Optimal energy management of small electric energy systems including V2G facilities and renewable energy sources

Optimal energy management of small electric energy systems including V2G facilities and renewable energy sources

Electric Power Systems Research 92 (2012) 50–59 Contents lists available at SciVerse ScienceDirect Electric Power Systems Research journal homepage:...

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Electric Power Systems Research 92 (2012) 50–59

Contents lists available at SciVerse ScienceDirect

Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr

Optimal energy management of small electric energy systems including V2G facilities and renewable energy sources C. Battistelli a,∗ , L. Baringo b , A.J. Conejo b a b

Electrical & Electronic Engineering Department, Imperial College, South Kensington Campus, London SW7 2AZ, United Kingdom Department of Electrical Engineering, University of Castilla – La Mancha, Campus Universitario s/n, 13071 Ciudad Real, Spain

a r t i c l e

i n f o

Article history: Received 2 December 2011 Received in revised form 20 March 2012 Accepted 12 June 2012 Available online 10 July 2012 Keywords: Microgrid Robust optimization Smart energy management Vehicle-to-grid

a b s t r a c t The emerging of plug-in hybrid vehicles results not only in the increase of electric vehicles as means of transportation, but also in the utilization of vehicle batteries for grid support, which is referred to as vehicle-to-grid (V2G). However, V2G is still at a conceptual stage, and the lack of practical and realistic frameworks to help moving from concept to implementation causes serious challenges to its adoption. In this context, this paper proposes a practical model for the assessment of the contribution of V2G systems as a support to energy management within realistic configurations of small electric energy systems (SEESs) including renewable sources, such as Microgrids. Considering the uncertainty factors related to renewable power sources and gridable vehicles, the model materializes into a robust linear optimization problem suited to be easily integrated in the Energy Management System of SEESs, to support – in operation or operation planning – SEESs’ participation in the electricity market. The paper also presents a practical methodology to model the aggregation of gridable vehicles, contributing to the literature in the field and helping towards the actual implementation of V2G. The efficiency and usefulness of the developed aggregation and optimization models are shown using a realistic SEES case study. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved.

1. Introduction 1.1. Motivation, methodology and objectives Against the worldwide economic crisis, the exhaust emissions and the ever-increasing oil prices, plug-in electric vehicles (PEVs), such as electric cars (BEVs) and plug-in hybrid (PHEVs), could be in the near future a valuable, economic and clean means to provide the power grid with demand response services by either delivering electricity into the grid or throttling their charging rate [1,2]. Moreover, from a small electric energy system (SEES) perspective, PEVs could be a support for intentional islanding [3]. The entire concept of using PEVs as a distributed resource – load and generation/storage device – by their integration into the grid is known as vehicle-to-grid (V2G). V2G can be used with such gridable vehicles, that is, BEVs and PHEVs, with grid capacity. Since most vehicles are parked an average of 95% of the time, their batteries could be used to let electricity flow from the car to the power lines and back. This typically could happen in residential or industrial garages and parking areas, where cars would be parked without charging for most of the time (being the charging time much shorter

∗ Corresponding author. Tel.: +44 7845 553 490. E-mail addresses: [email protected] (C. Battistelli), [email protected] (L. Baringo), [email protected] (A.J. Conejo).

than the parking time), thus making available a certain quantity of electrical energy, which corresponds to a percentage of the available power stored in batteries. Since the electricity would flow from batteries to power lines just for a limited part of the time during which cars are parked, it could also be possible to time vehicles support to the grid within the parking period. That is, to time V2G power production to fit within driving requirements, while meeting the time-critical power “dispatch” of the electric system. Clearly, all this realizes not only a technical but also an economic value [4]. There is some distrust among experts about the mass rollout and implementation of V2G. This technology, though interesting, still shows a number of undefined aspects, particularly for what regards the evaluation of the impact, the reliability and the availability of the V2G service. The general belief of the sceptics is that V2G is too expensive and that there are easier ways to store energy and support the power grid in the electricity supply. However, peerreviewed studies by Kempton et al., who are currently conducting research on the V2G technology and its performance when used on the grid, show that the V2G plan is technically and economically promising and feasible [5]. The development of PEVs impacts not only urban and private transport, but also public transport serving communities more or less distributed throughout a country. The dispersion of the electrical power needed to charge vehicle batteries will depend on the typology and structure of the transportation service, as well as on the composition of the fleet into which the single electric vehicles

0378-7796/$ – see front matter. Crown Copyright © 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2012.06.002

C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

will be aggregated based on open or closed jurisdictions. Thus, the penetration levels of distribution networks bended or bendable to V2G will be diverse, and, similarly, the charging stations (garages, parking areas) will play at different participation levels in the technical and economic aspects of the energy market. In this paper, reference is made to a hypothetical participation of aggregated PEV units within SEESs such as a Microgrid (MG), which can result in a significant contribution to the total internal energy balancing. This is the case, for instance, of a typical urban/rural – central or outlying – context, where there are two medium-capacity garages in presence of a local energy infrastructure, which is organized as a SEES including small-medium wind and biomass power generating systems. Although keeping in mind that the original MG concepts were developed with reference to LV networks, in line with the last years tendency of increasing MG exploitation potentials through MV applications, this paper makes use of the MG concepts for the characterization of the case study, given the particular structure considered, which includes – in the same small area – local generation, controllable loads and energy storage (in this case V2G). Therefore, in the following the term MG is used with the broader meaning of small electric system that can be part of a MV or LV network. The aim of this paper is developing a practical model to assess, in operation or operation planning, the impact of V2G on the energy balancing of a SEES, according to the objective of optimal economic management of the SEES itself. The expected result is a flexible tool suited to the Energy Management (EM) of the SEES. The proposed model materializes into a simple linear dispatch algorithm that can be easily integrated in the Energy Management System (EMS) of a system operator. In the case of the system under study, the EMS can be thought as physically installed at the interface point between the SEES and the macrogrid, that is, where the Smart Grid is located. Nevertheless, it is worth mentioning that there can also be EMSs installed so as to manage single areas of the V2G system; in this case, the operational integration of different EMSs on a hierarchical basis can be implemented as a Multi-Agent System (MAS) [6]. The setting of the proposed optimization model is conceptually general and can thus support SEESs in their active participation in the electricity market. The flexibility of the model makes it suitable for the analysis of many aspects related to “smart” EM of SEESs with V2G. Specifically, the reference case-study is a SEES that manages all the functions available locally, with the aim of assessing and optimizing the exploitation of the energy contribution provided by the electrical vehicles charge and management stations on a daily basis. Uncertainties that characterize the problem under study are considered in a probabilistic framework, employing appropriate techniques for their account. In particular, uncertainty associated to aggregation is accounted for into the EM model via robust optimization (RO), whereas uncertainty related to renewable power production is addressed via stochastic programming. 1.2. State of the art on V2G So far, V2G research has mainly focused on how to connect the vehicle batteries to the power grid [7,8], on proving the validity of the V2G concept [9], on characterizing its feasible services [8], and on identifying new markets [10,11]. In particular, frequency regulation is viewed as one of the most promising and practical services with V2G, given the fast charging rate of batteries [7,11,12]. In recent years, attention has also been paid to the optimal operation of V2G, with some efforts to integrate V2G into the Unit Commitment (UC) [13]. However, the approach proposed in [13] to account for the uncertainty related to V2G is heuristic, and, in addition, vehicles are considered just as generating units that are assumed to be charged only from renewable sources, which might be unrealistic.

