Comparison of two methods for long-run marginal
cost-based transmission use-of-system pricing
A.Bakirtzis, PBiskas, A.Maissis, A.Coronides, J.Kabouris and M.Efstathiou
Abstract: Two methods that provide geographically differentiated transmission usage tariffs, based
on the long-run marginal cost of transmission, are presented and compared: investment cost-related
pricing and the DC load flow pricing. The basic assumptions and approximations behind their design
are analysed. Very efficient implementations of both methods, based on sensitivity analysis, are
presented. Both methods are applied to the computation of transmission usage tariffs in the Greek
power system, and the resulting tariffs are compared.
List of symbols
SB = system power base (MVA)
p.
ei
=
=
E
=
e..!I
=
PDi
cy =
xij =
f. =
!I
0
=
P =
B’
=
eij
=
net real power injection at node i (MW) (peak
demand conditions)
power demand at node i (MW)
voltage phase angle at node i (rad)
expansion constant (f/MW/km/yr)
length of line ij (km)
annual cost of line ij per MW (€/MWlyr) (eo = ? .
CIJ)
reactance of line i j @.u.)
power flow of line ij (MW)
voltage phase angle vector (phase angle of reference
node is excluded)
real power injections vector (reference node is
excluded)
negative of network admittance matrix: [BG]= -l/xo,
[Bii]= C,l/x,, (row and column that correspond to
reference node are excluded)
vector with all its elements zero, except for the element that corresponds to node i, which equals +1,
and the element that corresponds to nodej, which
equals -1
e23
1
=
i
if 8,
2 0,
- e t J , if OZ < 0,
Introduction
The restructuring of the power industry is based on the
separation of electricity generation, transmission, distribu0IEE, 200 1
IEE Proceedwigs o n h e no. 20010408
DOL 10.1W9/ip-gtd:200IONX?
Paper first received 13th July 2000 and in revised form 18th January 2001
A. Bakutns and P. Biskas are with the Department of Electrical & Computer
Engineering,Aristotle University of Thessaloniki,540 06 Thessaloniki,Greece
A. Maissis, A. Coronides, J. Kabouris and M. Efstathiou are with the Department of Generation and Transmission Studies, Public Power Corporation, 89
Deirachiou St., 104 43 Athens, Greece
IEE Proc.-Gener. Trurism. DisIrih., Vol. 148, No. 4, July 2001
tion and retailing. Electricity transmission and distribution
are considered natural monopolies, whereas generation and
retailing are open to competition. Open access to the transmission system and fair, cost reflective pricing of transmission services are very important for healthy competition in
the power sector. To ensure fair and non-discriminatory
transmission access and pricing, most new electricity
markets have introduced an independent transmission
system operator (TSO), who is responsible for the operation and pricing of the transmission system.
Owing to the economies of scale in electricity transmission [I], it is problematic to price transmission services
solely on the basis of short run marginal costs (SRMC)
since collected revenues cannot cover the revenue requirements of transmission owners [ 2 4 ] .The charges for transmission services introduced in countries that have
restructured their power sectors are usually separated into
three components [7-IS].
(i) Connection charge: this charge covers the cost of network reinforcements required to provide service to a transmission customer. It is characterised as ‘deep’ or ‘shallow’,
depending on how far from the customer site the customer’s liability extends.
(ii) Transmission use-of-system charge (capacity charge):
this charge compensates the transmission owner for the
sunk costs of the existing transmission system assets, as well
as the transmission system operating and maintenance
costs.
(iii) Transmission operating charge (energy charge). This
charge covers the costs incurred in the electricity market
due to the existence of a ‘non-perfect’ transmission system.
These are the costs of transmission losses and transmission
limitations (congestion). The revenues collected from
energy charges are used to compensate the providers of the
corresponding services (generation adjustment to cover
losses, generation or demand adjustment to relieve congestion) [9, 15-18]. If based on SRMC, energy charges leave
the TSO with a profit, which can be used to either reduce
the transmission use-of-system charges, or compensate
holders of capacity rights [16, 191.
Our focus in this paper is on the transmission use-ofsystem (TUoS) charge, which constitutes the largest part of
transmission service charges. There are two broad categories of TUoS charging method,
411
(a) Uniform tariff methods: these methods (also referred to
as postage stamp methods) uniformly charge all transmission customers, irrespective of their location within the
grid, according to a measure of their usage of the transmission network [2]; this is usually their system-peak-coincident demand (kW) or annual energy demand (kWh). The
postage stamp methods define a uniform tariff (in f k W or
E/kWh) for all grid users. They are simple, but fail to
provide locational s ignals to the transmission customers.
