WP EN2014-24

A comparative study of imbalance reduction strategies for virtual power plant

operation

J. Zapata Riveros, J. Vandewalle and W. D’haeseleer

TME WORKING PAPER - Energy and Environment Last update: October 2014

An electronic version of the paper may be downloaded from the TME website:

http://www.mech.kuleuven.be/tme/research/

A COMPARATIVE STUDY OF IMBALANCE REDUCTION STRATEGIES FOR VIRTUAL POWER PLANT OPERATION

J. Zapataa,b, J. Vandewalle 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

The penetration of a large amount of distributed generation (DG) technologies with intermittent output, such as photovoltaic installations and wind turbines, yields an important challenge to the electric grid. It is believed that aggregating them with controllable technologies such as cogeneration devices (CHP) can help to balance fluctuations of renewable energy. This work evaluates the ability of virtual power plant (VPP) to reduce the imbalance error of renewables generators. The study is undertaken in a VPP that consists of several cogeneration devices and photovoltaic (PV) installations. The virtual power plant operator bids electricity to the day-ahead market using the forecast for solar irradiation and for the thermal demand. During the actual day, the imbalance due to deviations between the forecasted electricity delivered and the real output has to be settled in the balancing market. Thus, in order to compensate these errors and possible economic drawbacks, the operation of the CHP is adjusted periodically in a so called reschedule. Two different rescheduling strategies are compared against a reference scenario in which the imbalance error is settled in the market. The first one (‘forced strategy’) aims at reducing the imbalance error every time step regardless of the imbalance prices. The second (‘economic strategy’) considers the imbalance prices and takes only action if it is economically appropriate and thus intends to reduce the total operational cost. The results show that the rescheduling technique is able to reduce the imbalance error (up to 90% depending on the season and the strategy). Additionally, the total operational cost is estimated. However the nowadays imbalance prices only lead to a slightly financial advantages that is unlikely to motivate real life operators to perform a rescheduling strategy.

Highlights

The dispatch of the VPP is controlled by a day-ahead optimization followed by a rescheduling

strategy.

The maximum theoretical reduction of the schedule deviation was found using ‘forced rescheduling strategy’ which aims at decreasing the imbalance error regardless of the price. It was found that the imbalance can be reduced up to 90% during the winter. This strategy is best to support the grid, however it leads to an increase of the operational costs.

A second approach ‘economic rescheduling strategy’ takes the imbalance price into account and is

more efficient in reducing the operator’s total cost -a cost reduction of 3% appears in the summer.

Even a rough imbalance price forecast can be used in the economic rescheduling strategy without severely compromising the cost reduction.

Keywords: cogeneration, virtual power plant, balancing market, photovoltaic, optimization.

1 Corresponding author. Email: William.Dhaeseleer@mech.kuleuven.be Tel. +32 16 322510, Fax. +32 16 3 22985.

Nomenclature

( ) Total fuel cost of the CHP system [€]

( ) Total revenues of the CHP system [€]

( ) Fuel cost of the CHP prime mover [€]

( )

Fuel cost of the auxiliary boiler [€]

( )

Savings due to the local use of electricity [€]

( )

Revenues for the electricity fed into the grid [€]

( ) Heat demand [kW]

( ) Thermal power of the CHP [kW]

( ) Thermal power of the boiler [kW]

( ) Thermal (dis)charging power to the storage tank [kW]

( ) Thermal capacity of the storage tank [kWh]

Storage tank loss factor [%]

Time step [h]

( ) Electric power of the CHP [kW]

( ) Primary energy use of the CHP [kW] ( ) Self- consumption of electricity [kW]

( ) Electricity sent to the grid [kW]

( ) Electric power of the ‘ith’ CHP device[kW]

( ) Real output of the VPP [kW]

( ) Forecasted output of the VPP [kW]

Forecasted PV output [kW]

Forecasted CHP output [kW]

Actual PV output [kW]

Actual CHP output [kW]

( ) Electricity traded with the balancing market [kW]

( ) Total imbalance cost [€]

Negative imbalance of the VPP during one time interval [kWh]

Negative imbalance price [c€/kWh]

Positive imbalance of the VPP during one time interval [kWh]

Positive imbalance price [c€/kWh]

Spot market prices [c€/kWh]

Net regulating volume [kWh]

1. Introduction

The large penetration of distributed generation (DG) in the electric grid yields an important challenge to the operation of the energy system. Several DG technologies have an intermittent output that is very difficult to forecast (i.e. wind and solar).This rises the imbalance error of the system. To balance out the planned feed-in, control reserve power is used. Increasing the use of reserve power adds a significant cost factor for operating the grid. In order to counterbalance this problem, it is proposed to group different distributed generation technologies in what is known as a virtual power plant. A virtual power plant as defined in [1] is an agglomeration of distributed generators, controllable loads and storages devices, aggregated in order to operate

