Trends in German and European Electricity Working Papers
WP-GE-08
Nodal Pricing in the German Electricity Sector –
A Welfare Economics Analysis, with Particular
Reference to Implementing Offshore Wind
Capacities
Kristin Dietrich, Uwe Hennemeier, Sebastian Hetzel, Till Jeske,
Florian Leuthold, Ina Rumiantseva, Holger Rummel, Swen
Sommer, Christer Sternberg, and Christian Vith
Final report of the study project: ‘More Wind?’ (2005)
Dresden University of Technology
Chair of Energy Economics and
Public Sector Management
Chair of Energy Economics and Public Sector Management
EE²
Dresden University of Technology
Faculty of Business Management and Economics
Nodal Pricing in the German Electricity Sector –
A Welfare Economics Analysis, with Particular Reference
to Implementing Offshore Wind Capacities
Final report of the study project: ‘More Wind?’
Authors:
Kristin Dietrich, Uwe Hennemeier, Sebastian Hetzel, Till Jeske,
Florian Leuthold, Ina Rumiantseva, Holger Rummel, Swen Sommer,
Christer Sternberg, Christian Vith
Academic Advisors:
Christian von Hirschhausen, Franziska Holz, Ferdinand Pavel
Dresden, September 2005
Table of Contents
Abbreviations .................................................................................................................................................. IV
Nomenclature ....................................................................................................................................................V
List of Figures.................................................................................................................................................. VI
List of Tables.................................................................................................................................................. VII
List of Tables.................................................................................................................................................. VII
1 Introduction .................................................................................................................................................. 8
2 Background of the Study.............................................................................................................................. 9
2.1 DENA grid study ...................................................................................................................................9
2.2 Pricing mechanisms .............................................................................................................................10
2.2.1
Present situation: uniform pricing.......................................................................................... 10
2.2.2
Zonal pricing.......................................................................................................................... 12
2.2.3
Nodal pricing ......................................................................................................................... 13
2.2.4
Empirical studies on nodal pricing ........................................................................................ 15
2.3 Technical specifics ..............................................................................................................................17
2.3.1
Transmission capacity constraints ......................................................................................... 17
2.3.2
Kirchoff’s laws ...................................................................................................................... 18
2.3.2.1 Kirchhoff’s first law (current law) ............................................................................ 18
2.3.2.2 Kirchhoff’s second law (voltage law)....................................................................... 19
3 Model and Data .......................................................................................................................................... 19
3.1 Optimization problem..........................................................................................................................19
3.1.1
Cost minimization under uniform pricing.............................................................................. 20
3.1.2
Nodal pricing ......................................................................................................................... 20
3.2 The DC Load Flow Model...................................................................................................................22
3.2.1
Why DC ................................................................................................................................. 22
3.2.2
The model .............................................................................................................................. 22
3.2.2.1 Foundations............................................................................................................... 22
3.2.2.2 Real power flow between two nodes ........................................................................ 23
3.2.2.3 Losses of real power between two nodes.................................................................. 23
3.3 Description of the GAMS modeling process.......................................................................................24
3.4 Data......................................................................................................................................................26
3.4.1
Mapping the high voltage-network........................................................................................ 26
3.4.2
Line specific data ................................................................................................................... 27
3.4.3
Node specific capacities......................................................................................................... 28
3.4.4
Generation costs..................................................................................................................... 29
3.4.5
Demand.................................................................................................................................. 30
4 Scenarios, Results and Interpretation ......................................................................................................... 31
II
4.1 Scenarios..............................................................................................................................................31
4.2 Results and Interpretation ....................................................................................................................33
4.2.1
Existing HV-grid: scenario 1 vs. scenario 2 .......................................................................... 33
4.2.1.1 Low load ................................................................................................................... 34
4.2.1.2 Average load ............................................................................................................. 34
4.2.1.3 High load................................................................................................................... 34
4.2.1.4 Interpretation............................................................................................................. 34
4.2.2
Offshore wind energy input: scenario 3 vs. scenario 2 .......................................................... 35
4.2.3
Offshore model grid extension: scenario 4 vs. scenario 3 ..................................................... 37
4.3 Comparison of all models....................................................................................................................41
5 Conclusions ................................................................................................................................................ 42
References ....................................................................................................................................................... 43
Appendix A:
Inverse Demand, Nodal Price and Welfare ........................................................................... 47
Appendix B:
Implementing the optimization problem in GAMS............................................................... 49
Appendix C:
Assumptions for calculating transmission losses in the DCLF ............................................. 53
Appendix D:
Result data ............................................................................................................................. 54
III
Abbreviations
A
Ampere
ISO
AC
alternating current
kV
kilovolts
Al
aluminum
kW
kilowatts
BETTA
British Electricity Trading and
kWa
kilowatt years
Transmission Arrangements
L
ratio of losses against demand
Bundesnetzagentur
LBMP
location-based marginal pricing
(German Regulatory Agency for Post
LMP
locational marginal price
and Telecommunications)
MC
marginal cost
California Independent System
MCP
market clearing price
Operator
MW
megawatts
CLP
competitive locational price
MWh
megawatt hours
CMSC
Congestion Management settlement
NETA
New Electricity Trading Arrangements
BNetzA
CAISO
Credits
DESTATIS Statistische Bundesamt Deutschland
independent system operator
(England and Wales to Scotland)
NYISO
(German Federal Statistical Office)
New York Independent System
Operator
DC
direct current
OC
opportunity cost
DCLF
DC Load Flow model
P
real power
DENA
Deutsche Energie-Agentur (“German
PJM
Pennsylvania-New Jersey-Maryland
Energy Agency”)
Transmission Organization
GDPG
GDP of Germany
Q
reactive power
GDPF
GDP of a Federal State
St
steel
HOEP
Hourly Ontario Energy Price
HV
high voltage
IMO
Independent Electricity Market
Operator (Canada)
IV
Nomenclature
Symbols:
surface area [m2]
A
Pi
transmission capacity constraint at line i
a
prohibitive price [€/MWh]
Β
line series susceptance [1/Ω]
b
slope
pref
reference price [€/MWh]
C
total costs of production [€]
p*
equilibrium price [€/MWh]
demand at node n [MWh]
pn*
nodal price at node n [€/MWh]
reference demand at node n [MWh]
Ri
line resistance [Ω]
equilibrium demand [MWh]
Vj,k
voltage magnitude at a node [volts]
dn*
equilibrium demand at node n [MWh]
W
welfare [€]
G
line series conductance [1/Ω]
Xi
line reactance [Ω]
gn
generation at node n [MW]
Xm
line reactance for m circuits [Ω/km]
gnt
generation of plants of type t at node n (*)
Z
line impedance [Ω]
[MW]
δj,k
voltage angle at a node [rad]
maximum generation capacity of plants of
ρ
specific electrical resistance (material
dn
dn
d
ref
*
gnt,max
Pi
real power flow at line i [MW]
max
[MW]
type t at node n [MW]
characteristic) [Ωm]
Imax
maximum allowable current line flow [A]
ε
demand elasticity at reference demand
Ljk
losses of real power [MW]
Θjk
voltage angle difference [rad]
l
length of a line [m]
Pjk
real power flow between two nodes [MW]
Indices:
i
line between node j and node k
n
nodes within the network
j
node within the network
ref
reference
k
node within the network
t
type of generation plant
m
number of circuits
max
maximum
(*) Types of plants are denominated according to the energy source or technique used for generation. See
section 3.3.
V
List of Figures
Figure 1: Two node example for line congestion .............................................................................................14
Figure 2: Kirchhoff’s first law..........................................................................................................................18
Figure 3: Social welfare and market clearing price ..........................................................................................21
Figure 4: Example for an auxiliary node ..........................................................................................................26
Figure 5: Nodal prices and uniform price within the average load scenario ....................................................35
Figure 6: Nodal price difference (“without offshore” minus “plus 8 GW”) ....................................................36
Figure 7: Change in optimal demand: scenario “nodal price plus 8 GW” vs. “nodal price plus 8 GW” .........39
Figure 8: Nodal price difference (“plus 8 GW” minus “plus 13 GW”)............................................................39
Figure 9: Congested lines around the North Sea 13 GW average ....................................................................40
Figure 10: Welfare gain under nodal pricing compared to cost minimization .................................................41
Figure 11: Nodal prices without offshore wind (low load) ..............................................................................54
Figure 12: Nodal prices without offshore wind (high load) .............................................................................57
Figure 13: Nodal prices “plus 8 GW” (average load).......................................................................................60
Figure 14: Nodal prices “plus 8 GW” (low load) .............................................................................................63
Figure 15: Nodal prices “plus 8 GW” (high load)............................................................................................66
Figure 16: Nodal prices “plus 13 GW” (average load).....................................................................................69
Figure 17: Nodal prices “plus 13 GW” (low load) ...........................................................................................72
Figure 18: Nodal prices “plus 13 GW” (high load)..........................................................................................75
Figure 19: Congestions close to the North Sea: Nodal price plus 8 GW (low demand) ..................................78
Figure 20: Congestions close the North Sea: Nodal price plus 8 GW (high demand) .....................................79
Figure 21: Congestions close to the North Sea: Nodal price plus 13 GW (low demand) ................................80
Figure 22: Congestions close to the North Sea: Nodal price plus 13 GW (high demand) ...............................81
VI
List of Tables
Table 1: Network access and demand fees of the German transmission providers (high-voltage level). ....... 11
Table 2: Details of the high voltage-network .................................................................................................. 27
Table 3: Values for reactance and resistance................................................................................................... 28
Table 4: Values for reactance and resistance................................................................................................... 28
Table 5: German power plant capacities ......................................................................................................... 29
Table 6: Marginal costs of power generation per fuel..................................................................................... 30
Table 7: Demand per federal state................................................................................................................... 31
Table 8: Scenarios ........................................................................................................................................... 33
Table 9: Results for cost minimization and nodal pricing............................................................................... 34
Table 10: Maximum possible input without grid extension (scenario 3) ........................................................ 36
Table 11: Congested lines within the “plus 8 GW” scenario (average load) .................................................. 37
Table 12: Assumed grid extension .................................................................................................................. 37
Table 13: Maximum wind offshore energy with extended grid (scenario 4)................................................ 38
Table 14: Congested lines (X) for the “plus 13 GW” scenario ....................................................................... 38
Table 15: Ratio of losses against demand ....................................................................................................... 42
Table 16: Spreadsheet: Parameters.................................................................................................................. 52
Table 17: Prices per node: without offshore wind (low load) ......................................................................... 56
Table 18: Prices per node: without offshore wind (high load) ........................................................................ 59
Table 19: Prices per node: “plus 8 GW” (average load) ................................................................................. 62
Table 20: Prices per node: “plus 8 GW” (low load)........................................................................................ 65
Table 21: Prices per node: “plus 8 GW” (high load)....................................................................................... 68
Table 22: Prices per node: “plus 13 GW” (average load) ............................................................................... 71
Table 23: Prices per node: “plus 13 GW” (low load)...................................................................................... 74
Table 24: Prices per node: “plus 13 GW” (high load)..................................................................................... 77
Table 25: Losses in different scenarios ........................................................................................................... 77
VII
1 Introduction
Based on a reference scenario for 2020, a recent study by the German Energy Agency (DENA) has indicated
high costs of the integration of additional offshore wind capacities in the North Sea. However, this study was
based on a uniform pricing model, and might thus overestimate the effects of additional wind energy in the
network. An alternative approach is the concept of nodal pricing, which is increasingly becoming the
benchmark of electricity pricing in U.S. markets as well as in Europe. Theory proves nodal pricing to be the
most efficient mechanism from the economic point of view while simultaneously respecting physical laws of
electricity networks.
Within the scope of a study project of the Chair of Energy Economics and Public Sector Management (EE2)
at the Dresden University of Technology graduate students compared the results of uniform and nodal
pricing in the German electricity sector. The basic interest was to find out about consequences of switching
from the current regime to a spatial dependent nodal pricing system. The model also simulates – similarly to
the DENA study – the effects of increasing offshore wind capacities in the North Sea. Therefore, the model
was gradually varied from the current 0 GW to 8 and 13 GW.
The model of the German electricity system includes 425 lines and 310 nodes of the 380-kV and the 220-kV
grid. Power flows are calculated and dynamically optimized using the DC Load Flow Model. Nonetheless,
the model is time static as it assumes constant flows during one hour. Demand is approximated by linear
demand functions based on actual reference demands for each node and a reference price per MWh based on
EEX data. Generally, plant type specific marginal costs of electricity generation were considered in the
formulation of the maximization problem. Wind energy, however, was valuated at the basis of opportunity
costs arising from necessary balancing and response capacities. This was necessary as marginal costs of wind
energy generation are negligible and therefore do not represent real costs occurring when using wind energy.
Output of the installed wind capacities was assumed to be constant and available during the considered hour
(onshore and offshore). A further simplification is the neglect cross-border flows. Finally, note that the
model calculates competitive results only and does not consider market power issues and strategic behavior.
The optimization problem is perceived as a welfare maximization problem which is solved in GAMS.
The present report summarizes the results of the study project including theoretical background information
and a detailed description of the model. Section 2 gives a review of the DENA study, theoretical concepts
and examples from practice regarding electricity pricing, and the results of recently published studies on
nodal pricing. Additionally, basic physical laws of energy flow in electricity grids are briefly described.
Section 3 explains the underlying model and how required data were collected and integrated. First, the
optimization problem is examined depending on the particular pricing mechanism. The second part of
section 3 reviews the DC Load Flow Model as proposed by Schweppe et al (1988) and recently explained by
8
Stigler and Todem (2005). It is often used for economic analysis of electricity networks with respect to
physical constraints. The final part informs from which sources data was received and how it was integrated
into the model. This part is to support comprehension and evaluation of the study’s results. Section 4
presents the four scenarios of the study. After modeling the present situation (Status quo with uniform
pricing), nodal pricing is introduced without any changes in the network’s design. In a second step, the feedin from offshore wind energy plants in the North Sea is raised up to the network’s capacity limit, which
allows constructing 8 GW offshore plants. The last scenario assumes 13 GW offshore wind energy provided
four additional extra high-voltage lines at the North Sea in order to at least get the wind energy into the grid
at the coast. All scenarios are varied according to three demand levels. Section 5 analyzes received results. A
conclusion from this study is drawn and its limitations are mentioned in Section 6.
2 Background of the Study
2.1
DENA grid study
A recent study from the German Energy Agency (DENA 2005a) indicates for a reference scenario for 2015
high additional costs caused by the integration of additional wind plants into the existing grid. Particularly,
the grid extensions due to emerging network bottlenecks would be cost-intensive. For the further
development of renewable energy in Germany an efficient integration of especially onshore and offshore
wind energy into the existing power system is very important. Several capital-intensive investments would
have to be made to keep the grid system reliable.
Therefore the Deutsche Energie-Agentur (DENA) has commissioned the study “Planning of the Grid
Integration of Wind Energy in Germany onshore and offshore up to the year 2020” (DENA Grid Study). The
goal of this study is to enable fundamental and long-term energy-economic planning, which is supported by
all participating partners of the DENA study.
The study is divided into three parts:
I. Development of energy scenarios in which the proportion of renewable power stations and the
electricity generated by them, and the development of the conventional power station is established
for the years 2007, 2010 and 2015.
II. Examination of the effects this would have on the national grid, with a special focus on the
reinforcement and extension measures required and on grid management.
9
III. Development of the systems requirements in the power stations with the main focus on the optimum
provision of normal and contingency reserve energy.
The study develops strategies for the increased use of renewable energies and their effects on the grid until
2015. The study focuses on the integration of the approximately 37 GW wind capacity – on- and offshore –
into the electricity grid since on a mid-term basis wind has the highest potential of increasing the share of
renewable energies in power generation. The DENA grid study is based on the current German uniform
pricing model. The major results of the study are (DENA, 2005b, pp. 4-15):
•
Approximately 400 km of the existing 380 kV grid has to be upgraded; approximately 850 km new
construction is needed.
•
Reliable energy supplies on today's standards can be guaranteed if certain technical measures are
implemented.
•
Approximately 20 to 40 million tons CO2 emissions can be avoided until 2015 according to the
structure of the power plans in operation.
•
The additional costs for the expansion of wind energy will cost private households between 0.39 and
0.49 Cent € per kWh in 2015.
2.2
Pricing mechanisms
Competitive markets for electricity determine either a uniform marginal price, a set of nodal or locational
marginal prices (LMP), or only a few zonal marginal prices. Although theory proves LMPs to be the most
efficient, critics find the large number of LMPs – compared to one uniform or several zonal prices confusing. They claim a uniform- or zonal-based model to be more transparent. The following section briefly
describes the present pricing mechanism in Germany and the theoretical concepts of uniform, zonal and
basic prices.
