2011 IEEE First International Workshop on Smart Grid Modeling and Simulation (SGMS) - at IEEE SmartGridComm 2011
Optimization models for consumer flexibility aggregation in smart grids: the ADDRESS approach Alessandro Agnetis, Gabriella Dellino, Gianluca De Pascale, Giacomo Innocenti, Marco Pranzo, Antonio Vicino
emerge from an analysis of the present state of the art in the management of electricity distribution networks:
Abstract— This paper addresses the problem of optimal management of consumer flexibility in an electric distribution system. Aggregation of a number of consumers clustered according to appropriate criteria, is one of the most promising approaches for modifying the daily load profile at nodes of an electric distribution network. Modifying the daily load profile is recognized as one of the strongest needs both for safe and efficient operation of the network. The paper proposes an optimization approach allowing the aggregator, i.e., the operator which manages the aggregated consumers, to gather flexibility and generate bids for the energy market, with the aim of maximizing its revenue. It is shown that this problem can be solved through mixed integer linear programming. Numerical simulation results are provided for validating the proposed approach.
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I. I NTRODUCTION The ever increasing diffusion of renewable energy sources in electricity systems has considerably raised the need for responsive and resilient power delivery systems. Linking electricity systems to the most recent methods and technologies in communications and computer control has been recognized as the most appropriate path to meet the requirements deriving from this new scenario. The vision of the ‘smart grids’ as founding pillars of the economy of the 21st century has found a solid ground in the very promising results achieved by several important research projects and initiatives developed in recent years ( [1]–[6]). The design of intelligent, self-healing electricity networks allowing for intensive data flow among system components, system operators, generators, market traders, retailers and consumers is the primary objective of these and other projects which are posing important challenges to the information and communication research community, including the control community ( [7]–[12]). In this context, the ADDRESS European project (Active Distribution networks with full integration of Demand and distributed energy RESourceS) [13], [14] aims at the development of an ‘Active Demand’ (AD) view to the smart grids, allowing for the active participation of both domestic and small commercial consumers in the network management, letting them play an active role in the energy market through the newly introduced operator called ‘Aggregator’ [15]. The rationale of the approach is based on different facts which
the presence of intermittent generators, typically renewable energy sources, poses serious problems to the network operation (power unbalances management, voltage regulation, etc.); well assessed investigations on domestic consumptions state that at least 10% of the domestic load is ‘flexible’, in the sense that it can be time-shifted, specifically in the presence of economic incentives as well as environmental concerns; safe electric system operation requires the continuous presence of a power ‘reserve’ to be used for facing possible problems arising in the network.
The basic idea underlying the AD approach is to exploit household and small commercial consumption flexibility to reduce as much as possible the generation reserves which represent a significant cost for safe operation of the system, as well as to accomodate unbalances caused by distributed renewable energy sources. The ADDRESS approach takes into account different types of equipment and appliances present at the consumers’premises, from distributed generation, such as photovoltaic or co-generation plants, to thermal and electrical storage devices and purely passive loads. The main issues involved in the flexibility evaluation are related to the features of devices and their usage and control. In this sense, air conditioning, space and water heating plants show the highest potential with respect to flexibility. Also, plugin vehicles, although not explicitly tackled in the ongoing ADDRESS project activities, are devices with high potential for flexibility procurement. The main focus of the project is on the Aggregator, which is conceived as an intermediary party between the consumers and the energy market. This player enrolls consumers through signing appropriate contracts with them on the basis of their typical daily load profile and features like geographical position, type of devices installed, number of people in the house etc. The aggregator gathers flexibility from its affiliated consumers, asking them to adjust their daily load profile according to an optimized schedule. This way, he is able to prepare bids for the market in the form of (ancillary) services, consisting in power reduction (or The authors are with the Dipartimento di Ingegneria dell’Informazione & Centro per lo Studio dei Sistemi Complessi, Universit`a di Siena, 53100 increase) over specific time intervals. The actuator signals Siena, Italy. the aggregator uses to interface with its consumers are Email: {agnetis,dellino,pranzo,vicino}@ing.unisi.it; price-volume signals, through which he offers a reward to
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consumers for their willingness to modify their load profile. According to the setup outlined above, the purpose of this paper is to propose an optimization framework for solving the basic decision problem the aggregator has to solve in his activity on the energy market. On the basis of forecasts of the energy price, he has to make decisions on which kind of bids to submit to the market, by evaluating the expected consumer responses in terms of daily load profile changes to price-volume signals. We will focus on the dayahead market and formulate an optimization problem whose solution allows the aggregator to design an optimal daily business strategy for maximizing his revenue. It is shown that the problem can be cast as a mixed integer linear program, whose solution provides an optimal schedule of bids to the day-ahead market, as well as the related price-volume signals to be sent to the affiliated consumers to gather the required energy. In addition, simulation results are illustrated, highlighting advantages and limitations of the approach in terms of computational burden. The paper is structured as follows. Section 2 introduces the problem formulation and the related key concepts. Section 3 provides the formulation of the aggregator short term business plan as a mixed integer linear programming problem, while simulation results are reported in Section 4. Concluding remarks are given in Section 5.
