District Microgrid Management Integrated with Renewable Energy Sources, Energy Storage Systems and Electric Vehicles*

District Microgrid Management Integrated with Renewable Energy Sources, Energy Storage Systems and Electric Vehicles*

Proceedings of the 20th World Congress Proceedings of 20th The International Federation of Congress Automatic Control Proceedings of the the 20th Worl...

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Proceedings of the 20th World Congress Proceedings of 20th The International Federation of Congress Automatic Control Proceedings of the the 20th World World Congress Proceedings of the 20th9-14, World The Federation of Automatic Control Toulouse, France, July 2017 The International International Federation of Congress Automatic Control Available online at www.sciencedirect.com The International of Automatic Control Toulouse, France, July Toulouse, France,Federation July 9-14, 9-14, 2017 2017 Toulouse, France, July 9-14, 2017

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IFAC PapersOnLine 50-1 (2017) 10015–10020

District Microgrid Management Integrated District Microgrid Management Integrated District MicrogridEnergy Management Integrated with Renewable Sources, Energy with Renewable Energy Sources, Energy  with Renewable Sources, Energy Storage Systems Energy and Electric Vehicles  Storage Electric Vehicles  Storage∗ Systems Systems and and Electric Vehicles ∗ ∗ ∗∗

M. P. Fanti ∗ A. M. Mangini ∗ M. Roccotelli ∗ W. Ukovich ∗∗ M. M. P. P. Fanti Fanti ∗∗ A. A. M. M. Mangini Mangini ∗∗ M. M. Roccotelli Roccotelli ∗∗ W. W. Ukovich Ukovich ∗∗ M. P. Fanti A. M. Mangini M. Roccotelli W. Ukovich ∗∗ ∗ Maria Pia Fanti, Agostino M. Mangini, Michele Roccotelli are with ∗ ∗ Maria Pia Fanti, Agostino M. Mangini, Michele Roccotelli are with Pia Fanti,ofAgostino M.and Mangini, Michele Roccotelli are with the Department Electrical Information Engineering of the ∗ Maria Maria Pia Fanti, Agostino M. Mangini, Michele Roccotelli are with the of Electrical and Information Engineering the Department Department of Electrical and Information Engineering of of the the Polytechnic of Bari, Bari, Italy (e-mail: mariapia.fanti, the Department of Electrical and Information Engineering of the Polytechnic of (e-mail: Polytechnic of Bari, Bari, Bari, Bari, Italy Italy (e-mail: mariapia.fanti, mariapia.fanti, agostinomarcello.mangini, [email protected]) of Bari, Bari, Italy (e-mail: mariapia.fanti, ∗∗ Polytechnic agostinomarcello.mangini, [email protected]) agostinomarcello.mangini, [email protected]) Walter Ukovich is with the Department of Engineering and ∗∗ agostinomarcello.mangini, [email protected]) ∗∗ Walter Ukovich is Department of and is with with the the of Department of Engineering Engineering and Architecture of the University Trieste, Trieste, Italy (e-mail: ∗∗ Walter Ukovich Walter Ukovich is with the of Department of Engineering and Architecture of the University Trieste, Trieste, Italy (e-mail: Architecture of the University of Trieste, Trieste, Italy (e-mail: [email protected]) Architecture of the University of Trieste, Trieste, Italy (e-mail: [email protected]) [email protected]) [email protected]) Abstract: This paper addresses the problem of the energy management of cooperative district Abstract: paper the problem of energy cooperative district Abstract: This paper addresses thethe problem of the the energy management ofand cooperative district microgrids: This the goal is addresses minimizing additional energy tomanagement be purchasedof maximizing the Abstract: This paper addresses thethe problem of the energy management ofand cooperative district microgrids: the goal is energy to be purchased maximizing the microgrids: the goal bought is minimizing minimizing the additional additional energy to To be this purchased and maximizing the utilization of energy at the day-ahead energy market. purpose the District Energy microgrids: the goal bought is minimizing the additional energy to be this purchased and maximizing the utilization of at day-ahead energy market. the Energy utilization of energy energy at the the day-ahead energy consumption market. To To this purpose the District District Energy Management Systembought (DEMS) predicts the energy of purpose the district and minimizes utilization of energy bought at the day-ahead energy consumption market. To this purpose the District Energy Management System (DEMS) predicts the energy of the district and minimizes Management Systemenergy (DEMS) predicts the energyintegrating consumption of the energy districtsources, and minimizes additional real-time requests by optimally renewable storage Management Systemenergy (DEMS) predicts the energyintegrating consumption of the energy districtsources, and minimizes additional real-time requests by renewable storage additional real-time energy requests byTooptimally optimally integrating renewable energy sources, storage systems and district electric vehicles. solve this problem two approaches are considered. In additional real-time energy requests by optimally integrating renewable energy sources, storage systems district solve problem considered. In systems and districtweelectric electric vehicles. Toenergy solve this this problem two two approaches are considered. In the first and approach, assumevehicles. that theTo consumption, the approaches cumulative are production of the systems and district electric vehicles. To solve this problem two approaches are considered. In the first we that the consumption, the production of the first approach, approach, we assume assume thatcosts the energy energy consumption, theacumulative cumulative production of the the renewable energies and the energy are known. In this case, linear programming problem the first approach, we assume that the energy consumption, the cumulative production of the renewable energies and costs this case, aa linear programming problem renewable energies and the thebyenergy energy costs are are known. Indeal thiswith case,the linear programming problem is formulated and solved the DEMS. In known. order toIn parameters uncertainty, we renewable energies and theby energy costs are known. Indeal thiswith case,the a linear programming problem is formulated and solved the DEMS. In order to parameters uncertainty, we is formulated and solved by the DEMS. In order to deal with the parameters uncertainty, we propose a second approach formulated as a stochastic linear programming problem. is formulated andapproach solved by the DEMS.asIn order to deal with the parameters uncertainty, we propose propose aa second second approach formulated formulated as aa stochastic stochastic linear linear programming programming problem. problem. propose a second approachFederation formulated as a stochastic programming problem. © 2017, IFAC (International of Automatic Control)linear Hosting by Elsevier Ltd. All rights reserved. Keywords: Energy management, Energy storage, Renewable energy, Optimization, Stochastic Keywords: Keywords: Energy Energy management, management, Energy Energy storage, storage, Renewable Renewable energy, energy, Optimization, Optimization, Stochastic Stochastic programming. Keywords: Energy management, Energy storage, Renewable energy, Optimization, Stochastic programming. programming. programming. 