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Demand-side management in smart grid operation considering electric vehicles load shifting and vehicle-to-grid support
Electrical Power and Energy Systems 64 (2015) 689–698
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Demand-side management in smart grid operation considering electric vehicles load shifting and vehicle-to-grid support M.A. López ⇑, S. de la Torre, S. Martín, J.A. Aguado Department of Electrical Engineering, Universidad de Málaga, Spain
a r t i c l e
i n f o
Article history: Received 12 February 2014 Received in revised form 16 July 2014 Accepted 19 July 2014
Keywords: Demand-side management Electric vehicles Smart grid Vehicle-to-grid
a b s t r a c t Demand fluctuation in electric power systems is undesirable from many points of view; this has sparked an interest in demand-side strategies that try to establish mechanisms that allow for a flatter demand curve. Particularly interesting is load shifting, a strategy that considers the shifting of certain amounts of energy demand from some time periods to other time periods with lower expected demand, typically in response to price signals. In this paper, an optimization-based model is proposed to perform load shifting in the context of smart grids. In our model, we define agents that are responsible for load, generation and storage management; in particular, some of them are electric vehicle aggregators. An important feature of the proposed approach is the inclusion of electric vehicles with vehicle-to-grid capabilities; with this possibility, electric vehicles can provide certain services to the power grid, including load shifting and congestion management. Results are reported for a test system based on the IEEE 37-bus distribution grid; the effectiveness of the approach and the effect of the hourly energy prices on flattening the load curve are shown. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction The transition towards the Smart Grid (SG) requires to incorporate new functionalities and capabilities to the existing electricity grid. Among some identifiable features, distributed generation is a common characteristic of the SG and, in addition, the nature of these generators is varied since they can be non-dispatchable renewable, such as wind turbines or photovoltaic panels, combined heat and power, fuel cells, microturbines or diesel-powered plants. Devices which are able to store energy, like electric fixed batteries, can help the system to smooth the intermittent behavior of renewable sources enabling an easier integration. The next generation of the electricity grid will also pave the way to electrified transportation [1]. SGs comprise different entities that can interact with each other bidirectionally, giving the possibility to establish commercial relationships to serve and request electric energy or to solve technical problems that could arise, thus empowering the consumer. These entities within the SG can respond to changes in the prices at which the energy is bought and sold to the main grid with the objective of minimizing the costs of the energy they need or ⇑ Corresponding author. E-mail addresses: [email protected] (M.A. López), [email protected] (S. de la Torre), [email protected] (S. Martín), [email protected] (J.A. Aguado). http://dx.doi.org/10.1016/j.ijepes.2014.07.065 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
maximizing the income from the energy they sell. Among the many features that make a grid smart, the essential aspect is the integration of power system engineering with information and communication technologies. In turn, this integration can allow for advances in reliability, efficiency and operational capability [2]. Among other interesting characteristics of SGs, the concept of Demand-Side Management (DSM) has attracted the attention of many researchers and, among DSM strategies, demand response has been widely considered [3–5]. Demand response can be understood as voluntary changes by end-consumers of their usual consumption patterns in response to price signals [6]. Along with the savings regarding electricity bills, this kind of schemes can be used to avoid undesirable peaks in the demand curve that take place in some time periods along the day, resulting in a more beneficial rearrangement [7–10]. Through the use of DSM, several benefits are expected, like the improvement in the efficiency of the system, the security of supply, the reduction in the flexibility requirements for generators or the mitigation of environmental damage, although some challenges have to be overcome starting from the lack of the necessary infrastructure [11]. In addition, the introduction of DSM has to be conceived taking into account other distributed energy resources technologies that could be present in SGs [12,13]. In regard to this, several SG projects worldwide are underway or have been completed [14,15].
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Nomenclature Pmin v Indexes and sets t; T index and set for time periods, t 2 T e; E index and set for the scenarios used to model the uncertainty, e 2 E i; R index and set for renewable generators belonging to the agent, i 2 R j; G index and set for non-renewable generators belonging the agent, j 2 G b; B index and set for batteries belonging to the agent, b 2 B v; H index and set for electric vehicles belonging to the agent, v 2 H n; A index and set for demand nodes of the agent, n 2 A tm ; T M index and set of transitions periods for the electric vehicles belonging to the agent, t m 2 T M jaj the cardinality of a set a Parameters We probability of scenario e ^ kbt main grid hourly forecasted buying price in time period t (cents €/kWh) ^ kst main grid hourly forecasted selling price in time period t (cents €/kWh) PR;e renewable power output for generator i in time period t i;t for scenario e (kW) X parameter related to capacity constraints of the agents Hn;t total demand prior to load shifting for bus n in time period t (kW) fe fraction of the total demand that can be shifted /n;t fixed demand for bus n in time period t (kW) cn;t maximum shiftable demand for bus n in time period t (kW) k maximum number of periods that demand can be shifted (hours) k rate between maximum shiftable demand and fixed demand, constant for all periods and nodes kd upper bound for the change in the value of shiftable demand between two consecutive periods, constant for all the periods and nodes (kW) lj variable cost for non-renewable generator j (cents €/ kW) ij fixed cost for non-renewable generator j (cents €) fj start-up cost for non-renewable generator j (cents €) 1j shut-down cost for non-renewable generator j (cents €) Pmin g;j
Pd;max b
minimum power output for non-renewable generator j (kW) maximum power output for non-renewable generator j (kW) maximum discharging power for battery b (kW)
Pc;max b
maximum charging power for battery b (kW)
Smax b
maximum state of charge for battery b (kWh) charging efficiency for batteries discharging efficiency for batteries
Pmax g;j
gC gD
In order to simplify the implementation of the proposed approach in real systems, most of the actions in the SG are taken by the agents. In order to take these actions, the agents act on their own interest; sometimes, however, they make use of additional information provided by the SG operator. The individual decisions of the agents can only be slightly corrected by the SG operator (centralized correction) in order to correct the violation of technical constraints in the SG, in case they arise.