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The consumer flexibility is currently not exploited, and the aim of the ADDRESS project is to introduce a new market player, the Aggregator, able to gather the consumers’ flexibility and use it on the market. To this end, each consumer is provided with an “Energy Box” which interfaces the consumer directly with the Aggregator. The Energy Box is a device able to control and coordinate household appliances and loads. Each Energy Box receives signals from the Aggregator to modify the load profile of the consumers by leveraging on shiftable and flexible loads: as a payoff the consumer receives a reward. The flexibility request signals describe a request of load reduction (increase) for a given time period and specify the monetary reward if the consumer fulfills the request. Therefore, as shown in Fig. 1, the Aggregator task is twofold: •
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II. P ROBLEM FORMULATION Let us start by briefly recalling the typical mechanism behind energy markets. Here, there are mainly two kinds of players. On one side, energy “producers” who aims at selling the energy they produce either through contracts with other players or by selling it directly on the wholesale market. On the other side, “retailers” who aims at buying energy from the producers and selling it to their customers. Both producers and retailers submit bids to the market specifying the price, the time and the amount of energy they want to sell or buy. The energy price is fixed by matching demands with offers and typically changes during the day. Finally, the TSO (Transmission System Operators) and DSO (Distribution System Operator), a third category of players, verify whether the energy flows are compatible with the transmission and distribution networks structure and possibly curtail some offers to prevent congestion risks and guarantee safe operation of the network. The above activities are repeated in two stages, characterized by different time horizons and known as the day-ahead and the intra-day markets. In such a framework, the consumers are not aware of the presence of the energy market since their counterpart is simply the retailer they are related through a contract. However, it is well known that the energy consumptions of domestic and small commercial consumers is characterized, at least to some extent, by a certain degree of flexibility, essentially due to: •
“adjustable loads”, whose power profile can be modified within a proper threshold; unnecessary consumptions, usually associated to wastage or comfort excess.
On the consumer side: he gathers flexibility by suitably proposing incentives to consumers in order to shape their load profile; On the energy market side: he sells flexibility into the energy market and he may provide a balancing service to DSO.
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Relations with market and consumers
To carry out this task the Aggregator groups its affiliated consumers into clusters. A cluster includes all the consumers sharing similar characteristics in terms of kind and usage of the appliances, number of people at the premises, their habits and geographical region to which they belong. We assume that the behavior of the cluster, in the absence of flexibility requests, can be represented as a baseline load profile curve, representing the cluster load profile during the day. Besides, the Aggregator is assumed to know how each cluster reacts in response to each admissible price-volume signal sent to it. In other words, the different clusters response functions to the price-volume signals are known and utilized in order to optimize the bids presented to the market. In Fig. 3 we show the baseline load profile of a cluster and the response
“shiftable loads”, whose starting time can be freely set on a specific interval up to a certain extent;
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function to a fixed power reduction signal. Observe that, due to the presence of shiftable loads, the modified load profile shows a payback effect just after the end of the power reduction time interval. This means that consumers reducing consumption in one period, tend to recover their scheduled program in the successive time slots. This behavior introduces dynamics in the process which must be accounted for in the aggregator scheduling optimization. The Aggregator job is to optimize the available flexibility that can be gathered by its consumer portfolio and to present bids on the market when the energy price is most favorable. Moreover, he has to take into account the possibility of bids curtailment from DSO, in case his matched market bids will be deemed unfeasible in the service validation process.