1. INTRODUCTION On the other hand, Fathi and Bevrani (2013) and Nguyen 1. On the Fathi (2013) and 1. INTRODUCTION INTRODUCTION On the other hand, Fathi and and Bevrani (2013)management and Nguyen Nguyen and Le other (2013)hand, investigate the Bevrani online energy 1. INTRODUCTION On hand, Fathi and Bevrani (2013)management and Nguyen andthe Le other (2013) investigate the online energy energy and Le (2013) investigate the online management Renewable Energy Sources (RESs) and Energy Storage problem by considering that renewable energy generations and Le (2013) investigate the online energy management Renewable Energy Sources (RESs) Energy Storage considering renewable generations Renewable Energy Sources (RESs) and Energyproduced Storage problem problem byare considering that renewableInenergy energy generations Systems (ESSs) are the key to reduceand pollutants loadsby stochasticthat estimations. both approaches, Renewable Energy Sources (RESs) and Energyproduced Storage and problem byare considering that renewableInenergy generations Systems (ESSs) are the key to reduce pollutants and loads stochastic estimations. both approaches, Systems (ESSs) fossil are the key to reduce pollutants produced and loads are stochastic estimations. Inused. both In approaches, by conventional fuel power plants and to limit energy stochastic optimization problems are a recent Systems (ESSs) are the key to reduce pollutants produced and loads are stochastic estimations. In both approaches, by conventional fossil fuel plants and to energy stochastic optimization problems are used. In a by conventional fossil fuel power power plants andThe to limit limit energy stochastic optimization problems are used. In studying a recent recent purchasing costs (Rahbar et al. (2015)). concept of work, Rahbar et al. (2015) address a MM problem by conventional fossil fuel power plants andThe to limit energy stochastic optimization problems are used. In studying a recent purchasing costs (Rahbar et (2015)). of Rahbar al. address MM purchasing costscan (Rahbar et al. al. (2015)). The concept concept of work, work, Rahbar et et al. (2015) (2015) address aa for MMaproblem problem studying microgrids that integrate and share both RESs and the real-time energy management single microgrid purchasing costscan (Rahbar et al. (2015)). The concept of work, Rahbar et al. (2015) address a for MMaproblem studying microgrids that and share RESs and energy management microgrids that appealing can integrate integrate and emerging share both bothsmart RESsgrids and the the real-time real-time energy management a single single microgrid microgrid ESSs becomes for the system that is constituted by a for renewable microgrids that can integrate and share both RESs and the real-time energy management for a single generation microgrid ESSs becomes appealing for the emerging smart grids system that is constituted by a renewable generation ESSs becomes et appealing for The the emerging Management smart grids system that is constituted by a renewable generation (Hatziargyriou al. (2007)). an ESS, and an aggregated load. The authors ESSs becomes et appealing for The the Microgrid emerging Management smart grids system, system that is constituted by a renewable generation (Hatziargyriou (2007)). system, an and an load. The (Hatziargyriou et al. al. (2007)). The Microgrid Microgrid Management system, an ESS, ESS, the andtotal an aggregated aggregated load. The authors authors (MM) can be seen as an optimization problem, which illusaim to minimize energy cost. Moreover, Zhang (Hatziargyriou et al. (2007)). The Microgrid Management system, an ESS, the and an aggregated load. The authors (MM) can be as problem, which illusto minimize energy cost. Moreover, Zhang (MM) can be seen seennetworks as an an optimization optimization problem, whichenergy illus- aim aim to minimize the atotal total energy cost. Moreover, Zhang trates electricity interconnecting various et al. (2013) consider MM problem constituted by several (MM) can be seen as an optimization problem, which illusaim to minimize the total energy cost. Moreover, Zhang trates electricity networks interconnecting various energy consider MM constituted by trates electricity networks interconnecting various energy et et al. al. (2013) (2013) equipped consider aa with MM problem problem constituted by several several generation elements (supply side) with energy consumpmicrogrids RESs and ESSs. Their aim trates electricity networks interconnecting various energy et al. (2013) consider a MM problem constituted by several generation elements (supply side) with consumpmicrogrids equipped with RESs ESSs. Their generation elements (supply side) with energy energy consumpmicrogrids equipped withmicrogrid RESs and and ESSs. Their aim aim tion elements (demand side) and storage devices (Stluka is to minimize the total costs. However, the generation elements (supply side) with energy consumpmicrogrids equipped withmicrogrid RESs and ESSs. Their aim tion elements (demand side) andofstorage storage devices (Stluka is to the total costs. However, the tion elements (demand side) and devices (Stluka is to minimize minimize the totaland microgrid costs.problem However, the et al. (2011)). The integration RESs and ESSs in a optimal energy offering purchasing in tional.elements (demand side) andofstorage devices (Stluka is to minimize the totaland microgrid costs. However, the et The RESs and ESSs aa optimal offering purchasing in et al. (2011)). (2011)). The integration integration of by RESs and authors ESSs in infor optimal energy energy offering and (Parvania purchasingetproblem problem in the the microgrid is studied and