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Other studies have focused on Aggregators, to show that they are required in order to fully realize the benefits of V2G [1,14,15], or to propose ideas on aggregation modelling [1,15,16]. Such aggregation is required to effectively integrate the fleet of battery vehicles into the grid as Distributed Energy Resources (DERs). In [1], emphasis is put on the Information Technology (IT) potential to handle the defined control signals and communication flows between the various agents, e.g., the PHEV owner, the Aggregator and the Transmission System Operator (TSO), and simulations are performed on an electric vehicle fleet used for commuting purposes to study the regulating power capability. A detailed mathematical interpretation of the role of the aggregator is found in [15]. Using dynamic programming the authors maximize the customer benefit, identifying the State Of Charge (SOC) before the next trip for cars, and the total revenue of the aggregator. The economic analysis of V2G technology has been widely addressed in the literature. For instance, Kempton and Tomic [11] use the effective generation capacity of three different types of EVs to evaluate revenue and costs associated to the electricity supply to three distinct markets, namely, peak power, spinning reserve and regulation. Similarly, Zhong and Cruden make assessments in the context of the UK electricity market [17], and a recent study has been published by National Grid and Ricardo examining the UK V2G market [18]. Another aspect studied in several publications is the control of V2G, which is necessary to decide whether the EV should be charged/discharged or provide frequency regulation at each hour. A few V2G control algorithm have been proposed in the literature: for example, in [19] the problem of maximising the EVs owners’ profit by selling excessive energy to grid is considered, and a V2G control algorithm is proposed that is based on the application of a binary particle swarm optimization technique. Some relevant findings are presented in [20], where the real-time control problem is studied considering price uncertainty. Many studies have focused on the optimization of different V2G assets. In [21], an optimal bidding formulation for EVs performing regulation up and down with only unidirectional power flow is developed. In [15], an optimal charging sequence for EVs selling only regulation is formulated, whereas smart charging optimization without V2G and optimized V2G with only regulation are formulated with some simplifications in [22]. Also, the very recent work in [23] addresses the optimal simultaneous bidding of V2G energy and ancillary services for aggregator profit maximization, formulating the model as a linear problem that can be easily and efficiently solved for large groups of EVs. The adoption of the V2G aggregator concept associated to the MG operation, which is also the subject of this paper, has been already presented in the literature. For instance, it is relevant the work recently presented in [24], where a general micro-source and V2G models are developed and simulations of voltage regulation and renewable energy support are performed in order to prove the appropriate performance of the proposed structure and control strategy. Lately, significant and comprehensive work has been done in [25], where the impact of EVs integration is investigated in details from both the technical operation and the electricity market perspectives. In [25] the impact of EVs penetration on voltage profiles and power lines congestion is evaluated based on steady state and dynamic behaviour analyses, and the benefits arising from smart charging are analysed. Simulations conducted on a MV semiurban network show that smart charging can allow higher levels of EVs penetration without the need of grid reinforcements. It is relevant to note that the studies recently presented in the literature contribute in giving a satisfactory description of how a V2G scheme should act within the system or interact with the main grid, and that several of the mentioned papers also present practical and realistic aggregation frameworks for V2G systems. Within this

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context, this paper adds further contributions to the state of the art, delivering – on one hand – a complete methodology for realistic V2G aggregator modelling and integration in the EM of a SEES, and – on the other hand – a methodological proposal for taking into account the uncertainties associated to the charging/discharging pattern of EVs in optimization problems. Although V2G is still in the conceptual stages and waiting for its implementation, the approach in this paper represents a conceptual and practical framework to help move from concept to implementation. 1.3. Paper organization The remaining of this paper is structured as follows. Section 2 discusses the methodology, its flexibility and the possible extension of its application area. In Section 3 the methodological approach to model the electrical vehicle aggregation is presented and discussed. The proposed optimization model, in its initial (non-robust) and stochastic-robust formulations, is described in Section 4. The results of the application of the proposed models to a realistic case study are presented and discussed in Section 5. Finally, Section 6 summarizes the main results and conclusions of the paper, and gives some hints about possible future developments.

