WP EN2015-6
Bidding strategies for Virtual Power
Plants considering CHPs and
intermittent renewables
J. Zapata Riveros, K. Bruninx, K. Poncelet, and
W. D’haeseleer
TME WORKING PAPER - Energy and Environment
Last update: March 2015
An electronic version of the paper may be downloaded from the TME website:
http://www.mech.kuleuven.be/tme/research/
Bidding strategies for Virtual Power Plants considering CHPs and intermittent renewables
J. Zapata Riveros a,b, K. Bruninx a,b, K. Poncelet a,b, and W. D’haeseleer a,b,1
a University of Leuven (KU Leuven) Energy Institute, TME Branch, Heverlee, Belgium
b Energyville (joint venture of VITO NV and KU Leuven), Genk, Belgium
Abstract
Energy efficiency and renewable-energy sources (RES) are fundamental parts of the European energy policy.
For this reason, efficient distributed generation technologies such as combined heat and power coupled to
district heating (CHP-DH) and RES based electricity are largely promoted. Additionally, the flexibility that CHPDH offers to the power system is seen as an option to balance the intermittent output of RES based generation.
This could be done by aggregating RES based electricity generation and CHP DH in a virtual power plant (VPP).
In this framework, the present work presents a methodology to evaluate the optimal bidding strategy of a VPP
composed of a CHP-DH and RES based generators. The objective is to investigate the optimal bidding strategy
for a VPP that uses CHP DH to compensate for the uncertainties regarding electricity generation and market
prices. The VPP operator nominates its energy to the day ahead market the day before the actual delivery (D1). In real time, any deviation from the day-ahead schedule is settled in the imbalance market. The
uncertainties are modeled using a two stage stochastic programming.
Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’. The major difference
between the studied strategies lies in the dispatch decisions. The ’static’ strategy does not adjust the scheduled
output of the CHP. Whereas, the ‘flexible DA’ and ‘flexible RT’ strategies differ from each other on the
information available at the moment of performing the reschedule (second stage decision). The ‘flexible DA’
reschedules the CHP output for the whole day depending on the RES scenario, but under uncertainty regarding
the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at each time step depending
on the RES generation and imbalance price scenarios.
The results show that in comparison with the ‘static‘ strategy, the ‘flexible DA’ operation results in a profit
increase during summer (5,900 €/week), the intermediate season (2,800 €/week) and winter (2,700 €/week).
This increase is moderate when compared against the total fuel cost in these seasons. Better results are
obtained when the ‘flexible RT’ strategy is applied. Using this strategy larger profits are achieved for all
seasons. For instance, during winter the difference between the ‘flexible RT’ operation and the ‘static’ case
amounts to 22,600 €/week, approximately 5 % of the fuel cost.
Keywords: Virtual power plant, cogeneration, renewable energy, imbalance markets, stochastic programming.
1
Corresponding author. Email: [email protected] Tel. +32 16 322510, Fax. +32 16 3 22985.
1
Introduction
In the fight against climate change, the European Union (EU) has committed itself to reach a set of targets set
under the Climate and Energy Package. This package, also known as the "20-20-20" package, sets three main
objectives for 2020: a 20% reduction in EU greenhouse gas emissions based on 1990 level; raising the share of
EU end energy originated from renewable resources to 20% and a 20% improvement in energy efficiency.
In this context, it is assumed that combined heat and power (CHP) devices connected with district heating can
play an important role [1]. Furthermore, photovoltaic (PV) facilities and wind farms are seen as a partial
replacement of fossil fuel-based electricity generation.
The present paper aggregates a hypothetical CHP connected to district heating with a large amount of RES
based electricity generators, in a virtual power plant (VPP). In [2] a virtual power plant is defined as an
agglomeration of distributed generators, controllable loads and storages devices, aggregated in order to
operate as a single power plant and being able to participate in the power exchange market. According to [2]
the use of a VPP can bring benefits such as increasing the flexibility of the electric grid without a large
investment in infrastructure. It is also mentioned that the VPP operation could help to displace the fossil
generation during peak hours and solve grid balance problems [2].
Nevertheless, all the benefits expected from the VPP operation depend largely on the interaction between the
VPP and the electric power market. Currently, the largest volume of energy is traded the day before (D-1) on
the day-ahead market which consequently has the largest liquidity. The day-ahead market is supervised by the
transmission system operator (TSO). The TSO expects that the participants give unbiased bids; this means that
the nominations should equal the expected generation. The deviations between demand and generation are
settled in the imbalance market which is controlled by the TSO. In order to incentivize the participants to
reduce their imbalance, imbalance tariffs are in place.
The TSO has the final responsibility to keep the balance between generation and consumption. To achieve this
task, a certain amount of capacity has to be kept steady (idle or offline). These reserves are activated in case of
positive (generation surplus) or negative (lack of generation) imbalance. The price that the TSO pays to the
reserves providers2, is transferred directly as imbalance tariff to penalize those players that caused the
imbalance.
Trading in the power exchange market brings along several uncertainties, specifically due to errors in the
forecast of renewable generation and the evolution of the day-ahead and imbalance prices. The objective of
this paper is to develop a methodology to coordinate the participation of CHP-DH and RES in the day-ahead
market (DA) and to compare different bidding strategies for the VPP, exploiting the flexibility of CHP-DH to
compensate for the uncertainty on day-ahead prices, RES forecast and imbalance tariffs. The uncertainties are
explicitly modeled using a two-stage stochastic program.