grows exponentially with the number of admissible flexibility requests present in the database. With reference to the optimization cost function, we assume that the aggregator main objective is to maximize its revenue. Hence, the objective function is composed of two terms: the income from selling the energy on the market, and the cost to be paid to the consumers for their participation in the service. The main constraints of the model account for the following facts: • Each cluster can receive at most one flexibility request per day by the aggregator. • The payback at the level of the load area where the aggregator operates must not exceed a given minimum/maximum threshold profile. • Each single offer to the market must have a minimum and a maximum volume. • The request to each consumer cluster cannot exceed a maximum threshold related to the reliability of the cluster. Notice that the aggregator can promptly react to a curtailment request coming from the DSO. In fact, if the total load (of the load area) resulting from market clearing turns out too large to pass DSO validation in certain critical time slots, the optimization model can be re-run after the constraint on the maximum load of the load area (in the critical time slots) has been suitably tightened. Possibly, when the model is run again, flexibility requests in the previous optimal solution that are not related to those involved in the curtailment can be fixed, if we wish the new flexibility plan to be only partially different from the previous round.
III. T HE OPTIMIZATION MODEL In this section, we show how the problem of preparing bids for the energy market in the different time slots of the relevant time horizon, can be formulated as a mixed integer linear programming problem. Computational complexity issues of the optimization model are discussed. First, we provide a brief description of the model we developed, without entering into mathematical details. Mathematical formulation of the model is introduced in subsection III-A in which the mathematical optimization model used in the day-ahead market is presented. The optimization model involves the following groups of decisions (variables): • A first group of boolean variables represents whether the aggregator is able to propose offers to the market for the various time slots. • A second group of variables specifies the amount of energy gathered in the various time slots. • The last group of boolean variables characterizes the participation of which cluster to which offer of the aggregator. Notice that there exist two different time scales in the problem. A first time scale is used to represent time as seen from the market point of view. A different time scale may represent the time slots as seen from the clusters point of view. The input data required by the optimization model are mainly given by load profiles of the consumer clusters; i.e., “baseline” load profiles (in absence of aggregator flexibility requests) and load profiles corresponding to each possible flexibility request of the aggregator. Of course, the cluster flexibility is represented by the difference of these profiles. In our model we assume that, for each possible flexibility request, the aggregator is able to retrieve the information about the overall price to be paid when the cluster accepts its proposal. The availability of such data allows the optimization algorithm to handle multi-level price/volume signals consisting of multiple volume thresholds and corresponding price levels. Moreover, the aggregator optimization process can cope with complex flexibility requests in which, for each time slot, a different (multi-level) signal is sent to the cluster. Clearly, the computational burden of the algorithm
A. Aggregator Toolbox Optimization Model for the dayahead market The indices used in the mathematical formulation of the model are: • k: denotes the k-th cluster of consumers; k = 1, . . . , K, where K is the number of clusters in the load area. • h: denotes the h-th flexibility request that the aggregator may send to cluster k; more specifically, it consists of a (possibly multi-level) price/volume signal and the duration of the request. We assume that the aggregator may formulate a finite number of proposals (corresponding to different combinations of price-volume signals, in different time slots), which we denote by H. Therefore, h = 0, 1, . . . , H, where we set h = 0 for the case in which no request is sent by the aggregator to the consumers. • t: denotes the t-th market time slot; t = 1, . . . , TM , TM being the number of market time slots within the selected time horizon. • τ denotes the τ -th consumer time slot; τ = 1, . . . , TC , TC being the number of consumer time slots within the selected time horizon. To run the optimization model, the aggregator needs the following input data, that he will get from the database:
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πt : denotes the energy price forecast at market time slot t. Pkh : gives the overall cost that the aggregator has to pay to its consumers if the h-th flexibility request is sent to cluster k. τ1h : denotes the starting time (expressed in consumer time slots) of the flexibility request h. τ2h : denotes the ending time (expressed in consumer time slots) of the flexibility request h. fk0 (τ ): gives the baseline load profile of cluster k. The discrete values of the load profile are given for daily consumer timeslots τ = 1, . . . , TC . The baseline load profile is expressed in kWh. fkh (τ ): gives the load profile of cluster k when the flexibility request h is activated. The discrete values of the modified load profile are given for daily consumer time slots τ = 1, . . . , TC . Lmin (τ ): is the minimum load compatible with the load area for each consumer time slot τ . It is expressed in kWh. Lmax (τ ): is the maximum load compatible with the load area for each consumer time slot τ . It is expressed in kWh. ω is the minimum threshold value for the size of the bid to be made on the energy market. Ω is the maximum threshold value for the size of the bid to be made on the energy market. ρk : denotes the maximum “risk” for cluster k. It imposes an upper limit on the request that each cluster can receive from the aggregator. It is measured in kWh. σk : is an indicator of cluster k reliability. It ranges from 0 to 1, 1 being the maximum reliability.