They are used in many countries, due to their simplicity,
especially when combined with energy charges that provide
the necessary locational signals to the customers. In this
case, they can be theoretically justified as additive revenue
reconciliation adjustment to SRMC-based transmission
prices [24].
(b) Locational tariff methods: these methods differentiate
the TUoS tariff according to the customers’ location
within the grid. Usually, they separate the entire network
into different zones of charge, with a uniform tariff within
each zone. The intention behind their design is to send
long-term signals for the positioning of new generators
and new loads in the grid, so as to avoid network reinforcements as far as possible.
In this paper we present two locational TUoS tariff
methods based on the long-run marginal cost (LRMC) of
electricity transport: investment cost-related pricing (ICRP)
and DC load flow Firicing (DCLFP). In fact, both pricing
methods are investment cost-related, but we reserve the
name ICRP for the transport model method originally
developed by the EIritish National Grid Company [20].
Both methods lead to zonal TUoS tariffs. The assumptions behind their design and the design methodology are
analysed. Fast LRMC computations by both methods,
based on efficient seiisitivity analysis, are presented. Transmission tariffs prodiiced by both methods for the Greek
transmission system are presented and compared.
2 Transmission pricing using long-run marginal
cost
The calculation of the LRMC of transmission is related to
the construction of an optimum transmission network.
The optimum network is the minimum cost network that
serves the users under specified reliability standards. The
LRMC of transporling electric power to (from) a user is
the reinforcement cost of the optimum network, required
for servicing a unit increase in the demand (production) of
the particular user. The LRMC of transmission is calculated by sensitivity analysis around the solution of the
problem of constructing the optimum transmission network.
The precise calculation of the LRMC of transmission is
very difficult and must be based on a variety of assumptions about the future. An approximate calculation of the
LRMC of transmission is usually performed in practice,
based on several simplifying assumptions concerning the
optimum network. ‘Two methods for the approximate calculation of LRMC of transmission, are analysed below:
ICRP and DCLFP.
2.I Investment cost-related pricing
2.I. I Basic assumptions: The following simplifying
assumptions, used for the construction of the optimum network by the ICRP method, were developed by the British
National Grid Company (NGC) [20].
(i) The optimum network is constructed using only the
existing routes of the current network.
478
(ii) The optimum network is constructed assuming peak
demand conditions. The system load is allocated to the
generators in proportion to their registered capacity (pro
rata), with no regard to economic criteria. The underlying
assumption is that maximum transmission system stress
occurs under peak demand conditions, which is not always
correct [2].
(iii) All the lines of the optimum network are of the same
type. Their cost is proportional to their length. The length
of the cables is scaled up, to reflect their higher price relative to that of the overhead lines.
(iv) The transmission capacity of the lines of the optimum
network is taken to be precisely equal to the power transported from generators to loads at peak demand conditions. The construction of the optimum network does not
take into account the required network redundancy ( N - 1
or hgher) and ignores the fact that network expansions
take place in discrete quantities.
(v) When constructing the optimum network, it is assumed
that electric power can be routed at will on the existing
routes. The flow of electric power in the optimum network
conforms to the real power balance equations, but ignores
Kirchhoff s voltage law. Consequently, many routes of the
existing network become useless, and the optimum network
is very sparse; in fact, it is radial. The shorter routes are
being used, whereas the longer routes are not used and do
not contribute to the optimum network construction cost.
2.1.2 Construction of optimum network: The optimum network is constructed by solving the optimisation
problem:
[MW.km]
23
S.t.
Cft3
= Pt,
for every node i ( l b )
3
The annualised network construction cost is subsequently
computed by multiplying the total MW.km with the network expansion constant C (average annual transmission
cost in fIMWIkmlyr.).
The optimisation problem (eqn. 1) is easily transformed
into a linear programming (LP) problem of the linear network flow type. In our implementation of ICRP, the linear
network flow problem is efficiently solved using the
RELAX code [21].
2.1.3 Computation of LRMC of transmission: The
LRMC of transmission is computed by sensitivity analysis
around the optimal solution of the problem in eqn. 1.