Towards this aim, two different bidding approaches will be considered: ‘Static’ and ‘flexible’ VPP operation. In
the first ‘Static’ strategy, the electric power delivered by the CHP is equal to the DA schedule. Consequently,
the resulting imbalance that stems from renewables forecast errors is settled in the imbalance market. On the
other hand, in ‘flexible’ operation the CHP is allowed to reschedule its electric output in order to compensate
for the forecast error of RES. Thus the total imbalance volume might be reduced. Furthermore, it is considered
that the rescheduling can be performed at two different moments in time. In the ‘flexible DA’ case it assumed
that the CHP schedule is adjusted just once after having a more accurate idea of the realization of the RES
2
In Belgium, these prices correspond to the maximum price paid for up regulation (Marginal incremental) and the
minimum received for down regulation (Marginal decremental price).
generation but not of the imbalance prices. On the other hand, the ‘flexible RT’ case, where RT stands for real
time, considers that the rescheduling is done every time step once the actual imbalance price is known.
In the literature, several studies about optimal bidding strategies and imbalance cost minimization can be
found. For instance, the optimal dispatch of industrial cogeneration devices in a liberalized market is studied in
[3]. The benefits of using a micro-CHP device to balance the portfolio of a VPP (‘self-balancing’) are assessed in
[4], [5]. Both studies result in little or no incentive for ‘self-balancing’. Nevertheless, these studies are based on
deterministic techniques that disregard the uncertainties of the system. Taking uncertainties into account could
make the ‘self-balancing’ approach more valuable.
Stochastic programming has been extensively used to thoroughly account for uncertainties. The case of optimal
wind power integration in the electric power system has been extensively studied [6]–[9]. In [7] stochastic
programming is used to generate an optimal bid for a short-term power market. Results show that using a
stochastic approach leads to higher profits compared with a deterministic methodology. Similarly, [8] considers
the bidding of a wind power plant (WPP) in the different energy markets (i.e, day-ahead, intraday and
balancing market). In addition, [6] includes a risk aversion model to analyze the different optimal offering
strategies of a WPP depending on the risk attitude. In [6]–[9] only wind generators are studied.
Joint participation of a WPP and dispatchable generators is an interesting field of study. The case study in [10]
consists of a wind farm and a pumped hydro storage plant (PHS). The authors of [10] use two-stage stochastic
programming to account for the uncertainties in the day-ahead prices and wind power. However, it does not
take into account the available information regarding imbalance prices. The results show that aggregating WPP
and PHS can lead to larger profits and reduce the imbalance cost.
From the reviewed literature only one model [11] considers simultaneously imbalance price and wind power
forecast uncertainties as well as coordinated participation in the day-ahead market. The authors propose a
two-stage stochastic optimization of a VPP that aggregates a WPP with a PHS and a conventional electric power
plant. The results show substantial profits increase when these power plant operate together. Nevertheless it
does not assess the benefits that a VPP can obtain from using its flexibility in real-time to react to the
imbalance prices, nor the specific interaction with a heat demand (CHP unit).
Compared to the literature, the contributions of this paper are:
•
A stochastic program that coordinates the operation of RES generators with a CHP used for DH
including uncertainties in day-ahead prices, imbalance prices and renewable energy generation and
the specific constraints characteristics of a DH system (e.g., the heat demand should be met all the
time);
A comparison between three different strategies: a ‘static’ case in which no rescheduling for balancing
the forecast error is implemented, a ‘flexible DA’ that assumes uncertainty regarding imbalance prices
when rescheduling the CHP and a ‘flexible RT’ case in which it is assumed that the VPP can react to the
actual imbalance prices.
The paper continues as follows: Section 2 provides a detailed description of the optimization model and the
characteristics of the case study. The results are presented and discussed in Section 5. Finally, Section 0
presents the conclusions and further work.
•
2
Methodology
The present study assesses the optimal dispatch of a hypothetical virtual power plant in Belgium. The VPP
system consists of a CHP-DH together with uncontrollable RES based electricity generation (i.e., photovoltaic
and wind energy). Figure 1 gives an overview of the studied system. The CHP-DH plant or CHP system consists
of a prime mover, an auxiliary boiler and a thermal storage unit that meet the heat demand of the community.
The electricity generated by the VPP is sold in the electric power market. In other words, the DH plant is not
responsible for meeting the electrical demand of the community.
Figure 1: Distribution of the electricity and heat connections for the studied case. The CHP system is composed of a prime
mover, an auxiliary boiler and a thermal buffer. The electricity generated is traded in the electricity market.
The VPP controller makes a nomination on the day-ahead market considering the expectations for renewable
energy generation in its portfolio, DA and imbalance prices, while the heat demand is assumed to be known.
During real time, the deviations between the day-ahead nomination and the actual dispatch have to be settled
in the balancing market.
In order to account for the uncertainties that the VPP faces, a stochastic program is developed. In a stochastic
program the uncertainty is represented using a set of scenarios.
The stochastic program studied in this work is illustrated in Figure 2. When bidding electricity in the day-ahead
market, the decision process can be split into two different stages. In the first stage, the decisions have to be
taken under uncertainty regarding the future RES generation and prices. In this study, the first stage decisions
correspond to the day-ahead bidding. The day-ahead bid (i.e., first stage decision) is obtained using a
combination of 10 day-ahead, 10 imbalance and 10 renewables scenarios which result in a total of 1000
scenarios.