2.2.1
Present situation: uniform pricing
Electricity pricing in Germany is based on a mixed price calculation, containing a fixed component for
network access and a variable demand charge. The latter is paid per unit of energy actually purchased. By
paying a fixed network access charge, the customer rents a particular band which will be reserved for his
energy delivery. This payment covers costs from losses, ancillary services, voltage transformation and access
to networks at lower voltage levels.
10
Basic principles of pricing mechanisms are defined in the association agreement between energy producers
and industrial consumers “VV II plus” (VDN, 2001) in conformity with the EU directive on electricity
96/92/ EG and the resulting German Energy Industry Act (Energiewirtschaftsgesetz, EnWG, last modified
and enacted on July, 13, 2005). The VV II plus agreement demands pricing mechanisms on the basis of cost
recovery and a separation of prices for transmission and allocation of electricity. The present current “cost
plus” accounting for grid fees1 will be replaced from 2006 by historic cost accounting with inflation-adjusted
returns for investments in new assets.
Transmission provider
Network access fee
Demand fee
Network access fee
Demand fee
(EUR/ kWa)
(ct/ kWh)
(EUR/ kWa)
(ct/ kWh)
Annual load utilization period
EnBW AG
< 2,500 h/a
3.38
≥ 2,500 h/a
1.28
34.44
0.04
37.30
0.04
Incl. transformation
6.24
1.28
Annual load utilization period
RWE AG
< 2,500 h/a
4.03
≥ 2,500 h/a
0.96
23.28
0.19
27.97
0.19
Incl. transformation
8.72
0.96
Annual load utilization period
E.ON Netz GmbH
≤ 3,000 h/a
3.49
> 3,000 h/a
0.99
32.22
0.03
35.53
0.03
Incl. transformation
6.80
0.99
Table 1: Network access and demand fees of the German transmission providers (high-voltage level).2
Sources: EnBW AG (2005), RWE AG (2005b), E.On Netz AG (2005).
Additionally, structural classes are defined on the basis of population density, demand density, cabling
degree and location (East/West) in order to find structurally comparable transmission providers. This will
provide a basis for the new Regulatory Agency for Post and Telecommunications (BNetzA) to regulate grid
fees, which have to be approved by BNetzA ex-ante.
Transmission providers have adapted to the VV II plus principles and calculate separate prices for network
access and individual demand. Price schemes mostly depend on the load’s average annual power
consumption. Consumer with relatively high annual consumption rates are charged a higher fixed price while
1
2
A general example of regulatory current cost accounting for grid fees in Germany is presented in RWE AG (2005a, p. 148).
Prices do not include purchase tax and further markups for counting and deviating voltage levels.
11
paying a per unit price significantly lower than for loads with low annual consumption. In consequence,
prices paid by loads depend on their individual contracts and vary significantly. (Table 1)
The currently implemented pricing schemes are a form of uniform pricing: the same price will be charged for
loads with identical consumption rate magnitudes – regardless of the individual characteristics of its bus
(particularly losses and congestion on adjacent lines).
Uniform pricing has been applied in Finland (since 1998), Sweden (since 1996), Alberta (since 2001) and
Ontario (since 2002)3 and was in operation in the former England/ Wales-Pool (1990-2005), PJM (19971998) and in the first phase of the New England market from 1999 to 2003 (see Fuller, 2003). It is typically
pool-based and works efficiently only in the absence of congestion. Otherwise, in the case of congestion, an
uplift payment is required, which covers overall costs from congestion but does not send adequate market
signals as do nodal prices (see Krause, 2005). Therefore uniform pricing is not able to ensure an optimal
allocation of energy and transmission capacities in a situation of congestion as seen e.g. in the case of New
England (see Hogan, 1999). Xingwang et al (2003) sum this problem up as the incapability of uniform
pricing to achieve harmony between market liquidity and efficient pricing.
2.2.2
Zonal pricing
One attempt to solve incentive problems of the uniform pricing approach was to introduce zonal pricing,
which is currently applied in Norway (since 1991), Australia (since 1998), New York (since 1999, for load),
Texas (since 2001) and Denmark (since 2000). The California ISO used zonal pricing from 1998 to 2002
(see Fuller, 2003).
According to this approach, the market is divided into several zones depending on their respective
congestion costs. Higher prices are paid in zones where demand exceeds system capacity of transmission.
The price of the respective reference node is applied to the whole zone. Zones are usually pre-defined and
fix. In Norway, however, zones may vary depending on the actual situation in the grid regarding
congestion.4 Consequently, if the system is unconstrained there is only one zone (and the same price as
under uniform or unconstrained nodal pricing), which was the case for 43.8% of the hours in 1998 (see
Johnsen et al, 1999, p. 34). There were maximal six zones due to congestion (0.4% in 1998).
3
4
The Independent Electricity Market Operator (IMO) in Canada has been calculating so far its uniform price as the sum of the
Hourly Ontario Energy Price (HOEP), Congestion Management settlement Credits (CMSC) uplift and losses uplift. A comparison
of nodal and IMO uniform pricing can be found at http://www.ieso.ca/imowebpub/200405/mo_pres_NodalAnalysis
_2004jan14.pdf. For a detailed explanation of CMSC see http://www.ieso.ca/imoweb/pubs/consult/cmsc/cmsc_overview.ppt.
Johnsen et al. (1999, p. 3) state that the distinction between a nodal or zonal system in Norway is– for the reason of varying zonesless clearly defined. However, Norway’s system is usually referred to as zonal.
12
Proponents of zonal pricing claim that it would balance well equity concerns and efficiency goals and is less
complex and therefore more transparent to market participants (see Alaywan et al, 2004, p. 1).
On the other hand, the zonal approach is criticized for its potential of market power abuse during periods of
high demand and resulting congestion (see e.g. Borenstein et al, 2000). Johnsen et al (1999), however, could
not find clear empirical evidence in a study on Norway.
Hogan (1999) rejects the model of nodal prices for a number of reasons. He calls zonal pricing “[…] an
effort to treat fundamentally different locations as though they where the same […]” (p. 1). It would create
more administrative rules, poorer incentives for investments, demands to pay generators not to generate
power, and finally it is much more complicate to define zonal than nodal prices.5 Complications regarding
the ability to offer transmission rights that match the system real capability could be observed in Australia,
England and California (in the end of the nineties) as well. Contrarily, Krause (2005, p. 34) claims the zonal
pricing system working fairly in Australia and Norway (see also Johnsen et al, 1999, p. 1). However,
according to Alaywan et al (2004, p. 1), the zonal market design of California was considered having
contributed to the energy crisis in 2000 and 2001.
Anyway, regarding the evolution of market structures worldwide, nodal pricing seems to become,
increasingly the benchmark of congestion management for its simplicity, effectiveness in practice and
conformity with economic theory and physical laws.
2.2.3
Nodal pricing
Nodal pricing6 is a method of determining prices in which market clearing prices are calculated for a number
of locations on the transmission grid called nodes. Each node represents a physical location on the
transmission system including generators and loads. The price at each node reflects the locational value of
energy, which includes the cost of the energy and the cost of delivering it (i.e. losses and congestion). Nodal
prices are determined by calculating the incremental cost of serving one additional MW of load at each
respective location subject to system constraints (e.g. transmission limits, maximal generation capacity).
Differences of prices between nodes reflect the costs of transmission.
Central to the nodal price approach are congestions on lines (see section 2.3.1). Without any congestion the
market clearing price results from the intersection of the aggregated supply (“merit order”) and customers’
5
Hogan cites the 1997 PJM attempt to install zonal pricing as an example, where the system collapsed as soon as constraints
occurred. Generators rather run than respect transmission constraints – just responding to (distorted) signals from zonal pricing.
6
There are at least three alternative denominations of “nodal prices”: “Locational Marginal Price/ LMP” (PJM), “Location-Based
Marginal Pricing/ LBMP” (NYISO) and ”Competitive Locational Prices/ CLP” (Stoft, 2002).
13
demand. In result, the price will be equal for every node in the grid disregarding losses. In case of congestion
on line there is a need for load to be shed or more expensive generation to be dispatched on the downstream
side of the constraint. Prices on either side of the constraint will differ.
Congestion occurs if both of the following two conditions are fulfilled (Stoft, 2002, p. 392):
1. The marginal costs of production differ between nodes.
2. Overall demand exceeds supply ability of the “cheapest” generator due to limited production or
constrained line capacity. A line constraint can be caused when a particular branch of a network
reaches its thermal limit or when a potential overload will occur due to a contingent event on another
part of the network (e.g. generator black out). The latter is referred to as a security constraint.
remote supplier
local supplier
€ (20+Q/50)/MWh
€ (40+Q/50)/MWh
A
B
500-MW-Limit
Bus 1
demand: 100 MW
Bus 2
demand: 800 MW
Figure 1: Two node example for line congestion
Source: Stoft (2002, p. 391)
In case of congestion the price of the right to transmit power over a line is positive as the following simple
example from Stoft (2002, p. 391) may demonstrate (Figure 1). Assume a generator A at bus 1 representing a
remote supplier with a marginal cost function below the marginal costs of a local supplier (B) at bus 2. Bus 1
demands 100 MW, bus 2 800 MW. The line between the buses is limited to 500 MW. In this situation the
cheaper generator A produces 100 MW for its own consumption and exports 500 MW to bus 2 (total
generation: 600 MW). A has opportunity costs from 300 MW which it can not supply to Bus 2 due to
congestion. Bus 2 imports 500 MW from bus 1, B generates 300 MW for own consumption. Calculating
nodal prices on the basis of the cost functions gives ([20+600/50] EUR/MWh =) 32 EUR/MWh at bus 1 and
46EUR/MWh at bus 2 respectively. A will demand from consumers in bus 2 the same price B is demanding
for its power supply because A is maximizing his profit and knows that consumers in Bus 2 are willing to
pay B’s price. The transmission price over a line is defined as the difference between the nodal prices of the
related buses and gives 14 EUR/MWh.
To optimize dispatch in the whole system a classic supply and demand equilibrium price has to be
developed: The marginal generator is determined by matching offers from generators to bids from loads at
each node. This process is carried out for a specific time interval (e.g. every 15 minutes) at each input and
exit node on the transmission grid. The prices take into account the losses and constraints in the system, and
14
generators are dispatched by the system operator, not only in ascending order of offers (or descending order
of bids), but in accordance with the required security of the system. This results in a spot market with bidbased, security-constrained, economic dispatch with nodal prices as proposed by Hogan (2003, p. 2).
Apparently, nodal prices reflect the actual situation in the grid more transparently than uniform prices and
represent adequate allocation signals. The calculation nodal prices is one of several important considerations
in analyzing where to site additional generation, transmission and load. The implementation of efficient
congestion management methods on the basis of nodal pricing is crucial to cope with scarce transmission
capacities and to ensure security of supply. In combination with further political measures there might be
saved costly investments in transmission lines (see Bower, 2004).
Nodal pricing was first implemented in New Zealand (1997), followed by some US markets (e.g. PJM 1998,
New York 1998, New England 2003).7 On 1 April 2005, the British Electricity Trading and Transmission
Arrangements (“BETTA”) were introduced in UK extending the earlier “New Electricity Trading
Arrangements” for England and Wales (NETA) to Scotland. With BETTA, nodal pricing was introduced for
the Great Britain grid on the basis of marginal transmission investment requirements (Tornquist, 2005). The
California ISO is actually redesigning the procedures by which it performs forward scheduling and
congestion management; CAISO plans to introduce nodal pricing by 2007 CAISO (2005).
2.2.4
Empirical studies on nodal pricing
Empirical analyses using the nodal pricing concept have been provided, e.g. for England/Wales, Austria,
Italy and, most recently, for California. A contentious issue is how to model the electrical grid properly and,
thereupon, how to calculate corresponding nodal prices. On the basis of data from the U.S. Midwest region
the full AC model was compared to the less complex DC Load Flow model.
Green (2004) developed a thirteen node model of the transmission system in England and Wales
incorporating losses and transmission constraints. The study analyzes the impact of different transmission
pricing schemes (LMP, zonal and uniform pricing). Green shows that the introduction of the LMP concept
would raise welfare by 1.5% compared to the uniform model on behalf of the larger consumer welfare
(+2.6%) while generator profit would decrease by 1.1%. To strengthen these results, Green applies different
values for demand elasticity (-0.1, -0.25, -0.4) and shows that the increase of welfare is higher with a larger
absolute elasticity value.
For the Austrian high voltage grid, Todem (2005) has analyzed the economic impact of a nodal price based
congestion management. Against the background of scarce transmission capacities in the East of Austria,
7
According to Fuller (2005), nodal pricing was introduced even earlier in some Latin American states (Chile 1982, Argentina 1992,
Peru 1993, Bolivia 1994).
15
Todem developed an optimization model with 165 nodes applicable to the bilateral Austrian electricity
market.8 On the basis of January 2004 data, it could be shown, in which places congestion occurs and which
prices would be optimal. The author suggests a division of the network into two pricing zones according to
their congestion situation. The most efficient solution to overcome the congestion problem would be to build
an additional 380-kV line – the so called ‘Steiermark’-line.
Interesting results regarding the distribution of economic surplus under nodal, uniform and zonal pricing
provides a study from Ding and Fuller (2005). They show for the Italian 400 kV grid that there is no loss in
(total) social surplus using uniform or zonal pricing with a nodal pricing dispatch compared to a full nodal
price system (dispatch and pricing nodal-based). The authors therefore calculated optimal dispatch on the
basis of an optimal power-flow model, respecting transmission constraints and losses while defining uniform
(respectively zonal) prices for financial settlements. The results, however, show that the distribution of
economic surplus between supply and demand sides will vary depending on the pricing model. More
importantly, the authors reveal perverse incentives for generators that are dispatched at different levels than
uniform or zonal prices would suggest. “Constrained-on” generators, which are dispatched at higher levels,
may receive a smaller surplus than under nodal pricing settlement, even though the extra generation is
needed (and vice versa for “constrained-off” generators). However, as economic data of the study where not
completely realistic, the authors did not draw firm conclusions.
The California ISO has – in the run-up to the planned implementation of its Market Redesign and technology
Upgrade (MRTU)9- provided several studies on locational marginal pricing. The most recent one (August
2005) uses schedules and market bids of previous years, conditions of the future MRTU structure and the
ISO’s full network model in an Alternating Current (AC) Optimal Power Flow (OPF) simulation to estimate
prices that may occur in the ISO’s real-time market if it were based on locational marginal prices (CAISO
2005, p. 1). Prices were calculated and given as average per zone (total of 29 zones). The resulting LMPs are
generally moderate, apart from some exceptions: less 1% of the nodal prices exceeded $100/MWh, and 91%
of the nodal prices were below $65. Furthermore, prices within one zone were generally very similar while
significant zonal price variations last only a few hours per year. In conclusion, it was found that LMP pricing
would produce stable and predictable prices. This result may refute concerns regarding the potential for high
LMPs in certain constrained areas of the grid, where the cost of delivering energy to customers is increased
due to frequent, severe congestion.
8
9
Other electricity markets using the nodal price approach are usually centrally organized (PJM Interconnection, NYISO and New
Zealand).
The MRTU proposes a forward and real-time congestion management procedure that adjusts generation, load, import, and export
schedules to clear congestion using an Alternating Current (AC) Optimal Power Flow algorithm (OPF) and a Full Network
Model (FNM) that includes all buses and transmission constraints within the CAISO Control Area. (CAISO, 2005, p. 4)
16
2.3
Technical specifics
2.3.1
Transmission capacity constraints
The transmission of energy by electricity follows specific physical laws. Every current flow in a transmission
line rises the temperature of the line. Each line has a maximum temperature it can sustain (thermal limit).
The change in temperature is proportional to the resistance of a transmission line. An easy example for the
relationship of a line resistance is given by:
R = ρ*
l
A
(2.1)
The circuit resistance depends on its cross section (and the resulting surface area), the length of the line, and
the used material. Moreover, the transmission capacity depends on several factors such as the number of
circuits, the environmental temperature and wind conditions. Accordingly, the transmission limit is not a
constant value but changes along with external factors. Hence, equation (2.1) is accurate for illustrative
reasons but not applicable in real transmission systems. Under real conditions, empirically acquired data for
resistances and reactances are used that already include the above mentioned characteristics.10
Altogether, physical facts implicate that the maximum energy flow is limited. In case the thermal limit is
passed, undisturbed operation is not longer guaranteed and therefore requires a regulation of flows. If the
overstepping is high in magnitude or lasts for a longer period, respectively, transmission lines may tear apart
due to decreasing mechanical strength. This situation is referred to as congestion on line.