2. Methodology Being the system under study a small network conceived as a MG, which is typically characterized by stochastic supply, due to the presence of uncertain renewable generation, and by a demand that responds to market signals and hence can be uncertain, it is clear that a deterministic approach is more suited for preliminary analyses, but for any more accurate and reliable analysis a probabilistic framework should be used. With respect to this, this paper proposes a model that is based on a stochastic methodology, considering, in particular, uncertainty related to power generation from wind and from PEVs. The proposed EM model is flexible and hence suited for different applications, in different stages of analysis, based on the time horizon considered and on the definition of the variables of the problem. With reference to short term horizons (a day, a week, a month), the tool can be used for analyses pertaining to SEES operation and short-term management. Such is the case in this paper, where a daily time horizon is considered for analyses in operation or operation planning. For longer horizons (a quarter of year and over) the application of the tool can be extended to planning analyses, such as investment or resource planning, or scenario analyses, such as reliability assessment, risk analysis, etc. The following subsections discuss in detail the approach used to properly model the contributions in power production given by wind and PHEVs/BEVs. 2.1. Wind power generation modelling Wind power generation is modelled via scenarios, and the related uncertainty is addressed by referring to one of the well-established methodological approach proposed in literature [26–29]. Monte Carlo Simulation (MCS) technique is used to generate a large number of scenarios, each assigned a certain probability. Then, scenario reduction [1] is employed to eliminate scenarios with very low probability and to aggregate close scenarios, in order to decrease the computational burden of MCS while maintaining good approximation. Since the modelling pattern is similar to the one provided in [26], and since a full discussion on wind analysis is beyond the scope of this paper, for a complete discussion on this modelling framework the reader is referred to [26].

2.2. Robust optimization Many sources of uncertainty can affect PHEVs/BEVs power production, such as vehicle parking time, duration of the period during which vehicles are plugged into the grid, SOC of the car batteries, vehicle storage, etc. [30]. Clearly, this has to be considered in the modelling. To this aim, RO [31] is used in this paper to properly account for uncertainty related to PHEVs/BEVs in the proposed EM model, since this technique is particularly adequate when dealing with uncertain but bounded parameters, just like power from/to PHEVs/BEVS can be assumed in short-term. The general approach of RO entails reformulating the original optimization problem with uncertainty into a deterministic program (robust counterpart optimization problem), so that each solution of the new program is feasible for all allowable realizations of the uncertain data. The uncertain data are assumed to be unknown but bounded, and most studies assume convexity for the uncertainty space. Compared to stochastic programming, RO does not require information about the probability distribution of the uncertain data, and thus the uncertainties are modelled as random variables that are constrained to lie within a known range. 2.3. Plug-in electric vehicles aggregation Central to the V2G concept is the integration of the PHEVs/BEVs aggregation into the grid so that their batteries can give beneficial contributions to the electrical network. In fact, the battery of a single vehicle is a very small resource whose impact on the grid is negligible and only represents a noise. Therefore, PHEVs and BEVs need to be aggregated for the grid to take advantage of their presence, both on the supply side (to provide power for demand balancing) and on the demand side (to consume at appropriate times). The aggregator, responsible for grouping PHEVs and BEVs to act as a DER, and for interfacing them with the Independent System Operator (ISO) or Regional Transmission Organization (RTO), is the critical entity to make the V2G concept implementable. With respect to this, this paper proposes a novel and practical methodology to model the aggregator, which develops in several steps based on the conceptual framework associated to plug-in electric vehicles. The versatility of the modelling makes it suitable as a support tool for the implementation of V2G into real-world applications. 3. Aggregator model The principal utility of PEVs lies in their availability to provide clean and economic transportation to owners rather than to support power grid operations. Therefore, PHEVs and BEVs may not always be plugged into the grid; moreover, since every vehicle may travel different distances every day, its battery storage may differ from that of the other PHEVs/BEVs at the time it interconnects with the distribution network. All this must be taken into consideration when constructing an appropriate model of aggregator, under a set of reasonable assumptions. In modelling the aggregator, some assumptions have been introduced for the sake of simplicity, as follows: 1. Each PHEV/BEV in the aggregation has the same efficiency and the same battery type. 2. Losses in PHEV and BEV batteries are negligibly small. 3. The storage capability of batteries does not change during the study period (one day). These assumptions are reasonable for the study undertaken, but also consistent with reality. Particular attention deserves the last two hypotheses, as battery degradation and power loss are

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3.2. Assumptions and application of the method With respect to the case study addressed in this paper, that is, a local energy infrastructure organized as a SEES including autonomous renewable power sources and two garages suited to V2G (the “aggregators”), which is analysed for operation’s purposes during a time horizon of one day, the following assumptions are considered in the application of the method described in Section 3.1: Fig. 1. Classification of possible PHEV/BEV states.

spontaneous phenomena that in principle cannot be ignored. Generally speaking, batteries over time degrade and eventually stop working; declining capacity, increasing internal resistance, elevated self-discharge, and premature voltage cut-off on discharge are all complex technical issues that do more to cause battery degradation and power loss that a typical battery car owner could ever do. However, deepening the basic mechanisms of batteries behaviour is beyond the scope of this paper, which instead aims to provide some insight and methodological contributions for the modelling of V2G. Moreover, in the new-generation batteries for PHEVs and BEVs, which are currently in production or will be available within the next few years, yearly losses are expected to be small (less than 10%). Considering all this, and also considering that the reference time frame for our study (a day) is very small compared with a year, make allowance for the assumptions above. Nevertheless, it is worth to clarify that such assumptions can be relaxed or removed if sufficient data is available. 3.1. Method The power that the aggregation of PHEVs/BEVs can supply or demand to the grid mainly depends on factors such as type of batteries (lead acid, nickel metal hydride, lithium-ion, zebra, etc.), size and type of vehicles (CV: plug-in charge only vehicle, non suitable for V2G; DV: plug-in charge/discharge vehicle, suitable for bidirectional communication with the grid and therefore for V2G), PHEVs/BEVs state (which depends on the driving pattern of each vehicle), state of the batteries, charge/discharge rates of the batteries, [32]. These factors are affected by uncertainty [1,30], hence generating uncertainty in the power that the aggregator can demand or supply. Fig. 1 shows a classification of PHEVs/BEVs states based on their type (CV or DV). For the study undertaken, which addresses SEESs including V2G, this paper focuses on DVs only. In this case, the DV power supply/demand aggregation, PGARAGEj,t , at time t can be calculated as a function of all the factors mentioned above, and according to the classification of Fig. 1, as follows [32]: (2.1)

PGARAGEj,t = −rCt · nt

(2.2)

+ rDt · nt

(2.3)