We now introduce the mathematical model in terms of objective function, functional and technical constraints, which results in a Mixed Integer Linear Programming (MILP) formulation. max
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E t πt −
t=1
K X H X
Pkh xkh
(1)
k=1 h=0
subject to H X
xkh = 1, ∀k
(2)
h=0
Lmin (τ ) ≤
K X H X
xkh fkh (τ ) ≤ Lmax (τ ), ∀τ
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k=1 h=0
ωYt ≤ Et ≤ ΩYt , ∀t H X
(1 − σk )
h=0 K X k=1
X
xkh
(4)
(fk0 (τ ) − fkh (τ )) ≤ ρk , ∀k (5)
τ ∈[τ1h ,τ2h ]
(fk0 (τ ) −
H X
xkh fkh (τ )) ≥ Rt , ∀τ ∈ t, ∀t
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h=0
(1 − Yt )(−M ) ≤ Rt , ∀t
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Et ≤ Rt + (1 − Yt )(−M ), ∀t
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The objective function of the model – Equation (1) – aims at maximizing the aggregator’s profits and it is composed of two terms. The first term takes into account the gains from selling the flexibility to the markets, while the second term accounts for the costs that the aggregator has to pay to its consumers. The functional constraints of the model are as follows. Equation (2) enforces that each cluster k receives exactly one flexibility request for each day. Recall that if a cluster does not receive a flexibility request then xk0 = 1. Constraint (3) guarantees that in each consumer time slot the load profile of the whole load area remains bounded within two threshold values. Equation (4) is used to avoid that the aggregator produces offers that are below a minimum and beyond a maximum value. Observe that, due to the presence of variable Yt , if no offer is presented in the market time slot (i.e., Yt = 0), then the aggregator cannot sell energy to the market (i.e., Et = 0). The constraints expressed in Equation (5) are used to limit risks (i.e., excessive requests to unreliable clusters) for the aggregator business. This is obtained by imposing an upper bound on the energy requested to each cluster and also by taking into account the reliability of each cluster. More specifically, the higher the cluster reliability, the bigger the bound on the overall flexibility the aggregator can collect from cluster k. Notice that this constraint could also be “disabled” (by setting σk = 0 and ρk = ∞), so that it would not be active in the optimization model.
The variables involved in the model are: •
TM X
Yt ∈ {0, 1}, t = 1, . . . , TM . This family of boolean variables is used to represent the offer on the energy market. If Yt is 1 then the aggregator is able to present an offer in the market time slot t. Otherwise it assumes value of 0. Et , t = 1, . . . , TM . This continuous variable represents the amount of energy that the aggregator is able to offer to the market at time slot t. xkh ∈ {0, 1}, k = 1, . . . , K, h = 0, . . . , H. This family of boolean variables is used to represent the signals sent from the aggregator to its consumers. If xkh = 1, then the cluster k receives a flexibility request h from the aggregator. Otherwise, the variable is equal to 0. Recall that h = 0 denotes the baseline scenario, in which no flexibility is requested to the cluster. Rt , t = 1, . . . , TM . This variable represents the difference between the baseline load profile and the actual load profile of the entire load area in the t-th market time slot. It may assume either positive values (if the clusters reduce their consumption) or negative values when the clusters increase their consumption (note that this may happen during the paybacks).