As explained above, a current flow causes a change in temperature. Unfortunately this comes along with an
energy loss in this transmission line:
-
Ohm’s law:
V=R*I
(2.2)
-
Power law:
P=V*I
(2.3)
P=R*I2
(2.4)
Inserting equation (2.2) in (2.3) yields:
-
Loss of a DC transmission line:
An AC model fully considers the line impedance Z consisting of resistance (real part) and reactance (reactive
part). Section 3.2 describes how the DC Load Flow model simplifies the problem.
10
See section 3.4 for the approximate values that are used in this report.
17
2.3.2
2.3.2.1
Kirchoff’s laws
Kirchhoff’s first law (current law)
The electrical DC current is equal to the number of charge carriers flowing through a line within a specific
time or, in case of AC, the frequency with which the charge carrier pulsate. Kirchhoff’s first law – also
called: current law – specifies that these charge carriers cannot disappear. The sum of incoming flows must
equal the sum of outgoing flows. Defining the incoming current as positive and the outgoing as negative, the
sum will be zero:
∑I
µ
=0
(2.6)
µ
At one node, there are, basically, four types of current flows (Figure 2):
-
incoming flows from other nodes (via transmission lines): +pn
-
outgoing flows to other nodes (via transmission lines): -pn
-
power supply (by a local generator) at this node: g
-
power demand (by a local consumer) at this node: d
Figure 2: Kirchhoff’s first law
Applying this denotation to equation (2.6) yields:
∑p
n
−d + g =0
(2.7)
n
However, losses are not considered here. They may occur through transformation while withdrawing or
injecting energy as well as through transportation – losses on transmission lines. Losses can be regarded as
outgoing flows into the environment.
Important, however, is the fact that current does not leave a node arbitrarily through all possible lines.
Different outgoing lines act as current divider.11 That means that current flows leave a node reciprocally
11
For further information see relevant technical literature, e.g. Lunze (1987), Stoft (2002).
18
proportional to the resistances of the respective lines. The effect is that one cannot inject more energy at this
node once on of the outgoing lines is congested even if other lines are still able to work with higher load.
This is, particularly, decisive in highly meshed networks. For those meshed networks, the second Kirchhoff
law has to be considered as well.
2.3.2.2
Kirchhoff’s second law (voltage law)
Voltage describes the difference between two electric potentials. You could say voltage makes current
flow.12 Power plants create and sustain a potential difference throughout the grid. If energy was consumed
without energy injection into the grid voltage would collapse. Hence, consumption can be understood as
voltage drain. The second law of Kirchhoff states that the sum of all voltages within a mesh equals zero –
equation (2.8).
Vν = 0
∑
ν
(2.8)
The above explained technical specifics are not primarily of economic relevance. However, they make up the
framework for an economic consideration of electricity networks. For deeper matter compare Koettnitz and
Pundt (1967), Koettnitz et al (1986), Lunze (1987).and Stoft (2002).
3 Model and Data
3.1
Optimization problem
A standard DC load flow model was used to simulate the German high voltage transmission system. The grid
comprises 291 nodes (plus 19 auxilliary nodes, see section 3.4.1) and two voltage levels (380 and 220 kV).
For more detailed information about the DC Load Flow model and underlying assumptions see section 3.2.
This report follows the path described by Schweppe et al (1988). His work provides the mathematical basis
for our model. According to the programming example outlined by Todem (2004, pp. 85-101) and with
valuable personal help of Mr Todem himself, the modelling software GAMS13 is utilized to implement the
necessary mathematical equations.
In case of a convex problem, GAMS solves a set of equations by means of iteration processing. GAMS
therefore offers a set of solvers varying in the way of finding a solution. Generally spoken, the type of
12
13
For further information see relevant technical literature, e.g. Lunze (1987), Stoft (2002).
GAMS optimizes an objective function and fulfils additional side conditions simultaneously.
19
problem, e.g. linear or nonlinear, determines the range of possible solvers. In our experience the solvers
Pathnlp and Conopt are appropriate for this model which is non linear. Both lead to the same results.
In this study, a static approach was chosen. Different scenarios were computed separately, analysed, and,
subsequently, compared to each other. The period of time referred to is one hour. For reasons of simplicity,
we do not consider a transmission reliability margin [(N-1)-constraint]. The model stresses transmission lines
up to 100% of their thermal limit. This must be taken into account while analyzing results.
3.1.1
Cost minimization under uniform pricing
In both the nodal and the uniform pricing model social welfare is the objective value to maximize. The
welfare equals total consumers’ benefit minus costs of generation, what is identical to the sum of producers’
and consumers’ surplus (Figure 3).14 The model determines optimal dispatch quantities of generation and
loads as well as the voltage angles at each bus while respecting the physical laws of power flow, particularly
Kirchhoff’s laws, capacity constraints of lines and generators, and demand characteristics. In the case of a
uniform price, the price and demand per node are fixed. This is an admissible simplification for the static
approach. In order to maximize welfare, the cost minimal dispatch has to be found. Hence, it becomes a cost
minimization problem.
W (d nref
max
⎛ dnref
d nref
⎜
ref
ref
) = ∑ ⎜ ∫ p ref (d n ) d ⋅ d n − ∫ c(d nref ) d ⋅ d nref
n ⎜ 0
0
⎝
Pi ≤ Pimax
s.t.
∑ gn = ∑ dn + L
n
n
t
t , max
∑ gn ≤ ∑ gn
n ,t
⎞
⎟
⎟
⎟
⎠
(1)
line flow constraint
(2)
energy balance constraint
(3)
generation constraint (per type of plant)
(4) 15
n, t
Total costs comprise only marginal costs of production at the power plants. Other costs as e.g. those arising
from network operation and maintenance are neglected.
3.1.2
Nodal pricing
In the case of nodal prices, welfare is maximized by finding the optimal demand for each node (Figure 3).
Hence, the following set of equations has to be solved.16
14
Aee Appendix A.
For a detailed description of all equations and constraints as used in the GAMS code see Appendix Appendix B.
16
Constraints to be obtained are the same as above. Compare also: Hsu (1997) and Green (2004).
15
20
d n*
⎛ d n*
⎞
*
*
*
⎜
max W (d n ) = ∑ ∫ p (d n ) d ⋅ d n − ∫ c(d n * ) d ⋅ d n * ⎟
⎟
n ⎜ 0
0
⎝
⎠
*
Pi ≤ Pi max
(5)
line flow constraint
(6)
∑ gn = ∑ dn + L
energy balance constraint
(7)
t
t , max
∑ gn ≤ ∑ gn
generation constraint (per type of plant)
(8)
s.t.
n
n
n, t
n, t
price
inverse demand
function
merit order
(supply)
pnref
consumer
surplus
pn
producer
surplus
dnref
dn*
supply, demand
(quantity of power)
social welfare
costs of production
Figure 3: Social welfare and market clearing price
Having the optimal dispatch for every node dn*, the corresponding market clearing nodal price pn is given by
the inverse demand function:17
pn = pn
17
ref
1
ref
+ ⋅ pn
ε
⎛ d n*
⎞
⋅ ⎜⎜ ref
−1⎟⎟
⎝ dn
⎠
(9)
Derivation of this equation is presented in Appendix A.
21
3.2
The DC Load Flow Model
3.2.1
Why DC
In general, Schweppe et al (1988) showed that the DC Load Flow Model (DCLF) can be used as an
instrument for an economic analysis of electricity networks. They apply it to their nodal price approach for
electricity pricing. As calculations in electricity networks are sophisticated due to the occurrence of reactive
power and the flow characteristic of electricity in highly meshed HV networks, simplifications are necessary.
The DCLF helps to simplify the modeling of such networks in case of symmetrical steady states. The DCLF
focuses on real power flows. It is, in particular, applicable for economic purposes as the transport of real
power is the main task of electricity networks (Todem et al, 2005, p. 5). Hence, real power is the main
commodity that customers demand and that generates benefits.18
Overbye et al (2004, p. 2) emphasize three advantages of the DCLF compared to an AC model:
1. The problem becomes smaller (about half the size).
2. The solution is noniterative.
3. The network topology does not depend on the power flowing and has to be factored once only.
Furthermore, they come to the conclusion that the DCLF is adequate for modeling LMPs albeit there are
some buses at which the deviation is significantly high. The latter occurs particularly on lines with high
reactive power and low real power flows (Overbye et al, 2004, p. 4). This is easily understandable because as
above mentioned reactive power is ignored by the DC approach.
3.2.2
3.2.2.1
The model
Foundations
Schweppe et al (1988, pp. 272-274) describe the way from a complete AC Load Flow to a DCLF. Therefore,
a decoupled AC Load Flow model is generated which assumes that real power P flows according to the
differences of the voltage angles Θjk between two nodes as well as reactive power flows Q is caused by
differences in voltage magnitudes V. Consequently, one can model the real power flow by only focusing on
voltage angle differences. The paper of Stigler and Todem (2005, pp. 114-115) explains the basic equations
that are described by Schweppe et al in detail:
Pjk = Gi V
2
j
- Gi V j V k · cos Θ jk + Bi V j V k · sin Θ jk
(3.10)
18
Relevant reactive power issues such as the necessity or influence, respectively, of investments in compensation facilities can not be
modeled by DC flows.
22
Θ jk = (δ j − δ k )
Bi =
Gi =
(3.11)
Xi
(3.12)
X i2 + Ri2
Ri
(3.13)
X i2 + Ri2
Equation (3.10) is the basis for all further calculations – both the lossless DC load flow and the transmission
losses (Stigler and Todem, 2005, pp. 116-118). Moreover, two basic assumptions must be made (Schweppe,
1988, p. 314):
1. The voltage angle difference Θjk is very small.
2. The voltage magnitudes V are standardized to per unit calculation. Hence, they can be considered to
be equally one at each node (Vj ≈ Vk).
3.2.2.2
Real power flow between two nodes
The calculation of lossless real power flows is the first step along the way to use the DCLF in a dynamic
economic model of an electricity network. In order to approximate the lossless line flows, one can suppose
that:
cos Θ jk ≈ 1
(3.14)
sin Θ jk ≈ Θ jk
(3.15)
This yields a linear equation for the lossless line flows:
P jk = Bi ⋅ Θ jk
3.2.2.3
(3.16)
Losses of real power between two nodes
The second step along the way is the estimation of losses occurring along the lines. Losses are important as
they cause the sum of generation not to equal the sum of demand. Thus, transmission lines are stressed not
only by demand but by demand plus losses. In order to approximate the losses on a line, equation (3.14)
must be complemented by the second order term of the Taylor series approximation:
cos Θ jk ≈ 1 -
Θ 2jk
2
(3.17)
23
Then, after some further assumptions and conversions19 transmission losses can be calculated by:
L jk = Ri ⋅ Pjk2
(3.18)
Both equations (3.16) and (3.18) provide us with the required relationship between demand and generation
as well as the resulting real power flow. One can now start to implement the model in order to observe
changes in line flows caused by changes in demand or generation, respectively. Combining this with a set of
economic information such as demand and supply functions for each node will enable us to assign a specific
price for each node of the network.
3.3
Description of the GAMS modeling process
For a better understanding of the GAMS code the modeling process will be described exemplarily for the
nodal price approach following the code which is divided into 5 parts.20
During the optimization process GAMS changes demand in the system in conformity with a given demand
function21, which defines the price the consumer is willing to pay at most. This is done by means of varying
the voltage angles at each node. Following the merit order of generation and given the reference price,
GAMS herewith calculates the maximum welfare at each node and – after aggregation - for the whole
system.
Part I
First of all, each node is assigned a number from 1 to 310. Similarly, each line is given a number from 1 to
407. For subsequent standardization fixed base values are defined for apparent power and the two voltage
levels. Additionally, fixed demand elasticity for all demand functions is introduced.
Part II
Here, data in from of fixed parameters representing the real situation in Germany is included into the GAMS
code. Parameters are:
•
reference points per node (prices and demands),
•
thermal limits of each line,
•
generation capacities per node and costs per plant type.
19
See Appendix C.
The uniform pricing model is calculated respectively merely modifying the objective function as described in section 3.1.2.
21
See section 3.4.5 and Appendix A for more detailed information about the underlying demand function.
20
24
The thermal line limit is calculated according to Lunze (1987, p. 222)22:
Pmax = 3 V I max
(3.19)
In (3.19) V is the given voltage level of the line. I represents the given maximum current at a line without
overheating and damaging the line.
The mix of generation plant types defines the maximum supply capacity per node. Except wind stations,
different marginal costs of production are defined for each type. Wind mills do not have variable costs and
therefore no marginal costs. However, they increase the need for balancing and response capacity within the
network because the intensity and duration of wind is difficult to predict. These costs are estimated and taken
into account as opportunity costs.
Part III
The transfer matrix H and the network susceptance matrix B are computed. They contain all necessary
information about the network topology and the normalized reactances and resistances of the lines. H is the
product of the line susceptance vector (B-Vector, see Appendix Appendix B, p. 51) and the incidence
matrix. B is the sum of the products of the incidence matrix and the transfer matrix H over all lines. Node 1
is appointed to be the swing bus of the network.
Part IV
Power input per node is calculated as the sum of nine sub variables representing the nine different plant types
that are, generally, able to contribute to the nodes power generation. In order to calculate the total variable
costs of generation per node the amount of power generated by a plant is multiplied by its marginal costs of
production. Consequently, this sum is a variable, too.
The net input is calculated as the difference between input and demand plus losses. In case of a net input
unequal zero, there is a voltage angle between the node’s voltage vector and the voltage vector at the swing
bus, which results in a flow of power.
Part V
Respecting all necessary constraints, the welfare function as described above is maximized. The resulting
optimal quantity of power demanded at every node dn* is used to calculate nodal prices pn on the basis of the
inverse demand equation as given in (A.8). This is the price a consumer at node n is at most willing to pay
for the calculated quantity of power.
22
Note that in a DC world apparent power (S) equals real power (P).
25
3.4
Data
The subsequent section describes the empirical data used in the model. First of all, a survey of the required
input variables is given; afterwards the calculations and the underlying approaches are explained.
3.4.1
Mapping the high voltage-network
The nodes are taken as the substations from the German integrated network (VGE, 2000, UCTE, 2004). Only
substations of the high and extra high voltage level were taken into consideration under the assumption that
the entire electricity transportation for all voltage levels takes place through high voltage transmission.
Hence, 291 regular plus 19 auxiliary nodes within the 380 kV and the 220 kV levels were detected (Table 2).
Auxiliary nodes became necessary where lines split up without a node or where the course of a line is
ambiguous (Figure 4).
Figure 4: Example for an auxiliary node
Source: UCTE (2004).
Lines of different voltage levels are listed separately, so the there may be more than one connection between
two nodes, e.g. one 380 kV double circuit and one 220 kV double circuit. Our model embraces 426
electricity lines for Germany. It does not include cross-border flows.
26
Object
Quantity
Nodes
Length [km]
292
Auxiliary nodes
19
Connection of nodes / lines
(220 kV)
Connection of nodes / lines
(380 kV)
172
15225
256
22617
Table 2: Details of the high voltage-network
3.4.2
Line specific data
A line’s characteristic can be described by three main factors: maximum thermal limit, line resistance and
line reactance. The maximum thermal limit is, basically, influenced by the type and the length of the line as
well as by the voltage level (see section 2.3.1). For Germany, we assumed four cables23 per wire for 380 kV
circuits and two cables24 per wire for the 220kV level (Pundt, 1983, p. 11 et seq., Pundt and Schegner, 1997,
p. 38 et seq.). An adequate value for the apparent power S is 1500 MVA for the 380 kV level up to a length
of 100 km, and, respectively, 400 MVA for a 220 kV level circuit up to a length of 90 km (Pundt, 1983,
p. 11). In fact, the admissible apparent power decreases for a continuous line longer than the given lengths
(ibid.).
From equation (3.19) maximal current can be derived as follows:
I max =
S
(3.20)
3 *V
In our model the possible current doubles when using a double circuit line, and is three times larger for a
triple circuit line. These maximal current values are necessary for the maximum power flow constraint in the
model.