Pmax v Smax v
jtv #
minimum charging or discharging power allowed for electric vehicles (kW) maximum charging or discharging power allowed for electric vehicles (kW) battery capacity of electric vehicle v (kWh) kilometers covered by electric vehicle v in time period t (km) average battery consumption (kWh/km)
Variables PS;e power sold in time period t for scenario e (kW) t PtB;e
power bought in time period t for scenario e (kW)
C G;e t;j
non-renewable generation cost for generator j in time period t for scenario e (cents €) power output for non-renewable generator j in time period t for scenario e (kW) discharging power for battery b in time period t for scenario e (kW) charging power for battery b in time period t for scenario e (kW) discharging power for electric vehicle v in time period t for scenario e (kW) charging power for electric vehicle v in time period t for scenario e (kW) optimal demand for bus n in time period t for scenario e (kW) optimal shiftable demand for bus n in time period t for scenario e (kW) amount of demand that goes from time period t to time period t 0 for bus n and scenario e (kW) state of charge for battery b in time period t for scenario e (kWh) state of charge for electric vehicle v in time period t for scenario e (kWh)
PG;e r j;t Pd;e b;t Pc;e b;t Pd;e v ;t Pc;e v ;t
Uen;t
Cen;t M en;t;t0 Seb;t Sev ;t
Binary variables bet binary variable that takes the value ‘‘1’’ if the agent is buying in time period t for scenario e, and ‘‘0’’ otherwise v G;e binary variable that takes the value ‘‘1’’ if generator j is t;j running in time period t for scenario e, and ‘‘0’’ otherwise yG;e binary variable that takes the value ‘‘1’’ if generator j t;j starts up in time period t for scenario e, and ‘‘0’’ otherwise sG;e binary variable that takes the value ‘‘1’’ if generator j t;j shuts down in time period t for scenario e, and ‘‘0’’ otherwise yd;e binary variable that takes the value ‘‘1’’ if electric vehiv ;t cle v is discharging in time period t for scenario e, and ‘‘0’’ otherwise yc;e binary variable that takes the value ‘‘1’’ if electric vehiv ;t cle v is charging in time period t for scenario e, and ‘‘0’’ otherwise
To make decisions each agent poses an optimization problem to maximize its profit over a set of periods, they can perform DSM strategies and Vehicle-to-Grid (V2G). As energy prices are usually higher for high demand periods, the optimization problems result in a flattened load curve. Following the regulatory trends in many countries, in particular in countries in Europe [16], the renewable generation in the model is also prioritized over the conventional generation. The framework considers market and technical
M.A. López et al. / Electrical Power and Energy Systems 64 (2015) 689–698
operation of the grid, and it is illustrated in a case study modeling a SG based on IEEE 37-bus distribution grid. The rest of the paper is organized as follows: in Section 2, the related work and paper contributions are introduced. Then, Section 3 presents a proposal for the SG operation, referred as problem statement, including the description of the operational algorithm steps previously mentioned. Section 4 focuses on DSM strategies, describing the optimization problems in detail and providing models of the different elements included. The case study and results are presented in Section 5. Finally, conclusions are drawn in Section 6.
Related work and contributions Many works are found in the literature investigating DSM benefits and SG modeling. Some of them cover problems regarding scheduling appliances based on pricing models; for instance, in [17], a voluntary household load shedding model is studied in order to keep the system in secure conditions with respect to demand peaks. Using two different methodologies, the benefits of DSM for both the consumers and utilities are shown in [18,19], stressing the importance of identifying the flexible loads. In comparison to these works, in this paper, operation of appliances is not considered and, instead, a fraction of the initial demand is assumed to be shiftable. In addition, agents with generation or storage assets are included in our formulation, while the previous works only stress the role of consumers. Other authors study how the demand can be allocated through optimization problems based on utility functions and other specific constraints. In [20], the objective of the proposed model is to maximize the utility of a consumer subject to a minimum daily consumption level and restrictions over load levels including price uncertainty. Authors in [21] consider the problem of maximizing the social welfare expressed as the sum of utilities of consumers minus the energy provider costs. In [22], a similar approach is proposed but uncertainty in renewable power generation is addressed and supply and demand are coordinated in two different time scales. The extension to several energy providers and the joint consideration of distributed and renewable generation units, storage devices, active demand and EVs is studied in [23]. One common aspect in these works is that the demand is calculated depending on the constraints, while in our work the total demand over the time horizon is known and it is only arranged differently. Moreover, the proposed model considers the maximization of the agents profit, whereas the social welfare or the utility functions are considered in [21–23]. Finally, only in [23] several elements present in SGs are modeled in a similar way to our proposal and, although some aspects are similar the way the demand is allocated is completely different. Finally, DSM can also be applied to EVs and, for this reason, they may be also influenced by price signals changing their location or their consumption pattern if needed. We propose a optimizationbased model applicable to EVs considering that EV load can be shifted based on charging prices. V2G can be also performed to get additional profits. Some related papers are described next. The impact of EVs on the demand profile is analyzed in [24] and, in [25], the authors try to integrate EVs with demand response strategies involving the consumer. In these works, EVs contribution is included through simple policies with no formal mathematical modeling of EVs load management and without considering V2G. In [26], a game theoretic approach is proposed to schedule EVs charging for peak shaving and valley filling while, in [27], V2G is also considered for this purpose; developing an optimization problem that aims at getting a final load profile close to a target load curve. In [28], a coordination mechanism is proposed
691
to allocate EVs charging efficiently, stressing the role of renewable energy. EVs can also be managed to solve technical problems, like line congestion, through the change in the initial expected charging pattern [29]. Other authors consider a specific smart load management approach that can be applied to EVs but focusing on technical aspects like losses minimization or voltage limits without including market issues [30]. According to the ideas presented, the main contributions in this work are: The formulation of a particular DSM strategy based on optimization problems where the profit maximization of all the involved agents is pursued. An algorithm to optimize the hourly allocation of demand and generation, taking into account technical constraints and enabling the EVs and renewable resources integration.