+ rSDt · nt

(2.3) nt

(2.3)

nt ) are known. 3. Batteries: the same battery type, with the same specifications (capacity, charge/discharge/self-discharge rates) is considered for all vehicles. In particular, Chevy Volt’s lithium-ion batteries [33] are considered in all cases. These batteries have a theoretical (nominal) capacity of 16 kWh, but, for the sake of preserving efficiency and life time, no more of 90% of the this capacity should be used, as well as discharge should not go under the 25%. Optimal charging time is 6–8 h if using a 110 V outlet [33]. The hypothesis of considering the same battery type for all vehicles is for the sake of simplicity, and anyhow reasonable for the type of analysis undertaken. As for the hypothesis on garages, both number of parking spaces and hourly occupancy are forecastable based on typical garage operation program, and hence this assumption can be considered realistic. The same holds true for the assumption on vehicles, the state of which is considered known, as this state is predictable based on typical load profiles (residential, commercial or industrial) and vehicles users’ behaviour. On the basis of the above hypothesis, the power profiles of the garages (power demanded or available for grid support) is directly determined through Eq. (1). The uncertainty pertaining to these profiles is analysed in Section 4.2.

4. Energy management model for small electric energy systems This section describes in detail the optimization models proposed to address the study of the EM of a SEES with V2G. Being the analysis devoted to assess the interaction between the SEES and the main grid from an operational perspective, the problem can be formulated as an EM model, where the objective is determining the power output of the dispatchable generating units (DGUs), as well as the power output/input of garages and main grid, in order to minimize the total operating costs of demand supply satisfying appropriate constraints.

(1)

In (1), rCt , rDt and rSDt are the rates of charge, discharge and selfdischarge in kW at time t, respectively, whereas

1. Garages: the number of parking spaces reserved to PHEVs/BEVs is defined, and the occupancy of these spaces at a certain hour t of the day is known. (2.1) (2.2) 2. Vehicles: their numbers and states at hour t (i.e., nt , nt and

(2.1) nt ,

(2.2) nt

and

denote the number of vehicles at time t in state 2.1 (charging), 2.2 (discharging) and 2.3 (inactive), respectively. Based on type of batteries, type of PEV (i.e., number of (2.1) (2.2) (2.3) CV and DV), vehicles states (i.e., nt , nt and nt ) and charge/discharge rates, it is possible determining, for each aggregator participating in the V2G, at every hour t, the power available for supplying the grid or demanded, by using Eq. (1). It is worth mentioning that the formulation in (1) is obtained considering DVs only, but can be easily extended to cases including also CVs.

4.1. Initial (non-robust) model Disregarding uncertainty related to V2G, the initial model is formulated as follows:

Min

C =

H  Scwind

 I N−1  

(Scwind )

t=0

+ Cgrid,t · (Pgrid,t ) +

i=1 J  j=1

CDGUi ,t · (PDGUi ,t,Scwind )



CGARj ,t · (PGARj ,t,Scwind )

(2.1)

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C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

Subject to :



i ∈ ˝nDGU

=



Pflowk ,t,Scwind +

k|s(k)=n



PGARj ,t,Scwind

j ∈ ˝nGAR







PDGUi ,t,Scwind + Pgrid,t +



PLl −

l ∈ ˝nLoad

Pflowk ,t,Scwind

k|r(k)=n

(2.2)

PWm ,t,Scwind

Wm ∈ ˝nWind

∀t, Scwind , n ≡ n¯ : connected to bulk grid ≡ reference bus

 i ∈ ˝nDGU







min PGAR ≤ PGARj ,t,Scwind ≤ P¯ GARAGEj,t ,

PGARj ,t,Scwind

j

j ∈ ˝nGAR



Pflowk ,t,Scwind +

k|s(k)=n

=



PDGUi ,t,Scwind +

PLl −

l ∈ ˝nLoad

Pflowk ,t,Scwind

if P¯ GARAGEj,t < 0 (grid to vehicle) Pflowk ,t,Scwind

PWm ,t,Scwind

∀t, Scwind , ∀n = / n¯

(2.3)

if P¯ GARAGEj,t > 0 (vehicle to grid)

(2.15)

Wm ∈ ˝nWind

1 = (ı − ır(k),t,Scwind ) ∀k ∈ Line, t, Scwind xk s(k),t,Scwind (2.4)

min max ≤ Pflowk ,t,Scwind ≤ Pflow Pflow

∀k ∈ Line, t, Scwind

(2.5)

min max PDGU ≤ PDGUi ,t,Scwind ≤ PDGU

∀i, t, Scwind

(2.6)

k

k

i

i

min max ≤ |Pgrid,t | ≤ Pgrid Pgrid

0 ≤ PWm ,t,Scwind ≤

∀t

(2.7)

max PW m ,t,Scwind

∀m, t, Scwind

(2.8)

PDGUi ,t,Scwind − PDGUi ,t+1,Scwind ≤ RDNi

∀i, t, Scwind

(2.9)

PDGUi ,t+1,Scwind − PDGUi ,t,Scwind ≤ RUPi

∀i, t, Scwind

(2.10)

− ≤ ın,t,Scwind ≤ 

¯ ∀t, Scwind ∀n = / n,

= 0 ∀t, Scwind , ın,t,Sc ¯ wind

n¯ : reference bus

min max PGAR ≤ PGARj ,t,Scwind ≤ PGAR j

(2.14)

0 ≤ PGARj ,t,Scwind ≤ P¯ GARAGEj,t ,

k|r(k)=n



It is worth mentioning that the 24-h power profile of the garages/aggregators determined by means of the method described in Section 3 should represent, for each hour t, a load (when PGARAGEj,t < 0 → grid to vehicle) or a possible contribution in power generation to support the SEES and the main grid in load supply (when PGARAGEj,t < 0 → Vehicle to grid). When PGARAGEj,t > 0, PGARAGEj,t represents the maximum amount of power that the jth garage could produce if required by the SEES, and hence can be viewed as the maximum limit for the variable PGARj ,t,Scwind (PGARj ,t,Scwind : optimal power output of garage j). On the contrary, when PGARAGEj,t < 0, PGARAGEj,t represents the demand of the jth garage at hour t. Based on these considerations, in the implementation of model (2), constraint (2.13) is reformulated as follows:

j

∀j, t, Scwind

It must be mentioned that inequality (2.14) is used in place of expression PGARj ,t,Scwind = P¯ GARAGEj,t ,

if P¯ GARAGEj,t < 0 (grid to vehicle)(2.16)

to represent the behaviour of garage j as a load, just for the purpose of formulating a model suitable for RO application in the next step of the proposed methodology, as RO technique requires the constraints on which it operates to be inequalities [31]. In any case, for the minimization of generation costs both expressions (2.14) and (2.16) provide the same optimal solution. Model (2) is the deterministic equivalent of a stochastic model due to the presence of renewable generation from wind, which is modelled via scenarios as described in Section 2.1. 4.2. Robust counterpart optimization model