As mentioned in section 2.3.1, realistic values for the resistances and reactances of high voltage circuits can
not be derived easily and are subject to empirical experiences. Pundt and Schegner (1997, p. 39) give a
satisfactory approximation for reliable values within the German grid (Table 3).
Number of circuits
Single Circuit
23
24
Voltage level [kV]
Resistance [Ω/km]
380
Reactance [Ω/km]
n.s.
n.s
240/40 AlSt.
185/32 AlSt.
27
Double circuit
220
n.s
n.s
380
0.03
0.26
220
0.078
0.29
Table 3: Values for reactance and resistance
Source: Pundt and Schegner (1997, p. 39).
In our model, the impedance of a single circuit is 1.8 times the impedance of a double circuit. This is a
simplified experience approach, too. Theoretically, the factor is supposed to equal two. However, the two
circuits influence each other due to electromagnetic fields. The degree of influence depends on the distance
between the circuits. Hence, the value for one double circuit differs from the value for two single circuits.
Although to a much lesser amount, values may also vary between differently constructed double circuits.
Altogether, the need for a simplification is evident. Accordingly, all values for lines with m circuits can be
(3.21).25
calculated using equation
X m = X 1 * 1.8 − m +1
Quantity of lines
(3.21)
Voltage Level [kV]
Single Circuit
Triple Circuit
Resistance [Ω/km]
Reactance [Ω/km]
380
0.054
0.468
220
0.140
0.522
380
0.016
0.014
220
0.043
0.016
Table 4: Values for reactance and resistance
Source: Own calculations.
3.4.3
Node specific capacities
The evaluation of the capacity of all German power plants was based on several sources, mainly the
‘Yearbook on European Energy and Raw-Materials Industry 2005’ (VGE, 2004)26. It provides the latest and
most complete data accessible to public. The yearbook also includes a CD-ROM with information about the
whole German plant fleet and further details about the European Energy Market. It contains an excel sheet27
about all German power plants exceeding 100 MW capacity, their locations and/or their names, their owners,
the installed capacity with the primary fuel of every unit and some remarks. In cases where the grid
integration was not clear, facilities were attached to their geographically closest node. For Power plants with
the possibility to run with an alternative type of fuel, only the main type of fuel was regarded. So it is
25
1.8 is an approximate value.
See also http://www.energy-yearbook.de/.
27
This database embraces all facilities up to January 1st 2004.
26
28
feasible to cover the demand with the most convenient power plants, because it is required that the main fuel
is the most advantageous fuel for every plant.28
The data for wind energy converters were taken from the German Wind Energy Association’s report on
installed wind energy capacity (DEWI, 2005). The total capacity amounts to nearly 17 GW. In 2005 over
17000 wind energy converters were installed in Germany. To simplify the data integration, wind
concentration zones were established comprising three to five zones per federal state. The cumulated
installed capacity per federal state was divided by the number of wind concentration zones in the specific
state and allocated to the concentration zones. The capacity of each concentration zone was allocated equally
to surrounding nodes located a maximum of 50 km from the zone. The simplification may lead to higher
congestion at nodes near concentration zones than in reality. A more detailed allocation has to be part of an
update of this study
Fuel
Installed capacity [GW]
Fuel
Installed capacity [GW]
Coal
31.222 Wind (onshore)
16.695
Brown coal
20.982 Natural gas
18.146
Nuclear Power
20.680 Fuel oil
Pump water
6.078
5.950 Total
103.058
Table 5: German power plant capacities
Source: VGE (2004), own calculations.
3.4.4
Generation costs
The node specific generation costs are calculated on a marginal cost basis. There are several studies and
approaches to estimate marginal costs of power generation (see EIA, 2004, p. 49, Pfaffenberger and Hille,
2004, DENA, 2005a, p. 278). In this study the marginal costs are based on the costs of the fuel excluding
operating and service costs. An exception is the wind power generation, which was priced at opportunity
costs as given in the DENA grid study (DENA, 2005b, p. 14). Wind opportunity costs may arise from
control and backup capacities. For all other power plant, we use the average marginal generation cost per
plant type according to Schröter (2004, p. 7) as they seem to form a mean compared to the DENA study.
(Table 6)
Fuel
Costs [€/MWh]
Fuel
Costs [€/MWh]
Nuclear Power
10.00 Fuel oil
50.00
Coal
18.00 Pump water
13.33
28
As an example: The best way to run a coal-fired power plant, which has the opportunity to fire with oil or gas, is with coal.
29
Brown coal
15.00 Running wasser
0.00
Natural Gas
40.00 Wind
4.05
Table 6: Marginal costs of power generation per fuel
Source: DENA (2005b) and Schröter (2004).
3.4.5
Demand
In order to derive node-specific demand, we assume a positive correlation between economic income and
total electricity demand. We split the federal states into administrative local districts and identified their
population figures (DESTATIS, 2005). Inhabitants per node were calculated distributing a district’s
population figure equally to all nodes of the district. In a second step, annual per capita energy consumption
had to be determined for every node. Therefore, the annual average per capita energy consumption of
Germany as given by German Federal Statistical Office (DESTATIS, 2005) was multiplied by the ratios of
Germany’s total GDP and the federal states specific GDP (Statistik-Portal, 2005). This resulted in a weighted
per capita consumption for every federal state. All nodes within one federal state were assumed to have the
same per capita consumption. Multiplying the annual per capita consumption of a node by its population
figure and dividing this by 8,760 finally gives the hourly node specific demand. Summing up the nodes’
demand resulted in a total demand of 56,241 MWh.
A disadvantage of the received data is that the results are average values. This lowers the signification of the
model because the variability of demand remains unconsidered. In order to solve this problem, the node
specific demands will be modified in different scenarios and adjusted by system load data of the respective
transmission system operators.
Federal state
Ratio
Number of local
Hourly demand per
GDPF/GDPG
districts
federal state [MWh]
Baden-Wurttemberg
1.10
44
8,287
Bavaria
1.11
96
9,720
Berlin
0.85
1
2,053
Brandenburg
0.66
18
1,198
Bremen
1.32
2
0,669
Hamburg
1.66
1
2,065
Hesse
1.19
26
5,100
Mecklenburg-Western Pomerania
0.64
18
0,784
Lower Saxony
0.86
46
5,006
North Rhine-Westphalia
0.96
54
12,294
Rhineland-Palatinate
0.85
36
2,400
30
Saarland
0.90
6
0,650
Saxony
0.66
29
2,010
Saxony-Anhalt
0.66
24
1,196
Schleswig- Holstein
0.88
15
1,690
Thuringia
0.66
23
1,119
Total
56,241
Table 7: Demand per federal state
Source: DESTATIS (2005).
4 Scenarios, Results and Interpretation
4.1
Scenarios
Four basic scenarios were considered, with variations of the applied pricing model and installed offshore
wind capacity:
1. Status quo: no additional offshore wind energy plants using the cost minimization approach
(“uniform pricing”).
2. Nodal prices without offshore wind: no additional offshore wind energy plants using the nodal
pricing model.
3. Nodal prices plus 8 GW: additional 8 GW offshore wind energy plants using the nodal pricing
model.
4. Nodal prices plus 13 GW: additional 13 GW offshore wind energy plants and grid extension using
the nodal pricing model.
Furthermore, for all of these scenarios reference demand was varied. Average demand was assumed to equal
56,241 MW. According to VDN (2005), peak load in Germany was 77,200 MW in 2004, being almost 1.4
times the average load. For this reason, high demand was calculated multiplying average demand by 1.3.
Low demand was assumed to be 0.7 times average demand.
The installed onshore wind energy capacity was allocated to different wind power generation zones, which
were then assigned to certain nodes.29 For the calculation of the load flow it was assumed that the feed-in of
offshore and onshore generated electricity is at most equal to the aggregated installed capacity of the wind
plants.
31
It was first checked whether nodal pricing was superior to cost minimization under uniform pricing regarding
the respective social welfares (section 4.2.1). To ensure comparability of these scenarios, the same input data
were used. Within the nodal price scenario demand and price could vary, whereas, the cost minimization
approach works with a given uniform price. Neither of these scenarios considers the integration of additional
offshore wind energy. Thus, the impact on social welfare of introducing a competitive nodal pricing scheme
in Germany compared to the current situation is obtained.
In a next step additional offshore wind energy plants were integrated into the existing grid (section Fehler!
Verweisquelle konnte nicht gefunden werden.). The aim was to find out how much offshore wind energy
could be fed into the grid at most without any extension of lines. Consequently, they were not considered in
the model, which is based on marginal costs. Offshore wind energy from the North Sea was supposed to be
fed in completely at nodes along the coastline (Brunsbüttel, Emden, Wilhelmshaven). Having calculated
occurring congestions, GAMS would reduce input of offshore energy if congestion costs exceeded
opportunity costs of wind energy. Therewith, this scenario shows the maximum possible offshore feed in
considering the existing grid.
Finally, a scenario was run considering additional 13 GW offshore wind energy plant (section 4.2.3).30 In our
model, this would require an extension of the grid by four lines and an upgrade of two lines.31 Fix costs from
an expansion of plant and grid capacity were neglected and offshore energy supposed to be fed into nodes at
the coast.
Scenario
Demand at
Price
loads
Capacity of offshore
Grid capacity
wind energy plants
low
1. Status quo
average
fix
0 GW
existing lines
nodal
0 GW
existing lines
nodal
8 GW
nodal
13 GW
high
2. Nodal prices without
offshore wind
low
average
high
low
3. Nodal prices plus 8 GW
average
high
existing lines
(full capacity)
low
4. Nodal prices plus 13 GW
average
grid extension
high
29
In this study no geographical differences in the strength of wind (e.g. strong wind vs. light wind) were adopted. In case of
distinguishing wind generated electricity by regions, a higher load on the transmission lines from North to South and from East to
West would result (DENA, 2005a, p. 75 et sqq.).
30
The DENA grid study (DENA, 2005a) proposes offshore wind capacities of 20 GW until 2020.
31
These lines are planned to construct according to VGE (2000).
32
Table 8: Scenarios
In the subsequent chapter results will be discussed. Scenarios will be compared as following:
•
Status quo vs. nodal prices without offshore wind (scenario 1 vs. scenario 2)
•
Nodal prices without wind vs. nodal prices plus 8 GW (scenario 2 vs. scenario 3)
•
Nodal prices plus 8 GW vs. nodal prices plus 13 GW (scenario 3 vs. scenario 4)
4.2
4.2.1
Results and Interpretation
Existing HV-grid: scenario 1 vs. scenario 2
First we compared nodal pricing with the cost minimization under uniform pricing. The results refer to
hourly values. Marginal cost bidding and a demand elasticity of -0.25 at the reference point are supposed. In
order to define the reference price, the EEX average price32 for the relevant period – same as for demand
calculation – was estimated using the 200-day-line.
32
Note that the EEX volumes at the moment only account for approximately 10% of the entire market volume.
33
Cost minimization
Scenario
Nodal pricing
Welfare
Demand
Losses
Welfare
Welfare
Demand
Demand
Losses
[Mio. €]
[GWh]
[MWh]
[Mio. €]
change
[GWh]
change
[MWh]
Low
3.19
39.4
1446
3.23
+ 1.3%
44.4
+ 12.9%
1365
Average
4.44
56.3
1544
4.48
+ 0.9%
62.0
+ 10.3%
1547
High
5.67
73.1
1720
5.67
+ 0.6%
79.2
+ 8.4%
1890
Table 9: Results for cost minimization and nodal pricing
4.2.1.1
Low load
The greatest welfare gain occurs in the low load case. Here, the welfare under nodal pricing exceeds the
welfare under uniform pricing by 1.3% (Table 9). Although the demand in the nodal price scenario is greater
than in the cost minimization scenario, losses are lesser under nodal pricing. Hence, energy is allocated more
efficiently as only nodes with a high willingness to pay justify a loss-intensive transport, whereas, under a
fixed price the allocation is independent from the willingness to pay.
4.2.1.2
Average load
The welfare gain through nodal pricing in this scenario amounts to 0.9%. Losses are greater than in the low
load scenario and equal approximately losses in the cost minimization case. However, as the optimal demand
again increases, energy is allocated more efficiently.
4.2.1.3
High load
The welfare gain in this case amounts to 0.6%. The demand again increases. The ratio between losses and
demand is approximately the same. Thus, energy transport is at the same efficiency level. Under nodal
pricing, however, energy is allocated according the willingness to pay. Therefore, welfare is greater albeit the
relative losses are the same.
4.2.1.4
Interpretation
The variations in welfare gain between the scenarios result from two facts. First, the introduction of nodal
prices allows prices to vary from node to node which means that energy is allocated according to the
willingness of pay at each node (pictured by the demand curve for each node). Second, onshore wind input
causes low opportunity cost which we treat as marginal cost of wind supply. In the low load case, demand is
satisfied by low marginal cost generators (onshore-wind, nuclear, lignite). Hence, the price differences
34
between nodal prices and the uniform price is greatest.33 Combining this with the two facts mentioned above,
it can be shown that the welfare spread between uniform and nodal pricing is largest during low load periods
as the uniform price error is largest. Onshore wind generators, however, are predominantly located in
Northern and Central Germany but inject energy into many different nodes and can, thus, be sufficiently
transmitted throughout the country. Remarkably, the same lines are congested comparing uniform and nodal
pricing scenario. Taking congestions into account and thus pricing energy efficiently leads to higher demand
and lower – but differing – prices (Figure 5).
35,00
30,00
€/MWh
25,00
20,00
15,00
10,00
5,00
0,00
1
17 33 49 65 81 97 113 129 145 161 177 193 209 225 241 257 273 289 305
node
nodal price
uniform price
Figure 5: Nodal prices and uniform price within the average load scenario
Altogether, the welfare under nodal pricing is greater for all three demand scenarios – low, average and high
load. For the average case, the annual welfare gain amounts to 350 million Euros. Hence, nodal pricing is the
economically more efficient tool. Note, that offshore wind has not been included, yet. Subsequently, we will
simulate the injection of offshore wind energy into the grid. Therefore, we use the nodal pricing approach as
we have proven that it creates greater social welfare than cost minimization under uniform pricing.
4.2.2
Offshore wind energy input: scenario 3 vs. scenario 2
The constant input of wind onshore power is the result of a German law that guarantees fixed prices for
power of windmills. That is why the maximum possible input of wind onshore power has to be taken as
input. As for the wind offshore power, the amount of input is capped due to the available line capacities that
depend on demand levels. The opportunity costs of generating one unit of wind energy were set to
4.05 €/MWh.
33
See Appendix D:
Result data for figures showing the nodal prices for the other scenarios.
35
Wind offshore [MW]
Wind onshore [MW]
Average load
7812
16695
Low load
7085
16695
High load
7894
16695
Table 10: Maximum possible input without grid extension (scenario 3)
Compared to the nodal pricing model without offshore wind parks an additional welfare gain of 1% occurs.
The average nodal price drops about 10% to 15.4 €/MWh. Particularly the nodes in Northern Germany
benefit from the additional wind energy (Figure 6). Overall, the southern part of Germany is less affected by
offshore wind generation. Anyway, Northern and Central German nodes benefit from the low wind price.
This result is independent from the demand case.
18
16
14
€/MWh
12
10
8
6
4
2
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
node
Figure 6: Nodal price difference (“without offshore” minus “plus 8 GW”)
As handled in the model the German grid was loaded with an excessively high offshore energy input: On the
one hand this gives the maximum possible value without extension in the net, on the other hand this step
helps to find out, which lines are critically loaded by the wind offshore energy.
36
Line
Description
From Bus
To Bus
3
Wilhelmshaven to Conneforde
2
3
4
Conneforde to Emden
3
4
298
299
18
Dt. Bucht 1 to Dt. Bucht 2
27
Sottrum to Landsbergen
17
46
31
Dollern to Wister
18
21
46
Hamburg Hafen to Hamburg Ost
28
30
168
Rommerskirchen to Niederaußen
115
116
369
Neuenhagen to Marzahn
266
267
Table 11: Congested lines within the “plus 8 GW” scenario (average load)
4.2.3
Offshore model grid extension: scenario 4 vs. scenario 3
One scenario of German energy policy makers is to install offshore wind energy plants with up to 15 GW.
This study implemented a goal of 13 GW by building and upgrading electricity lines in the north of
Germany. Some of them have already been planned (VEG, 2001). Although this study applies a very
ambitious extension (Table 12), the maximum offshore capacity could not be raised higher than 13.3 GW.