analyzed several Day-Ahead Market (DAM) al. (2014)) is et al. (2011)). The integration of by RESs and authors ESSs infor a optimal energy offering and (Parvania purchasingetproblem in the microgrid is studied and analyzed several Day-Ahead Market (DAM) al. (2014)) microgrid is studied and analyzed by several authors for not Day-Ahead Market (DAM) (Parvania etThe al. Day-Ahead (2014)) is is different purposes. considered in the above cited papers. microgrid is studied and analyzed by several authors for Day-Ahead Market (DAM) (Parvania etThe al. Day-Ahead (2014)) is different not in above papers. different purposes. purposes. not considered considered inisthe the above cited citedmarket papers. in The Day-Ahead Energy Market a short-term which energy different purposes. considered inisthe above citedmarket papers. in The Day-Ahead Some papers deal with the off-line MM energy problem not Energy Market short-term energy Energy Market is aa for short-term market in which which energy prices computed the following 24 hours (Kwon and Some papers deal with the MM energy problem Energyare Market is a for short-term market in which energy Some papersthe dealtotal withenergy the off-line off-line MM energy problem to minimize drawn from the power grid prices are computed the following 24 hours (Kwon and prices are computed for the following 24 hours (Kwon and Some papers deal with the off-line MM energy problem Frances (2012), Fanti et al. (2015a), Fanti et al. (2015b)). to minimize the total energy drawn from the power grid prices are computed for the following 24 hours (Kwon and to minimize the total energy drawn from the power grid by knowing a priori the renewable energy generations and Frances (2012), Fanti et al. (2015a), Fanti et al. (2015b)). Frances (2012), Fanti et al. (2015a), Fanti et al. (2015b)). to minimize the total energy drawn from the power grid In this context, some authors face the problem of balancing by knowing aa et priori the renewable renewable energy generations and Frances (2012), Fanti et al. (2015a), Fanti et al. (2015b)). by knowing priori the energy generations and loads (Atzeni al. (2013), Matamoros et al. (2012))In parIn this this context, context, some authors face face the the problem problem of balancing balancing authors of by knowing a priori the renewable energyal. generations parand In energysome interconnecting elements with loads (Atzeni al. (2013), In this context, some authors facegeneration the problem of balancing loads (Atzeni etet al.al. (2013), Matamoros et al. (2012))In (2012))In par- real-time ticular, Atzeniet (2013)Matamoros propose a et general grid model real-time energy interconnecting generation elements with real-time energy interconnecting generation elements with loads (Atzeni et al. (2013), Matamoros et al. (2012))In parloads. Chang et al. (2013) propose a multi-stage stochastic ticular, Atzeni et al. (2013) propose a general grid model energy interconnecting generation elements with ticular, Atzeni et al.distributed (2013) propose general gridstorage model real-time that accommodates energyaa production, loads. Chang et al. (2013) propose aa multi-stage stochastic loads. Chang et al. (2013) propose multi-stage stochastic ticular, Atzeni et al. (2013) propose general grid model optimization problem, aiming at minimizing the expected that accommodates distributed energy storage loads. Chang problem, et al. (2013) propose a multi-stage stochastic that accommodates distributedManagement energy production, production, storage and a day ahead Demand-Side (DSM) mechoptimization aiming at minimizing the expected optimization problem, aimingcost at minimizing theMoreover, expected that distributedManagement energy production, storage real-time power unbalancing of the retailer. and aaaccommodates day Demand-Side mechproblem, aimingcost at minimizing theMoreover, expected and day ahead Demand-Side Management (DSM) mechanism. In ahead Matamoros et al. (2012) a central(DSM) approach is optimization real-time power unbalancing the real-time power unbalancing cost of of (Fanti the retailer. retailer. Moreover, and a day ahead Demand-Side Management (DSM) mechthe authors in a previous paper et al. (2015a)) anism. In Matamoros et al. (2012) a central approach is power unbalancing cost of the retailer. Moreover, anism. In Matamoros etminimize al. (2012) a total centralcost approach is real-time introduced in order to the resulting the authors authors in aa previous previous paper (Fanti (FantiSystem et al. al. (DEMS) (2015a)) the in paper et (2015a)) anism. In Matamoros etminimize al. (2012) a total centralcost approach is present a District Energy Management introduced in order to the resulting authors in a previous paper (FantiSystem et al. (DEMS) (2015a)) introduced in generation order to minimize the total cost resulting from energyin and transportation, while each the present aa District Energy Management present District Energy Management System (DEMS) introduced order to minimize the total cost resulting that forwards the purchased day ahead power profile to from energy generation and transportation, while a District Energy Management System (DEMS) from energy generation and transportation, while each each present microgrid satisfies its local power demand. that forwards the purchased day ahead power profile to that forwards the purchased day ahead power profile to from energy generation and transportation, while each each district building that in turn minimizes its real-time microgrid that forwardsbuilding the purchased day ahead power profile to microgrid satisfies satisfies its its local local power power demand. demand.  each district that in turn minimizes its real-time This work is supported by the project Smart Cities and Commueach district building that in turn minimizes its real-time microgrid satisfies its local power demand. power consumption and costs by respecting the comfort  This work is supported by the project Smart Cities and Commueach district building that in turn minimizes its real-time  power nities and Social Innovation 2014-2016 - ASMARA. work is supported byPilot the project Smart Cities and Commupower consumption consumption and and costs costs by by respecting respecting the the comfort comfort  This This work is supported byPilot the project Smart Cities and Commupower consumption and costs by respecting the comfort nities nities and and Social Social Innovation Innovation Pilot 2014-2016 2014-2016 -- ASMARA. ASMARA.