According to optimisation theory [2], the LRMC of transporting electric power to node i is the Lagrange multiplier
A,, associated with the power balance equation at node i
(eqn. 16); this gives the sensitivity of the optimum network
construction cost with respect to the power demand at
node i:
The LRMC of power transport to node i is calculated multiplying Aiwith the expansion constant c:
L R M C , = E . A,
[e/MW/yr]
(3)
2.1.4 Physical interpretation of LRMC of transportation: reference node: Since the optimum network is radial, there is a unique route from a given node to
another. A generation node is arbitrarily chosen as a reference node.
I E E Proc.-Genrr. Transm. Disfrib., Vol. 148. No. 4. July 2001
The LRMC of transporting electric power to node i (a,)
expresses the total MW.km of reinforcement of the optimum network required to serve a 1MW increase in the
demand of node i. it is implied that the demand increase at
node i will be supplied by an equal increase of the reference
node generation. The required reinforcement of the optimum network is the addition of 1 MW of transport capacity to all the lines along the unique path from the reference
node to node i. Therefore, d,is the distance (in km) from
the reference node to node i, traversing the optimum network. The concept of distance is used for the efficient computation of the nodal LRMCs.
s.t. B' . e = -S1pB
To solve the optimisation problem in eqn. 5, the DC load
flow equations (eqn. 5b) are first solved for 6, and the
resulting vector 8 is then substituted in eqn. 5a, to compute
the total M W . h of the optimum network. The annualised
cost of the optimum network can then be computed by
multiplying the total MW.km with the expansion constant
-
c.
2.2 DC load flow pricing
2.2.7 Basic assumptions: The following simplifying
assumptions are used for the construction of the optimum
network by the DCLFP approach.
(i) The optimum network is identical to the existing network as far as the topology and the electrical characteristics
of transmission lines are concerned.
(ii) The optimum network is constructed assuming peak
demand conditions. The system peak load is allocated to
generators either pro rutu or based on economic criteria.
(iii) The cost of the optimum network is computed based
on either of the following:
( U ) the equipment cost of the optimum network is the
replacement cost of the equipment of the existing network.
(b) all the lines of the optimum network are of the same
type; their cost is proportional to their length; the length
of the cables is scaled up, to reflect their higher price
relative to that of the overhead lines.
(iv) The transmission capacity of the lines of the optimum
network is taken to be precisely equal to the power transported from generators to loads at peak demand conditions. The construction of the optimum network does not
take into account the required network redundancy ( N - 1
or higher) and ignores the fact that network expansions
take place in discrete quantities.
(v) The optimum network satisfies Kirchhoffs laws. DC
load flow simplifications are assumed.
2.2.2 Construction of optimum network: The optimum network is constructed by solving the optimisation
problem (in the following analysis it is assumed that all
lines are of the same type):
2.2.3 Computation of LRMC of transmission: The
LRMC of transmission is computed by sensitivity analysis
around the optimal solution of the problem in eqn. 5.
However, since the optimisation problem in eqn. 5 is trivial
(it has no degrees of freedom), the transportation LRMC
can be computed by a sensitivity analysis around the solution of the base-case load flow.
The LRMC of power transportation at node i of the
network represents the change in construction cost of the
optimum network (in €'yr or MW.km) required for servicing an incremental change of 1MW in the demand at node
i. it is considered that an increase in demand at node i is
covered by an equal increase in the reference node generation.
The calculation of the LRMC of power transport to
node i involves the solution of an additional DC load flow
problem (change-case load flow). This case differs from the
base-case load flow, in that the generated power at the reference node and the power demand at node i are increased
by 1 MW. The LRMC of node i is computed as the difference between the MW.km of the change-case and the basecase load flows.
The solution of N change-case load flows is required for
the computation of the LRMCs of all nodes of the network. As a consequence, the computation of all LRMCs
requires N forward-back substitutions with the table of factors of B'.
Using sensitivity analysis around the solution of the basecase load flow, the LRMCs of all nodes of the system can
be calculated more efficiently, requiring only one fonvardback substitution. Differentiating eqn. 5u with respect to
the power demand vector, Po we get:
Using eqn. 5b
S.t.
1
-(Oz
223
Pi
- 0,) = - for every node i
SB
(4b)
The constraints of the optimisation problem in eqn. 4 have
no degrees of freedom. Therefore, the solution of the optimisation problem coincides with the solution of a DC load
flow problem. Owing to the linear dependence of the power
flow equations (eqn. 4b), a generation node is selected as
the reference node and its voltage phase angle is arbitrarily
set to zero. The power balance equation of the reference
node is omitted when writing the load flow equations
(eqn. 4b).