The latter is caused by additional congestions in Northern Germany. The results show that a grid extension
has to be planned very carefully to maximize the additional benefits. Often new congestions appear in the
downstream grid limiting the effect of the extension.
From node
To node
Type of line
1.
Emden
Diele
double 380 kV
2.
Wilhelmshaven
Conneforde
double 380 kV
3.
Diele
Cloppenburg
double 380 kV
4.
Cloppenburg
St. Hülfe
double 380 kV
5.
Emden
Coneforde
upgrade to 380kV
6.
Cloppenburg
Coneforde
upgrade to 380kV
Table 12: Assumed grid extension
37
Offshore wind [GW]
Average load
12.6
Low load
11.1
High load
13.3
Table 13: Maximum wind offshore energy
with extended grid (scenario 4)
For the “plus 13 GW” scenario, we might expect demand to fall due to occurring congestions from the
additionally injected wind energy, which leads to rising prices (Table 14). However, the low marginal costs
of wind energy more than compensate that effect making available energy cheaper to customer. The average
price decreases about 2.5% to 15.06 €/MWh. Again, mainly nodes in Northern Germany benefit from the
grid extension. In consequence, total demand increases (Figure 7). Due to falling energy supply costs and
rising demand the additional welfare gain is about 0.8% compared to the situation in the grid without
extension.
Line Location
Average load
Low load
High load
-
X
X
10 Niederlangen to Meppen
X
X
X
18 Dt. Bucht I to Dt. Bucht II
-
-
X
31 Dollern to Wilster
X
-
X
34 Brunsbuettel to Wilster
-
-
X
46 Hamburg Hafen to Hamburg Ost
X
X
X
76 Luestringen to Wehrendorf
X
-
X
103 Polsum to Kusenhorst
-
X
X
168 Romerskrichen to Niederaussen
X
-
X
274 Daxlanden to Weiher 2
-
-
X
339 Grossdalzig to Eula
-
-
X
369 Neunhagen to Marzahn
X
-
X
414 Ludwigsburg to Neckarwestheim
-
-
X
426 Emden to Diele
-
-
X
3 Wilhelmshaven to Conneforde
Table 14: Congested lines (X) for the “plus 13 GW” scenario
38
1,60%
1,40%
Demand change
1,20%
1,00%
0,80%
0,60%
0,40%
0,20%
0,00%
low
average
nodal plus 8 GW
Figure 7:
high
nodal plus 13 GW
Change in optimal demand: scenario “nodal price plus 8 GW” vs.
“nodal price plus 8 GW”
Surprisingly, some nodes have prices below their costs of generation. This is caused by the welfare
maximizing attempt. If additional demand at one node enables supply a node with a higher willingness to
pay, the welfare gain from this node can be higher than the loss from the first node. This phenomenon only
occurs in few cases in Northern Germany enabling a higher flow of cheap wind energy to the South.
However, due to these congestions some nodes face a serious price increase (Figure 8).
20
15
10
€/MWh
5
0
-5
-10
-15
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
-20
node
Figure 8: Nodal price difference (“plus 8 GW” minus “plus 13 GW”)
39
Since only a limited amount of wind energy can be transported to the demand centers in the south, only
Northern Germany would contribute to the welfare gain and benefit from the offshore wind input (Figure 9).
Moreover, it must be considered that thenetwork extension ivestments are not taken into account in the
welfare analysis. Further, grid constructions are likely to become political issues. Under these circumstances,
the welfare gain from grid extensions must be regarded differently to the welfare gain from introducing
nodal pricing. Because only a limited amount of wind energy can be transported to the demand centers in the
south, in a nodal pricing regime only Northern Germany would participate in the welfare gain resulting from
offshore wind. The analysis shows that the German electricity grid is not suited for a high amount of offshore
capacity. The highly meshed network rather seems to be designed for decentralized input.34
Figure 9: Congested lines around the North Sea 13 GW average
34
Note that, here, ‘decentralized’ refers to units significantly smaller than 8 GW.
40
4.3
Comparison of all models
The analysis showed that the nodal model approach is superior to the cost minimization approach under
uniform pricing as well as additional input of offshore wind energy increases the welfare (Figure 10). The
latter is, particularly, caused by the comparably low opportunity costs of wind energy. Increasing the costs
would lead to a decrease of the welfare benefits. Eventually, the gain could turn into a loss if the opportunity
costs are higher than the marginal costs of nuclear and lignite energy. In this case the political feed-in
guarantee for wind energy would lead to a drawback of cheaper fossil energy and, thereby, cause welfare to
decrease. On the other hand, if the opportunity cost is lower than the value estimated in the DENA study, the
welfare gain would become much more significant. However, while this is important for the offshore wind
scenarios, it does not influence the result about the superiority of the nodal pricing approach.
3,50%
3,00%
Welfare Gain
2,50%
2,00%
1,50%
1,00%
0,50%
0,00%
low
average
nodal
nodal+8GW
high
nodal+13GW
Figure 10: Welfare gain under nodal pricing compared to cost minimization
Another interesting circumstance is the impact of wind energy on grid losses. The dispatch of energy is more
efficient under nodal pricing and thus the ratio of losses to demand is lower. By injecting additional offshore
energy into the grid, this ratio increases significantly (Table 15). An explanation, therefore, consists in the
fact that energy is injected only at three nodes in Northern Germany. This highly centralized energy input
has to be transported to demand centers in Central and South Germany since not the entire wind energy can
be consumed at Northern German nodes. The welfare maximizing approach takes account of this problem.
Since lost energy has to be generated, it increases the total costs of generation. The calculated scenarios
represent the optimal dispatch under the assumed conditions.
41
Demand
Scenario 1:
Scenario 2:
Scenario 3:
Scenario 4:
uniform pricing
nodal pricing
nodal +8GW
nodal + 13 GW
Low
0.037
0.031
0.052
0.059
Average
0.027
0.025
0.046
0.050
High
0.024
0.024
0.039
0.043
Table 15: Ratio of losses against demand
Congestions occur in all of the nodal pricing scenarios. However, the number of congested lines increases
strongly in the scenarios with additional offshore wind capacities. In short, the DENA study shows fewer
congested lines. The congestions, furthermore, differ from the congestions pointed out by the DENA grid
study (2005a). There is only one congested line in this model that corresponds to the DENA congestions.
But, the congestions occur in similar regions. An important reason is that the DENA did assume offshore
wind facilities in the Baltic Sea, too. This changes the stress on the lines and allows a better distribution of
the energy throughout the grid. However, at this point of time, it seems that large wind parks are much more
likely to be erected in the North Sea, if they come about at all.
5 Conclusions
This paper has analyzed the implication of additional wind supply into the German high-voltage grid, using a
nodal pricing approach.35 First of all, it is shown that a nodal pricing scheme is economically superior to cost
minimization under a uniform price. Welfare increases between 0.6% and 1.3% within the nodal price
approach. Note that this seems to be quite low but means a large number in absolute terms. Demand
increases significantly under nodal pricing, whereas a demand increase is not allowed by definition in the
cost minimization scenario due to the uniform price.
Moreover, it has been illustrated that there is an additional welfare increase of about 1% on average in case
of additional offshore wind input into the German power grid. However, the results show that there is a limit
of wind energy distribution at about 8 GW. Beyond that we were forced to extent the modeled grid in order
to supply with further wind energy. Even though, the welfare increases again by 0.8% when escalating the
wind supply after the grid extension, the downstream grid cannot carry the burden and congestions occur on
lines leaving the adjacent nodes. Consequently, the prices at the inland nodes do not differ significantly as
their demand is accommodated by the same generating pool as before.
42
Note as well that the 8 GW boundary for the current grid already includes that only offshore wind facilities
generate in Northern Germany, whereas existing large-scale plants would not be dispatched. However, these
facilities might be necessary for balancing and response power. Problems may arise, if the construction of
offshore wind mills sets negative incentives for investments in other types of generation plants. This is not
represented in our straightforward marginal consideration.
References
Alaywan, Ziad, and Tong Wu (2004): Transitioning the California Market from a Zonal to a Nodal
Framework: An Operational Perspective. In: Proceedings of the Power Systems Conference and
Exposition,
2,
862-867.
Retrieved
September
01,
2005,
from
http://www.caiso.com/docs/09003a6080/32/2c/09003a6080322c6d.pdf
Bohn, Roger E., Caramanis, Michael C., and Fred C. Schweppe (1984): Optimal pricing in electrical
networks over space and time. In: Rand Journal of Economics, 15, 360-375.
Borenstein, Severin, Bushnell, James, and Frank Wolak (2000): Diagnosing Market Power in California’s
Deregulated Wholesale Electricity Market. PWP-064, University of California Energy Institute.
Retrieved September 01, 2005, from http://www.ucei.berkeley.edu/ucei/PDF/pwp064.pdf
Bower, John (2004): Electricity Infrastructure & Security of Supply: Should EU Governments Invest in
Transmission Capacity? Oxford Institute for Energy Studies. Retrieved August 31, 2005, from
http://www.oxfordenergy.org/comment_prn.php?0403
CAISO (2005): Market Redesign and Technology Upgrade. Locational Marginal Pricing (LMP) Study 3B.
Retrieved August 31, 2005, from http://www.caiso.com/docs/2005/08/24/2005082414133610519.pdf
Chen, Luonan, Suzuki, H., Wachi, T., and Y. Shimura (2002): Components of nodal prices for electric power
systems. In: IEEE Transactions on Power Systems, 17, 41-49.
DENA (2005a): dena-Netzstudie, Energiewirtschaftliche Planung für die Netzintegration von Windenergie in
Deutschland an Land und Offshore bis zum Jahr 2020. Deutsche Energie-Agentur.
DENA (2005b): Summary of the Essential Results, Planning of the Grid Integration of Wind Energy in
Germany Onshore and Offshore up to the Year 2020 (dena Grid study). Deutsche Energie-Agentur.
DESTATIS (2005): Statistik regional 2004. Statistisches Bundesamt Deutschland. Retrieved July 21, 2005,
from http://www.destatis.de/allg/d/veroe/proser211_d.htm.
DEWI (2005): Deutschlands Windindustrie bleibt Weltmeister. Deutsches Windenergie-Institut. Retrieved
September 06, 2005, from www.dewi.de/dewi_neu/deutsch/themen/statistic/pdf/pm28072005.pdf.
35
Note that we did not consider the case without onshore wind energy availability. Balancing and response power are regarded to
exist to a sufficient degree and cause marginal costs that are, here, referred to as opportunity costs for wind.
43
Ding, Feng, and J. David Fuller (2005): Nodal, Uniform, or Zonal Pricing: Distribution of Economic
Surplus. In: IEEE Transactions on Power Systems, 20, 875-882. Retrieved September 01, 2005, from
http://ieeexplore.ieee.org/iel5/59/30784/01425584.pdf?arnumber=1425584
E.On Netz AG (2005): Netznutzungsentgelte für die Netznutzung das Stromversorgungsnetz der E.ON Netz
GmbH.
Retrieved
August
29,
2005,
from
http://www.eon-
netz.com/Ressources/downloads/netznutzungsentgelte.de.pdf.
EIA (2004): Electric power Annual 2003. Energy Information Administration. Retrieved September 06,
2005, from http://www.eia.doe.gov/cneaf/electricity/epa/epa.pdf.
EnBW
AG
(2005):
Preisblätter
Netznutzung.
Retrieved
August
29,
2005,
from
http://www.enbw.com/content/de/netznutzer/strom/netznutzung/preisblaetter.
Energyquote (2005): UK Market Bulletin 13th April 2005. Retrieved August 31, 2005, from
http://www.energyquote.co.uk/markets/news_commentary.html
Fuller, J. David. (2004): Uniform, Nodal and Zonal Pricing in Electricity Markets. University of Waterloo,
Department
of
Management
Sciences.
Retrieved
August
31,
2005,
from
http://www.gerad.ca/fichiers/congres/2004-05-07-Fuller.pdf
Green, Richard (2004): Electricity Transmission Pricing: How Much does it Cost to Get it Wrong?
University of Hull Business School.
Hogan, William W. (1998): Transmission Investment and Competitive Electricity Markets. Harvard
University, John F. Kennedy School of Government, Center for Business and Government.
Hogan, William W. (1999): Transmission Congestion: The Nodal-Zonal Debate Revisited. Harvard
University, John F. Kennedy School of Government, Center for Business and Government. Retrieved
August 29, 2005, from http://ksghome.harvard.edu/~whogan/nezn0227.pdf
Hsu, Michael (1997): An Introduction to the Pricing of Electric Power Transmission. In: Utilities Policy, 6,
257-270.
Johnsen, Tor Arnt, Verma, Shashi Kant, and Catherine Wolfram (1999): Zonal Pricing and Demand-Side
Bidding in the Norwegian Electricity Market. PWP-063, University of California Energy Institute.
Retrieved September 01, 2005, from http://www.ucei.berkeley.edu/ucei/PDF/pwp063.pdf
Koettnitz, Harald, and Hans Pundt (1967): Berechnung elektrischer Energieversorgungsnetze, Band I:
Mathematische
Grundlagen
und
Netzparameter.
Leipzig,
VEB
Deutscher
Verlag
für
Grundstoffindustrie.
Koettnitz, Harald, Winkler, Gert, and Klaus-Dieter Weßnigk (1986): Grundlagen elektrischer
Betriebsvorgänge in Elektroenergiesystemen. Leipzig, VEB Deutscher Verlag für Grundstoffindustrie.
Krause, Thilo (2005): Congestion Management in Liberalized Electricity Markets – Theoretical Concepts
and International Application. EEH – power systems laboratory, Swiss Federal Institute of
Technology
Zurich.
Retrieved
August
31,
2005,
from
http://www.eeh.ee.ethz.ch/downloads/psl/publications/krause_congestion_management.pdf
Lunze, Klaus (1987): Berechnung elektrischer Stromkreise. Berlin, VEB Verlag Technik.
44
Ma, Xingwang, Sun, David I., and Kwok W. Cheung (2003): Evolution Toward Standardized Market
Design. In: IEEE Transactions on Power Systems, 18, 460-469. Retrieved September 01, 2005, from
http://ieeexplore.ieee.org/iel5/59/26968/01198273.pdf?isnumber=&arnumber=1198273
Overbye, Thomas J., Cheng, Xu, and Yan Sun (2004): A Comparison of the AC and DC Power Flow Models
for LMP Calculations. In: Proceedings of the 37th Hawaii International Conference on System
Sciences 2004.
Pfaffenberger, Wolfgang, and Maren Hille (2004): Investitionen im liberalisierten Energiemarkt: Optionen,
Marktmechanismen, Rahmenbedingungen. Final Report, University of Bremen, Bremer Energie
Institut.
Pundt, Hans (1983): Elektroenergiesysteme: 5. Lehrbrief. Zwickau, Zentralstelle für Lehr- und
Organisationsmittel des Ministeriums für Bildung.
Pundt, Hans, and Peter Schegner (1997): Wissensspeicherheft: Elektroenergiesysteme. Dresden University of
Technology, Institute for Electrical Power Supply.
RWE
AG
(2005a):
Facts
&
Figures
2005.
Retrieved
September
01,
2005,
from
http://www2.rwecom.geber.at/factbook/en/servicepages/downloads/files/electricity_grid_rwe_fact.pdf.
RWE AG (2005b): Preise für die Nutzung des Netzes der RWE Transportnetz Strom GmbH. Retrieved
August
29,
2005,
from
http://www.rwe-
transportnetzstrom.com/generator.aspx/netznutzung/netznutzungspreise/language=de/id=75492/netznu
tzungspreise-home.html.
Schröter,
Jochen
(2004):
Auswirkungen
des
europäischen
Emissionshandelssystems
auf
den
Kraftwerkseinsatz in Deutschland. Diploma thesis, Berlin University of Technology, Institute of
Power
Engineering.
Retrieved
September
01,
2005,
from
http://basis.gruene.de/bag.energie/papiere/eeg_diplarbeit_schroeter_lang.pdf.
Schweppe, Fred C., Caramanis, Michael C., Tabors, Richard D., and Roger E. Bohn (1988): Spot Pricing Of
Electricity. Boston, Kluwer.
Stigler, Heinz, and Christian Todem (2005): Optimization of the Austrian Electricity Sector (Control Zone of
VERBUND APG) under the Constraints of Network Capacities by Nodal Pricing. In: Central
European Journal of Operations Research, 13, 105-125.