During the second stage, the day-ahead prices are known. It t is also assumed that at this point the VPP
operator has a more accurate forecast regarding the realization of the RES based generation and thus decisions
regarding the dispatched volume are taken.
Figure 2: Two-stage stochastic programming for the VPP. The first stage decisions correspond to the day-ahead bids,
whereas the second stage decisions are related to the actual dispatch.
The second stage decisions or actual dispatch decisions are obtained in a ‘re-evaluation’ process. This process is
performed once the day-ahead bid is obtained (i.e., after the first stage decisions are taken) and it makes use of
a larger set of scenarios (50 imbalance and 50 renewables scenarios). Figure 3 visualizes the entire optimization
process.
Figure 3: During the first stage decision process the DA bid is obtained. Afterwards the results are evaluated in a larger set
of scenarios and the second-stage decisions (or the actual dispatch) are taken.
Three different bidding strategies are studied: ‘static’, ‘flexible DA’ and ‘flexible RT’ as stated in Table 1. The
major difference between the studied strategies lies in the second stage decision process. The ’static’ strategy
does not adjust the scheduled output of the CHP.
On the other hand, the ‘flexible DA’ and ‘flexible RT’ strategies have the same day-ahead bid. They differ from
each other on the information available at the moment of performing the reschedule (second stage decision).
The ‘flexible DA’ reschedules the CHP output for the whole day depending on the RES scenario, but under
uncertainty regarding the imbalance price. The ‘flexible RT’ strategy allows the VPP to adjust its position at
each time step depending on the RES generation and imbalance price scenarios which are assumed to be
known. The ‘flexible RT’ case is performed using a rolling-horizon approach, at each time step once the
observed imbalance prices of each scenario are obtained, the dispatch decisions are taken.
Table 1: Summary of the different bidding strategies: ‘static’, ‘flexible DA’ and ‘flexible RT’
Case
Dispatch
Static
Dispatch equals to DA schedule.
No reevaluation
Flexible DA
One dispatch per RES scenario.
•
Day-ahead price
•
RES generation
•
Day-ahead price
•
RES generation
•
Actual imbalance price
Flexible RT
Reevaluation Variables Considered
during the 2nd stage
One dispatch per RES and Imbalance
prices scenarios.
It is important to remark that both the ‘flexible DA’ and ‘flexible RT’ correspond to two extreme cases. When
deciding on the actual dispatch, the ‘flexible DA’ assumes that the VPP operator has no knowledge regarding
the imbalance prices. In contrast, the ‘flexible RT’ assumes complete knowledge of the imbalance prices for the
current time step. In reality, the Belgian TSO provides, actualized information every 3 minutes on the current
imbalance volume. From this information the VPP can obtain a very accurate forecast of the imbalance price in
order to perform ‘passive balancing’3. However, the forecast can still deviate from the actual imbalance price as
the response of other market participants is unknown and thus the real benefits lie between the economic
savings of these two cases ‘flexible DA’ and ‘flexible RT’ operation.
This stochastic optimization procedure was formulated as a mixed integer linear program (MILP). The model
has been developed in GAMS, and is solved using the commercial solver CPLEX.
3
Stochastic optimization model
The objective is to maximize the revenues obtained by the VPP as stated in Equation (1):
+
#$%
()
∀, ∀, ∀, ∀:max = ,! + ,,,
− ',,
*
(1)
In this equation, , is the time horizon, in this particular case, two days from which only the first one is
implemented (the second day is considered to enforce an optimal behavior in the storage tank). The studied
time period is divided in 15 minute time steps. Furthermore in Equation (1), S, R and I represent the sets of
scenarios of day-ahead prices, RES based generation and imbalance prices, respectively.
The revenues result from the difference between the profits obtained in the DA and imbalance (IMB) market
()
#$%
#$%
respectively and the operational cost of the CHP-DH ',,
. Recall that ,,
is the result from
! and ,,
settling the deviations between the planned and delivered electricity in the imbalance market for this reason,
this variable can take positive or negative values. The revenues are weighted over all scenarios. The probability
of occurrence of each scenario is equal to for the day-ahead prices scenarios, for the RES generations
scenarios and for the imbalance price scenarios.
The electric power scheduled to be traded on the day-ahead market -. ! is calculated in Equation (2):
3
Passive balancing is a measure implemented by the Belgian TSO to allow the market participants helping reduce the total system
imbalance on real time.
∀:-. ! = -./0) + -.1 *
(2)
In this equation, -./0) corresponds to the scheduled electric power output of the CHP and -.1 to the traded
RES generation. It is important to remark that the electric power scheduled to be traded on the day-ahead
market -. ! does not depend on the scenarios.
On the other hand, the DA RES nomination -.1 is limited to the maximum and minimum possible values
achieved by the RES scenarios at each time step.
∀:-.1 = 0
(3)
or
. . 1 ≤
∀: 34
-, * ≤ -
1
367
. 1
-, *
8
The actual electricity dispatched -.,,
depends on the realization of the scenarios as stated in Equation (4):
/0)
1
8
(4)
∀, ∀, ∀ ∶ -.,,
= -.,,
+ -.,
*
/0)
#$%
Where -.,,
is the actual output of the CHP. The imbalance error ∆-.,,
represents the difference between the
actual electric power generated and the day-ahead schedule. This is expressed in Equation (5):
#$%
8
∀, ∀, ∀:∆-.,,
= -.,,
− -. !