nities and Social Innovation Pilot 2014-2016 - ASMARA. Copyright 10430Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © © 2017 2017, IFAC IFAC (International Federation of Automatic Control) Copyright © 2017 10430 Copyright © under 2017 IFAC IFAC 10430Control. Peer review responsibility of International Federation of Automatic Copyright © 2017 IFAC 10430 10.1016/j.ifacol.2017.08.2035

Proceedings of the 20th IFAC World Congress 10016 M.P. Fanti et al. / IFAC PapersOnLine 50-1 (2017) 10015–10020 Toulouse, France, July 9-14, 2017

preferences. In the related literature, few contributions consider the integration of plug-in Electric Vehicles (EVs) into the microgrids. Indeed, EVs can be considered mobile ESSs of the microgrid: Musio et al. (2014) propose a novel approach for determining the charging profile of EVs suitable for their integration into microgrids. This paper addresses the problem of district MM with the goal of maximizing the utilization of energy bought at the DAM by optimal policies to distribute the real time energy among the microgrid resources. More in detail, once the DAM is closed, the DEMS performs the optimal policies to store the exceeding energy in the ESSs and EV batteries in case the energy demand is overestimated, and requiring energy by them when the district needs additional energy. To this aim, two approaches are considered. In the first approach, the district energy consumption, the cumulative production of RESs and the energy cost are assumed known a priori. In this case, a Linear Programming (LP) problem is formulated and solved by the DEMS with the objective of minimizing additional energy requests and maximizing the energy stored in the ESSs and EVs batteries. In the second approach, the district energy consumption, the cumulative production of RESs and the energy cost are assumed affected by uncertainty and a scenario-based Stochastic Linear Programming (SLP) problem is defined and solved by the DEMS. The main novelties of this paper are summarized as follows: • with respect to Musio et al. (2014), the proposed MM strategy integrates not only RES and standard ESSs but also an EV fleet; • considering the contributions of Atzeni et al. (2013), Rahbar et al. (2015), the presented approach minimizes the real-time energy costs of cooperative microgrids by considering sustainability objectives; • unlike Nguyen and Le (2013) and Chang et al. (2013), the formulated LP problem exhibits polynomial complexity. The paper is organized as follows. Section 2 presents the district energy management model. Section 3 specifies the DEMS optimization problems and in Section 4 a case study shows the benefits of the stochastic approach. Finally, Section 5 summarizes the conclusions. 2. DISTRICT ENERGY MANAGEMENT MODEL In this section the district energy management model is presented. In particular, Fig. 1 illustrates the scheme of a simplified energy system consisting of the district grid composed of the N building microgrids, which are connected with the main Power Grid (PG). The DEMS works as load aggregator for the district buildings and purchases the forecast energy profiles at the day-ahead market. We assume that the DEMS satisfies the district energy demand by purchasing energy at the prices that are determined by the market (Fanti et al. (2015a)). Successively, the DEMS works as energy manager to satisfy the real-time district energy demand with two objectives: i) minimizing the energy purchased in real time by the district, managing and integrating RESs, ESSs and EVs if the building requires more energy; ii) maximizing

the utilization of the purchased energy by storing the surplus in the ESSs and the EV batteries.