Statistik-Portal: Volkswirtschaftliche Gesamtrechnungen. Bruttoinlandsprodukt. Retrieved June 23, 2005,
from http://www.statistik-portal.de/Statistik-Portal/de_jb27_jahrtab65.asp
Stoft, Steven (2002): Power System Economics: Designing Markets for Electricity. Piscataway, NJ, IEEE
Press, Wiley-Interscience.
Todem, Christian (2004): Methoden und Instrumente zur gesamtsystemischen Analyse und Optimierung
konkreter Problemstellungen im liberalisierten Elektrizitätsmarkt. Dissertation, Graz University of
Technology, Department of Electricity Economics and Energy Innovation.
Todem, Christian, Stigler, Heinz, Huber, Christoph, Wulz, Christoph, and Hannes Wornig (2004): Nodal
Pricing als Analyseinstrumentarium zur Untersuchung der volkswirtschaftlichen Auswirkungen eines
45
marktbasierten Engpassmanagements bei Engpässen im Verbundsystem. Graz University of
Technology, Department of Electricity Economics and Energy Innovation.
Törnquist, Jonas (2005): UK Transmission System Challenges. The Office of Gas and Electricity Markets.
Retrieved September 01, 2005, from http://www.iea.org/textbase/work/2004/transmission/tornquist.pdf
UCTE (2004): Interconnected Network of UCTE. Dortmund, Abel Druck.
VDN (2001): Verbändevereinbarung über Kriterien zur Bestimmung von Netznutzungsentgelten für
elektrische Energie und über Prinzipien der Netznutzung, 13.12.2001. Retrieved August 29, 2005,
from http://www.vdn-berlin.de/verbaendevereinbarung_ii_plus.asp
VDN (2005): Jahreshöchstlast Strom 2004 im europäischen Vergleich. Retrieved August 20, 2005, from
http://www.vdn-berlin.de/akt_jhoechstlast_2005_07_28.asp.
VGE (2000): Elektrizitäts-Verbundsysteme in Deutschland. Essen, Verlag Glückauf.
VGE (2005): Jahrbuch der europäischen Energie- und Rohstoffwirtschaft 2005. Essen,Verlag Glückauf
GmbH.
46
Appendix A:
Inverse Demand, Nodal Price and Welfare
Assume a linear inverse demand function of the general form as given in (A.1) with the slope b being
negative. Hence, the demand function is pictured in equation (A.2).
p(d ) = a + b ⋅ d
d ( p) = −
a 1
+ ⋅p
b b
(A.1)
(A.2)
Now calculating the demand elasticity according to (A.3), yields equation (A.4). This will subsequently lead
to the calculation of the slope b (A.5).
ε=
δd p
⋅
δp d
(A.3)
1 p
b d
(A.4)
ε= ⋅
In order to derive prohibitive price a and slope b, we assume that the demand elasticity ε equals -0.25 at the
reference point. Prohibitive price a and slope b for each node can, then, be calculated on the basis of given
reference price and demand – (A.5) and (A.6).
p ref 1
⋅
d ref ε
(A.5)
a = p ref − b ⋅ d ref
(A.6)
b=
Applying (A.6) and (A.5) yields, after simplifications, (A.7).
p= p
ref
p ref 1 ref
p ref 1
− ref ⋅ ⋅ d + ref ⋅ ⋅ d
ε
ε
d
d
1
⎛ d
⎞
p = p ref + ⋅ p ref ⋅ ⎜ ref −1⎟
ε
⎝d
⎠
(A.7)
For the optimal demand at node n (dn*), the node specific reference demand and price36, we finally get the
nodal price:
pn = pn
ref
*
⎞
1
ref ⎛ d n
+ ⋅ p n ⋅ ⎜⎜ ref
−1⎟⎟
ε
⎝ dn
⎠
(A.8)
Social welfare is calculated as the sum over the welfare of every node. Therefore, total costs C are subtracted
from the benefit given demand dn*. The benefit describes the value that the consumption of one unit of
electrical power gives to the customer. It is pictured by the area below the inverse demand function. Hence, it
can be derived by integrating the inverse demand function from zero to the optimal demand point.
36
Within the scope of this study, the reference price was assumed to be identical for all nodes.
47
dn
⎞
⎛ dn
*
*
*
*
*
⎜
W (d n ) = ∑ ∫ p (d n ) d d n − ∫ c(d n ) d d n ⎟
⎟
⎜0
n
0
⎠
⎝
*
*
*
⎡
1 1⎛
= ∑ ⎢ pnref d n* (1 − ) + ⎜⎜ d n*
ε 2⎝
n ⎢
⎣
( )
2
1 p nref
⋅
ε d nref
(A.9)
⎞⎤
⎟⎟⎥ - C
⎠⎥⎦
48
Appendix B:
Implementing the optimization problem in GAMS
First part
As for the scalars, Nodes, N and NN denote all the nodes form no. 1 to no. 308. Similarly all the lines from
no. 1 to no. 407 are represented by Line, L or LL. With the scalars MVABase, VoltageBase1 and
VoltageBase2, which are values of apparent power, first and second voltage level respectively, the
normalization bases ZBase1 and ZBase2 are computed. They are needed in the next part. In addition a fixed
demand elasticity ε for all demand functions is given as a scalar.
Second part
Almost all parameters are imported directly from excel sheets without conversion:
FromBus(L) and ToBus(L) are the numbers of the starting node and the end node linked directly with
each other by a line.
LineVoltage(L) is the voltage level of a line.
ThermalLimit(L), as mentioned above, is the maximum current through a line without overheating
and damaging the line.
Demand0(N) is the reference demand of power at a node.
Price0(N) is the reference price at a node.
There are nine types of power stations in this model. Each of them has a maximum supply capacity per node.
This is memorised in Max_Generation_[name](N) whereas name is the short name for the type of power
station. Except wind stations, each type of power station has different marginal costs of production that are
denoted MC_[name](N) whereas name is again the short name of the power station type. The opportunity
cost of wind supply are memorised in OC_wind(N).
Some parameters are converted:
The given resistances and reactances of the lines are divided by ZBase1 or ZBase2 to get the normalized
parameters Resistance(L) and Reactance(L). As a result both parameters are expressed in a per unit system.
The maximum possible load flow through a line for thermal reasons is calculated with (1) and memorised in
parameter PowerFlowLimit(L).
PowerFlowLimit(L) = 3 * LineVoltage(L) *ThermalLimit(L)
(1)
49
Third part
The information about the network topology in FromBus(N) and ToBus(N) is written into an incidence
matrix called Incidence(L,N). With the help of BVector(L) the matrixes H(L,N) and B(N,N) are made (2) and
(3). Node 1 is nominated swing bus slack(N) of the network.
H(L,N) = Bvector(L) × Incidence(L,N)
(2)
L max
∑ [H ( L, NN ) ∗ Incidence( L, N )]
B(N,NN) =
(3)
L =1
Fourth part
There are variables for demand of power Demand(N) and power injection Generation(N). The latter one
consists of several sub variables called Generation_[name](N) with the same denotation for name as in the
parameter marginal costs. Cost(N) are the total costs of generation per node and TotalCosts are the total
costs of the entire network. NetInput is the difference between demand and power injection at a node. The
amount of power flowing through a line is described by LineFlow(L). Delta(N) is the voltage angle in regard
to the swing bus voltage angle. Last but not least, social welfare is the variable Welfare.
Fifth part
Each node has a linear inverse demand function that is defined by Price0(N), Demand0(N) and ε:
p(N) = a + b(N)*d(N)
b( N ) =
p ref
d ref ( N )
(2)
∗ε
(3)
a = pref*(1-ε)
(4)
This yields equation (x).
Integrating the inverse demand function from 0 to Demand(N) yields the social benefit.
Subtracting
TotalCosts, then, yields the Welfare:
Demand ( N )
Welfare =
∫ Nodalp[( Demand ( N )]dDemand ( N ) − TotalCosts
(4)
0
Totalcosts means the sum of the costs of generation at all nodes.
The cost of generation at a node is the marginal cost of a power plant type times its output.
The following equations concern physical constraints:
50
For a network without losses NetInput equals B times Delta for all nodes. Losses are calculated with the
second summand and are added to the nodes at the ends of a line in equal shares. (5)
LineFlow is H times Delta. (6)
N max
NetInput(N) =
∑ {B( N , NN ) ∗ Delta( NN ) } ∗ MVABase
NN =1
+ 0,5 ∗
N max
∑{
Resistance(L) ∗ (LineFlow( L) ∗ Incidence( L, N ) )
2
}
(5)
N =1
N max
LineFlow(L) =
∑ {H ( L, N ) ∗ Delta( N ) }
(6)
N =1
The modulus of LineFlow faces an upper bound. (7a) (7b)
The Delta is fixed at 0 for the swing bus. (8)
No power injection of a power plant type is allowed to exceed its maximum capacity of generation. (9)
LineFlow(L) ∗ MVABase ≤ PowerFlowLimit(L)
(7a)
LineFlow(L) ∗ MVABase ≥ - PowerFlowLimit(L)
(7b)
Slack(N) ∗ Delta(N) = 0
(8)
Generation_type(N) =L= Max_Generation_type(N)
(9)
Spreadsheet: Parameters
Name
Schweppe`s notation
BVector(L)
Ω
Incidence(L,N)
A
description
incidence
matrix:
line-nodes
identity
H(L,N)
Ω *A
transfer matrix for calculation
[p.u.]
B(N,N)
AT* Ω *A
system susceptance matrix
[p.u.]
LineVoltage(L)
voltage level of a line [kV]
ThermalLimit(L)
maximum possible current [A]
51
LineFlow(L)
z
power flow through a line L [A]
NetInput(N)
y
difference between demand and
supply [MW] at node N
Delta(N)
δ
voltage angle at node N [rad]
Demand(N)
d
demand of power [MW] at node
N
Generation(N)
g
amount of power [MW]
provided by all power plants
together at node N
Generation_[typex](N)
amount of power generation
provided by typex power
plants ant node N
Nodalp
Cost(N)
ρ
nodal price [Euro] at node N
costs of generation per node
[Euro] at node N
TotalCosts
total costs of generation of the
market [Euro]
Welfare
social welfare of the market
[Euro]
Table 16: Spreadsheet: Parameters
52
Appendix C:
Assumptions for calculating transmission losses in the
DCLF
According to Todem (2004, pp.130-131), transmission losses are made up by the sum of the load flows along
a line. Those can flow in both directions, so that:
L jk = Pjk + Pkj
(C.1)
Furthermore it can be stated that:
Gi = G jk = Gkj
(C.2)
Bi = B jk = Bkj
(C.3)
sinΘ jk = - sinΘ kj
(C.4)
cosΘ jk = cosΘ kj
(C.5)
Under the assumptions that
X i ff Ri
(C.6)
one can insert equation (3.10) into (C.1) and then simplify the resulting equation by inserting equations
(3.16), (3.17), (C.2), (C.3), (C.4) and (C.5). These steps lead to the equation for estimating transmission
losses (3.18).
53
Appendix D:
Result data
20
18
16
14
10
8
6
4
2
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
0
1
€/MWh
12
Node
Figure 11: Nodal prices without offshore wind (low load)
54
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
11.72
46
13.27
91
13.79
136
14.42
181
14.56
226
15.06
271
14.20
2
11.81
47
13.67
92
13.32
137
14.42
182
14.15
227
15.24
272
13.90
3
11.93
48
13.51
93
13.65
138
14.32
183
14.09
228
14.83
273
14.13
4
10.94
49
13.51
94
14.56
139
14.60
184
14.31
229
14.86
274
14.10
5
12.47
50
13.64
95
14.95
140
14.67
185
14.30
230
14.77
275
14.08
6
12.80
51
13.35
96
15.09
141
14.70
186
14.10
231
14.61
276
13.63
7
12.22
52
13.29
97
15.17
142
14.72
187
14.48
232
14.71
277
13.64
8
11.83
53
13.30
98
14.08
143
14.73
188
14.48
233
14.58
278
13.68
9
11.92
54
13.27
99
14.07
144
14.96
189
14.79
234
14.10
279
13.71
10
11.87
55
13.42
100
14.20
145
15.24
190
14.51
235
14.09
281
13.45
11
11.91
56
13.29
101
14.27
146
15.14
191
14.79
236
14.25
282
13.82
12
12.52
57
13.09
102
14.34
147
15.22
192
15.69
237
14.11
283
13.61
13
12.36
58
13.74
103
14.47
148
15.02
193
15.50
238
14.11
284
13.46
14
12.45
59
13.57
104
14.72
149
14.88
194
14.91
239
14.08
285
13.81
15
11.24
60
13.81
105
14.83
150
15.37
195
15.05
240
13.79
286
13.81
16
11.68
61
15.38
106
14.15
151
14.77
196
15.06
241
13.48
287
13.71
17
12.28
62
15.05
107
16.54
152
14.67
197
13.33
242
13.52
288
13.32
18
11.97
63
15.08
108
16.54
153
16.33
198
13.36
243
13.62
289
13.35
19
11.60
64
15.10
109
15.01
154
17.87
199
14.82
244
13.51
290
13.34
20
11.65
65
14.95
110
15.02
155
14.81
200
14.95
245
14.21
292
14.30
21
11.67
66
14.90
111
15.02
156
14.82
201
15.46
246
13.75
293
14.33
22
11.62
67
14.85
112
15.01
157
14.76
202
15.43
247
13.91
294
14.43
23
11.52
68
14.91
113
15.00
158
16.84
203
14.40
248
13.97
295
16.97
24
9.94
69
14.82
114
15.00
159
16.69
204
15.46
249
14.17
296
14.76
25
11.67
70
14.66
115
15.01
160
14.56
205
14.42
250
13.67
297
13.68
26
11.67
71
14.93
116
15.00
161
14.42
206
14.40
251
13.73
298
11.88
27
11.86
73
14.63
117
15.09
162
14.54
207
14.36
252
13.88
299
12.20
28
11.93
74
14.61
118
15.06
163
14.55
208
14.08
253
13.79
300
11.35
29
11.95
75
14.64
119
15.00
164
14.59
209
14.66
254
13.82
301
11.65
30
12.10
76
14.60
120
15.00
165
14.44
210
15.64
255
14.04
302
13.29
31
12.19
77
14.58
121
15.00
166
14.28
211
17.08
256