as a unique power plant. Due to the characteristically low generation capacity of individual DG units, combining them into a VPP will also enable their participation in the exchange market. The power exchange is performed the day before in the so called day-ahead market (DA). The operation of this market can be explained as follows: on the day before actual electricity delivery, the participants bid into the market. Based on the submitted bids the market determines the clearing price.2 The bids that have prices lower than the clearing price are accepted in the market. In principle, the prices are based, amongst other factors, on the variable operation and maintenance cost of the generation facilities. Since photovoltaic (PV) and wind energy have minimal variable costs, their bids are generally granted. Nonetheless, the low predictability of these technologies increases the cost to compensate the imbalance between the projected electricity and the actual supply, due to forecast error. This imbalance is considered as a major barrier to introduce renewable energy sources (RES) in the exchange market. The present work aims to answer two main questions: First, can a VPP conform by micro-CHP technologies help to integration renewable energy (specifically PV) in the electricity market by reducing the imbalance due to the imperfect forecast? And second, which kind of optimization strategy should be used and what is the economic benefit?

1.1. Literature review and contributions In the literature several studies explore similar questions. For example [2] assesses the unit commitment problem of distributed resources and highlights the benefits to aggregate different energy producers in a VPP, the study uses the energy hub model [3] which is based on a Mixed integer linear program (MILP) optimization and aims to produce the most economical dispatch using different energy carriers. Similarly, [4] also performs a MILP optimization to control the operation of five cogeneration devices. It concludes that large economic advantages can be obtained by operating the CHP taking into account the Spot or DA prices. Additionally, it states that using a VPP configuration can help to balance fluctuations of renewable energy. Nevertheless, this observation is not further assessed as it is done in this study. Additionally,[5] highlights the complementary characteristics of PV and CHP technologies when operating together in a microgrid. It finds out that these two technologies together with a small electrical storage device can supply steady power to an isolated microgrid. Furthermore, the ability to reduce imbalance by making use of CHP technology has been explored in several works. In [6] different optimization strategies (MILP, Heuristics) are used to control a VPP conformed by CHPs that offer electricity to the DA market and reserve market. It was proven that a VPP can comply with a predefined schedule even under deviations between the forecasted and actual load. The

2 Clearing price or Marginal is the cost of the generation of one additional unit of electric energy in MWh.

author in [6] employs a rescheduling strategy similar to the one used in this work however no RES are taken into account which is one of the major aims of this project. The same rescheduling strategy also called Model PredictiveControl (MPC )or rolling horizon optimization is applied in [7] to control individual households with micro-CHP installations. It is demonstrated that including predictions on the system control leads to considerable economical savings. The same author in [8] evaluates the ability to reduce the imbalance of a wind farm making use of residential micro-CHPs aggregated in a VPP. Limited economic advantages were found when performing imbalance reduction. Yet, the VPP operation does not make use of optimization strategies applied for individual households (i.e, MPC). This paper applies rolling horizon approach to operate the VPP. Another common technique utilized to control VPPs in order to reduce the imbalance error, is the multi-agent control, as reported in [9]. This techniques apply distributed control assuming that all devices operate in an economically optimal way and the only information exchanged between them are the prices?. The results of a field test that uses multi-agent technique to reduce imbalance due to forecast errors are documented in [10].The VPP consist of Wind power production, heat pump installation and a large CHP. The report shows that with the aggregated operation it is possible to reduce the overproduction of wind almost completely, but it fails to compensate underproduction. Both [9] and [10] do not give an estimate of the economic benefits of reducing the imbalance, the present work tackles this point. Finally, other works such as [11],[12] report the use of VPP to reduce imbalance of RES. In the first study a VPP that consist of a wind farm, a solar installation and a conventional gas turbine is simulated. It is found that it is better to cover the forecast deviations buying the electricity from the day-ahead market than using the gas turbine. The latter work assesses the possibility to balance a large scale PV installation making use of an industrial CHP unit; the results predict a possible imbalance reduction of more than 80%. Both studies involve large installations instead of micro-generators as the ones that concern to this work.

1.2. Contributions and content of the present paper In conclusion with respect to the reviewed literature the contributions of this work can be summarizes as:

1. The ability of residential micro-CHP devices to reduce imbalance due to forecast errors of RES is assessed by applying rolling horizon optimization to a VPP.

2. A comparison between different imbalance reduction strategies is performed in terms of imbalance error reduction and economic benefits achieved.

The rest of this paper is organized as follows: Section 2 describes the methodology applied and explains the optimization algorithm. Section 3 defines the assumptions. In section 4 the mechanism of the balancing market in Belgium and the procedure applied to forecast the imbalance prices are described. The results are presented and analyzed in section 5. Finally, conclusions are stated in section 6.

2. Methodology

2.1. Problem description The present study evaluates the ability of residential micro-CHPs to reduce the imbalance of small decentralized PV installations. Real residential gas and electric demand profiles have been made available by the LINEAR project3 . This data has been collected during measurements performed on 57 houses and it represents a characteristic sample of the Flanders region with respect to annual consumption, dwelling type and number of inhabitants. The data is subject to confidentiality and further/detailed information cannot be published. In order to obtain a realistic heat profile based on the gas demand it is assumed that both variables are proportional. This assumption is justified by the fact that 83% of the residential gas demand in Flanders is used for space heating. Hence, the converting factor is equivalent to the boiler efficiency.