(5)
The profits are calculated as the sum of the revenues obtained from trading electricity in the day-ahead market
and the imbalance market as stated in Equations (6) and (7):
∀:,! = -. ! ∙ <,! ∙ ∆
#$%
#$%
#$%
∀, ∀, ∀, ∀:,,,
= ∆-.,,
∙ <,
∙ ∆
(6)
(7)
#$%
In Equations (6) and (7) <,! corresponds to the day-ahead price and <,
to the imbalance price in [€/MWh].
The imbalance revenues can be either negative or positive depending on the nature of the system imbalance
(SI) and the imbalance tariff. In addition ∆is the time step of the simulation in this case 15 minutes.
The heat balance is described in Equation (8):
/0)
%(#>1
/0
∀, ∀, ∀:=./0) + =.%(#>1 * + ∆=.,,
+ ∆=.,,
= =.?@364? + =.,,
(8)
According to this equation the optimization must ensure that the heat demand is met during every time step
for all the scenarios, using the CHP =./0) , the boiler =.%(#>1 or the heat that is charged to or discharged from
/0
/0)
%(#>1
the thermal storage buffer =.,,
. Additionally, the variables ∆=.,,
and ∆=.,,
represent the difference
between the actual thermal power delivered by the CHP and backup boiler and their planned thermal power
output, respectively.
The CHP plant is constituted by three internal combustion gas engines. Equation (9) states the relationship
between the electrical and thermal power output of each unit. Similarly, Equation (10) links the primary energy
use to the thermal and electrical power production. Looking at this equation is clear that once the optimal
electrical output is selected, simultaneously the thermal output is settled and vice versa.
/0)
/0)
∀, ∀A: -.,4
= =.,4
B
C1
EF
CD ,4
(9)
(10)
.
∀, ∀A: G,4
/0)H
JKL
1.I,H
=
MN
F,4 = JKL
D.I,H
MO
F,4
. /0)H is the primary fuel consumption of each individual CHP unit A, CD and C1 are,
In these equations,G,4
respectively, the thermal and electrical efficiency of the CHP plant. F,4 is a binary variable that indicates the
on/off status of each CHP unit. This variable is independent of the scenarios and cannot change during real
time generation.
The total electricity generation -./0) and primary energy G. /0) use of the CHP plant are estimated as the sum of
the total electricity generation and fuel consumption among the individual units, as stated in Equations (11) and
(12):
∀:-./0)
∀: G. /0)
PQRS
/0)
= -.,4
(11)
4
PQRS
. /0)H = G,4
(12)
4
The start-up cost is calculated using Equation (13):
6_UV
∀, ∀A:',4
6_UV
≥ <,4
F,4 − FX,4 *
(13)
6_UV
In this Equation <,4
is a positive parameter that represents a fixed cost for starting up the machines. The
fuel consumption of the boiler G. %(#>1 is calculated as shown in Equation (14):
∀:G. %(#>1 =
=.%(#>1
,
YZ[\@
(14)
It is assumed that the boiler has constant efficiency YZ[\@ . The total operational cost of the system is
estimated as the sum of the primary energy cost of the CHP system and the start-up cost: see Equation (15):
()
. /0) + ∆G,,
. %(#>1 * + '6_UV
∀:',,
= <]^1> ∙ ∆ ∙ G. %(#>1 + G. /0) + ∆G,,
(15)
. /0) and ∆G,,
. %(#>1 correspond to the fuel use difference that appears when the CHP system
In Equation (15) ∆G,,
is rescheduled and <]^1> is the fuel price.
(/
The state of charge (SOC) of the storage tank =,,
is calculated using Equation (16). The efficiency of the
/0
4
storage tank Y is assumed to be constant. Recall that =.,,,
is the average thermal power (kWth) that is
charged to/discharged from the storage tank during every time step; consequently, it can take both positive or
negative values:
(/
(/
/0
∀, ∀, ∀:=,,
Y ∙ =X,,
" =.,,
∙ ∆
(16)
Equations (17)-(18) ensure that the optimization does not exceed the operational limits of the CHP:
/0)
/0)
/0)
/0)
∀, ∀A, ∀, ∀: =.34
5 =.,4
" ∆=.,4,,
5 =.367
(17)
/0)
/0)
/0)
/0)
∀, ∀A, ∀, ∀:-.34
5 -.,4
" ∆-.,4,,
5 -.367
(18)
Equations (19) and (20) prevent exceeding the operational limits of the storage tank and boiler:
3.1
(/
(/
∀, ∀, ∀: 0 5 =,,
5 =367
(19)
%(#>1
%(#>1
%(#>1
%(#>1
∀, ∀A, ∀, ∀:=.34
5 =.,4
" ∆=.,4,,
5 =.367
(20)
Case Specific Constraints
The previously explained equations apply to the ‘flexible DA’ case; in this subsection, the necessary
modifications to these equations for the other cases are described.
/0)
/0)
%(#>1
. /0) , ∆G,,
. %(#>1 to zero. In
First, the ‘static’ case is modeled by forcing the variables ∆-.,,
, ∆=.,,
, ∆=.,,
, ∆G,,
other words, the CHP is not allowed to deviate from its scheduled output.