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TABLE I
The flexibility requests to be examined by the aggregator optimization module are derived as follows. We consider
C LUSTER DETAILS Cluster ID 1 2 3 4
Size 900 800 1250 1020
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Reliability 1 1 0.6 0.8
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Besides the functional constraints discussed before, we need to add some technical constraints to guarantee consistent solutions. This family of constraints described in Equation (6) defines the variables Rt as the minimum difference between baseline and actual load profiles in the whole load area. In the last two constraint, we define M as an arbitrarily large constant. The Equation (7) is a family of constraints introduced to link the two families of decision variables, Yt and Rt . In fact, Rt must be positive whenever the aggregator is able to present an offer to the market (i.e., Yt = 1). The last family of constraints (Equation (8)) guarantees that – whenever the aggregator is able to present an offer to the market (i.e., Yt = 1) – the energy offered to the market is at most equal to the overall flexibility gathered by the aggregator.
two price levels; namely, 0.01e and 0.02e; a single volume reduction level of 1 kW; two options for the duration of a flexibility request; namely, 2 hours (i.e., 8 time slots) and 3 hours (i.e., 12 time slots).
To control the overall computational effort, we do not account for all the possible level combinations of the three factors, limiting the number of flexibility requests for each cluster to 90 signals. The minimum and maximum size of the bid have been fixed to ω = 100 kWh and Ω = 1 MWh, respectively. For each possible flexibility request, the response function of the cluster is known; an example is given in Fig. 3.
IV. N UMERICAL SIMULATION RESULTS In this section, numerical results provided by the optimization algorithm in a simulated scenario are presented together with a discussion on advantages and limitations of the approach. We perform our experiments assuming that consumers belong to four clusters, whose characteristics (namely, size and reliability) are specified in Table I. Although the optimization model is flexible, in our tests we assume 24 one hour time slots for the market time scale and 15 minutes time slots for the consumer time scale. The energy price forecasts over the 24-hour time horizon have been derived based on historical data, and are depicted in Fig. 2.
Fig. 2.
Energy price forecasts for the day-ahead market
Fig. 3. Baseline load profile and response function of a cluster to a flexibility request
Based on this input data, we solve the optimization problem formulated in Section III-A using CPLEX [16]. The optimal solution consists of the following bid made on the energy market: from 9 to 10, the aggregator offers 187 kWh; from 10 to 11, he offers 1 MWh; from 11 to 12, he offers 975.8 kWh and from 12 to 13 he offers 1 MWh. The resulting bid is depicted in Fig. 4, represented by the red bars. The blue profile shown in this figure represents the total amount of power collected by the aggregator. Notice that in two time intervals (from 10 to 11 and from 12 to 13) the aggregator would be able to offer more than it does, due to a slightly higher amount of power collected over the whole market time slot; however, having fixed a threshold Ω = 1 MWh, the aggregator is not allowed to exceed this value. The energy collected by the aggregator is due to the following flexibility requests sent to the clusters: clusters 1 and 2 receive a reduction request of 1 kW lasting 3 hours, from 9 to 12, with a corresponding reward of 0.02e; clusters 3 and 4 receive a reduction request of 1 kW from 11 to 14, with a corresponding reward of 0.02e. We point out that the aggregator formulates his bids over the time slots corresponding to higher forecasted energy prices, as it is evident from Fig. 2. The overall aggregator’s profit for the optimal solution found by the algorithm is equal
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techniques. V. C ONCLUSIONS
Fig. 4.
In this paper an optimization approach has been proposed allowing the aggregator to gather consumer flexibility in an electricity distribution network, for generating services and bids to be submitted to the energy market. With reference to the day-ahead market, it is shown how the aggregator problem can be formulated and solved through mixed integer linear programming. Simulation results are provided, showing the effectiveness and the flexibility features of the proposed approach. Besides the environmental impact, the optimal solution found suggests considerable daily savings for consumers participating in the active demand. Extensions of the presented approach to deal with the intraday market as well as the management of derivatives in the wholesale energy market are the subject of ongoing work.