3 For more information http://www.linear-smartgrid.be/

The case study of this paper considers only the houses whose annual heat demand is larger than 20.000 kWh , since according to [13] considerable benefits when using micro-CHP instead of traditional heating systems (i.e., condensing boilers) can only be obtained in households with large heat demand. Only three of the studied profiles fulfill this condition. Therefore the considered VPP consist of three detached dwellings. Each of them with a micro-CHP system (CHP prime mover, boiler and thermal storage tank) and a small solar power station with maximum output of up to 32 kW. The studied micro-CHP technology is an internal combustion engine. Its characteristics will be further explained in section 3.1. This kind of technology was selected since it represents the largest number of CHPs that are installed in Belgium at the moment [14]. There is no heat grid connection between the houses. Nevertheless, the electricity generated by micro-CHP can be used either to meet the common electric demand or can be sold in the exchange market. On the other hand,since the solar power station is not attached to the houses the PV output will always be sold on the DA market. It will never be used for self-consumption. It is assumed that, the VPP operator will bid a certain amount of electricity on the market using a prediction of the solar irradiation and heat demand. In real time, if the VPP fails to deliver the contracted electricity, the difference is settled in the balancing market. For this reason, during every time step the CHP production is rescheduled in order to reduce the imbalance. The analysis is performed for three representative weeks for three different seasons (summer, intermediate and winter). The imbalance reduction and the economic advantages are compared among the different seasons and scenarios. Since the study evaluates the reduction of imbalance errors caused by the forecast deviation of PV output, other error sources such as deviations of heat demand and electricity price ?forecast are not considered.

2.2. Optimization The optimization uses a MILP model that is solved by the optimization software CPLEX. It is performed at two different points in time: the day previous to the delivery and in the actual day. The first optimization (DA optimization), has the objective to find an operational schedule for the CHP and boiler that minimize the energy cost of the households. The results of this optimization are the base for the three analyzed rescheduling strategies as shown in Figure 1. In the DA optimization, a large part of the electricity generated by the CHP is used to meet the local demand; this is due to the fact that the spot prices are most of the time not high enough to motivate the use of the CHP for selling electricity into the grid. Nevertheless, the system allows to feed excess electricity into the grid and thus this part of the optimization also estimates he amount of electricity produced by the CHP that is going to be sold in the DA-market. In the actual day (D), a rescheduling strategy is performed using a rolling horizon approach. At each time step the actual PV output is obtained and the imbalance error is estimated. The optimization is performed for the entire time horizon, yet only the first time slot is implemented, the procedure is repeated during the next periods. Two different approaches are evaluated for the rescheduled strategy. First, a ‘forced strategy’ reduces the imbalance error regardless of the price. This strategy gives the maximum theoretical possible imbalance reduction under the optimization conditions. A second approach or ‘economic strategy’ intends to minimize the total operational cost including the imbalance cost. These strategies are compared against a ‘Reference scenario’ in which no reschedule strategy is performed, thus the forecast deviations are settled in the imbalance market. Furthermore, the ‘economic strategy’ is evaluated considering both perfect prediction of the imbalance prices and a forecast that is performed using autoregressive models (ARIMA) as explained in section 4.2.

In summary, four scenarios are studied, namely a Reference Scenario (REF), a forced reschedule strategy (FS) and an economic reschedule strategy with perfect prediction (ES-P) and with forecast (ES-F).

Figure 1: Two step optimization. On the Day- ahead (D-1) the optimization decides the optimal schedule of the CHPs. In the actual day (D) a reschedule routine is performed aiming to reduce the imbalance error.

2.3. Day-ahead optimization algorithm The objective of the cost optimization algorithm to minimize the operational cost of the system is expressed in equation (1) and extended in equation (2). The operational cost is the sum of the fuel cost of the CHPs and boilers (CCHP, Cboiler). On the other hand, the savings include the revenues due to the electricity that is sold to the grid (Ggrid) and the savings due to the self-consumption of the electricity generated by the CHP (Glocal):

∑( ( ) ( ))

(1)

∑( ( ) ( ) ( ) ( ))

(2)

The relationship between the electric and the thermal output of the CHP is described in equation (3). In a similar way, equation (4) relates the electric output and the primary energy. The parameters ath ,bth, ap, and bp are calculated from measured data of commercial CHP provided by the IEA annex 54 and reported in [15]. Figure 2 shows the linearization of the micro-CHP Ecopower plus. On the other hand ϒ is a binary variable that indicates the on/off status of the CHP.

( ) ( ) ( ) (3)

( ) ( ) ( )

(4)

The optimization is constrained by several operational and technical conditions. The operational constraints ensure that the heat demand ( demand) will always be met using the CHP ( chp), the boiler

( boiler) or the heat that is discharged from the thermal storage buffer ( c), as described in equation (5):

( ) ( ) ( ) ( )

(5)

DA

OPTIMIZATION

(D-1)

Heat demand

Electric demand

Local price

Spot price

Gas price

PV forecast

PV actual

+-

Fix previous values

(D)

RE-SCHEDULE

(Imbalance)

DA schedule Real output

The state of charge of the storage tank (Qst) is calculated using equation (6). The efficiency of the storage tank4 (ηst) is assumed to be constant. The time step ( ) of the analysis is 15 minutes:

( ) ( ) ( )

(6)

It is assumed that the boiler has a constant efficiency and thus the primary energy can be estimated as in equation (7).