The problem in eqn. 4 can be written using vector
notation:
IEE Proc.-Gener. Tninsm. Df.s.trib., Vol. 148. No. 4, July 2001
Using eqn. 6, the LRMCs of all nodes A; are computed,
except for the LRMC of the reference node, which equals
zero. The calculation involves only one forward-back substitution of the vector inside the large parentheses in eqn. 6
with the triangular factors of matrix B'. The nodal LRMCs
in [€/MW/yr] are computed using eqn. 3.
2.3 Properties of LRMC of transmission
The nodal LRMCs computed by both methods have the
following properties.
(U) The LRMC of the reference node is zero.
419
(6) Changing the choice of reference node results in a
constant shift of all nodal LRMCs, thus preserving the
geographical differentiation of nodal LRMCs. Additive
adjustment of the nodal LRMCs to satisfy the transmission
owner’s revenue requirements results in unique transmission tariffs, indepen’dentof the reference node selection (as
discussed later).
(c) The LRMCs for generation and for demand at the
same node are equal and opposite.
2.4 Computation of zonal TUoS tariffs
Charging every node in the system according to its LRMC
would be complex to implement in practice. For simplicity,
the system is separated into zones of TUoS charge. Each
zone of charge is a collection of neighbouring nodes with
similar LRMCs. Consumers within a zone are charged
according to their peak coincident demand. Producers are
charged according to their registered capacity. The tariff
within a zone is computed as the weighted average of the
LRMCs of the nodes within the zone, with the weights
being the corresponding nodal generator registered capacities or consumer peak coincident demands.
If the above zonal tariffs were applied to all generators
and loads, the revenues collected would represent only a
small fraction (e.g. 20Y0) of the transmission system sunk
costs. This is because during the optimum network
construction the network reliability (which increases considerably the network construction cost) was neglected. Therefore, if TUoS tariffs are solely based on LRMCs, the
revenues collected fi-om TUoS charges are not sufficient to
cover the transmission owner’s revenue requirements. An
additive adjustment of the LRMC-based TUoS tariffs is
required in order to cover the revenue requirements. The
zonal transmission tariffs are increased by a uniform
amount (calculated separately-for generators and loads).
The different uplift applied to the zonal transmission tariffs
for producers and consumers gives an additional degree of
freedom, so that the allocation of the revenue requirements
to producers and consumers can be arbifkily selected.
Imposing the revenue requirement constraints also results
in the derivation ol‘ unique transmission tariffs, independent of the initial refkrence node selection.
3 Calculation oif transmission use-of-system tariffs
for Greek power system
In this Section, we present and compare the TUoS tanffs
calculated by the ICRP and the DCLFP methods for the
Greek power systern. We also summarise the main findings
of a study undertaken by the Public Power Corporation
for the design of cost-reflective TUoS tariffs.
The Greek power system is characterised by bulk power
transfers from the lignite-rich North to the South, where
the densely populated Athens Metropolitan area is located.
Several critical operating conditions, mostly related to voltage instability, may lead to North-South transport limitations, with considerable generation rescheduling costs. In
order to send the appropriate locational signals to the
transmission users, a LRMC based locational TUoS tariff
was designed. For this purpose, the Greek power system
was separated into six TUoS charge zones, after careful
study of the system geography and the nodal LRMCs [22].
Fig. 1 shows the registered capacity and the peak coincident demand w i t h each zone, forecast for year 2001.
Total registered generating capacity is 9 61 3 MW. and peak
demand is 7819M’W. After examining the tariffs for different levels of allocation, a 500/0-50% allocation of the
480
charges between generators and loads (G-L) was selected
and all results presented in this Section are based on this
G-L allocation [22].
4
D
r
0
x 3
z
2
1
n
Athens
Central
South
West North-East
carpacity andpeuk couzcldeMt denwd u2 d$’rent
North
:ones of
13 registered cdpdcity
W peak coincident demand
The transmission system revenue requirements for the
year 2001 were projected to be fl80Miyr. The system
expansion constant (average annual p.u. line cost) was
calculated to be f34.2lMWlkmlyr. Assuming 50%G-50%L
allocation, the postage stamp tariff would be €9 362iMWl
yr for generators and €1 15lliMWlyr for the loads. The
network model used to compute the nodal LRMCs
consisted of 832 nodes and 1049 branches. Hydro plant
Plastiras, in Central Greece was selected as the reference
node. Both NGC’s [20] and our RELAX-based ICRP code
produced the same nodal LRMCs, but our code executed
45 times faster (134s compared to 3s on a P-11-350MHz
PC). The DCLFP approach produced slightly different
results when based on assumptions similar to ICRP (pro
vutu dispatch and uniform line type). The execution time of
the DCLFP approach was 2s on a P-11-350MHz PC.