Aggregator offers to the energy market
R EFERENCES [1] [2] [3] [4] [5] [6] [7]
Fig. 5. Baseline profile (dotted) of the load area and response profile (solid) to the aggregator’s offer
[8] [9]
to 442.79e: 54.37e will be paid by the aggregator to the consumers participating in the active demand, and the remaining amount is the net gain derived from selling the collected flexibility to the market, according to the formulated bids. Notice that the seemingly low reward received by a single consumer corresponds to a significant daily saving on the energy bill. Fig. 5 shows the response of the whole load area to the offer formulated by the aggregator; the dotted line represents the baseline profile of the load area, obtained by summing up the base profiles of the clusters belonging to that load area. This figure highlights the power reduction over the time intervals of the aggregator’s flexibility request, and the corresponding payback in the following hours, due to a shift in consumers’ loads. The dashed upper and lower lines denote the maximum and minimum loads compatible with the load area, over the 24-hour time horizon. This test has been performed using a 3 GHz Intel Core 2 Duo processor with 3.25 GB of RAM; the computation time required to find an optimal solution was about 3 minutes. Additional experiments with 4000 flexibility requests for each cluster have been executed, taking a computational time of approximately 45 minutes. In consideration of the fact that the problem is solved off-line (e.g. the day ahead), these computational times are practically feasible, i.e., the optimization model can be solved exactly with no need to resort to specific solution approaches such as dual decomposition or heuristic
[10] [11] [12]
[13]
[14]
[15]
[16]
http://www.fenix project.org/. http://www.eu deep.com/. http://intelligrid.epri.com/. http://gad.ite.es/index en.html. http://www.gridwiseac.org/. European Commission. European technology platform smartgrids: Vision and strategy for europe´s electricity networks of the future. 2006. A. Chakrabortty and J. H. Chow. Invited Session: Emerging applications of control theory in electric smart grids. In Proc. of 49th IEEE Conf. on Decision and Control, pages 182–218, Atlanta, December 2010. A. Papavasiliou, H. Hindi, and D. Greene. Market-based control mechanisms for electric power demand response. Proc. of 49th IEEE Conf. on Decision and Control, pages 1891–1898, December 2010. S. Meyn, M. Negrete-Pincetic, G. Wang, A. Kowli, and E. Shafieepoorfard. The value of volatile resources in electricity markets. Proc. of 49th IEEE Conf. on Decision and Control, pages 1029–1036, December 2010. A. Kiani and A. Annaswamy. The effect of a smart meter on congestion and stability in a power market. Proc. of 49th IEEE Conf. on Decision and Control, pages 194–199, December 2010. A. Roozbehani, M. Dahleh, and S. Mitter. On the stability of wholesale electricity markets under real-time pricing. Proc. of 49th IEEE Conf. on Decision and Control, pages 1911–1918, December 2010. A. Baitch, A. Chuang, G. Mauri, and C. Schwaegerl. International perspectives on demand-side integration. Proc. of 2007 CIRED - 19th International Conference on Electricity Distribution, Paper No. 0914, May 2007. R. Belhomme, R. Cerero Real de Asua, G. Valtorta, A. Paice, F. Bouffard, R. Rooth, and A. Losi. ADDRESS - Active demand for the smart grids of the future. Proc. of 2008 CIRED Seminar: Smart Grids for Distribution, Paper No. 0080, June 2008. E. Peeters, R. Belhomme, C. Battle, A. Paice, F. Bouffard, S. Karkkainen, D. Six, and M. Hommelberg. ADDRESS: scenarios and architecture for active demand development in the smart grids of the future. Proc. of 2009 CIRED - 20th International Conference on Electricity Distribution, Paper No. 0406, June 2009. M. Sebastian, J. Marti, and P. Lang. Evolution of dso control centre tool in order to maximize the value of aggregated distributed generation in smart grid. Proc. of 2008 CIRED Seminar: Smart Grids for Distribution, Paper No. 0034, June 2008. IBM ILOG. Cplex optimization studio v. 12.2 documentation. 2010.
VI. ACKNOWLEDGEMENTS The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 207643.
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