(7)

The cost of the CHP system (boiler and primary mover) can be calculated by multiplying the primary energy consumption by the gas price this is illustrated in equation (8).

( ) ( ) ( ) (8)

The electricity generated by the CHP ( chp) can be used inside the VPP ( local) or sold to the electricity

market ( grid):

( ) ( ) ( ) (9)

Consequently, the revenues obtained from selling or using the produced electricity are estimated in equation (10), where Pspot represents the DA market price and Plocal the price to buy electricity from the grid.

( ) ( ) ( ) ( ) (10)

On the other hand, some technical restrictions prevent exceeding the operational limits of the machines when they are turned on. This is expressed in equations (11)-(14) for the thermal storage, the boiler and the CHP, respectively:

( ) (11)

( ) (12)

( ) (13)

( ) (14)

Other technical constraints control the minimum start up time of the CHP device. This is performed as explained in [16] and it is important to consider this in order to avoid wearing out of the machine. As no heat grid connection exists between the houses, each system has to satisfy its individual heat demand; thus, equations (5)-(6) and (11)-(14) apply to every individual CHP. On the contrary, the electric demand is the aggregated electric demand of the houses. Therefore, the electricity generated by the VPP ( chp) is equal to the sum of the individual production of each CHP device:

( ) ( ) ( ) ( ) (15)

2.4. Actual day optimization (forced reschedule strategy) The objective function of the second optimization problem is to minimize the imbalance error. As stated in equation (16), this is the difference between the real output (OutReal) of PV and CHP and the forecasted output (OutForecast). This optimization is performed every time step once the real PV output is obtained.

∑| ( ) ( )|

(16)

4 The efficiency of the storage tank represents the percentage of heat that is preserved from the storage after it has been stored during one time step.

Although the objective function is different, the optimization has the same constraints previously explained and described in equations (5)-(15). Nevertheless, an additional constraint guaranties that the imbalance is always covered either by the actual CHP output (CHPReal) or through the electricity from the balancing market (EImb) (see section 4) as expressed in (17). The variable EImb can be positive or negative depending on the nature of the imbalance error.

( ) ( ) ( ) ( ) (17)

2.5. Actual day optimization (Economic rescheduling strategy) This optimization aims to reduce the total operational cost including the imbalance cost as expressed in equation (18). Thus, the VPP can decide every time step whether it is profitable to reduce its imbalance or whether it is better to settle the difference in the imbalance market.

∑( ( ) ( ))

(18)

The fee that the VPP has to pay for the imbalance depends on its own positions (i.e. if it is producing more of less than the forecasted output) and on the imbalance prices as shown in equation (19). It is important to remind that if the VPP has a positive imbalance the additional energy produced is sold to the TSO (Transmission System Operator) (see Table 1) and the VPP receives compensation (except in case of negative prices). Therefore the positive imbalance cost has a negative sign in equation (19):

( ) (19)

An additional constraint has been added to avoid that the VPP takes advantageous positions in the market that could be penalized by the TSO. Thus, equation (20) requires that the final imbalance is lower or equal than the imbalance caused by the PV installation (Δ PV) due to prediction errors:

( ) ( ) (20)

3. Assumptions

3.1. Cogeneration system The cogeneration system consists of a prime mover, a thermal buffer and an auxiliary boiler. The prime mover was sized for each house using the ‘maximum rectangle’ method as explained in [17]. It is assumed that all cogeneration devices are able to modulate and the modulation characteristics are similar to the commercial CHP device ‘Ecopower plus’ which are shown in Figure 2.

Figure 2: Technical characteristics of the Micro-CHP Ecopower Plus. The figure shows the linear relationship

Qchp = 2.5413*Echp+ 0.6886

Pprim= 3.8749*Echp + 0.7952

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between electric and primary energy (dashed line) and the electric and thermal energy (full line). The markers correspond to the measured data. The capacity of the storage tank is calculated in such a way that the buffer is able to store two hours of the maximum thermal output produced by the CHP. This was proven to be an optimal size for the tank from the economic point of view[18][19]. It is assumed that the storage tank starts and ends empty. The optimization does not allow dumping heat in the environment. Finally, the auxiliary boiler covers the remaining heat demand. The boiler efficiency is assumed to be constant and equal to 90%.