13.94
303
13.75
32
12.14
78
16.16
122
15.00
167
14.05
212
14.49
257
13.74
304
13.95
33
12.02
79
14.75
123
15.01
168
14.39
213
14.25
258
13.75
305
14.80
34
12.41
80
14.62
124
15.02
169
14.44
214
16.37
259
14.13
306
14.68
35
12.64
81
14.58
125
15.03
170
14.43
215
14.76
260
13.72
307
13.40
36
13.32
82
14.38
126
14.99
171
14.42
216
14.84
261
13.70
308
13.45
37
13.42
83
14.19
127
15.03
172
14.35
217
14.80
262
13.77
309
14.48
55
38
13.36
84
14.31
128
15.04
173
14.37
218
14.62
263
13.71
39
13.48
85
13.51
129
15.04
174
14.94
219
14.61
264
13.58
40
13.60
86
13.55
130
15.02
175
14.87
220
14.93
265
13.79
41
13.84
87
13.84
131
14.85
176
14.44
221
14.98
266
13.91
42
13.80
88
13.79
132
15.53
177
14.72
222
15.46
267
14.21
43
14.07
89
13.78
133
14.10
178
14.71
223
15.07
268
14.26
44
13.34
90
13.74
134
15.28
179
14.72
224
14.79
269
14.23
45
13.89
135
14.49
180
14.69
225
14.79
270
14.22
310
14.67
Table 17: Prices per node: without offshore wind (low load)
56
45
40
35
€/MWh
30
25
20
15
10
5
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Node
Figure 12: Nodal prices without offshore wind (high load)
57
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
16.52
46
17.98
91
18.32
136
19.56
181
21.16
226
21.44
271
25.24
2
16.64
47
18.21
92
18.00
137
19.57
182
18.49
227
21.38
272
12.71
3
16.75
48
18.00
93
18.29
138
19.45
183
18.00
228
20.36
273
23.85
4
15.52
49
18.04
94
21.57
139
18.96
184
19.31
229
19.21
274
23.78
5
17.04
50
18.29
95
22.59
140
18.98
185
19.39
230
19.40
275
24.20
6
17.20
51
18.01
96
22.97
141
19.03
186
19.57
231
19.21
276
18.75
7
17.48
52
17.97
97
23.18
142
19.06
187
17.29
232
19.81
277
18.80
8
16.72
53
18.00
98
18.62
143
19.05
188
17.30
233
19.18
278
18.88
9
16.99
54
17.88
99
18.49
144
19.29
189
17.96
234
18.07
279
18.96
10
16.87
55
18.00
100
18.71
145
20.02
190
20.84
235
18.06
281
17.12
11
17.20
56
17.34
101
18.74
146
19.79
191
21.92
236
18.45
282
12.93
12
18.19
57
17.35
102
18.68
147
19.91
192
39.53
237
18.02
283
12.93
13
17.93
58
17.62
103
18.86
148
19.32
193
34.71
238
18.00
284
15.48
14
18.00
59
17.65
104
19.00
149
18.96
194
22.51
239
17.97
285
13.87
15
16.45
60
17.84
105
19.11
150
19.21
195
24.42
240
17.45
286
13.87
16
17.06
61
18.71
106
18.37
151
17.88
196
22.91
241
17.08
287
14.57
17
17.71
62
18.00
107
19.69
152
17.77
197
15.54
242
16.55
288
15.50
18
17.17
63
18.00
108
19.59
153
18.34
198
15.58
243
16.70
289
15.70
19
16.66
64
18.01
109
18.00
154
18.00
199
26.27
244
16.53
290
15.71
20
16.92
65
18.07
110
18.00
155
18.02
200
24.51
245
17.31
292
19.41
21
16.94
66
18.02
111
17.98
156
18.00
201
24.37
246
15.00
293
20.94
22
16.91
67
18.09
112
17.84
157
18.14
202
24.27
247
16.99
294
21.32
23
16.85
68
18.00
113
17.77
158
18.00
203
21.17
248
17.46
295
27.94
24
14.69
69
18.02
114
17.61
159
18.76
204
24.41
249
17.90
296
21.74
25
17.23
70
18.00
115
17.80
160
18.44
205
21.31
250
16.63
297
22.30
26
17.23
71
18.03
116
15.00
161
18.57
206
21.26
251
16.73
298
17.21
27
17.29
73
18.05
117
18.72
162
18.70
207
21.13
252
16.94
299
17.67
28
17.30
74
18.07
118
18.63
163
18.58
208
20.66
253
16.75
300
16.59
29
17.72
75
18.00
119
17.86
164
18.78
209
21.90
254
16.92
301
17.19
30
17.46
76
18.05
120
17.96
165
19.35
210
24.15
255
17.42
302
17.99
31
17.45
77
18.08
121
17.96
166
19.41
211
28.34
256
17.18
303
18.06
32
17.60
78
19.46
122
17.94
167
19.15
212
21.10
257
15.68
304
18.42
33
17.64
79
18.59
123
17.96
168
19.80
213
20.93
258
15.71
305
19.03
34
17.64
80
18.00
124
18.00
169
20.49
214
25.74
259
17.62
306
20.25
35
17.80
81
18.21
125
18.54
170
20.61
215
21.81
260
15.20
307
15.95
36
18.17
82
18.12
126
18.77
171
20.72
216
21.97
261
15.00
308
17.12
37
18.23
83
18.06
127
18.71
172
20.96
217
21.92
262
16.26
309
21.10
38
18.27
84
18.72
128
18.57
173
20.95
218
21.52
263
15.00
310
21.31
58
39
18.36
85
17.59
129
18.77
174
24.48
219
21.49
264
16.49
40
18.18
86
17.75
130
19.01
175
24.27
220
21.65
265
14.20
41
18.42
87
18.33
131
17.89
176
21.06
221
21.57
266
12.50
42
18.69
88
18.31
132
20.30
177
21.43
222
22.87
267
27.89
43
18.97
89
18.30
133
18.45
178
21.39
223
21.72
268
27.43
44
18.15
90
18.27
134
18.55
179
21.43
224
21.00
269
27.15
45
18.60
135
19.26
180
21.33
225
20.64
270
26.40
Table 18: Prices per node: without offshore wind (high load)
59
25
20
€/MWh
15
10
5
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Node
Figure 13: Nodal prices “plus 8 GW” (average load)
60
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
5.63
46
16.01
91
16.26
136
17.36
181
17.85
226
18.19
271
17.72
2
4.05
47
16.11
92
15.37
137
17.37
182
17.36
227
18.39
272
14.69
3
10.00
48
16.14
93
15.78
138
17.48
183
17.29
228
17.70
273
17.33
4
4.05
49
16.13
94
17.42
139
17.25
184
17.56
229
16.88
274
17.30
5
11.75
50
15.93
95
18.08
140
17.17
185
17.55
230
16.99
275
17.46
6
12.78
51
15.12
96
18.32
141
17.12
186
17.35
231
16.84
276
15.49
7
10.35
52
15.17
97
18.45
142
17.16
187
17.15
232
17.15
277
15.52
8
10.00
53
15.32
98
16.30
143
17.25
188
17.16
233
16.87
278
15.58
9
8.43
54
14.78
99
16.29
144
17.45
189
17.66
234
16.10
279
15.62
10
10.45
55
14.86
100
16.47
145
18.06
190
17.83
235
16.09
281
15.09
11
6.39
56
14.22
101
16.52
146
17.90
191
18.30
236
16.42
282
14.71
12
4.06
57
13.64
102
16.59
147
18.00
192
19.51
237
16.11
283
14.51
13
3.98
58
14.71
103
16.83
148
17.48
193
19.43
238
16.11
284
14.84
14
4.02
59
14.82
104
16.91
149
17.18
194
18.50
239
16.09
285
14.85
15
4.56
60
15.21
105
16.97
150
17.61
195
18.80
240
15.62
286
14.86
16
3.58
61
16.75
106
16.14
151
16.38
196
18.76
241
15.06
287
14.92
17
0.70
62
16.25
107
18.05
152
16.28
197
15.41
242
15.00
288
14.73
18
11.64
63
16.26
108
18.00
153
17.39
198
15.46
243
15.12
289
14.80
19
11.29
64
16.25
109
16.03
154
18.00
199
18.47
244
15.02
290
14.79
20
4.05
65
16.12
110
16.02
155
16.92
200
18.62
245
15.54
292
17.54
21
3.51
66
16.11
111
16.01
156
16.93
201
19.83
246
15.00
293
17.71
22
4.59
67
16.11
112
15.89
157
16.98
202
19.76
247
15.39
294
17.90
23
3.88
68
16.11
113
15.83
158
18.00
203
17.83
248
15.77
295
22.17
24
3.37
69
16.06
114
15.68
159
18.25
204
19.84
249
16.08
296
18.16
25
3.96
70
15.94
115
15.85
160
17.10
205
17.87
250
15.31
297
16.59
26
3.96
71
16.09
116
15.00
161
16.95
206
17.85
251
15.39
298
5.31
27
5.81
73
16.03
117
16.58
162
17.10
207
17.76
252
15.56
299
3.89
28
6.56
74
16.04
118
16.52
163
17.11
208
17.41
253
15.43
300
4.60
29
5.92
75
16.00
119
15.92
164
17.76
209
18.20
254
15.52
301
3.95
30
9.20
76
16.05
120
16.01
165
17.71
210
19.70
255
15.95
302
15.31
31
10.00
77
16.03
121
16.01
166
17.54
211
22.41
256
15.79
303
16.21
32
10.69
78
17.71
122
16.00
167
17.29
212
17.67
257
15.14
304
16.19
33
2.60
79
16.43
123
16.01
168
17.62
213
17.47
258
15.16
305
16.92
34
10.78
80
16.07
124
16.05
169
17.79
214
20.87
259
16.09
306
17.89
35
11.66
81
16.16
125
16.46
170
17.80
215
18.17
260
15.00
307
14.87
36
14.47
82
15.95
126
16.61
171
17.79
216
18.26
261
14.95
308
15.10
37
14.79
83
15.83
127
16.69
172
17.74
217
18.24
262
15.33
309
17.83
38
14.54
84
16.44
128
16.49
173
17.76
218
18.02
263
14.98
310
17.98
39
15.00
85
15.42
129
16.67
174
18.60
219
18.00
264
15.14
61
40
15.11
86
15.56
130
17.09
175
18.47
220
18.26
265
14.90
41
15.73
87
16.22
131
16.15
176
17.81
221
18.27
266
14.65
42
15.77
88
16.23
132
17.99
177
18.06
222
19.10
267
18.31
43
16.10
89
16.24
133
16.23
178
18.03
223
18.24
268
18.24
44
14.91
90
16.23
134
16.42
179
18.06
224
17.77
269
18.16
45
16.15
135
16.88
180
18.00
225
17.59
270
18.00
Table 19: Prices per node: “plus 8 GW” (average load)
62
20
18
16
14
€/MWh
12
10
8
6
4
2
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Nodes
Figure 14: Nodal prices “plus 8 GW” (low load)
63
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
5.42
46
12.40
91
12.74
136
14.12
181
14.30
226
14.76
271
13.27
2
4.05
47
12.54
92
12.20
137
14.13
182
13.90
227
14.94
272
13.07
3
9.23
48
12.55
93
12.64
138
14.05
183
13.84
228
14.53
273
13.19
4
4.05
49
12.55
94
13.33
139
14.26
184
14.05
229
14.63
274
13.17
5
10.19
50
12.43
95
13.69
140
14.28
185
14.05
230
14.49
275
13.15
6
10.76
51
11.99
96
13.83
141
14.29
186
13.86
231
14.27
276
12.55
7
9.46
52
11.99
97
13.90
142
14.31
187
14.31
232
14.39
277
12.57
8
9.30
53
12.06
98
13.23
143
14.39
188
14.32
233
14.10
278
12.60
9
8.43
54
11.80
99
13.03
144
14.68
189
14.62
234
13.64
279
12.63
10
9.55
55
11.88
100
13.34
145
14.97
190
14.26
235
13.63
281
12.44
11
7.36
56
11.59
101
13.49
146
14.87
191
14.53
236
13.62
282
12.99
12
6.05
57
11.24
102
13.68
147
14.95
192
15.49
237
13.55
283
12.78
13
5.97
58
11.94
103
13.89
148
14.76
193
15.28
238
13.52
284
12.52
14
6.01
59
12.01
104
14.25
149
14.69
194
14.65
239
13.49
285
12.94
15
6.03
60
12.26
105
14.40
150
15.17
195
14.79
240
13.11
286
12.94
16
5.31
61
15.44
106
12.90
151
14.68
196
14.80
241
12.64
287
12.81
17
4.49
62
15.11
107
16.32
152
14.57
197
13.33
242
12.77
288
12.38
18
10.19
63
15.14
108
16.31
153
16.16
198
13.35
243
12.89
289
12.41
19
10.00
64
15.15
109
15.03
154
17.69
199
14.58
244
12.77
290
12.40
20
4.05
65
15.03
110
15.02
155
14.66
200
14.70
245
13.64
292
14.05
21
3.57
66
15.01
111
15.03
156
14.67
201
15.18
246
13.13
293
14.06
22
4.57
67
14.99
112
15.02
157
14.60
202
15.15
247
13.35
294
14.17
23
3.91
68
15.02
113
15.00
158
16.62
203
14.13
248
13.51
295
16.65
24
3.38
69
14.96
114
15.00
159
16.48
204
15.18
249
13.70
296
14.47
25
3.97
70
12.79
115
15.00
160
14.36
205
14.15
250
13.33
297
12.84
26
3.97
71
15.01
116
15.00
161
14.18
206
14.14
251
13.36
298
6.79
27
5.77
73
12.84
117
15.04
162
14.32
207
14.09
252
13.43
299
5.89
28
6.25
74
12.85
118
15.00
163
14.34
208
13.82
253
13.35
300
6.08
29
5.82
75
12.83
119
14.99
164
14.35
209
14.38
254
13.38
301
3.96
30
8.12
76
12.86
120
14.98
165
14.19
210
15.35
255
13.54
302
12.06
31
8.68
77
12.85
121
14.98
166
14.03
211
16.75
256
13.42
303
12.65
32
9.35
78
15.94
122
14.98
167
13.80
212
14.20
257
13.14
304
12.76
33
5.08
79
13.14
123
14.99
168
14.12
213
13.98
258
13.16
305
14.37
34
9.20
80
12.88
124
15.00
169
14.18
214
16.05
259
13.63
306
14.43
35
9.78
81
12.99
125
14.94
170
14.17
215
14.48
260
13.06
307
12.44
36
11.64
82
12.77
126
14.86
171
14.15
216
14.56
261
13.02
308
12.45
37
11.92
83
12.67
127
14.92
172
14.09
217
14.52
262
13.16
309
14.23
38
11.68
84
12.98
128
14.93
173
14.11
218
14.34
263
13.00
310
14.42
64
39
12.11
85
12.30
129
14.83
174
14.69
219
14.33
264
12.84
40
11.99
86
12.39
130
14.85
175
14.62
220
14.64
265
13.04
41
12.34
87
12.79
131
14.80
176
14.18
221
14.69
266
13.08
42
12.35
88
12.72
132
15.28
177
14.47
222
15.16
267
13.31
43
12.54
89
12.73
133
12.98
178
14.45
223
14.76
268
13.37
44
11.91
90
12.70
134
15.26
179
14.47
224
14.49
269
13.32
45
12.57
135
13.70
180
14.44
225
14.47
270
13.31
Table 20: Prices per node: “plus 8 GW” (low load)
65
45
40
35
€/MWh
30
25
20
15
10
5
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Nodes
Figure 15: Nodal prices “plus 8 GW” (high load)
66
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
6.88
46
17.29
91
18.05
136
19.41
181
20.98
226
21.26
271
22.88
2
4.05
47
17.87
92
17.14
137
19.42
182
18.45
227
21.21
272
13.33
3
14.55
48
17.64
93
17.60
138
19.34
183
18.00
228
20.19
273
21.80
4
4.05
49
17.64
94
20.78
139
18.79
184
19.21
229
19.06
274
21.76
5
15.46
50
17.82
95
21.77
140
18.79
185
19.29
230
19.23
275
22.17
6
15.99
51
17.19
96
22.14
141
18.83
186
19.44
231
19.02
276
17.71
7
15.19
52
17.13
97
22.34
142
18.86
187
17.20
232
19.62
277
17.75
8
14.64
53
17.18
98
18.17
143
18.89
188
17.21
233
18.92
278
17.83
9
14.24
54
17.01
99
18.23
144
19.14
189
17.87
234
17.83
279
17.90
10
15.00
55
17.22
100
18.40
145
19.87
190
20.68
235
17.81
281
16.50
11
13.69
56
16.71
101
18.41
146
19.64
191
21.74
236
18.17
282
13.51
12
18.19
57
16.43
102
18.39
147
19.76
192
39.19
237
17.75
283
13.45
13
17.82
58
17.12
103
18.60
148
19.18
193
34.41
238
17.72
284
15.32
14
18.00
59
17.17
104
18.78
149
18.84
194
22.33
239
17.69
285
14.19
15
12.70
60
17.49
105
18.90
150
19.11
195
24.22
240
17.09
286
14.20
16
13.05
61
18.71
106
18.18
151
17.84
196
22.72
241
16.49
287
14.72
17
16.13
62
18.00
107
19.56
152
17.74
197
15.46
242
16.12
288
15.31
18
15.92
63
18.00
108
19.46
153
18.30
198
15.50
243
16.27
289
15.46
19