Fig. 1. The district energy management scheme. 2.1 Problem Statement Let us consider a smart district including a set B = {i | i = 1, . . . N } of buildings and each building represents a microgrid. During the day-ahead, the DEMS purchases the energy necessary to satisfy the district demand from the energy market. Considering a time period divided in a set T = {t | t = 0, . . . , T − 1} of T time units, si (t) for t ∈ T denotes the energy purchased for satisfying the expected energy consumption of each building i ∈ B. Moreover, we denote by ui (t) the energy that building i ∈ B requires from the PG in real time during time t ∈ T . We define the following variables y i (t) that represent the additional energy to be purchased at time t ∈ T for building i ∈ B:  i y (t) = ui (t) − si (t) if ui (t) ≥ si (t) (1) y i (t) = 0 otherwise . Denoting by a(t) the predicted energy cost at time t ∈ T , the DEMS adopts a MM strategy in order to minimize the sum of the energy costs a(t)y i (t) for all i ∈ B and t ∈ T . The main innovative aspect of the proposed MM is that the considered buildings are equipped with ESSs, RESs and EVs plug-in devices. More in details, these components play a significant role in the minimization of the additional purchased energy y i (t): they allow storing energy and using it when building i ∈ B needs additional energy without exceeding the energy profile si (t). Moreover, the EV batteries act as mobile energy storages that can be shared by different buildings. Indeed, the EV can be a means to transfer the energy stored in its battery from a building to another one, according to the vehicleto-grid technology (Musio et al. (2014)). The proposed MM strategy has two advantages: i) the energy cost is minimized for the users since typically the costs of energy purchased in real time are higher than the day-ahead costs; ii) the strategy allows enhancing the reliability of the main PG (Rahbar et al. (2015)). 2.2 Renewable Energy Sources i We denote by rtot (t) the cumulative production of the i RESs and by r (t) the portion of renewable energy used by the DEMS to balance the energy consumption of building i ∈ B at time t ∈ T . Obviously, it holds:

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i 0 ≤ ri (t) ≤ rtot (t)

i∈B

t∈T.

(2)

i (t) = If building i ∈ B is not equipped with RESs, then rtot 0 ∀t ∈ T .

2.3 Energy Storage Systems Let us denote by S i = {k | k = 1, . . . K i } the set of K i ESSs of building i ∈ B. We define eis,k (t), eis,k,max and eis,k,0 the energy stored at time t ∈ T , the maximum possible value and the initial value of the stored energy in the ESS k ∈ S i of i ∈ B, respectively.

It holds: 0 ≤ eis,k (t) ≤ eis,k,max

∀i ∈ B,

eis,k (0) = eis,k,0

∀k ∈ S i ,

∀i ∈ B,

∀t ∈ T

∀k ∈ S i .

(3) (4)

Moreover, we take into account the scheduled maintenance operations of ESSs that are known a priori. Those operations are described by the following parameters zki (t) ∈ {0, 1} where:

if the ESS k ∈ S i is out of service (under zki (t) = 0 maintenance) at time t ∈ T ; zki (t) = 1 if the ESS k ∈ S i is correctly working at time t ∈ T .

If k ∈ S i is correctly working, then two cases may occur at time t: 1) energy cis,k (t) is stored in the ESS with efficiency i coefficient 0 < γc,s,k < 1; 2) energy dis,k (t) is used. The equation describing the energy stored in the ESSs is the following: i cis,k (t) − dis,k (t)] eis,k (t) = eis,k (t − 1) + zki (t)[γc,s,k ∀i ∈ B, ∀k ∈ S i ∀t ∈ T .

(5)

2.4 Electric Vehicles The set of the EVs shared among the buildings of B is denoted by V = {j | j = 1, . . . J}. Such vehicles require energy from the grid but also they can provide energy to the buildings that in real time need more energy than the purchased one. To this aim, the EVs can travel among buildings to transfer energy. The following variables are defined in order to describe the energy stored in the EV j ∈V: ev,j (t) energy stored by j ∈ V at time t ∈ T ; ci− v,j (t) energy requested by j ∈ V to building i ∈ B at time t ∈ T ; ci+ v,j (t) energy provided by building i ∈ B to EV j ∈ V at time t ∈ T and ready to be used; div,j (t) energy provided by EV j ∈ V to building i ∈ B at time t ∈ T . Now, we introduce the following parameters:

ev,j,min (t) minimum energy value that has to be stored in vehicle j ∈ V at time t ∈ T ; ev,j,max maximum energy value that can be stored in vehicle j ∈ V ; ev,j,0 energy stored in vehicle j ∈ V at time t = 0;

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qji (t) ∈ {0, 1} where qji (t) = 1 if j ∈ V is plugged-in to building i ∈ B at time t ∈ T else qji (t) = 0; 0 < γc,v,j < 1 efficiency coefficient describing the energy loss during the charging of j ∈ V ; 0 < γd,v,j < 1 efficiency coefficient describing the energy loss during the discharging of j ∈ V ; bip energy spent by each EV to travel from i ∈ B to p ∈ B with i = p.