(2.11) (2.12) (2.13)

Model (2), which includes a DC network representation, spans the N = 24 h of a day. The objective function (2.1) to be minimized is the expected operating cost of demand supply, where (Scwind ) is the probability/weight of wind scenario Scwind . Notice that variables PCGUi t,Scwind and PGARj t,Scwind take different values for different wind power scenarios, whereas variable Pgrid,t is assumed as independent of wind scenarios. In other words, the SEES operator uses the biomass unit (DGU) and the garages (GAR), which are under its control, as controlling devices but not the grid. Constraints (2.2) and (2.3) ensure the nodal power balance at every hour, with Eq. (2.2) pertaining to the bus connected to the main grid only, n¯ ≡ references bus. Constraints (2.4) define the power flow through each line. Constraints (2.5) limit the power flow in transmission lines. Constraints (2.6) enforce the power limits for DGUs, whereas constraints (2.7) enforce limits between the main grid and SEES system. Constraints (2.8) impose limits for the wind power generation and allow wind power curtailment if needed to satisfy transmission constraints. Constraints (2.9) and (2.10) are ramp down/up rates for DGUs. Also, inequalities (2.11) ensure voltage angle limits at every ¯ whereas Eq. (2.12) define the voltage angle at the ref/ n, bus n = erence bus. Finally, inequalities (2.13) represent the power limit constraints for the garages (the “PHEVs/BEVs aggregators”).

Model (2) does not account for the uncertainty brought in by PEVs. Therefore, it requires to be reformulated with a proper consideration of uncertainty in garages’ power profiles. Since these profiles can reasonably be assumed as uncertain but bounded parameters, they are modelled via a RO technique by using a forecast (expected) value and a “certainty interval” exp around such forecast, e.g., P¯ GARAGE ∈ [P¯ GARAGEj,t − , P¯ GARAGEj,t + ], j,t

with  indicating deviation from the expected value of garages’ charged/discharged power. The robust counterpart optimization model is thus formulated as follows [31]: Min

C =

H 

 I N−1  

(Scwind )

Scwind

t=0

+ Cgrid,t · (Pgrid,t ) +

CDGUi ,t · (PDGUi ,t,Scwind )

i=1 J 



CGARj ,t · (PGARj ,t,Scwind )

(3.1)

j=1

Subject to: Constraints (2.2)–(2.13) PGARj,t,Sc

wind

+ PDj,t,Sc

− P¯ GARAGEj,t · X + ZDj,t,Sc

(3.2)

wind

wind

· Dj,t

≤ 0 ∀t, Scwind , j if P¯ GARAGEj,t > 0

(3.3)

C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

PGARj,t,Sc

wind

− P¯ GARAGEj,t · X + ZCj,t,Sc

+ PCj,t,Sc

wind

wind

· Cj,t

≤ 0 ∀t, Scwind , j if P¯ GARAGEj,t < 0

min ≤ PGARj,t,Sc PGAR j

(3.4)

∀t, Scwind , j (if P¯ GARAGEj,t < 0)

wind

(3.5)

∀t, Scwind , j (if P¯ GARAGEj,t > 0)

0 ≤ PGARj,t,Sc

wind

ZDj,t,Sc

wind

+ PDj,t,Sc

ZCj,t,Sc

wind

+ PCj,t,Sc

wind

wind

55

(3.6)

≥ D · Y

∀t, Scwind , j

(3.7)

≥ C · Y

∀t, Scwind , j

(3.8)

X≤Y

(3.9)

X=1

(3.10)

0≤Y

(3.11)

PDj,t,Sc

wind

, PCj,t,Sc

wind

, ZDj,t,Sc

wind

, ZCj,t,Sc

wind

≥ 0 ∀t, Scwind , j

(3.12)

Model (3) is obtained using duality properties and exact linear equivalences [31]. Variables PDj,t,Sc , PCj,t,Sc , ZDj,t,Sc and wind

ZCj,t,Sc

wind

wind

wind

are dual variables of the initial problem (2), used to

account for the known bounds of garages’ charge/discharge power (ZDj,t,Sc and PDj,t,Sc for discharging; ZCj,t,Sc and PCj,t,Sc for wind

wind

wind

wind

charging), whereas X and Y are auxiliary variables, the former used to obtain equivalent linear expressions and the latter to formulate the robust problem. Parameters  C and  D denote deviations from the expected values of power charged and discharged by garages, respectively. Also, Cj,t and Dj,t are control parameters (Cj,t for charging and Dj,t for discharging) introduced to maintain a certain level of robustness in the objective function. These parameters take values between 0 and 1, so that if  C ,  D = 0 (subscripts j, t dropped for clarity) the influence of garages power deviations is ignored (nonconservative “optimal” solution), whereas if  C ,  D = 1 all garages power deviations are considered (conservative “optimal” solution). Constraints (3.3)–(3.6) limit the garages’ power output, with inequalities (3.3) and (3.6) used in discharge phase, and inequalities (3.4) and (3.5) in charging. The minimum and maximum values should be chosen in accordance with the battery charging requirements provided by manufacturers. In particular, for a Chevy Volt Li-ion battery (the reference battery type of this paper), the charge should not exceed the 85–90% of the nominal (theoretical) capacity [33]. 5. Case study Numerical results of applying the proposed EM model to a test SEES are presented and discussed in this section. Both models (2) and (3) are applied to demonstrate their effectiveness and usefulness, and the corresponding results are compared to show the differences between the non-robust and robust approaches. 5.1. System configuration The considered configuration of SEES including V2G is shown in Fig. 2. It is a 20 kV 4-bus network, connected to the main grid at bus 1 (“slack bus”, 132 kV), and consisting of: a biomass power plant (DGU) and a wind farm (WF) at buses 3 and 4, respectively; a residential garage (G1) and a “office” garage (G2) at buses 2 and 3, respectively; and loads in all buses. All these components are assumed as part of the same jurisdiction. All distribution lines have the same characteristics, with reactance of 0.097 . The two garages have space for a certain number of PHEVs/BEVs and are able to support the SEES and/or the bulk grid in the electrical power supply, since they include V2G technology. The main