On the other hand, the ‘flexible DA’ and ‘flexible RT’ have the same day-ahead schedule; thus, it is only
necessary to modify the equations that involve RT decisions. This is because in ‘flexible DA’ the imbalance
#$%
#$%
volume decision ∆-.,,
is considered independent of the of the imbalance price <,
scenarios. In other
words, the imbalance volume is settled before knowing the imbalance prices but with knowledge of the RES
generation and day-ahead prices.
In contrast, in the ‘flexible RT’ case the imbalance volume is estimated depending on the imbalance price
/0)
,
scenarios and thus several variables become dependent of these scenarios such as:-.,,,
/0)
/0)
8
(/
/0)
/0)
%(#>1
#$%
. /0) , ∆G,,,
. %(#>1 , ∆-.,,,
-.,,,
, =.,,,
, -.,,,
, =,,,
, ∆-.,,,
, ∆=.,,,
, ∆=.,,,
, ∆G,,,
and consequently the
equations where these variables appear are also dependent on the imbalance tariffs.
4
Application to a case study
The developed methodology is applied to a hypothetical case study that assumes a large penetration of
renewable energy and the installation of a district heating facility in the city of Leuven (Belgium) which
resembles a typical small European city. The heat demand profile is approximated through a bottom-up
4
The efficiency of the storage tank represents the percentage of thermal energy that is preserved by the storage after it has been stored
during one time step of 15 minutes. For example, a storage tank with an efficiency of 90 % is charged with 1kWhth after 15 minutes, only
0.9 kWhth remains.
approach. Data concerning the building stock of Leuven provided by the municipality [12] is combined with
heat demand benchmarks [13] and synthetic load profiles [14] to create the heat demand profile.
It is assumed that the thermal energy is sold to the community at a constant retail price. As consequence, this
do not influence the optimization results. For this reason these revenues are not included in the optimization.
The optimal size of the CHP is estimated using the maximum rectangle method explained in [15]. It is assumed
that the DH system is operated by three parallel internal combustion gas engines (ICGE). Each ICGE has a
maximum electrical output equal to 18 MWe. The electrical and thermal efficiency are C1 44 % and CD 48 %, respectively.
Regarding the renewable generation it is assumed that the total installed capacity amounts to 20 MWe from
which 14 MWe correspond to solar panels and 6 MWe to wind turbines. These numbers reflect the current
(2014) proportion of photovoltaic and wind installation in Belgium. The renewable energy scenarios are based
on data provided by the Belgian TSO [16].
The optimization will be performed for three different weeks each represent the behavior of a season
(summer, intermediate and winter). The total heat demand and the RES based generation of each of the
studied weeks are summarized in Table 2.
Table 2: Heat demand and RES based generation in the studied weeks.
Summer
Intermediate
Winter
Heat demand
[MWh /week]
1199
2598
6169
RES generation
[MWh /week]
1201
1011
879
Finally, the day-ahead and imbalance prices scenarios are also based on historic data of the Belgian electricity
market [16], [17]; the gas price is assumed to be constant and equal to 39 €/MWh. The gas price corresponds
to the average price that was paid by small and medium sized enterprises in 2014 [18].
4.1
Scenario Generation and Reduction
As mentioned before, to represent the uncertainty that stems from the renewable energy forecast errors, the
day-ahead and imbalance prices, the underlying stochastic processes are approximated using a group of
scenarios. A scenario corresponds to a possible realization of the stochastic process, thus a large enough
scenario representation should capture the distribution of the random variables.
The statistical scenario generation technique developed in [19], [20] and described in detail in [21] is used in
this thesis to generate a large set of scenarios. This technique makes use of historical forecast errors (e.g.,
difference between the forecasted variable and the measured output of this variable during the previous years)
to create different scenarios. Once the ‘error scenarios’ are obtained, they are added to the actual forecasted
variable (e.g., wind power forecast of the next day) to obtain the different scenarios for each variable (e.g.,
wind scenarios).
Yet, using a large number of scenarios is computational expensive. Therefore, a reduction technique is
necessary to trim down the number of scenarios. To this aim a modified version of the fast-forward scenario
reduction algorithm that includes the inherent characteristics of the optimization problem is implemented, as
described in [21], [22].
For the purpose of this work, a total of 200 day-ahead, 200 imbalance and 200 renewables scenarios were
generated independently. This was possible because currently very low correlationg between these variables is
observed. Nonetheless, for computational efficiency, the orginal set was reduced to 10 scenarios for each
parameter in the first optimization, resulting in a total number of 1000 combition of scenarios. Afterwards, as
explained before, the reevaluation process has used a larger number of scenarios (50 per set) leading to a total
of 25000 (10 day-ahead, 50 imbalance and 50 renewables scenarios) combinations of scenarios.
4.2
Limiting the Imbalance Volume
The results obtained when applying the optimization described in 3 during the intermediate season for the
‘flexible DA’ case are illustrated in Figure 4. In this figure, the black line represents the scheduled CHP electrical
power, the shaded area corresponds to the actual electrical power delivered by the CHP5. It can be observed
that at several moments the CHP was scheduled to operate at maximal output however, it delivers only the
minimum capacity (e.g., see Figure 4 between 14:00 and 16:00). In contrast, when the CHP was scheduled to
provide the minimum electrical power, it delivered the maximum power.