In each period t ∈ T the following conditions must be verified: ev,j,min (t) ≤ ev,j (t) ≤ ev,j,max ∀j ∈ V ∀t ∈ T (6) ev,j (0) = ev,j,0 ∀j ∈ V. (7)

Assuming the selected time units sufficiently large, each EV takes 1 time unit to travel from building i ∈ B to building p ∈ B. Each EV trip is scheduled the day ahead. The energy spent during a trip starting at time t − 1 from i to p can be denoted as: i i mi,p j (t) = [qj (t) − qj (t − 1)] bip

∀i, p ∈ B.

(8)

Since qji (t) = 0 and qji (t − 1) = 1, then mi,p j (t) = −bip . Hence, the energy stored in j ∈ V at time t ∈ T is the following: e v,j (t) = ev,j (t − 1)+ i− i [qji (t)(γc,v,j [ci+ v,j (t) + cv,j (t)] − dv,j (t))]+ (9) i∈B   qji (t − 1) mi,p (t) ∀j ∈ V, ∀t ∈ T . + j i∈B p∈B,p=i

In order to explain (9), assume that vehicle j leaves building i at time t − 1 to reach p at time t. Then at time t the energy stored by j is ev,j (t − 1) plus the energy exchanged with building p at time t (i.e., γc,v,j [ci+ v,j (t) + p (t)] − d (t)]) minus the energy spent during the travel cp− v,j v,j   i,p i,p (i.e., i∈B p∈B,p=i qji (t − 1) mj (t) = mj (t) = −bip , since qji (t − 1) = 1 and qji (t − 1) = 0 for i = i).

2.5 Building Energy Balance To satisfy the energy demand, each building can use, besides the PG, the ESSs, RESs and EVs. In order to introduce the building energy balance equations, the following additional quantities are specified:  i ni (t) = k∈S i γd,s,k zki (t) dis,k (t) energy required to the ESSs connected to building i at time t reduced by the i ; efficiency coefficient γd,s,k  i i v (t) = j∈V γd,v,j qj (t) div,j (t) energy required to the EVs plugged-in to the building i at time t reduced by the efficiency coefficient γd,v,j ; li (t) energy consumption of the loads of building i at the time t. Hence, the building energy balance is the following:  1 ci− (t) ui (t) + ri (t) + ni (t) + v i (t) = li (t) + γc,v,j v,j

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j∈V

∀i ∈ B and ∀t ∈ T ,

(10)

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where the second term of (10) is the energy demand of building i, i.e., the sum of the consumption of the building loads and the energy ci− v,j (t) necessary to recharge j ∈ V . 3. DISTRIC ENERGY MANAGEMENT SYSTEM STRATEGY

Then we optimize the two objectives in lexicographic order (Ehrgott (2006)): we first minimize F and then we maximize FS , while keeping F at its minimum. The obtained mathematical formulation is the following LP problem: lexmin [F, −FS ]

In this section, we define the DEMS strategy to minimize the costs of the energy purchased in real time in each time unit t ∈ T . More in detail, the DEMS strategy consists in i) accumulating energy in the ESS and EV batteries, when the profile si (t) is sufficient to satisfy the building demand; ii) using energy of RES, ESS and EV batteries when the energy profile si (t) is not sufficient to satisfy the building demand. The following constraints impose that the energy saved with respect to the day-ahead profile si (t) at time t, i.e., si (t) − ui (t) with ui (t) < si (t), is stored in the ESS and EV batteries:  qji (t)ci+ zki (t)cis,k (t) + v,j (t) ≤ k∈S i i

j∈V

i − u (t) + si (t) + y i (t) + rtot (t) − ri (t) ∀i ∈ B, ∀t ∈ T . (11)

More in detail, at time t, the term −ui (t) + si (t) + y i (t) is the day-ahead purchased energy that the building i ∈ B does not use to satisfy the energy demand. Indeed, −ui (t) + si (t) + y i (t) = −ui (t) + si (t) if ui (t) < si (t) because y i (t) = 0. Otherwise, −ui (t) + si (t) + y i (t) = 0 if ui (t) ≥ si (t) because y i (t) = ui (t) − si (t). Concerning the i RES, we accumulate the energy amount rtot (t) − ri (t) in the ESS and EV batteries. Now, we solve the district MM problem by two approaches. First, a known deterministic prior information is assumed about the loads energy consumption li (t), the production i of the RESs rtot (t) and the energy costs a(t) for t ∈ T . In this case a LP problem is formulated in order to minimize the additional energy district costs. In the second approach, uncertain information about the same parameters i li (t), rtot (t) and a(t) for t ∈ T is considered and a SLP problem is solved by considering several scenarios. In the two approaches, the optimization solutions provide to the DEMS the optimal distribution policy for both the charging operations and the energy utilization of the ESSs i− i i and EVs, defined by the variables cis,k , ci+ v,j , cv,j , ds,k , dv,j and ri .