Problem statement The problem is posed on a SG that includes distributed generation (renewable and non-renewable), and EVs that can perform V2G operations. We study the operation in a typical day on a hourly basis, under the assumption that a similar operation could be done for each day. The problem is multi-period and thought to be applied for planning purposes, that is, not in real time. The agents in the considered SG can be of two types: (a) EVs, these agents can move among the nodes in the network, also one agent could aggregate several EVs and (b) agents that are always connected to the same node, these agents can be composed of a combination of: loads, renewable generators, non-renewable generators, and batteries. The SG architecture and examples of possible agents in the SG are illustrated in Fig. 1. The focus is on load shifting made by agents in the SG (rescheduling their loads) based on their profit maximization (generators) or cost minimization (pure loads). The number of periods that loads can be shifted, forward or backward, is referred to as ‘‘k’’, and it is an exogenous parameter in the proposed model. We study the results for different values of ‘‘k’’ because of two main reasons: (I) to evaluate the incentive (difference in profit or cost) that agents have to perform load shifting, and the resulting system performance (integration of renewable generation, losses, line apparent power flows, etc.) and (II) to evaluate the feasibility of the strategy, the higher the value of ‘‘k’’ the more difficult the strategy will be to apply for the agents in the real systems. In practice, it is interesting to understand what different values of parameter ‘‘k’’ mean for consumers and know other papers dealing with similar concepts. For instance, values of ‘‘k’’ below 3 h could be applied to cooling
Fig. 1. Agents considered in the smart grid.
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devices, through appropriate control signals, due to temperature restrictions [31]. In addition, air conditioning in commercial and residential areas has turned out to be the main responsible of demand peak in some countries and, thus, it is an ideal candidate for load shifting with higher values of this parameter [32,33]. Values between 2 h and 8 h have been considered by some authors as well to study reductions in distribution losses [34]. The agents can sell or buy energy, if it is technically feasible for them, (from/to) (other agents/the main grid). Each agent makes its own decisions, and there are not centralized decisions. The main grid is considered as a slack node with infinite capacity. The proposed model for the SG operation consists of two sequential stages, first a market based solution is calculated, and second the technical feasibility of the previous solution is checked in a technical operation stage. The SG operation along with these stages can be integrated in an specific operational algorithm, Fig. 2. In the first stage each agent makes decisions, for each period, about the quantities to generate, to buy from the main grid or the SG, its load shifting, and to sell its generation to the main grid or to the SG. Agents can choose between trade among them inside the SG, then the energy prices (selling and purchase) are determined by an internal auction based on the agents bids, or to trade with the main grid. The internal auction is ruled by the SG operator. Agents have to face two sets of parameters with uncertainty, on one hand the energy selling/purchase prices to/from the main grid, and on the other hand the available generation of the renewable resources. Both sets or parameters are modeled through scenario trees. They are also data, the initial energy demand for each agent (for each period) and the rate of that demand they can shift. To make their decisions, each agent poses an optimization problem. This problem is a mixed integer linear programming in the general case and a linear programming in some particular cases. We give a general description of these optimization problems in
what follows, and they will be described in detail in the next section. These optimization problems consists of an objective function and a set of constraints. Agents make decisions based on their profit maximization, thus the objective function is the expectation on the set of scenarios of the agents profit. The agents profit is defined as the income from selling energy minus the costs from generation and/or energy purchase. The set of constraints is made up of the technical constraints for each particular component of the agent, for instance, the capacity bounds for generators, and the bounds for the energy flow from/to batteries or EVs. Finally, in the second stage, a load flow is used to check the technical feasibility of the previous solution. In this stage, the active losses in the network lines are calculated (we only consider the active losses) in the network lines and the technical constraints are checked, in particular the node voltage bounds and the apparent power in the lines. If some bounds are violated then a correction to the initial solution is applied, and the new result is again checked. We apply the correction algorithm described in [35], that minimizes the changes with respect to the initial solution. Description of the agent strategy In this section, the strategy followed by the agents to make their decisions regarding load shifting is described. In what follows, first the different SG elements of the agents and the main related parameters and variables are introduced. Then, the agent optimization problem, consisting of an objective function and a set of constraints, is presented. Smart grid elements The SG elements considered in this work are presented here. Each agent is considered to be formed of four possible components: loads, generators, batteries or EVs. Loads are characterized by a fraction of the total demand that can be shifted and they depend on the time period and the node in the more general case. Thus, the initial predicted demand Hn;t is defined as the sum of fixed demand /n;t and the shiftable component cn;t , expressed as a fraction f e of the total demand, in every node and time period; this can be written as:
Hn;t ¼ /n;t þ cn;t ¼ /n;t þ f e Hn;t
8t;
8n
ð1Þ
Once the agent makes the decision, based on the results from its optimization problem, the total demand changes to Uen;t and the optimal shiftable demand to Cen;t . Fig. 3 illustrates the limits for demand in the proposed load shifting mechanism. The maximum number of periods that loads can be shifted forward or backward is an exogenous parameter ‘‘k’’, explained in the previous section. It is assumed that part of the agent loads can be
Fig. 2. Flow chart of the operational algorithm.
Fig. 3. Parameters and variables related to the demand.