Figs. 2 and 3 give the zonal TUoS tariffs for generators
and loads calculated by ICRP and DCLFP for 500/oG5O%L allocation. The zone sequence in all the Figures is
such that generator tariffs (Fig. 2) are in ascending order.
The following conclusions can be drawn from the results.
(i) Both the ICRP and DCLFP methods lead to heavy
charges for generators located in the North and consumers
in the metropolitan area of Athens. These charges provide
economic incentives for the location of new generators in
the South and of new loads in the North.
(ii) In most of the cases, the ICRP method leads to greater
differentiation of charges between zones. This is a major
feature of the ICRP method; in some cases, this is desirable
as it produces stronger economic signals.
(iii) Both the ICRP and DCLFP methods provide the same
ranking of the zones with respect to generation tariffs
(Fig. 2). The South and West systems are interchanged in
the ranking of the zones with respect to load tariffs (Fig. 3).
Differentiation of the charges calculated by the ICRP and
DCLFP methods is mainly attributed to the following
reasons:
(U) The Greek transmission system consists of two parallel networks of 400kV and 150kV voltage levels. The
absence of a 400kV network in the North-East leads to
lower marginal prices for those areas when calculated by
the ICRP method (Fig. 3). On the contrary, for areas
where a 400kV network dominates (i.e. the North), the
marginal prices calculated by both methods are sirmlar.
(b) The Western part of the country is an area with high
production and low load (exporting area). Despite this,
IEE P i o c -Gener T r u n m Dtrrrrb
Vol 148, N o 4, July 2001
the load charging (especially by DCLFP) is quite high
(Fig. 3). This is because the load, although not high, is
dispersed over a wide area through long transmission
lines.
*O1-
P
$ 10
W
:5
Athens
Central
South
West
North-East North
und DCLFP
Fig.2 Zonul trcuzsniisxun tLirfls for generutors by ICRP
upproid (5iMG-jO‘YL.ullocution)
0 ICRP
4
Conclusions
Two locational transmission use-of-system tariff methods,
based on long run marginal cost of transmission, have been
presented and compared: investment cost related pricing
and DC load flow pricing. Transmission usage tariffs have
been computed using both methods for the Greek power
system. These tariffs provide adequate incentive to increase
generation in the vicinity of high consumption via a tariff
diversification of 5:l between high and low tariff zones for
generators. Reasonable incentive for loads to move near
the production areas is also given by a 1:3 tariff diversification for load charging zones. The designed TUoS tariffs are
capacity tariffs and charge the users according to their peak
demand usage (in kW). Work is under way for the development of energy usage tariffs to account for losses and congestion in the transmission network, as well as connection
tariffs.
5
DCLFP
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-
Athens
Central
South
West
North-East
North
Fi . 3 Zonul trun~mlssionturgs for lods by ICRP curd DCLFP upprouch
(j8vd-joxLulionrtion)
0 ICRP
W DCLFP
The DCLFP method was finally selected for the TUoS tariff calculation in the Greek power system, since it provides
more realistic power flows. The disadvantage of the
method is that it requires more input information than the
ICRP method.
Of particular interest to market participants engaged in
bilateral contracts is the TuoS-related cost per transported
MWh. Table 1 gives the TUoS charge per MWh of a bilateral contract from one zone to another. A 80% load factor
of the contract is assumed. The contract TUoS charge
ranges from a low of €l/MWh for Athens-to-North transport to a high of €3.6/MWh for North-to-Athens transport.
Table 1: Bilateral contract transmission charge in E per
MWh (80% loadfactor)
~-
-
From generator
North- North Central Athens South West
east
Toload
Northeast
2.4
2.8
1.7
1.5
1.9
2.2
North
1.9
2.3
1.2
1.0
1.4
1.7
Central
2.7
3.1
2.0
1.8
2.2
2.5
Athens
3.2
3.6
2.4
2.2
2.7
3.0
South
2.8
3.2
2.0
1.8
2.3
2.6
West
2.9
3.3
2.2
2.0
2.5
2.7
IEE Prm-Geiier. Trrmsni. Distrih., Vol. 148, No. 4, July 2001
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