Fig. 2. SEES configuration.

grid can sell or buy energy, depending on loads demand and on the trading with the SEES. Loads vary during the day according to residential or commercial/industry load profiles, whereas generation vary according to the typical production profiles of the considered generating units, as controlled by the SEES operator. 5.2. Data and assumptions 5.2.1. Generation H = 30 different scenarios of wind power generation are considered in the numerical simulations. These scenarios are obtained by a re-elaboration of the data provided in [26], which were built through the combined use of MCS and scenario reduction technique, as discussed in Section 2.1. Generation data for the biomass cogeneration power plant and the main grid are provided in Table 1. The hourly mean values of the considered wind power production scenarios are provided in the second column in Table 2. 5.2.2. Load Load data are derived from typical residential and industrial profiles. These data are provided in the third and fourth columns of Table 2. Residential loads (L1 and L2) are considered at buses 1 and 2, whereas manufacturing loads (L3 and L4) are assumed connected to buses 3 and 4. 5.2.3. Energy costs Prices of energy from the main grid and garages are provided in the fifth and sixth columns of Table 2, respectively. These prices are considered variable during the day depending on the load demand. The main grid energy prices correspond to historical data for the Spanish area of the electricity market of the Iberian Peninsula [34], whereas the prices associated to the garages’ energy production have to be derived or arbitrarily selected. In particular, since V2G participation in the electricity market is still at a conceptual stage and V2G is not yet integrated in the actual markets, no recognized standards or rules exist to price V2G, but different criteria can be proposed and followed to define how much the energy from EVs could cost. A possibility is to use the price of fuel to derive a constant electricity price for the EVs [35], or to use electricity market prices. This paper follows the latter approach, assuming that the price of the electrical energy from the garages is 10% lower than the price of the electricity obtained from the main grid. The cost of energy from the biomass cogeneration plant is assumed constant during the day (in particular, equal to

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C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

Table 1 Biomass cogeneration unit and main grid data. min PCGU (kW)

max PCGU (kW)

RDNi (kW/h)

RUPi (kW/h)

max Pgrid (kW)

0

250

100

100

1000

i

i

Table 2 Wind, load and energy price data. t

Mean PWm (kW)

L1 and L2 (kW)

L3 and L4 (kW)

Cgrid,t (D/MWh)

CGAR1,2 ,t (D/MWh)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

36.75 57.31 60.99 66.34 67.97 67.53 81.72 80.41 63.93 51.39 81.02 74.58 67.97 65.00 63.81 25.36 3.31 6.44 8.26 4.18 4.85 45.09 67.27 42.89

50.0 37.5 30.0 27.5 25.0 27.5 32.5 37.5 36.0 37.5 40.0 42.5 45.0 45.0 45.0 42.5 60.0 70.0 80.0 100.0 110.0 100.0 75.0 62.5

5.0 5.0 5.0 5.0 5.0 5.0 5.0 75.0 175.0 185.0 210.0 162.0 100.0 175.0 125.0 115.0 115.0 100.0 37.5 20.0 10.0 5.0 5.0 5.0

44.80 41.03 36.10 33.00 33.00 36.46 43.01 47.05 46.06 45.51 46.06 44.50 45.61 45.42 39.28 41.16 42.01 43.00 41.16 41.63 42.00 41.16 41.87 36.81

40.32 36.93 32.49 29.70 29.70 32.81 38.71 42.35 41.45 40.96 41.45 40.05 41.05 40.88 35.35 37.04 37.81 38.70 37.04 37.47 37.80 37.04 37.68 33.13

30 D/MWh), since this is typically the case, and cheaper than the other types of available generation sources. 5.2.4. Garages A residential garage (G1) and an “office” garage (G2) are considered, including 200 and 100 PHEVs/BEVs parking spaces, respectively. Garages power profiles are determined by means of the methodology described in Section 3, considering the batteries capacity being 14 kWh (90% of nominal capacity) after full recharge, and 4 kWh (25% of nominal capacity) after full discharge. Charge and discharge rates of 2.1 kW are assumed in all cases, which are reasonable considering the manufacturer’s specifications on the optimal charge/discharge times of the chosen battery type (Li-ion Chevy Volt’s). Self-discharge rate was assumed equal to 0.1 kW. For the RO model, a constant deviation of ±10% from the mean value is applied. Fig. 3 shows the ranges of variation (upper and lower bounds) for garages G1 and G2.

Fig. 3. Power profile for garages (upper and lower bounds).

During the night, cars are parked in the residential garage G1, charging their batteries, while no activity exits in the office garage G2. On the other hand, during the working hours, some cars stay in G1 and are able to provide power to the grid. In these hours and after the trip home-office, some cars charge their batteries in G2 while others can contribute to power generation. 6. Results and discussion Problems (2) and (3) are solved using CPLEX 11.2.1 [36] under GAMS [37] on a Linux-based Server with four processors clocking at 2.9 GHz and 250 GB of RAM. For both problems the optimal solution is achieved in less than 1 s. The robust model is tested for different values of the control parameters  C and  D . The effect of augmenting such parameters from 0 up to 1 can be seen in Fig. 4, which shows the minimum

Fig. 4. Trend of the optimal objective function depending on parameter I.

C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

(a)

57

(b)

Fig. 5. Mean values of the power of garage G1: (a) robust solution; (b) difference between non-robust and robust solution.