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shifted [36]. The agent can access to the necessary information, like hourly energy prices, generation costs or weather historical data, to decide how and when it is more favorable to satisfy its demand. Generators can be of two types: non-renewable and renewable. Non-renewable generator j is characterized by its operational cost, that is made up of the variable cost lj , fixed cost ij , start-up cost fj and shut-down cost 1j . Its operation is mainly conditioned on the relation between generation costs and energy prices. Techmax nical bounds for power output, P min g;j and P g;j , are also considered. The power supplied by renewable generators, namely photovoltaic panels and wind turbines, is modeled as a set of scenarios. The specific values are calculated using real generator models and real values of wind speed and solar radiation; these values are combined to get an overall number of different scenarios corresponding to representative situations that take place during the year. We follow the current regulatory trends, proposed in many countries, in particular in Europe [16], that prioritize the use of low emission renewable generators over the conventional generators, even if some subsidy is needed to make the operation feasible. In this regard in our model the renewable generation is prioritized over the conventional generators in the optimization problems assuming a zero generation cost for them (but we do not consider subsidies explicitly in the model). We consider the renewable generation as a parameter with values given by an scenario tree, and that all the available renewable generation is used in the system (no spillage). In case the renewable generation is greater than the demand in the SG, the excess of generation is transferred (sold) to the main grid through the connection node. Fixed storage devices are represented by bank of electric batteries in this work. Fixed batteries are modeled taking into account the following aspects: (i) A battery can charge (absorb energy from the grid) or discharge (inject energy to the grid) considering operational efficiencies gC and gD respectively, (ii) there is a limit for the power drawn or supplied by a battery b; Pc;max and Pd;max , and b b (iii) the energy contained in the battery is tracked considering its State of Charge (SOC) Seb;t . Finally, mobile storage devices are represented by electric vehicles. Similar aspects enumerated for fixed batteries are applied for electric vehicles although some additional considerations are needed to define appropriately the mobility model. We consider two models for the EVs, the uncontrolled operation and the operation controlled by an aggregator [37], because they model two common situations in real systems, the individual user and a company fleet. In the uncontrolled situation we assume that EVs follows a fixed pattern, that is defined by three kinds of time periods: Transition, charging periods, and resting periods. During the transition periods the EVs move on the network and they consume the energy in their battery. In the charging periods the EVs consume energy from the network. And during the rest periods the EVs neither consume their own energy nor charge energy from the network. In this case the values of the energy flows in each periods are also fixed quantities. Two parameters are needed to determine the energy consumption (kWh) in transitions: (i) Parameter jtcm is the amount of kilometers covered in time period t m and (ii) parameter # that represents the energy consumption in kWh/km. In the case of operation controlled by an aggregator only the transition periods and their corresponding energy consumption are fixed. For the other periods, the aggregator makes the decision on when to charge and the quantity to consume from the network, they can perform V2G in these periods. Optimization problem description In this section, the mathematical relationships between the parameters and variables with respect to the elements of each
agent are developed in the form of an optimization problem, for the general case it is a mixed integer linear programming. First the objective function is described, and next the set of common constraints (balancing and DSM), and the set of constraints for each possible component of the agents (generators, batteries, EVs) according to the ideas described in Section 4.1 are presented. The number of equations, continuous variables, binary variables and execution time for the optimization problem of each agent, as described in Section 5.1, is given in Table 1. The corresponding values mainly depend on the SG elements of each agent and they can be calculated with the following equations: The number of equations is:
jTjjEj ð3 þ 2jGj þ 4jBj þ 3jHj þ 3jAjÞ þ jEj ðjBj þ jHj ð1 2jT M jÞÞ The number of continuous variables is:
jTjjEj ðjGj þ 3jBj þ 2jHj þ 2Þ þ jAjjEj ð2jTjk k ðk þ 1ÞÞ The number of binary variables is:
jTjjEj ð3jGj þ jBj þ 2jHj þ 1Þ The simulations were carried out in a computer Intel Core 2 Duo @ 3 GHz with 4 GB RAM. The software GAMS (using the CPLEX optimizer) was used to perform the optimization problems linked with MATLAB as a support to coordinate the execution of these problems, store data and make graphical representations. Regarding the objective function, the agents maximize their expected profit, that in the more general case is defined by: tf jEj jGj X X X ^kb PS;e ^ks P B;e We C G;e nmaximizeo t t t t t;j P S;e ;PB;e ;C G;e t t t;j
e¼1
t¼t 0
! ð2Þ
j¼1
where ^ kbt and ^ kst are the hourly forecasted buying and selling market prices (parameters), P B;e and P S;e are the hourly power bought and t t G;e sold (variables) and C t;j represents the function of generation costs for non-renewable generator j, defined in Section 4.2.2, t 0 is the initial time period and t f is the final time period. For a particular agent, some terms in Eq. (2) are fixed to zero depending on the agent composition, for instance if it contains only generators or only loads. From the historical data in real power systems, for instance in the Spanish system [38], we observe that average prices are higher for higher demand. Thus, the consequence of profit maximization for agents is that they try to shift their load to the periods with the lowest prices, and the demand curve is flattened. Common constraints (balancing and DSM) The constraints common to all the optimization problems include the energy balancing and DSM constraints. The balancing constraint relates PB;e and PS;e with the power t t supplied from generators, the bus load and the power drawn or