subject to:  Equations (2) − (11)     (15a)  y i (t) ≥ ui (t) − si (t) ∀i ∈ B  i y (t) ≥ 0 ∀i ∈ B (15b)  i i i i   r (t), u (t), e (t), e (t), c (t), v,j s,k s,k    i− i i cv,j (t), ci+ (t), d (t), d (t) ≥ 0 ∀i, k, j, t s,k v,j v,j

i∈B t∈T

Moreover, we define the secondary objective function expressing the total stored district energy during the day as follows:   FS = eis,k (t) + ev,j (t). (13) i∈B k∈S i t∈T

j∈V t∈T

(15)

where lexmin denotes the lexicographic min of the two functions within brackets. Note that constraints (15a) and (15b) are imposed to satisfy equation (1): this occurs because the objective function (14) minimizes the decision variable y i (t). The LP problem is formulated by T · [3N + N 3 i=1 K i + J + 3N J] non-negative real variables subject N N to T · [3N + 3J + 3 i=1 K i ] + J + i=1 K i constraints.

3.2 Stochastic Approach

i In real cases some key parameters such as li (t), rtot (t) and a(t) are uncertain. Hence, in this section we reformulate the LP problem (15) as a SLP problem that minimizes the expected value E[F ] of the total district energy cost.

A stochastic programming problem can be formulated as a deterministic optimization problem whether several scenarios representing the uncertainty are available (Kall and Mayer, 2011). Let us consider H scenarios w1 , . . . , wH i where the parameters lhi (t), rtot (t) and ah (t) assume h different terns of values for h = 1, ..., H, with probabilities p1 , . . . , pH , respectively. Denoting by Fh the objective function of scenario wh , the expected value E[F ] can be written as the weighted sum: E[F ] =

H 

p h Fh .

(16)

h=1

Then, the stochastic programming problem can be formulated as the following SLP problem:

3.1 Deterministic Approach In this section, we formulate a LP problem that minimizes the costs of the additional energy to be purchased in real time by assuming the prior knowledge of consumptions and costs. We define the following primary objective function expressing the total district energy cost:  a(t)y i (t). (12) F =

(14)

min E[F ] =

H  

ph ah (t)yhi (t).

(17)

h=1 i∈B t∈T

subject to: Constraints (15)

for h ∈ 1, . . . , H

(18)

where yhi (t) denotes the additional energy to be purchased at time t in the considered scenario h for h = 1, ..., H. Since the variables in the set of constraints (18) are different for each scenario, the SLP problem is separable into H distinct LP problems (14) − (15).

The SLP problem solution represents the stochastic optimal control policy to schedule the charging and discharging operations of the ESSs and EV batteries.

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4. CASE STUDY

In this section we present a case study in order to show the benefits obtained by the DEMS strategies application to the district MM. The formulated LP and SLP problems are solved by a standard solver, i.e., GNU Linear Programming Kit (GLPK (2000)). The considered district is composed by 3 buildings of the set B = {1, 2, 3} connected to the main PG. The case study considers a large time horizon of T = 24 time units (with 1 t.u.=1 hour) so that it holds T = {t | t = 0, . . . , T − 1}. Moreover, the three buildings are equipped with a RES, a ESS and share a fleet of 3 EVs, i.e. S 1 = S 2 = S 3 = {1} and V = {j | j = 1, 2, 3}. The availability of each ESS z1i (t) for i = 1, 2, 3 and t ∈ T is provided according to the following scheduled maintenance: 1) the ESS of building 1 is not working at t = 0, 4, 5, 6, 10, 11, 19; 2) the ESS of building 2 is not working at t = 2, 6; 3) the ESS of building 3 is not working at t = 7, 13. Furthermore, the three buildings share a fleet of three EVs that accomplish the movements according to the following scheduled trip program. EV 1 is connected to building 1 from t = 4 to t = 13 and from t = 18 to t = 21; EV 1 is connected to building 3 from t = 0 to t = 3, from t = 14 to t = 17 and from t = 22 to t = 23. EV 2 is connected to building 1 from t = 0 to t = 4 and from t = 10 to t = 13; EV 2 is connected to building 2 from t = 5 to t = 9 and from t = 22 to t = 23; EV 3 is connected to building 3 from t = 14 to t = 21. EV 3 is connected to building 1 from t = 3 to t = 6 and from t = 10 to 15; EV 3 is connected to building 3 from t = 0 to t = 2, from t = 7 to t = 9 and from t = 16 to t = 23. In addition, the following parameters are chosen: • • • • • • •

Fig. 2. Energy consumption, day-ahead energy, renewable energy profiles of three buildings and energy cost in scenario w1 . Table 1. Most probable scenarios in the district. Scenario

w1

w2

w3

w4

w5

w6

w7

others

0.3

0.2

0.2

0.1

0.1

0.01

0.01

0.08

Prob. of occurrence

The optimal distribution policy for the charging and discharging of ESSs and EVs batteries is obtained by solving the LP problem (14)-(15) for scenario w1 by the deterministic approach. The total cost of energy resulting by the solution of the LP problem is F = 1, 72 e.