Figure 4: Resulting original DA bid (solid line) and actual dispatch of the CHP (gray area). The difference between da
schedule and real time dispatch creates large imbalance of the order of 40 MW.
This behavior creates very large imbalance volume, of the order of 40 MW. The reason of this large imbalance
volume is to profit from the price difference between the day-ahead and balancing markets.
This occurs because the VPP operator does not have enough information regarding the reactions of other
market players. The imbalance prices are calculated ex-post once the total system imbalance is known. If for
example the VPP operator expects large imbalance prices at certain hour (meaning that the system is short), he
as well as other market participants might decide to create large positive deviations from the DA schedule. This
might result in an overcompensation of the system leading to surplus of energy which is generally
characterized by very low imbalance prices. As a consequence the VPP will not only obtain lower profits than
expected in the imbalance market due to the behavior of other market players but also forgone some profits in
the DA market in order to be able to create large positive imbalances.
Similar results are reported [23] and [24] .The authors of [23] and [24] agree that, though the results are
‘optimal’ from a modeling perspective, a real player will have several reasons to avoid this behavior. One of
these reasons, apart from the profit loss, is that, as mentioned before, the TSO expects unbiased bids from the
market player. If the TSO realizes that a player is performing arbitrage, he can be penalized. The reason for this
is that the imbalance market will be affected if several players behave in this way.
5Keep in mind that the electric power traded in the day-ahead market is composed of the electricity generated by the CHP, and the RES
generation. Nevertheless, for illustration purposes only the electricity bided by the CHP appears in Figure 4.
Therefore, a penalty function is implemented to limit the imbalance volume caused by the VPP. In the present
work, a piecewise linear function is used to limit the imbalance volume, as in [23]. This function emulates the
expected behavior of the market by penalizing large deviations from the DA schedule.
The penalty function is illustrated in Figure 5. This function is regarded in [23] as a type of risk model named
‘Shortfall cost’. Thus the value of the parameters`1,,
,`2,, ,`3,, ,`de , `def and `deg , shown in Figure 5,
depends completely on the preferences of the user. In this particular case, if the total imbalance is between 0
and 20 % of the total installed capacity, the resulting penalization is equal to 3 % of the day-ahead price. For
deviations between 20 % and 30 % the penalty is equal to the day-ahead price realization. From 30 % and
above the marginal penalty is 10 times the value of the day-ahead price. As such, a player will only deviate
from his DA schedule if large profits are to be expected.
Figure 5: Shortfall cost function. This piecewise linear function was used to penalize imbalance volumes [23]. Large
deviations from the DA schedule are strongly penalized.
The following constraints are added to the model in order to include the penalty function. First, the absolute
value of the total imbalance is split in the three pieces that comprises the penalty function
`1,, ,`2,,
,`3,, as shown in Equation (21):
#$%
∀, ∀, ∀: h∆-.,,
h `1,, " `2,,
" `3,, (21)
Splitting the imbalance volume makes it possible to penalize large imbalance more than the small deviations as
shown in Equation (22):
1i
∀, ∀, ∀: ',,
0.3 ∙ `1,,
" `2,, " 10 ∙ `3,,
* ∙ <,! ∙ ∆
(22)
1i
In this equation ',,
corresponds to the total imbalance penalty. The variables`1,, ,`2,, and`3,, are
constrained using Equations (23)-(25):
i))
∀, ∀, ∀: `1,, 5 `de ∗ -.367
(23)
i))
∀, ∀, ∀: `2,,
5 l`def & `de m ∗ -.367
(24)
i))
∀, ∀, ∀: `3,,
5 l`deg & `def m ∗ -.367
(25)
Where `de , `def and `deg represent the percentage deviation of the schedule with respect to the total
i))
installed capacity of the VPP -.367
in this case 20 %, 30 % and 100 %, respectively.
Finally, the deviation penalty or shortfall cost is included in the objective function as follows:
+
#$%
()
1i
∀, ∀, ∀, ∀:max ! " ,,,
& ',,
& ',,
*
(26)
Recall that when applied to the ‘flexible RT’ case the previously stated Equations (21) to (26) are dependent also
on the imbalance prices scenarios.
The resulting DA schedule and actual dispatch using the designed penalty function are depicted in Figure 5. The
results correspond to the same analyzed scenario in the intermediate season shown in Figure 4. It can be
concluded that using a volume penalty function decreases the deviation between day-ahead schedule and
actual dispatch thus, more realistic day-ahead market bids are obtained. Following in Section 5, further results
using this model are reported.
Figure 6: Resulting DA bid (solid line) and actual dispatch of the CHP (gray area) when using an imbalance volume
penalty. This methodology is effective in limiting the schedule deviations.
5
Results and discussion
As stated in Equation (1) the total profits of the studied VPP can be estimated as the profits for trading the
electricity in the day-ahead and imbalance market minus the operational cost. These figures are broken down
in Table 3 for each of the studied strategies, for each of the weeks considered in the case study.
Table 3: Day-ahead profit, fuel cost and imbalance profit for the different bidding cases and studied seasons.
[k€/week].