Table 1 Solving time and number of variables for agents optimization problems. Agent 1 2 3 4 5 6 7 8
Equations
Continuous
Binary
Execution time (s)
36,960 19,584 28,800 23,040 19,584 20,736 17,280 3144
150,336 84,096 125,568 104,256 84,096 103,104 82,944 2160
3456 4608 8064 4608 4608 1152 1152 2088
1.155 0.577 0.796 0.671 0.592 0.827 0.561 0.032
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delivered from batteries for each agent. According to Eqs. (3)–(5), variables P S;e and PB;e cannot be different from zero at the same t t time period, that is, whenever one of them is different from zero, the other one must equal zero. Thus, an agent is not allowed to buy and sell simultaneously: B;e PS;e t Pt ¼
jRj jGj jBj jAj X X X X c;e P R;e PG;e ðP d;e Uen;t i;t þ j;t þ b;t P b;t Þ i¼1
j¼1
8t; 8e:
n¼1
b¼1
ð3Þ e 0 6 PB;e t 6 bt X 8t; 8e
ð4Þ
e 0 6 PS;e t 6 ð1 bt Þ X; 8t; 8e
ð5Þ
G;e d;e where PR;e i;t ; P j;t and P b;t are the hourly power supplied for renewable generator i, non-renewable generator j and battery b; Pc;e b;t is the hourly power absorbed by battery b and Uen;t is the total demand in node n. Note that terms for batteries are extensible for EVs. Eqs. (4) and (5), which constitute an application of the Big-M method [39], assure that an agent cannot buy and sell at the same time through binary variable bet . Finally, X is a large enough parameter that can be fixed taken into account the capacity constraints for a particular agent, for instance the capacity of the lines feeding the agent. The DSM constraints for each agent, which regulate how the loads can be shifted between periods, are expressed in the following way:
Uen;t ¼ /n;t þ Cen;t Uen;t
8t; 8n; 8e
X e X e ¼ Hn;t þ M n;t0 ;t M n;t;t0 t0
Cen;t ¼ cn;t þ
t0
t0
(
M en;t;t0 ¼ 0 if
8t; 8n; 8e 8t; 8n; 8e
kd 6 C
ð8Þ
t0
8t; 8n; 8e 0
t¼t; t þ k < t 0 or t 0 þ k < t
0 6 Cen;t 6 k /n;t 8t; 8n; 8e e n;tþ1
ð7Þ
t0
X e X e M n;t0 ;t M n;t;t0
X e M n;t;t0 6 cn;t
ð6Þ
C
e n;t
6 kd 8t; 8n; 8e
ð9Þ ðaÞ
8n; 8e ðbÞ
ð10Þ ð11Þ ð12Þ
In Eq. (6), the optimal demand Uen;t (variable) that is really consumed in time period t, is expressed as the sum of fixed demand /n;t (parameter) and Cen;t (variable) which represents the optimal shiftable for node n in time period t. Total demand for node n and period t is written in (7) in terms of the amount of energy that is shifted from other periods t 0 to the current period t; M en;t0 ;t , minus the amount of energy that leaves period t to other period t 0 ; M en;t;t0 , for each node n and scenario e. Eq. (8) defines a similar relation compared to (7) but in terms of the optimal shiftable demand. In practice, either (7) or (8) should be used. Eq. (9) expresses the limit for the total amount of energy that can be shifted to other time periods. The variable Men;t;t0 also has to satisfy logical relationships needed to model load shifting through parameter ‘‘k’’. Condition (10a) assures that the demand cannot be shifted to the same time period; condition (10b) sets that demand cannot be shifted more than k periods forward and backward and it has to stand true 8t and 8t0 . Finally, to allow for a smooth transition for the final demand curve, some conditions are applied. These conditions are represented by a bound in the demand that can be shifted and bounds for the slope of the curve expressed by Eqs. (11) and (12) respectively. Parameter k is set depending on the willingness of the agent to shift the loads conditioned by the activities it develops
in its area. Parameter kd can be chosen taking into account operational constraints in the grid, like the capability of supporting sharp demand changes between two consecutive time periods. Generators modeling The constraints and equations taken into consideration for agents with non-renewable generators are given next: G;e G;e G;e G;e C G;e 8t; 8j; 8e t;j ¼ lj P t;j þ ij v t;j þ fj yt;j þ 1j st;j
v
G;e t;j
Pmin g;j
6
PG;e t;j
6v
G;e t;j
Pmax g;j
8t; 8j; 8e
G;e G;e G;e yG;e t;j st;j ¼ v t;j v t1;j 8t; 8j; 8e
ð13Þ ð14Þ ð15Þ
Eq. (13) defines the generation cost for a non-renewable generator based on the operational costs defined previously. Binary variables G;e G;e v G;e t;j =yt;j =st;j are equal to 1 in case that during the current time period, the generator: Is already running/starts-up/shuts-down, and 0 in any other case. Eq. (14) establishes the power output technical bounds, and (15) sets the relation among the binary variables which represent start-up, shut-down and generator operation. Renewable generators are modeled following the ideas presented in Section 4.1. Fixed batteries modeling For electric fixed batteries the following constraints are included in the optimization problem: d;max d;e 0 6 P d;e 8t; 8b; 8e b;t 6 yb;t P b
ð16Þ
c;max d;e 8t; 8b; 8e 0 6 P c;e b;t 6 ð1 yb;t Þ P b
ð17Þ
06
Seb;t
6
Smax b
8t; 8b; 8e
ð18Þ
d;e Seb;t Seb;t1 ¼ gC Pc;e b;t ð1=gD Þ P b;t 8t; 8b; 8e
ð19Þ
Seb;t0
ð20Þ
¼
Seb;tf
8b; 8e
Eqs. (16) and (17) models the bounds for the hourly maximum and minimum power supplied and drawn from battery b; Pd;e b;t and d;max Pc;e and Pc;max . Binary variable yd;e b;t , through P b b b;t ensures that the battery is not charging and discharging at the same time. The battery SOC Seb;t has to lie between 0 and a maximum value Smax b expressed in (18). Eq. (19) represents the energy balance for the battery through charging and discharging efficiencies. Finally, Eq. (20) guarantees that the initial and final SOCs, Seb;t0 and Seb;tf respectively, must be identical in order to avoid non-realistic solutions. Electric vehicles modeling The constraints that a controlled EV adds to the optimization problem are similar to the constraints modeled by Eqs. (16)–(20) described in Section 4.2.3. However, to comply with the standard IEC 61851, charging and discharging power are modeled as semicontinuous variables: min d;e max d;e yd;e 8t; 8v ; 8e v ;t P v 6 P v ;t 6 yv ;t P v
ð21Þ
min c;e max c;e yc;e 8t; 8v ; 8e v ;t P v 6 P v ;t 6 yv ;t P v c;e d;e yv ;t þ yv ;t 6 1 8t; 8v ; 8e
ð22Þ ð23Þ
d;e where binary variables yc;e v ;t and yv ;t define if EV v is charging or discharging. According to Eqs. (21)–(23) an EV is not allowed to charge and discharge at the same time period, that is, if the variable representing charging power P c;e v ;t is positive and different from zero then the variable representing discharging power Pd;e v ;t is zero and vice versa. In addition, charging and discharging power can take values max within the minimum and maximum power bounds, Pmin v and P v respectively.