3.2. Forecasted and measured photovoltaic data The used PV profile was measured at a fixed rooftop PV installation at the KU Leuven Campus in Belgium. The data is available in fifteen minutes time steps [20]. As no meteorological information like the forecasted irradiation linked to the measured data was available, the historical power generation of the modules was used to obtain a simulated forecast. This was done making use of autoregressive models as explained in [21] and[22]. First, the PV data was normalized using a clear sky method [21].This kind of model assumes that the PV output can be explained by a combination of deterministic and stochastic factors. The clear sky method employs measurement from previous years to determine the output of the PV under clear sky conditions. The methodology is further illustrated in Figure 3. First the yearly PV output is arranged as function of the time of the day τd (i.e. as a fraction of the day being 1 the end and 0 the beginning) and day of the year τy

(see panel a). Afterwards, using quantile regression a smooth surface that covers closely the measured PV output is found. This is shown in the right panel. As in [22] no mathematical expression is derived from the surface, only interpolation is employed in order to find the clear sky model.

a) b)

Figure 3: Clear sky model. The left panels show the PV output as a function of the time of the day and the day of the year. The right panel presents a model of the PV output under clear sky conditions

Once the PV output is normalized, the deviation from the clear sky model is estimated making use of an autoregressive moving average technique (ARIMA). Details on how to fit an ARIMA model can be found in [23] The resulting model that best fits to the normalized PV output is a seasonal. ARIMA (0,1,2) (0,1,0)96. The seasonality corresponds to a daily correlation. Recall that the data is in 15 minutes time step and thus the total number of time steps per day is 96. A resulting example of the PV forecast using normalized PV output and ARIMA can be observed in Figure 4.

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Figure 4: The dashed line represents the forecasted PV output (‘forecast’); the gray line corresponds to the real PV output.

3.3. Electricity and gas prices For the present work it is assumed that the price for the local electricity corresponds to the residential tariff which amounts to 0.15 €/kWh at night and 0.22 €/kWh during the day. With regard to the DA price, the values are obtained from the BELPEX5 internet platform and correspond to the year 2012. It is also assumed that the VPP will pay a gas price equal to the price that is paid by small and medium sized enterprises which in the case of Belgium is equivalent to 0.039 €/kWh6. The imbalance prices are public available at the internet page of ELIA7. The working mechanisms of the Belgian balancing market are explained in section 4.

4. Belgian balancing market

The Belgian transmission system operator for electricity, ELIA, is responsible for ensuring the balance between generation and consumption inside the country [24]. This duty is shared with the different balance responsible parties (BRP)8 which are responsible to ensure that the energy supply corresponds to the forecasted consumption of energy in its balance area during a given period of time. The BRPs are charged for any imbalance that occurs on their perimeter. The imbalance prices are designed to encourage the BRPs to reduce the imbalance in their portfolio. Since January 2012, the Belgian imbalance system has changed and is described below.

4.1. Imbalance market mechanisms With the new balancing system, the imbalance pricing consist of a single price for both up and down regulation with additional incentive mechanisms α and β that are activated only in case of large imbalance. The imbalance bill that the BRP has to pay consists of the volume fee and the imbalance charge. The volume fee accounts mainly for the administrative cost. The imbalance tariffs are estimated taking into account several factors such as: The nature of the imbalance (the imbalance is positive when the BRP injects extra energy to the

system and negative in the contrary case of a off-take The cost of the activation

5 BELPEX is the Belgian Power Exchange for anonymous, cleared trading in day-ahead electricity. 6 Since the structure of the market for a VPP is not yet clearly established the model employs both retail and whole sale market prices. In the future the regulator should clarify the rules for the market. 7 ELIA is the Belgian transmission system operator (TSO) for electricity. 8 A BRP is a legal entity obligated to pay a TSO for the imbalances within its ‘Responsible’s Perimeter’.

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The position of the TSO The concept of the imbalance mechanisms is simplified in Table 1. In general four different cases can occur as shown in the table (situations A,B,C,D).

Table 1: Belgian balancing pricing [24]

Situation of ELIA Surplus Deficit

Imbalance in the BRP

Positive A B MDP-α MIP-β

Negative C D MDP+β MIP+α

If the TSO has a surplus of energy there is a need for down regulation. This means that the TSO will require some generators to reduce their output and will pay for this service. On the other side, when the TSO has a deficit there is a need for up regulation and some generators will be called to increase their output. The highest prices that the TSO will pay for up regulation and the lowest price for down regulation (usually negative values) are the marginal incremental and decremental price respectively. Consequently, in cases B and C, the position of the BPR helps to reduce the general imbalance. Thus, in case B, the TSO pays to the BRP the Marginal Incremental Price (MIP). Alternatively, in case C, the BRP pays to Elia the marginal price for down regulation or marginal decremental price (MDP). In contrast, in cases A and D the BPR position aggravates the total imbalance; thus it will receive the MDP or pay the MIP in case of positive or negative imbalance respectively. The variables α and β shown in Table 1 are only activated if the total system imbalance9 is larger than 140 MW. According to Elia β is usually set as zero and α is calculated based on the average of the 8 previous values of the system imbalance The average price for the last 10 months (January to October 2012) was 5.03 c€/kWh for negative imbalance and 5.24 c€/kWh for positive imbalance. This market nevertheless is very volatile and can reach larger values.