Flexible RT
Static
Flexible DA
Flexible RT
Static
Flexible DA
Flexible RT
Winter
Flexible DA
Intermediate
Static
Summer
DA revenues RES
62.9
64.8
64.8
62.5
62.0
62.0
34.9
34.7
34.7
DA revenues CHP
82.2
85.2
85.2
146.1
146.4
146.4
305.1
303.9
303.9
Fuel cost
96.3
95.5
91.7
193.9
191.6
180.8
416.8
415.8
398.9
Imbalance
revenues
-1.3
-1.1
1.3
-5.6
-4.9
-4.3
-4.7
-1.57
1.3
Total profits
47.5
53.4
59.6
9.1
11.9
23.3
-81.5
-78.8
-58.9
Table 3 shows that the operation of the VPP leads to economic profits during all seasons except for winter.
During winter, the total revenues are not enough to offset the fuel cost due to the large heat demand.
Nevertheless, it is important to recall that this cost should be reimbursed through sales of heat. Thus the
minimum heat unit cost that should be charged to the consumer to cover at least the operational cost of the
district heating during winter lies between 9.5 €/MWh and 13.6 €/MWh6. During the other seasons this heat
unit cost is negative. However, it is important to remind that in this work, the investment and maintenance
cost are not taken into account.
In addition, from Table 3, it can be deduced that in comparison with the ‘static’ operation, the ‘flexible DA’
operation results in a profit increase during summer (5,900 €/week) and the intermediate season
(2,800 €/week)7. Furthermore, during winter the profit increase (2,700 €/week) is low when compared against
the total fuel cost of this season8. The largest profits are achieved when the ‘flexible RT’ operation is applied.
During winter the difference between the ‘flexible RT’ operation and the ‘static’ case amounts to
22,600 €/week, approximately 5 % of the fuel cost.
As explained before, the main difference between the ‘flexible DA’ and ‘flexible RT’ relies on the information
available at the moment of taking the dispatch decisions. Figure 7 illustrates this further. The first column
corresponds, to the ‘static’ case, the second column to the ‘flexible DA’ case and the third column to the
‘flexible RT’ strategy. Results showed were obtained for a specific imbalance price scenario, between 8:00 and
14:00 during the intermediate season. The upper panel illustrates both the day-ahead and real time electrical
power generation of the CHP9. The same parameters are depicted in the second panel for the RES based
6
The heat unit cost was estimated dividing the total operational cost by the heat demand of the season.
Recall that the fuel cost in these seasons is of the order of 96,000 €/week in summer and 192,000 €/week in the intermediate season
thus, the profit change represent only 6 % and 1.5 % of this cost.
8 During winter the total fuel cost is of the order of 416,000 €/week, consequently the profit decrease corresponds only to a 0.6 % of this
cost.
9 Recall that the total bid is the combination of the CHP and RES expectation and the heat demand. Nevertheless, for illustration purposes,
Figure 7 shows the CHP and RES generation separately.
7
generation, the total remaining imbalance (RES error plus CHP deviation) are shown in the third panel. Finally,
in the bottom panels the DA and imbalance prices are shown.
Looking at the figures it can be observed that the ‘flexible DA’ strategy uses the cogeneration unit to
compensate the lack of generation of the RES. This is done by increasing the output of the CHP in real time. The
remaining imbalance is zero. This is done because during the dispatch optimization (re-evaluation) the ‘flexible
DA’ strategy does not have information on a specific imbalance price scenario, but on a large set of scenarios
that can take positive or negative values and thus, it decides to minimizes the total imbalance volume.
Figure 7: Comparison between ‘static’, ‘flexible DA’ and ‘flexible RT’ cases. The upper panel shows both the CHP
electrical power bided DA (solid line) and the actual electrical dispatch (gray area). The second pane depicts the
expected RES generation (solid line) and the actual RES output (gray area). The third panel shows the total
remaining imbalance of the VPP and finally, the last panel illustrates the day-ahead (black line) and imbalance
prices (gray line).
In contrast, in the ‘flexible RT’ the CHP does not compensate for the lack of generation of the RES but
decreases its generation to create a larger negative imbalance. The reason for creating this negative deviation
is the low imbalance tariff that appears in this scenario. In this case the VPP prefers to pay the imbalance
penalty and save fuel cost by turning the CHP off, as shown in Table 3.
The behavior of the different operating strategies among the three studied seasons is illustrated in Figure 8.
The first figure shows the heat demand (gray area), the thermal power generated by the CHP (blue line) and
boiler (red area) and the thermal power charge to (negative values) or discharge from (positive values) the
storage tank (blank line) of a characteristic day of each week. The illustrated parameters correspond to the
dispatched amounts for a specific scenario combination.
During the winter, due to the large heat demand, the CHP is running almost continuously leaving less flexibility
available. This explains why implementing the ‘flexible DA’ strategy during this season does not lead to a large
profit increase when compared against the ‘static ’strategy.
On the other hand, Table 3 shows that the cost reduction achieved using the ‘flexible RT’ operation is related to
a decrease in the fuel cost. This is also visible in Figure 8, during the intermediate and winter seasons. In
comparison with the other strategies, in real time, the ‘flexible RT’ operation uses the CHP less, activating the
boiler more often. As the day-ahead schedule of both the ‘flexible DA’ and ‘flexible RT’ is the same, it can be
deduced that the ‘flexible RT’ operation decreases its output, generating negative imbalance in order to obtain
benefits from the imbalance prices.
As explained before, creating an additional imbalance does not necessary aggravate the situation of the electric
grid (‘passive balancing’). In fact, in Belgium the imbalance prices are an indication of the status of the system.