1 2 3 γc,s,1 = 0.91; γc,s,1 = 0.81; γc,s,1 = 0.80. 1 2 3 γd,s,1 = 0.87; γd,s,1 = 0.83; γd,s,1 = 0.89. e1s,1,max = e2s,1,max = e3s,1,max = 50kW h. γc,v,1 = 0.87; γc,v,2 = 0.84; γc,v,3 = 0.82. γd,v,1 = 0.85; γd,v,2 = 0.88; γd,v,3 = 0.87. ev,1,max = ev,2,max = ev,3,max = 16kW h. b12 = b21 = 0.14kW h; b13 = b31 = 0.30kW h; b23 = b32 = 0.72kW h.

In realistic contexts, in order to deal with the parameters uncertainty, we consider 200 scenarios by analyzing historical data about energy consumption, production and cost of the three buildings. The case study refers to the period March-May over three consecutive years. For large-scale problems, a suitable technique can be used to reduce the number of considered scenarios, that consequently reduces the computational effort. The basic idea is not considering the scenarios characterized by very low probability and aggregating scenarios with close distances based on specific probability metric (Nguyen and Le (2013)). In the considered case study, the set of scenarios is reduced to H = 20. For the sake of the brevity, we show in Table 1 the seven most representative scenarios with high occurrence probability. Fig. 2 reports the renewable energy profiles i rtot (t), the day-ahead purchased energy profiles si1 (t) and 1 the energy consumption profiles l1i (t) for i = 1, 2, 3 and ∀t ∈ T for the three buildings in scenario w1 (the most probable one).

Fig. 3. Energy consumption, renewable profiles (left y axes) and energy cost profile (right y axes) in the 8 instances for building 1. The SLP solution is obtained by solving the H = 20 selected scenarios and the corresponding H LP problems (14)-(15) that provide E[F ] = 4, 91 e. We can observe that the cost increases if the uncertainty is taken into account. Now, we enlighten the effectiveness of the stochastic approach by considering 8 instances extracted by the initial 200 scenarios. Figures 3 depicts for each instance

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Table 2. Total costs obtained by the deterministic and stochastic solutions applied to the considered instances. Deterministic approach

Stochastic approach

B1

B2

B3

Total

B1

B2

B3

Instance

C1

C2

C3

C

C1

C2

C3

Total C

1

0, 51

1, 45

0, 91

2,87

0, 18

1, 39

1, 03

2,6

2

0, 23

0, 73

0, 33

1,29

0, 10

0, 62

0, 41

1,13

3

2, 77

4, 02

2, 91

9,7

2, 39

3, 94

3, 05

9,38

4

0, 61

1, 57

0, 98

3,16

0, 27

1, 51

1, 10

2,88 12,52

5

3, 81

5, 20

3, 85

12,86

3, 40

5.12

4, 00

6

2, 25

3, 43

2, 43

8,11

1, 88

3, 36

2, 56

7,8

7

0, 93

1, 94

1, 26

4,13

0, 59

1, 87

1, 38

3,84

8

3, 22

4, 54

3, 30

11,06

2, 82

4, 46

3, 45

10,73

the energy consumption, the RESs production and the energy costs for building 1. In each instance we apply the distribution policies obtained by the two approaches: i) the optimal distribution policy provided by the deterministic LP problem solution for the most probable scenario w1 ; ii) the optimal distribution policy provided by the scenariobased SLP. In order to compare the two approaches, the following indices are calculated:  i • building total costs C i = t∈T a(t)y (t) for i = 1, 2, 3;  • district total cost C = i∈B C i . The results are reported in Table 2 enlightening that the district total cost obtained by the application of the policy provided by the stochastic approach is in any case lower than the district total cost obtained by the application of the policy obtained by the deterministic approach. 5. CONCLUSIONS In this paper the complex problem of energy management of cooperative microgrids is addressed aiming at integrating Renewable Energy Sources (RESs), Energy Storage Systems (ESSs) and plug-in Electric Vehicles (EVs). To this aim, a Linear Programming (LP) problem minimizing the cost of the additional energy to be purchased in realtime is proposed under the assumption of deterministic prior information about the load energy consumption, the RES production and the energy costs. Moreover, a Stochastic Linear Programming (SLP) problem is formulated in order to consider the uncertainty about the same parameters. A case study is presented to show the effectiveness of the obtained policies applied by the District Energy Management System (DEMS). Future work will consider the possibility of selling the stored and renewable energy to the power grid. REFERENCES Atzeni, I., Ordonez, L.G., Scutari, G., Palomar, D.P., and Fonollosa, J.R. (2013). Noncooperative and cooperative optimization of distributed energy generation and storage in the demand-side of the smart grid. IEEE Transactions on Signal Processing, 61(10), 2454–2472. Chang, T.H., Alizadeh, M., and Scaglione, A. (2013). Real-time power balancing via decentralized coordi-

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