4.2. Imbalance price forecast Since in the economical rescheduling strategy, the objective is to minimize the total cost, a prognosis of the imbalance prices should be incorporated in the optimization. In [25] it is suggested that there is a linear relationship between the spot market price, the imbalance price and the net regulating volume (NRV)10. Using the market data of 2012 this relationship is plotted in Figure 5 The imbalance price is formulated as a linear combination of the NRV and the spot market price. A linear fit is expressed in equations (21) and (22) for the values of the year 2012. Note that both equations are very similar. This is due to the fact that, as mentioned before, in Belgium there is a single imbalance price for positive and negative regulation that only differs by α and β in case of large imbalance (see section 4).

Pimb_pos= Pspot+0.19*NRV+13.7 [c€/kWh] (21)

Pimb_neg= Pspot+0.18*NRV+15.5 [c€/kWh] (22)

9 The system imbalance is the difference between the expected and measured values of interchange in the Belgian

control area and the amount of reserve power activated. 10This is the reserve power that Elia had to activate in the specified 15 minutes to preserve the balance in the system.

Using a linear fit probes to be an accurate measure for the purpose of this research (see section 5). Other kind of relationship (e.g., piecewise function) may lead to more precise forecast, but is out of the scope of this work. Nevertheless, as explained before the algorithm was performed with and without perfect forecast in order to have an idea of the value of a perfect prediction.

Figure 5: Relationship between the NRV , the spot price and the imbalance price

As the DA price can be predicted with high accuracy it is assumed that the spot market prices are known in advance. Thus, only a forecast of the NRV is needed in order to predict the positive and negative regulating prices. Forecasting the NRV is a challenging task due to its unpredictable nature. Nevertheless, a good approximation can be found using autoregressive models as explained in [14]. Once the NRV forecast is obtained, the values are fitted to equations (21) and (22) and the positive and negative imbalance prices are estimated. An example of the positive imbalance price prediction is illustrated in Figure 6. The black line corresponds to the real imbalance prices whereas the red dotted line represents the forecast. It is clear that the forecast is able to reasonably follow the base line of the real price, but fails to predict the abrupt peaks. These peaks appear in the prices as result of the α and β mechanism that were explained above and thus are almost impossible to predict.

Figure 6: Real (black and solid) and forecasted (dashed line) positive imbalance price. The forecasted signal fails to predict the real peaks

5. Results and discussion

The results of the three different implemented strategies are compared. The first criterion to be evaluated is the ability to decrease the imbalance error or in other words the capacity to comply with the original day-ahead schedule. The second criterion is the total operational cost including the fuel cost and the imbalance cost. Since the DA revenues are the same for all scenarios (only differing between seasons) they are not included in the comparison.

5.1. DA schedule compliance Figure 7 illustrates the results of the DA schedule compliance on a typical winter day11.The left side of the figure depicts the reference scenario, whereas the plot in the middle corresponds to the forced reduction strategy and the right figure represents the economic approach using perfect prediction.12 In the figures, the black line indicates the amount of electricity that was bid into the DA market while the shaded area represents the real electric power that was delivered. Looking at the figures it is clear that even though the forced strategy gives the maximum theoretical possible reduction, using rescheduling techniques, either aiming to reduce the imbalance error or the total cost, the difference between the electricity bid DA and the real delivery (diagonal and horizontal shaded areas) can be largely reduced.

11 The calculations were performed for a week, the figures show only one day to facilitate the visualization. 12 The results of the Economic rescheduling with forecasted prices look very similar to those with perfect prediction and therefore are not shown.

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Figure 7: Reference and rescheduled scenarios on a winter day. In the reschedule scenarios (middle and right panels) the actual delivered electricity (diagonal and horizontal shaded areas) follows more closely the bid (black line). Figure 8: Reference and rescheduled scenarios on a summer day. Same convention as in Figure 7. Similarly, Figure 8 illustrates the studied scenarios on a summer day. In this case, only the forced reschedule approach decreases the difference between the real output and the DA bid. On the other hand, the economic strategy performs poor with respect to decrease the DA schedule deviations, suggesting that it is not profitable to do so during this day. This observation is elaborated further in the section 5.2. In a further step, the compliance with the DA schedule (i.e., imbalance error reduction) is calculated with respect to the reference scenario. Table 2 summarizes the results; in the first column the remaining imbalance in the reference case is shown. Afterwards, the corresponding positive and negative imbalance errors resulting from the rescheduling strategy is presented. It can be observed that the imbalance error (particularly the positive imbalance) in spring and summer is larger than in winter. From the table, it is inferred that it is theoretically possible to achieve a large compliance with the DA schedule using micro-CHP (up to 95 % in winter). Regarding the economic rescheduling strategies both with and without perfect price forecast, the results show that the amount of imbalance error reduction is lower (only 30% for the winter case). The numbers suggest that in some cases instead of using the CHP to reduce the imbalance it is better to settle the

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difference in the market. Particularly, in summer for example there is a minor effort to reduce negative imbalance (only 2.7 % lower than the reference case). This is due to the fact that, the low heat demand decreases the motivation to use the CHP in order to compensate for under production. Table 2: Remaining imbalance for the different scenarios [kWh]