(a)

(b)

Fig. 6. Mean values of the power of garage G2: (a) robust solution; (b) difference between non-robust and robust solution.

expected cost (objective function) for different values of  C and  D . It can be noticed that this cost raises as  C and  D increase, as expected due to the fact that the robust method becomes more conservative for greater values of  C or  D . The results obtained from the comparisons between the nonrobust problem (2) and the robust problem (3) for  C ,  D = 1 are provided in Figs. 5–8, where the depicted values are mean values (of all wind power scenarios) for vehicles and biomass and a single value for the main grid (as it is supposed to be independent on wind power profiles). Note in particular that the RO modelling mainly affects the optimal results of the garages (see Figs. 5(b) and 6(b)) and the main grid (see Fig. 8(b)), with a difference between the non-robust and robust solution that can reach 42 kW in the case of garage G1 and 22 kW in the case of garage G2, and which can be over 40 kW in the case of the main grid. On the contrary, no appreciable differences between non-robust and robust approach can be evidenced for the biomass cogeneration optimal

(a)

results (see Fig. 7(b): maximum difference between non robust and robust solution equal to 2.1 kW). The latter demonstrates that the optimal dispatch of the biomass cogeneration power plant is not sensitive to variations of power associated with garages (electric vehicles). For all generating sources the robust problem results present very slight deviations from those obtained from the non-robust model. This demonstrates that the aggregation model is capable of providing realistic characterization of PHEVs/BEVs behaviour. Next, we analyse the operation of the DGU in two different wind scenarios characterized by low and high wind power production, respectively. Fig. 9 depicts the power output of the DGU for these two scenarios. While the electric power bought/sold to the main grid has to be specified in advance and does not depend on the scenario realization, the DGU is flexible to cope with wind power variability. Thus, in the low wind scenario, the DGU provides its maximum power

(b)

Fig. 7. Mean values of the power of the biomass cogeneration plant: (a) robust solution; (b) difference between non-robust and robust solution.

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C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

(a)

(b)

Fig. 8. Power from/to the main grid: (a) robust solution; (b) difference between non-robust and robust solution.

(a)

(b)

Fig. 9. Power of the biomass cogeneration plant for a low and a high wind scenario: (a) robust solution; (b) difference between non-robust and robust solution.

output for almost all periods. However, for the high wind scenario, the DGU reduces its power output. On the other hand, the differences between the robust and nonrobust solution are not significant. This result is in line with that highlighted in Fig. 7 (b). Note that the DGU should be flexible enough to deal with the wind power variability. If the DGU cannot cope with wind power variability, a higher amount of energy has to be bought from the main grid that would materialize in an increase in the operation cost. In general, with respect to the non-robust approach, the robust model does not provide a more advantageous solution in absolute terms or from the perspective of costs minimization, but instead it provides a better and more effective solution for what concerns the robustness of the results, since it considers uncertainty. From this point of view, the robust method could turn out to be more conservative than needed, giving results that could seem disadvantageous from the perspective of optimally managing energy while minimizing costs. However, RO represents the best solution for studies aimed to operation planning (as in this paper), where data are generally gathered in short periods of time but with a level of uncertainty that materializes into small variations. 7. Conclusions This paper proposes a novel optimization tool for energy management within small electric energy systems including vehicle-to-grid systems. A methodology to properly model vehicles aggregation is also presented. The optimization model, which materializes in a linear programming algorithm, allows assessing the effect of vehicle-to-grid as a contribution to the management of energy resources of a SEES. Robust optimization is used to account for uncertainty associated to vehicle-to-grid. This method allows the uncertainty related

to vehicle-to-grid to be taken into account through estimated ranges of variation. A stochastic programming framework is used to take into account wind power scenarios. A detailed case study is used to show the effectiveness of the technique proposed for the economic and secure management of a SEES. The proposed methodology is flexible, so that further developments can be easily foreseen, for example by integrating improved evaluation methods of the various stochastic factors involved in the SEES. Appendix A. List of symbols The main notation used in the paper is provided below for quick reference. Other symbols are defined as required throughout the text. Indices and sets k index of transmission lines n index of buses r(k) receiving/sending bus of distribution line k Scwind index of wind power scenarios running from 1 to H t index of time periods running from 0 to N − 1 set of dispatchable generating units (i = 1, . . ., I) located at ˝nDGU bus n ˝nGAR set of garages (j = 1, . . ., J) located at bus n ˝nLoad set of loads (l = 1, . . ., L) located at bus n set of wind farms (Wm = 1, . . ., M) located at bus n ˝nWind Parameters CDGUi ,t price of energy obtained from dispatchable generating unit i at time t CGARj ,t price of energy obtained from garage j at time t

C. Battistelli et al. / Electric Power Systems Research 92 (2012) 50–59

Cgrid,t price of energy obtained from the main grid at time t PGARAGEj power demanded/produced by plug-in electric vehicles in garage j min /P max min/max power flow limits for line k Pflow flow k

k

i

i

min /P max PDGU DGU

min/max power output limits for dispatchable gener-

ating unit i min /P max min/max power limits for garage j PGAR GAR j

j

min /P max min/max power limits for the main grid Pgrid grid power demanded by load 1 at time t PL1 ,t PWm ,t,Scwind maximum power production of wind farm Wm at time t and under wind power scenario SCwind RDNi /RUPi ramp down/up limits for dispatchable generating unit i reactance of line k xk