15.44
64
18.00
109
17.95
154
18.00
199
26.04
244
16.11
290
15.47
20
4.05
65
18.05
110
17.94
155
18.02
200
24.30
245
16.91
292
19.30
21
19.48
66
18.01
111
17.92
156
18.00
201
24.19
246
15.00
293
20.78
22
6.09
67
18.07
112
17.78
157
18.11
202
24.09
247
16.60
294
21.16
23
17.49
68
18.00
113
17.71
158
18.00
203
21.01
248
17.20
295
27.73
24
15.25
69
18.00
114
17.55
159
18.73
204
24.23
249
17.64
296
21.57
25
17.88
70
17.94
115
17.73
160
18.34
205
21.14
250
16.40
297
20.56
26
17.88
71
18.01
116
15.00
161
18.45
206
21.10
251
16.50
298
13.32
27
10.48
73
18.04
117
18.62
162
18.58
207
20.96
252
16.71
299
17.44
28
9.90
74
18.05
118
18.53
163
18.47
208
20.50
253
16.52
300
12.80
29
10.77
75
18.00
119
17.80
164
18.66
209
21.73
254
16.69
301
17.84
30
12.60
76
18.01
120
17.89
165
19.23
210
23.97
255
17.20
302
17.17
31
13.15
77
18.04
121
17.89
166
19.29
211
28.13
256
16.97
303
17.99
32
14.69
78
19.33
122
17.88
167
19.06
212
20.93
257
15.58
304
18.18
33
14.45
79
18.54
123
17.89
168
19.68
213
20.76
258
15.61
305
18.83
34
13.80
80
18.00
124
17.93
169
20.35
214
25.54
259
17.40
306
20.09
35
14.51
81
18.16
125
18.44
170
20.47
215
21.64
260
15.15
307
15.65
36
16.72
82
18.04
126
18.66
171
20.58
216
21.79
261
14.99
308
16.50
37
17.01
83
17.95
127
18.61
172
20.80
217
21.75
262
16.07
309
20.92
38
16.82
84
18.54
128
18.47
173
20.79
218
21.35
263
15.00
310
21.13
67
39
17.20
85
17.41
129
18.63
174
24.27
219
21.33
264
16.10
40
17.40
86
17.54
130
18.89
175
24.06
220
21.48
265
14.43
41
18.00
87
18.05
131
17.84
176
20.89
221
21.40
266
13.17
42
17.98
88
18.04
132
20.15
177
21.25
222
22.69
267
24.91
43
18.54
89
18.02
133
18.21
178
21.21
223
21.53
268
24.60
44
16.96
90
17.96
134
18.47
179
21.24
224
20.82
269
24.35
45
18.04
135
18.93
180
21.14
225
20.46
270
23.77
Table 21: Prices per node: “plus 8 GW” (high load)
68
35
30
€/MWh
25
20
15
10
5
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Nodes
Figure 16: Nodal prices “plus 13 GW” (average load)
69
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
4.07
46
10.08
91
16.02
136
17.28
181
17.83
226
18.11
271
17.52
2
4.05
47
17.38
92
12.41
137
17.29
182
17.33
227
18.31
272
14.49
3
4.25
48
12.56
93
13.63
138
17.44
183
17.26
228
17.62
273
17.10
4
4.05
49
12.56
94
15.56
139
17.12
184
17.53
229
16.81
274
17.08
5
4.11
50
22.23
95
16.15
140
17.00
185
17.52
230
16.91
275
17.23
6
4.84
51
32.07
96
16.38
141
16.92
186
17.32
231
16.74
276
15.00
7
2.80
52
0.00
97
16.50
142
16.95
187
17.07
232
17.06
277
15.02
8
5.01
53
1.43
98
15.29
143
17.10
188
17.08
233
16.71
278
15.08
9
4.85
54
13.49
99
16.05
144
17.33
189
17.59
234
15.95
279
15.13
10
5.65
55
13.94
100
16.08
145
17.99
190
17.81
235
15.94
281
14.67
11
5.14
56
13.90
101
16.07
146
17.82
191
18.28
236
16.13
282
14.50
12
6.02
57
13.12
102
16.25
147
17.95
192
19.45
237
15.91
283
14.30
13
5.90
58
14.51
103
16.53
148
17.38
193
19.38
238
15.89
284
14.48
14
5.96
59
14.60
104
16.66
149
17.10
194
18.48
239
15.86
285
14.60
15
4.96
60
15.20
105
16.74
150
17.54
195
18.77
240
15.52
286
14.61
16
5.03
61
16.87
106
16.17
151
16.34
196
18.74
241
14.92
287
14.64
17
6.23
62
16.36
107
18.05
152
16.24
197
15.35
242
15.00
288
14.37
18
7.37
63
16.36
108
18.00
153
17.37
198
15.39
243
15.11
289
14.43
19
7.38
64
16.33
109
16.06
154
18.00
199
18.45
244
14.99
290
14.43
20
4.05
65
16.21
110
16.04
155
16.86
200
18.60
245
15.49
292
17.51
21
4.29
66
16.22
111
16.04
156
16.88
201
19.82
246
15.00
293
17.69
22
4.00
67
16.24
112
15.91
157
16.91
202
19.75
247
15.34
294
17.89
23
4.16
68
16.21
113
15.84
158
18.00
203
17.82
248
15.64
295
22.11
24
3.61
69
16.19
114
15.69
159
18.23
204
19.83
249
15.95
296
18.14
25
4.24
70
16.10
115
15.86
160
17.03
205
17.87
250
15.21
297
16.43
26
4.24
71
16.18
116
15.00
161
16.86
206
17.84
251
15.30
298
5.26
27
3.98
73
16.29
117
16.53
162
17.02
207
17.75
252
15.47
299
5.78
28
3.76
74
16.33
118
16.48
163
17.03
208
17.40
253
15.33
300
5.00
29
4.05
75
16.23
119
15.92
164
17.71
209
18.20
254
15.43
301
4.23
30
9.44
76
16.40
120
16.00
165
17.68
210
19.68
255
15.85
302
0.72
31
10.00
77
16.36
121
16.00
166
17.51
211
22.34
256
15.69
303
16.81
32
8.41
78
17.68
122
15.99
167
17.26
212
17.63
257
15.11
304
20.31
33
5.55
79
17.14
123
16.00
168
17.58
213
17.44
258
15.13
305
16.69
34
10.56
80
16.42
124
16.03
169
17.76
214
20.81
259
16.00
306
17.85
35
11.17
81
16.86
125
16.42
170
17.77
215
18.15
260
15.00
307
14.50
36
13.12
82
16.30
126
16.56
171
17.77
216
18.24
261
14.91
308
14.67
37
13.70
83
16.19
127
16.64
172
17.72
217
18.22
262
15.24
309
17.81
38
13.18
84
19.52
128
16.44
173
17.74
218
18.02
263
14.90
310
17.98
70
39
14.10
85
16.97
129
16.57
174
18.58
219
18.00
264
15.02
40
13.61
86
17.43
130
17.02
175
18.45
220
18.22
265
14.77
41
14.06
87
15.90
131
16.12
176
17.79
221
18.22
266
14.46
42
14.05
88
16.32
132
17.90
177
18.06
222
19.04
267
18.15
43
14.40
89
15.87
133
16.10
178
18.03
223
18.18
268
18.09
44
12.84
90
15.29
134
16.40
179
18.05
224
17.71
269
18.00
45
15.68
135
16.42
180
18.00
225
17.52
270
17.82
Table 22: Prices per node: “plus 13 GW” (average load)
71
20
18
16
14
€/MWh
12
10
8
6
4
2
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0
Nodes
Figure 17: Nodal prices “plus 13 GW” (low load)
72
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
4.17
46
8.40
91
9.56
136
13.64
181
13.89
226
14.35
271
12.25
2
4.05
47
9.21
92
9.85
137
13.65
182
13.49
227
14.51
272
12.13
3
4.64
48
8.91
93
10.54
138
13.63
183
13.43
228
14.12
273
12.17
4
4.05
49
8.91
94
11.25
139
13.67
184
13.64
229
14.33
274
12.16
5
3.89
50
9.01
95
11.56
140
13.57
185
13.64
230
14.14
275
12.14
6
2.34
51
8.27
96
11.67
141
13.51
186
13.46
231
13.90
276
11.42
7
5.46
52
7.62
97
11.73
142
13.53
187
14.01
232
14.01
277
11.43
8
5.02
53
6.65
98
11.47
143
13.78
188
14.02
233
13.65
278
11.46
9
4.88
54
8.58
99
10.61
144
14.16
189
14.31
234
13.21
279
11.49
10
5.36
55
9.10
100
11.52
145
14.48
190
13.85
235
13.21
281
11.37
11
4.94
56
10.00
101
11.91
146
14.38
191
14.11
236
12.58
282
12.05
12
5.41
57
10.48
102
12.46
147
14.46
192
15.13
237
12.85
283
11.85
13
5.34
58
9.89
103
12.82
148
14.27
193
14.90
238
12.73
284
11.50
14
5.38
59
9.90
104
13.34
149
14.32
194
14.23
239
12.70
285
11.97
15
4.59
60
9.91
105
13.57
150
14.80
195
14.38
240
12.28
286
11.97
16
4.51
61
16.08
106
10.32
151
14.47
196
14.37
241
11.71
287
11.83
17
5.51
62
15.75
107
15.92
152
14.37
197
13.33
242
11.91
288
11.37
18
6.26
63
15.70
108
15.91
153
15.83
198
13.34
243
12.05
289
11.39
19
6.27
64
15.63
109
15.24
154
17.34
199
14.18
244
11.91
290
11.38
20
4.05
65
15.70
110
15.15
155
14.38
200
14.29
245
12.93
292
13.63
21
4.41
66
15.81
111
15.21
156
14.39
201
14.75
246
12.39
293
13.66
22
3.86
67
15.95
112
15.08
157
14.29
202
14.72
247
12.65
294
13.76
23
4.17
68
15.76
113
15.00
158
16.22
203
13.73
248
12.96
295
16.18
24
3.60
69
15.91
114
15.00
159
16.07
204
14.75
249
13.14
296
14.07
25
4.22
70
9.33
115
15.01
160
13.98
205
13.75
250
12.74
297
11.91
26
4.22
71
15.67
116
15.00
161
13.75
206
13.74
251
12.75
298
4.96
27
3.57
73
9.52
117
14.85
162
13.92
207
13.69
252
12.80
299
5.26
28
3.28
74
9.57
118
14.81
163
13.95
208
13.42
253
12.72
300
4.63
29
3.60
75
9.46
119
14.95
164
13.95
209
13.98
254
12.74
301
4.22
30
8.31
76
9.61
120
14.89
165
13.79
210
14.92
255
12.92
302
7.25
31
8.60
77
9.62
121
14.89
166
13.63
211
16.29
256
12.81
303
9.40
32
7.25
78
15.55
122
14.90
167
13.40
212
13.82
257
12.40
304
9.67
33
4.92
79
10.00
123
14.91
168
13.69
213
13.59
258
12.41
305
13.54
34
8.86
80
9.62
124
14.91
169
13.75
214
15.60
259
13.01
306
14.01
35
9.14
81
9.88
125
14.75
170
13.75
215
14.07
260
12.26
307
11.42
36
10.02
82
9.79
126
14.64
171
13.74
216
14.15
261
12.20
308
11.38
37
10.45
83
9.90
127
14.68
172
13.68
217
14.11
262
12.39
309
13.81
38
10.06
84
9.85
128
14.70
173
13.70
218
13.94
263
12.16
310
14.00
73
39
10.74
85
9.71
129
14.45
174
14.28
219
13.93
264
11.98
40
10.10
86
9.82
130
14.54
175
14.21
220
14.22
265
12.17
41
10.12
87
9.86
131
14.65
176
13.77
221
14.27
266
12.15
42
10.01
88
9.57
132
14.84
177
14.05
222
14.73
267
12.32
43
10.29
89
9.57
133
10.50
178
14.04
223
14.38
268
12.37
44
9.96
90
9.45
134
15.17
179
14.05
224
14.11
269
12.32
45
9.79
135
12.09
180
14.02
225
14.10
270
12.30
Table 23: Prices per node: “plus 13 GW” (low load)
74
45.000
40.000
35.000
€/MWh
30.000
25.000
20.000
15.000
10.000
5.000
298
283
268
254
240
226
212
198
184
170
156
142
128
114
100
86
71
57
43
29
15
1
0.000
Nodes
Figure 18: Nodal prices “plus 13 GW” (high load)
75
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
Node
Price
1
4.60
46
13.00
91
17.64
136
19.13
181
20.65
226
20.92
271
19.01
2
4.05
47
18.46
92
14.46
137
19.14
182
18.39
227
20.88
272
14.30
3
6.21
48
14.96
93
15.58
138
19.12
183
18.00
228
19.89
273
18.44
4
4.05
49
14.96
94
18.47
139
18.46
184
19.03
229
18.78
274
18.45
5
7.34
50
21.99
95
19.37
140
18.43
185
19.11
230
18.91
275
18.82
6
7.77
51
28.94
96
19.71
141
18.44
186
19.20
231
18.66
276
15.93
7
6.24
52
3.73
97
19.89
142
18.47
187
17.00
232
19.26
277
15.97
8
7.00
53
5.67
98
17.08
143
18.56
188
17.01
233
18.44
278
16.04
9
5.94
54
15.20
99
17.77
144
18.84
189
17.67
234
17.37
279
16.10
10
7.86
55
15.76
100
17.82
145
19.58
190
20.38
235
17.36
281
15.42
11
5.08
56
15.87
101
17.77
146
19.35
191
21.43
236
17.62
282
14.41
12
18.19
57
15.26
102
17.83
147
19.47
192
38.79
237
17.24
283
14.24
13
17.79
58
16.46
103
18.09
148
18.89
193
34.03
238
17.19
284
15.00
14
18.00
59
16.48
104
18.35
149
18.61
194
22.00
239
17.17
285
14.67
15
5.89
60
17.03
105
18.49
150
18.93
195
23.88
240
16.45
286
14.67
16
9.57
61
18.71
106
17.90
151
17.78
196
22.40
241
15.49
287
14.91
17
14.25
62
18.00
107
19.30
152
17.67
197
15.28
242
15.42
288
14.95
18
10.17
63
18.00
108
19.20
153
18.23
198
15.32
243
15.57
289
15.02
19
10.00
64
18.00
109
17.85
154
18.00
199
25.69
244
15.42
290
15.03
20
4.05
65
18.01
110
17.83
155
18.00
200
23.95
245
16.20
292
19.10
21
12.28
66
18.00
111
17.82
156
18.00
201
23.85
246
15.00
293
20.48
22
5.25
67
18.01
112
17.67
157
18.05
202
23.76
247
15.90
294
20.86
23
11.27
68
18.00
113
17.60
158
18.00
203
20.71
248
16.72
295
27.33
24
9.83
69
17.94
114
17.43
159
18.69
204
23.89
249
17.15
296
21.25
25
11.53
70
17.84
115
17.62
160
18.13
205
20.84
250
15.98
297
17.70
26
11.53
71
17.96
116
15.00
161
18.20
206
20.80
251
16.08
298
4.60
27
7.86
73
18.01
117
18.42
162
18.35
207
20.66
252
16.28
299
17.37
28
7.56
74
18.03
118
18.34
163
18.25
208
20.21
253
16.09
300
5.93
29
8.08
75
17.96
119
17.67
164
18.43
209
21.42
254
16.26
301
11.51
30
9.21
76
18.03
120
17.75
165
19.01
210
23.62
255
16.81
302
5.38
31
10.00
77
18.03
121
17.75
166
19.07
211
27.73
256
16.59
303
18.00
32
9.92
78
19.07
122
17.74
167
18.88
212
20.60
257
15.39
304
20.92
33
11.48
79
18.82
123
17.75
168
19.46
213
20.44
258
15.42
305
18.42
34
10.78
80
18.00
124
17.80
169
20.09
214
25.17
259
17.01
306
19.80
35
11.65
81
18.43
125
18.24
170
20.20
215
21.32
260
15.05
307
15.11
36
14.41
82
18.00
126
18.43
171
20.30
216
21.47
261
14.97
308
15.43
37
14.86
83
17.89
127
18.40
172
20.50
217
21.43
262
15.74
309
20.61
38
14.49
84
20.54
128
18.26
173
20.50
218
21.04
263
15.00
310
20.80
76
39
15.17
85
18.26
129
18.37
174
23.92
219
21.01
264
15.46
40
15.17
86
18.62
130
18.67
175
23.71
220
21.16
265
14.77
41
15.91
87
17.58
131
17.74
176
20.58
221
21.07
266
14.23
42
15.92
88
17.88
132
19.86
177
20.92
222
22.35
267
20.06
43
16.39
89
17.54
133
17.82
178
20.88
223
21.17
268
19.99
44
14.48
90
17.09
134
18.33
179
20.91
224
20.47
269
19.79
45
17.32
135
18.27
180
20.81
225
20.10
270
19.49
Table 24: Prices per node: “plus 13 GW” (high load)
Demand
Nodal price without offshore
Nodal price plus 8 GW
Nodal price plus 13 GW
case
[MWh]
[MWh]
[MWh]
average
1548
2865
3125
low
1365
2312
2664
high
1890
3120
3485
Table 25: Losses in different scenarios
77
Figure 19: Congestions close to the North Sea: Nodal price plus 8 GW (low demand)
78
Figure 20: Congestions close the North Sea: Nodal price plus 8 GW (high demand)
79
Figure 21: Congestions close to the North Sea: Nodal price plus 13 GW (low demand)
80
Figure 22: Congestions close to the North Sea: Nodal price plus 13 GW (high demand)
81