Thus a low imbalance price suggests that there is surplus of generation in the grid. As a result, by slightly
decreasing the output of the CHP, the VPP owner is not only saving fuel but also helping the grid and will be
remunerated for this via the imbalance mechanism.
Figure 8: Comparison of the heat flow for the different strategies. The gray area corresponds to the thermal
demand. The blue line represents the thermal power output of the CHP. The gray line shows the average
power charge to (negative values) or discharged from (positive values) the storage tank. Finally, the red area
corresponds to the thermal power provided by the auxiliary boiler.
Conclusions and Further Work
This work was focused on developing a bidding strategy for a VPP composed by a CHP-DH and RES generation.
The bidding strategy was implemented using stochastic optimization. This optimization takes into account
uncertainty regarding RES electric power generation, day-ahead and imbalance price. As a consequence, the
CHP operation was scheduled not only to maximize the profit and cover the heat demand but also to
compensate for the possible forecast error of the RES.
Three different strategies were assessed: ‘static’, ‘flexible DA’ and ‘flexible RT’ operation. In the first strategy
the RES forecast errors are settled in the imbalance market and the CHP flexibility provided by its thermal
storage tank is not used. The other strategies use this flexibility to accommodate the forecast errors. In the
‘flexible DA’ case the CHP is rescheduled only once when accurate information regarding the RES generation is
obtained without knowledge on the imbalance prices. On the other hand, the ‘flexible RT’ adjust the CHP
output depending on the actual imbalance prices and RES generation. These strategies were applied to a
hypothetical case study that uses the Belgian city of Leuven as an example.
The results of the ‘flexible DA’ case show a profit increase during summer (5,900 €/week) and the intermediate
season (2,800 €/week), to be compared against the total fuel cost in these seasons (96,000 €/week in summer
and 192,000 €/week during the intermediate season). In contrast, during winter the difference between the
‘static’ and the ‘flexible DA’ case is low compared with this fuel cost. Better results are obtained when the
‘flexible RT’ strategy is applied. If the VPP is allowed to react to the imbalance prices changing its position close
to real time, the profits increase in all seasons.
This indicates that CHP-DH could help not only to reduce the cost due to the forecast errors but may also help
the grid to reduce the system imbalance. However, this economic advantage should be valued against the
additional investment needed to perform the accurate control on real time basis. Further work should assess
the investment, maintenance and operational costs needed to perform real time control and the effects of
considering other technologies such as heat pumps in the VPP. Additionally, estimating the impact of passive
balancing on the remaining imbalance of the system was out of the scope of this work.
Nomenclature
SYMBOL
DEFINITION
C@
Electrical efficiency of the CHP
[%]
Cn
Thermal efficiency of the CHP
[%]
F,4
On/off status of the CHP
#$%
∆-.,,
Electricity traded in the balancing market
[MW]
1
∆-.,o
Difference between RES electric power scheduled and dispatched
[MW]
/0)
∆=.,,
Difference between the planned and delivered thermal power of the CHP
[MW]
%(#>1
∆=.,o
Difference between the planned and delivered thermal power of the boiler
[MW]
∆
Time step of the optimization (15 minutes)
[h]
Yn
Thermal efficiency of the boiler
[%]
Y[
Storage tank loss factor
[%]
Probability of the imbalance scenarios
[%]
Probability of the renewable scenarios
[%]
Probability of the day-ahead scenarios
[%]
#$%
<,
Imbalance market prices
[€/MWh]
<,!
Day-ahead market prices
[€/MWh]
<]^1>
Gas prices
[€/MWh]
1i
',,
Deviation penalty
[€]
()
',,
Operational cost of the CHP
[€]
Start-up cost
[€]
6_UV
',4
UNITS
[-]
`de4
Limits of the piecewise deviation function
`p,,
Components x of the piecewise deviation function
[MW]
i))
-367
Installed capacity of the VPP
[MW]
8
-.,,
Electricity generated on real-time
[MW]
-./0)
Expected electricity generated by the CHP
[MW]
-. !
Total electric power traded in the DA market
[MW]
-.1
RES electric power traded in the DA market
[MW]
. /0)H
G,4
Primary fuel consumption of the CHP plant
[MW]
G. %(#>1
Primary fuel consumption of the boiler
[MW]
i
imbalance prices scenario
/0)
=.,4
Thermal power generated by the CHP
[MW]
=.%(#>1
Thermal power generated by the auxiliary boiler
[MW]
(/
=,,
State of charge of the storage
/0
=.,,,
Thermal (dis)charging power to the storage tank
#$%
,,
Imbalance market profits
[€]
!
Day-ahead market profits
[€]
r
Renewable energy scenarios
s
Day-ahead prices scenario
Acronyms
CHP
Combined Heat and Power District Heating
DA
Day-ahead
DH
District heating
EU
European Union
ICGE
Internal Combustion Gas Engine
IMB
Imbalance
MDP
Marginal Decremental Price
[%]
[€/MWh]
[MWh]
[MW]
[MW]
[€/MWh]
MIP
Marginal Incremental Price
NRV
Net Regulation Volume
PHSP
Pumped Hydro Storage Plant
PV
Photovoltaic
RES
Renewable Energy Sources
RT
Real time
SI
System Imbalance
SOC
State of Charge
TSO
Transmission System Operator
VPP
Virtual Power Plant
VSS
Value of the Stochastic Solution
WPP
Wind Power Plant
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