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In addition, two constraints are included representing the mobility model adopted:
Sev ;te ¼ Smax 8v ; 8e v Sev ;tm þ1 ¼ Sev ;tm jtcm #
ð24Þ t m 2 T M ; 8v ; 8e
ð25Þ
e
Eq. (24) states that EV SOC Sv ;t has to be maximum in period t e . The EV SOC is reduced according to (25) when it is moving during time period t m , that is, in transition between two connections to the grid [37,40]. Case study and results To illustrate how the proposed method works, it is applied to a case study for the SG depicted in Fig. 5. Different operating conditions characterized by the number of periods that loads can be shifted, parameter ‘‘k’’, are studied. The SG consist of 8 agents, with 2 renewable generators, 5 non-renewable generators, 2 batteries and 14 EVs on a network based on the IEEE-37 bus distribution grid [41]. In what follows, first the data for the case study are described and second the main results regarding the questions posed in Section 3 are presented and discussed. Case study data The data for the case study are: (i) the initial demand curve of the agents, (ii) the scenario tree for energy prices and renewable generation, and (iii) the parameters for the DSM constraints and the models for the technical operation of the agents. A typical demand curve from a real distribution grid is assumed and selling/purchase prices are set to represent three different scenarios; hourly average historical values for prices [38] are defined along with a high prices scenario, defined by the extreme value of the blue bar, and a low prices scenario, defined by the extreme value of the orange bar, and corresponding to the 110% and 90% of the average prices respectively, Fig. 4. The sum of the hourly demand along the 24 h of the day is constant although DSM operations can change the hourly values, that is, the demand is rearranged. Load buses, generators, batteries and EVs considered in the case study are represented in Fig. 5, where grid areas belonging to the seven defined SG agents are labeled with circled numbers. Another agent, an EV aggregator, is responsible for providing the energy needed by EV owners to perform their daily trips. In relation to renewable generators, Fig. 6 shows the hourly power output for the wind and the photovoltaic plants considered. Note that 4 scenarios are used for each renewable source. Combining them, 16 scenarios are obtained, representing typical situations. The values of f e ¼ 0:15 and k ¼ 2:5 are relatively small and have been considered in order to limit the load shifted without
Fig. 4. Demand curve and price scenarios.
Fig. 5. IEEE 37-bus distribution case study.
Fig. 6. Renewable generators scenarios.
implying non-realistic activities re-scheduling of the agents. Also, we consider a maximum value of k = 12, because a larger value implies in practical terms a great re-scheduling effort for agents, and the solutions would have to be defined over intervals of more than 24 periods (several days). The parameter kd is fixed to a value of 0.75 kW considering the average amount of energy trade in the system and the power capacity installed. A total number of 14 EVs is considered here. For the EVs uncontrolled charging pattern, EVs charge at a rate of 3.7 kW [42,43] during four time periods at the end of the day, as soon as they arrive from the last journey of the day; then the EVs idle for the remaining time periods. It is also considered that each EV performs two journeys, called transitions, and each one is attached to a particular time period. The assumption of two journeys per day and the charging timing preference is a reasonable assumption as shown for example in surveys like [44]. During transitions, EVs consume a certain amount of energy equal to half the total EV individual charging and they commute between the initial node represented
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in Fig. 5 and the closest node, assumed for the purpose of this work. Specifically, the battery consumption during journeys is taken as 6.66 kWh for uncontrolled and controlled charging while 3.33 kWh is chosen for controlled charging with V2G allowed, as described in next section. For an average energy consumption of 0.18 kWh/km, these values provide common daily travelled distances in European countries [37,40]. Maximum battery energy level is 16.5 kWh [45] for each EV and charging and discharging efficiencies are assumed to be 0.90 and 0.95 respectively. Table 2 shows the time periods for which either a transition or a charging operation takes place as explained in Section 4.2.4. Uncontrolled charging represents a probable charging pattern that EVs could follow in absence of control or price signals and it constitutes a reference to compare with other operation strategies. Similar approaches are found in [44,46]. In addition, a controlled operation where EVs respond to prices is considered. The performed journeys, and battery energy consumption, are the same as stated in Table 2 for uncontrolled charging, although the hourly charging power, and consequently the SOC, will be different because they are variables in the corresponding optimization procedure.
Fig. 7. Daily electricity load curves for several values of k.
Table 3 Standard deviation and demand range for different values of k. k
rk (kW) Drk (kW)
0
3
6
9
12
264.99 769.69
203.40 556.58
144.93 414.40
94.74 324.40
74.81 241.56
Case study results and discussion In order to illustrate the performance of the proposed model, some results referred to the final electricity load curve and EVs charging with DSM strategies are presented. According to the ideas presented in Section 3, the influence of parameter ‘‘k’’ on the agents profits and costs is studied and the system performance is analyzed in terms of active power losses and line apparent power flows. Firstly, the effect of the number of periods ‘‘k’’ that loads can be shifted on flattening the demand curve is shown in Fig. 7. For four different values of ‘‘k’’, the final electricity load curve is represented; obtained once the corresponding optimization problems are performed for each agent according to the ideas presented in Section 3. Results reveal that higher values of this parameter allocate the demand more efficiently, in other words, the total grid load is more uniformly distributed along time periods. Note that the load is shifted from time periods when higher prices are expected, for instance the end of the day, to time periods with lower expected prices, e.g. night and some afternoon time periods. To compare the final demand curve for different values of parameter ‘‘k’’, the standard deviation rk and demand range Drk , defined as the difference between the hourly maximum and minimum values of the demand, are given in Table 3. It is demonstrated that as the value of ‘‘k’’ is increased the standard deviation and demand range are reduced and, on that account, the load curve is flatter. The combined impact of EVs and DSM strategies on the load curve is analyzed next. For EVs operating under uncontrolled charging, considering the charging pattern given in Table 2, the demand peak is increased with respect to the initial load curve when DSM is not applied, Fig. 8. When EVs are charged responding to hourly prices, and DSM is performed at the same time, the load
Table 2 Electric vehicle connection pattern for uncontrolled charging. EVs EV1–EV4 EV5–EV6 EV7 EV8–EV9 EV10–EV11 EV12 EV13–EV14
Transitions
Charging periods
t7 ; t 19 t8 ; t 19 t8 ; t 18 t8 ; t 15 t9 ; t20 t9 ; t 19 t9 ; t 18
t 20 ; t21 ; t 22 ; t 23 t 20 ; t21 ; t 22 ; t 23 t 19 ; t 20 ; t 21 ; t 22 t16 ; t17 ; t18 ; t19 t21 ; t22 ; t23 ; t24 t 20 ; t21 ; t 22 ; t 23 t 19 ; t 20 ; t 21 ; t 22
Fig. 8. Daily electricity load curves with EVs charging.