Variables ın,t,Scwind voltage angle at bus n at time t and under wind power scenario Scwind PDGUi ,t,Scwind power output from dispatchable generating unit i at time t and under wind power scenario Scwind PGARj ,t,Scwind power input/output for garage j at time t and under wind power scenario Scwind Pgrid,t power input/output for the main grid at time t Pflowk ,t,Scwind power flow in line k at time t and under wind power scenario Scwind PWm ,t,Scwind power production of wind farm Wm at time t and under wind power scenario Scwind References [1] C. Guille, G. Gross, A conceptual framework for the vehicle-to-grid (V2G) implementation, Energy Policy 37 (2009) 4379–4390. [2] M. Musio, P. Lombardi, A. Damiano, Vehicles to grid (V2G) concept applied to a virtual power plant structure, in: XIX Intl. Conf. on Elec. Mach., 2010. [3] I. Grau, S. Skarvelis-Kazakos, P. Papadopoulos, L.M. Cipcigan, N. Jenkins, Electric vehicles support for intentional islanding: a prediction for 2030, in: NAPS 2009, 2009. [4] S.E. Letendre, P. Denholm, P. Lilienthal, Electric & hybrid cars: new load, or new resource? Public Utilities Fortnightly 144 (2006) 28–37. [5] The Grid-Integrated Vehicle with Vehicle to Grid Technology. http://www.udel.edu/V2G/. [6] S.D.J. McArthur, E.M. Davidson, V.M. Catterson, A.L. Dimeas, N.D. Hatziargyriou, F. Ponci, T. Funabashi, Multi-agent systems for power engineering applications—part I: concepts, approaches, and technical challenges, IEEE Transactions on Power Systems 22 (2007) 1743–1752. [7] T.B. Gage, Final Report: Development and Evaluation of a PHEV with Vehicleto-Grid Power Flow, AC Propulsion, Inc., 2003. [8] J. Tomic, W. Kempton, Using fleets of electric-drive vehicles for grid support, Journal of Power Sources 168 (2007) 459–468. [9] W. Kempton, S.E. Letendre, Electric vehicles as a new power source for electric utilities, Transportation Research D 2 (1997) 157–175.

59

[10] W. Kempton, J. Tomic, Vehicle-to-grid power implementation: from stabilizing the grid to supporting large-scale renewable energy, Journal of Power Sources 144 (2005) 280–294. [11] W. Kempton, J. Tomic, Vehicle-to-grid power fundamentals: calculating capacity and net revenue, Journal of Power Sources 144 (2005) 268–279. [12] A.N. Brooks, Vehicle-to-Grid Demonstration Project: Grid Regulation Ancillary Service with a Battery Electric Vehicle, AC Propulsion, Inc., 2002. [13] A.Y. Saber, G.K. Venayagamoorthy, Intelligent unit commitment with vehicleto-grid—a cost-emission optimization, Journal of Power Sources 195 (2010) 898–911. [14] A. Brooks, E. Lu, D. Reicher, C. Spirakis, B. Weihl, Demand dispatch, IEEE Power & Energy Magazine 8 (2010) 20–29. [15] S. Han, K. Sezaki, Development of an optimal vehicle-to-grid aggregator for frequency regulation, IEEE Transactions on Smart Grid 1 (2010) 65–72. [16] C. Sandels, U. Franke, N. Ingvar, L. Nordstrom, R. Hamren, Vehicle to grid—Monte Carlo simulations for optimal aggregator strategies, in: POWERCON, 2010. [17] X. Zhong, A. Cruden, Assessment of vehicle to grid power as power system support, in: Smart Grid & Mobility Europe Conf, 2009. [18] Bucks for balancing: can plug-in vehicles of the future extract cash – and carbon – from the power grid? National Grid and Ricardo joint White Paper. http://www.ricardo.com. [19] C. Hutson, G.K. Venayagamoorthy, K.A. Corzine, Intelligent scheduling of hybrid and electric vehicle storage capacity in a parking lot for profit maximization in grid power transactions, in: IEEE Energy 2030, 2008. [20] Wenbo Shi, V.W.S. Wong, Real-time vehicle-to-grid control algorithm under price uncertainty, in: SmartGridComm, 2011. [21] E. Sortomme, M.A. El-Sharkawi, Optimal charging strategies for unidirectional vehicle-to-grid, IEEE Transactions on Smart Grid 2 (2011) 131–138. [22] N. Rotering, M. Ilic, Optimal charge control of plug-in hybrid electric vehicles in deregulated electricity markets, IEEE Transactions on Power Systems 26 (2011) 1021–1029. [23] E. Sortomme, M.A. El-Sharkawi, Optimal scheduling of vehicle-to-grid energy and ancillary services, IEEE Transactions on Smart Grid 3 (2012) 351–359. [24] S. Cui, X. Liu, D. Tian, Q. Zhang, L. Song, The construction and simulation of V2G system in micro-grid, in: ICEMS, 2011. [25] J.P.A. Pecas Lopes, F.J. Soares, P.M.R. Almeida, Integration of electric vehicles in the electric power system, IEEE Proceedings 99 (2011) 168–183. [26] J. Wang, M. Shahidehpour, Z. Li, Security-constrained unit commitment with volatile wind power generation, IEEE Transactions on Power Systems 23 (2008) 1319–1326. [27] C. Battistelli, M. Uccelletti, Assessing wind power and electrical power systems interconnection: a methodological approach, in: PowerTech IEEE Trondheim, 2011. [28] J.M. Morales, R. Mínguez, A.J. Conejo, A methodology to generate statistically dependent wind speed scenarios, Applied Energy 87 (2010) 843–855. [29] J.M. Morales, S. Pineda, A.J. Conejo, M. Carrión, Scenario reduction for futures market trading in electricity market, IEEE Transactions on Power Systems 24 (2009) 878–888. [30] C. Guille, G. Gross, The integration of PHEV aggregations into a power system with wind resources, in: iREP Symposium, 2010. [31] D. Bertsimas, M. Sim, Robust discrete optimization and network flows, Mathematical Programming 98 (2003) 49–71. [32] D. Feng, Z. Xu, J. Østergaard, Redesign electricity market for the next generation power system of renewable energy and distributed storage technologies, in: PES General Meeting IEEE, 2010. [33] Chevrolet Volt Full Specifications. http://gm-volt.com/full-specifications/. [34] Iberian Electricity Pool, OMEL, Spain and Portugal. http://www.omel.es/. [35] J. Soares, T. Sousa, H. Morais, Z. Vale, P. Faria, An optimal scheduling problem in distribution networks considering V2G, in: IEEE CIASG, 2011. [36] The ILOG CPLEX, 2008. http://www.ilog.com/products/cplex/. [37] R.E. Rosenthal, GAMS, A User’s Guide, GAMS Development Corporation, Washington, DC, 2008.