SEASON REFERENCE FORCED STRATEGY ECONOMIC STRATEGY

PERFECT FORECAST POS NEG POS NEG POS NEG POS NEG Winter 69.3 105.4 15.6 5.0 32.2 73.7 19.2 81.0 Spring 267.8 206.5 139.7 100.2 205.0 144.4 206.5 150.9 Summer 300.1 137.4 163.4 56.8 190.0 133.7 180.6 133.6 POS =Positive imbalance ; NEG=Negative imbalance

5.2. Total operational cost The total operational cost is subject to evaluation. This cost includes the fuel cost of the CHP, the auxiliary boiler and the imbalance cost. The results are illustrated in Figure 9 , Figure 10 and summarized in Table 3. In Figure 9 the cost difference between the reference and the forced rescheduling scenario is illustrated. The three cost components are included (fuel cost for the boiler and CHP and the imbalance cost). In the graph, a positive amount indicates an increase of the cost and a negative amount a decrease. During winter the CHP is forced to produce more energy in order to compensate the amount that the PV installation fails to provide. Thus the cost of the CHP increases consequently, the cost of the boiler decreases since the CHP is simultaneously generating more heat. This is possible and still profitable in this season due to the large heat demand. Whereas in summer and spring there is a large positive imbalance (see Table 2). Thus, the CHP operation decreases in order to compensate for the excess of PV energy, this leads to an increase in the imbalance cost during both seasons since reducing positive imbalance (i.e., over production) lowers the profits obtained by selling this electricity in the imbalance market when the prices are large (see Figure 11 for an insight into this case). Consequently, the forced strategy only results profitable during winter (see Table 3).

Figure 9: Cost change for the ‘forced strategy’ with respect to the reference scenario. A positive change

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Figure 10: Cost change for the ‘economic strategy’ with respect to the reference scenario. A positive change denotes a cost increase while a negative change is a decrease

Similarly, Figure 10 illustrates the cost difference for the economic strategy with perfect prediction of the prices. Comparing with Figure 9, it can be seen that in this case there is a total cost reduction in all seasons (see Table 3). Particularly, it can be remarked that the CHP is used less to compensate negative imbalance in winter, leading to a larger cost reduction than the observed with the forced strategy. On the other hand, during summer the CHP production largely decreases due to two reasons: first the underproduction is mostly settled in the imbalance market and consequently increasing the imbalance cost, which is more convenient than using the CHP in this season due to the extra fuel cost. Second the CHP is turned off at some times to compensate the extra PV production, leading to savings in the primary energy cost. These results are also supported by the findings of the previous section (see Table 2 ). Table 3: Difference in the operational cost with respect to the reference scenario

DIFFERENCE [€/week]

WINTER SUMMER SPRING

FS ES-P ES-F FS ES-P ES-F PS ES-P ES-F

BOILER -9.27 -2.28 0.29 6.75 9.52 10.42 2.35 -1.25 -0.77

CHP 9.50 -1.42 -3.94 -5.74 -16.46 -17.00 -0.45 0.90 0.015

IMBALANCE -1.42 -0.44 0.07 2.18 3.02 3.58 1.12 -2.34 -1.12

TOTAL -1.18 -4.15 -3.57 3.20 -3.92 -3.01 3.02 -2.69 -1.87

FS= Forced strategy; ES-P=Economic strategy perfect prognoses; ES-F =Economic strategy with forecast Table 4 summarizes the total cost for the three studied strategies (and the cases with and without perfect prediction) and the percentage change of the cost. The first column corresponds to the reference scenario where the imbalance error is settled in the market. Afterwards the results of the forced rescheduling strategy and the economic rescheduling are shown, next to the total cost the percentage change between the studied case and the reference scenario is estimated. A negative percentage value indicates a cost increase. The main findings of Table 4 are summarized as follows:

The cost increase that occurs in summer and spring with the forced schedule reflects that even though it is theoretically possible to use micro-CHP devices to reduce imbalance, it is not always profitable to do so.

The perfect prediction gives always the maximum theoretical cost savings that can be achieved by reducing the imbalance error. Nevertheless, the difference between the forecasted and the perfect

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prediction is not large. In summer for example the cost of the economic strategy using perfect prediction is only 1.5 % lower than the cost when using a forecast (the difference in other seasons is of the same magnitude). This indicates that improving the quality of the forecast does not lead to a significant increase of the profits.