shifting makes it possible to reduce the demand peak and flatten the final load curve; shifting the charging to the night hours where prices are more favorable. If V2G is allowed, i.e. EVs discharge is permitted in the optimization problem, for a battery energy consumption in transitions according to Table 2, no V2G is finally carried out. This result can be justified taking into account that the particular EV constraints are satisfied if the SOC of the EVs is high enough to perform the arranged journeys and V2G. In other words, if consumption in transitions and the maximum SOC for EVs are of similar magnitude, there is no flexibility for allowing V2G in a economical way. If consumption in transitions is reduced to one half of the initial considered amount, V2G takes place in the most favorable time periods, Fig. 9. Similar results could have been obtained increasing the capacity of the battery of the EVs and keeping the previous battery energy consumption in journeys. Regarding EVs behavior, the SOC for EV1 vehicle, when different strategies are applied, is depicted in Fig. 10. For uncontrolled charging, the EV charges at the end of the day until maximum battery energy level. In case controlled charging is considered, the EV charges during night hours taking advantage of better buying prices. Additionally, if V2G is available, the EVs discharges at time periods t 20 and t21 when higher selling prices are expected providing additional profits. Finally, some economical and technical aspects of the proposed approach, profits/costs of the agents and system performance, are presented. For different values of the parameter ‘‘k’’, total income,
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Fig. 12. Total losses and maximum power.
Fig. 9. Daily electricity load curves with V2G allowed.
Fig. 13. Income and costs.
Fig. 10. State of charge for different strategies EV 1.
costs of non-renewable generation and costs of the energy bought, considering all the involved agents, are represented in Fig. 11. Although non-renewable generation cost increase as ‘‘k’’ grows, the income and costs of the energy bought increase and decrease respectively at a higher peace. Hence, the overall agents profit is improved through DSM utilization. From the technical point of view, total active losses slightly decrease as parameter ‘‘k’’ gets higher while average maximum line apparent power is reduced up to a certain limit, Fig. 12. The effect of DSM in losses is important at first but the variation is not very clear based on the value of ‘‘k’’ so that the power flow in lines is of similar magnitude in the different cases. However, the grid is less stressed during the last hours of the day when DSM is applied but high values of ‘‘k’’ can provoke the opposite behavior.
Fig. 11. Total income and costs.
In regard to EVs, in Fig. 13, total EVs charging costs and EVs discharging income are represented for the different cases considered. When EVs charge under the uncontrolled approach the average costs for an EV full charge can be estimated in 22.30 € while in controlled charging with and without V2G are roughly 9.90 € and 9.25 € respectively. Thus, DSM offers clear benefits to owners of EVs although the V2G use deserves a deeper consideration due to the small difference in charging prices. Conclusion A SG model relying on DSM strategies has been proposed. In this model, agents are modeled through optimization problems, with the possibility of flattening of the daily electricity load curve, shifting the demand from one time period to other time periods in response to hourly prices. It has been shown that it can be applied to common grid loads and EVs charging, helping to allocate the demand more efficiently. The particular characteristics of the load curve, the requirements for EVs mobility, as well as the hourly prices configuration, have been taken into account. Some input data of the model have to be chosen to allow for a suitable management of load shifting and EVs charging from each agent’s point of view, achieving a better use of the existing infrastructure through a reduction in losses and line power flows. For instance, small values of parameter ‘‘k’’, around 3 or 4 time periods, allow to maximize the expected profits or to minimize the costs of the agents and to improve the shape of the load curve. Results have shown that the deviations with respect to the mean for the final load curve can be decreased more than 70% with a significant reduction between the hourly maximum and minimum values of the demand. V2G capabilities have been also considered, thus including the possibility of obtaining additional profits for EVs owners and reducing the demand in time periods with high demand. The effect
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of the EVs on the load curve for the case study presented is small and bigger fleets of EVs have to be considered to improve the flattening of the load curve. Acknowledgment
[23]
[24] [25]
The authors would like to acknowledge the financial support from the Ministerio de Economía y Competitividad through Project ENE-2011-27495 and from the Junta de Andalucía through Proyecto de Excelencia with Ref. 2011-TIC7070.