Table 4: Cost of the different strategies and change with respect to the reference scenario (A negative change indicates a cost increase)

REFERENCE FORCED RESCHEDULE

ECONOMIC RESCHEDULE

PERFECT FORECAST

COST(€) COST(€) CHANGE (%)

COST(€) CHANGE (%)

COST(€) CHANGE (%)

Winter 406.70 405.50 0.28 402.50 1.02 403.10 0.88 Summer 93.25 96.45 -3.43 89.32 4.20 90.24 3.23 Spring 136.60 139.60 -2.20 133.90 1.96 134.72 1.37 Total 636.50 641.50 -0.78 625.70 1.69 628.10 1.33

Furthermore, observing the results of Table 3 and Table 4 it is important to highlight that the actual cost difference between the studied strategies is very small (of the order of zero to ten). This can result from the fact that the VPP consists of ICE. This kind of technology has a low electric efficiency and a large heat to power ratio. For that reason, the imbalance cost reduction does not compensate the increase of fuel cost of the CHP. Similar results are found in [8] and [2]. In [2] it is stated that the benefits provided by micro CHP technologies largely depend on the heat-to-power ratio and the load patterns. Thus the imbalance reduction might be evaluated in other kinds of buildings (e.g., service buildings) and with other kinds of CHP technologies (e.g., fuel cells). Nonetheless, this is out of the scope of this work. Finally, Figure 11 explains one of the reasons of the poor economic performance of the imbalance reduction technique. Figure 11 shows the remaining positive imbalance for the different strategies on a spring day. The upper panel illustrates also the real imbalance price (black) and the imbalance prediction (gray). The second and third panel corresponds to the ‘Economic strategy’ with and without perfect prediction respectively (black and dotted lines) and the panel at the bottom illustrates the ‘Forced strategy’ (dashed line). The shaded gray area represents the total imbalance when no rescheduling is applied (i.e., Reference scenario). Looking at the ‘Forced strategy’ (dashed line) the remaining imbalance is much lower than in the reference case (gray area), whereas in the other cases there is almost no change of the imbalance error. This is due to the fact that, as shown in the upper panel, the positive imbalance prices during this period are large (up to 27c€/kWh). The large prices reflect the need of the TSO for up-regulation, thus the TSO will pay to the VPP for its extra energy. As the forced strategy does not take the prices into account, it reduces the imbalance by decreasing the CHP operation, but therefore it loses the opportunity to make profit (from the positive imbalance).

Figure 11: Example imbalance price (gray line) and remaining imbalance for the different scenarios: Forced strategy (FS) and economic strategy with perfect prediction and with forecast (ES-P and ES-F). The FS strategy (dashed line) reduces the positive imbalance even when the imbalance prices are large. On the other hand though the forecast is not able to follow the peaks of the imbalance prices, the behavior of the economic strategy with and without perfect prediction is nearly the same. This can be explained using the concept of the profitable price that is elaborated in [18]. According to this concept in an economic optimization the CHP operates only if the price paid for the electricity is larger than the cost of the primary energy needed to produce the electricity minus the cost of the primary energy needed for the boiler to generate the same amount of heat (see equation (23))

(23)

This cost represents a threshold: once the electricity price is larger than this threshold (no matter how large) the CHP operation is considered profitable. Consequently the forecast does not have to predict the actual values but should be good enough to predict if the imbalance prices are larger than the production cost.

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An example is shown in Figure 11 around the hour 16:00. The prognosis fails to predict that the imbalance price will be larger than the production cost (dashed line first panel)13 and thus the economic strategy with forecast decides to decrease the CHP operation and meet the heat demand with the help of the boiler. During the rest of the time the forecast is good enough and the operation with and without forecast is the same.

6. Conclusion

In this work, an optimization algorithm was designed to operate a virtual power plant that consists of several micro-CHP systems and a PV installation. The optimization algorithm uses a mixed integer linear programming model that fixes the day before the amount of electricity that is going to be produced by the CHP. During the actual day a rolling horizon approach reschedules the operation of the CHP in order to compensate the imbalance error. Three different strategies are compared; the first or reference scenario does not make use of any rescheduling strategy but settles the imbalance error in the market. The second one or ‘Forced strategy’ forces to reduce the imbalance error without taking the prices into account. This gives an idea of the maximum reduction that is theoretically possible. The last approach aims to decrease the total cost (including the imbalance cost). The latter strategy was implemented with and without perfect prognosis. The results show that using the rescheduling strategy (either to reduce imbalance or cost) the deviation between the scheduled electricity and the actual delivery can be largely reduced (up to 90% in winter with the forced strategy approach). However, this operation is only profitable if the FORECAST of the imbalance prices are taken into account. Nevertheless, the obtained cost reduction seems not to be large enough to motivate a VPP operator to implement a rescheduling technique. These results provide valuable information since all the characteristics of the model come from realistic and measured data. Thus the low cost reduction can be explained by the fact that the studied technology (internal combustion engines) has a low electric efficiency (24.8%) and a large heat to power ratio. As a consequence imbalance cost reduction does not compensate the extra primary energy cost. It is recommended for further work to assess other micro-CHP technologies such as fuel cells whose electric efficiency is larger (up to 60%) and to study the rescheduling strategy in CHP installed in service buildings were the heat demand is higher and more spread around the year than in households.

Acknowledgment

The authors would like to thank the members of the IEA Annex 54, especially Dr. Steck (ENWIDA, Germany) for his active cooperation and interesting discussions.

The research of the first two authors has been supported by the Project ‘local intelligent networks and energy active regions’ (LINEAR) financed by the Flemish agency for innovation through science and technology (IWT).

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The operational cost changes with the electrical efficiency the one estimated for the example was calculated assuming the maximum electrical efficiency

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