[26]
[27]
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Demand-side management in smart grid operation considering electric vehicles load shifting and vehicle-to-grid support M.A. López ⇑, S. de la Torre, S. Martín, J.A. Aguado Department of Electrical Engineering, Universidad de Málaga, Spain
a r t i c l e
i n f o
Article history: Received 12 February 2014 Received in revised form 16 July 2014 Accepted 19 July 2014
Keywords: Demand-side management Electric vehicles Smart grid Vehicle-to-grid
a b s t r a c t Demand fluctuation in electric power systems is undesirable from many points of view; this has sparked an interest in demand-side strategies that try to establish mechanisms that allow for a flatter demand curve. Particularly interesting is load shifting, a strategy that considers the shifting of certain amounts of energy demand from some time periods to other time periods with lower expected demand, typically in response to price signals. In this paper, an optimization-based model is proposed to perform load shifting in the context of smart grids. In our model, we define agents that are responsible for load, generation and storage management; in particular, some of them are electric vehicle aggregators. An important feature of the proposed approach is the inclusion of electric vehicles with vehicle-to-grid capabilities; with this possibility, electric vehicles can provide certain services to the power grid, including load shifting and congestion management. Results are reported for a test system based on the IEEE 37-bus distribution grid; the effectiveness of the approach and the effect of the hourly energy prices on flattening the load curve are shown. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction The transition towards the Smart Grid (SG) requires to incorporate new functionalities and capabilities to the existing electricity grid. Among some identifiable features, distributed generation is a common characteristic of the SG and, in addition, the nature of these generators is varied since they can be non-dispatchable renewable, such as wind turbines or photovoltaic panels, combined heat and power, fuel cells, microturbines or diesel-powered plants. Devices which are able to store energy, like electric fixed batteries, can help the system to smooth the intermittent behavior of renewable sources enabling an easier integration. The next generation of the electricity grid will also pave the way to electrified transportation [1]. SGs comprise different entities that can interact with each other bidirectionally, giving the possibility to establish commercial relationships to serve and request electric energy or to solve technical problems that could arise, thus empowering the consumer. These entities within the SG can respond to changes in the prices at which the energy is bought and sold to the main grid with the objective of minimizing the costs of the energy they need or ⇑ Corresponding author. E-mail addresses: [email protected] (M.A. López), [email protected] (S. de la Torre), [email protected] (S. Martín), [email protected] (J.A. Aguado). http://dx.doi.org/10.1016/j.ijepes.2014.07.065 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
maximizing the income from the energy they sell. Among the many features that make a grid smart, the essential aspect is the integration of power system engineering with information and communication technologies. In turn, this integration can allow for advances in reliability, efficiency and operational capability [2]. Among other interesting characteristics of SGs, the concept of Demand-Side Management (DSM) has attracted the attention of many researchers and, among DSM strategies, demand response has been widely considered [3–5]. Demand response can be understood as voluntary changes by end-consumers of their usual consumption patterns in response to price signals [6]. Along with the savings regarding electricity bills, this kind of schemes can be used to avoid undesirable peaks in the demand curve that take place in some time periods along the day, resulting in a more beneficial rearrangement [7–10]. Through the use of DSM, several benefits are expected, like the improvement in the efficiency of the system, the security of supply, the reduction in the flexibility requirements for generators or the mitigation of environmental damage, although some challenges have to be overcome starting from the lack of the necessary infrastructure [11]. In addition, the introduction of DSM has to be conceived taking into account other distributed energy resources technologies that could be present in SGs [12,13]. In regard to this, several SG projects worldwide are underway or have been completed [14,15].
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Nomenclature Pmin v Indexes and sets t; T index and set for time periods, t 2 T e; E index and set for the scenarios used to model the uncertainty, e 2 E i; R index and set for renewable generators belonging to the agent, i 2 R j; G index and set for non-renewable generators belonging the agent, j 2 G b; B index and set for batteries belonging to the agent, b 2 B v; H index and set for electric vehicles belonging to the agent, v 2 H n; A index and set for demand nodes of the agent, n 2 A tm ; T M index and set of transitions periods for the electric vehicles belonging to the agent, t m 2 T M jaj the cardinality of a set a Parameters We probability of scenario e ^ kbt main grid hourly forecasted buying price in time period t (cents €/kWh) ^ kst main grid hourly forecasted selling price in time period t (cents €/kWh) PR;e renewable power output for generator i in time period t i;t for scenario e (kW) X parameter related to capacity constraints of the agents Hn;t total demand prior to load shifting for bus n in time period t (kW) fe fraction of the total demand that can be shifted /n;t fixed demand for bus n in time period t (kW) cn;t maximum shiftable demand for bus n in time period t (kW) k maximum number of periods that demand can be shifted (hours) k rate between maximum shiftable demand and fixed demand, constant for all periods and nodes kd upper bound for the change in the value of shiftable demand between two consecutive periods, constant for all the periods and nodes (kW) lj variable cost for non-renewable generator j (cents €/ kW) ij fixed cost for non-renewable generator j (cents €) fj start-up cost for non-renewable generator j (cents €) 1j shut-down cost for non-renewable generator j (cents €) Pmin g;j
Pd;max b
minimum power output for non-renewable generator j (kW) maximum power output for non-renewable generator j (kW) maximum discharging power for battery b (kW)
Pc;max b
maximum charging power for battery b (kW)
Smax b
maximum state of charge for battery b (kWh) charging efficiency for batteries discharging efficiency for batteries
Pmax g;j
gC gD
In order to simplify the implementation of the proposed approach in real systems, most of the actions in the SG are taken by the agents. In order to take these actions, the agents act on their own interest; sometimes, however, they make use of additional information provided by the SG operator. The individual decisions of the agents can only be slightly corrected by the SG operator (centralized correction) in order to correct the violation of technical constraints in the SG, in case they arise.
Pmax v Smax v
jtv #
minimum charging or discharging power allowed for electric vehicles (kW) maximum charging or discharging power allowed for electric vehicles (kW) battery capacity of electric vehicle v (kWh) kilometers covered by electric vehicle v in time period t (km) average battery consumption (kWh/km)
Variables PS;e power sold in time period t for scenario e (kW) t PtB;e
power bought in time period t for scenario e (kW)
C G;e t;j
non-renewable generation cost for generator j in time period t for scenario e (cents €) power output for non-renewable generator j in time period t for scenario e (kW) discharging power for battery b in time period t for scenario e (kW) charging power for battery b in time period t for scenario e (kW) discharging power for electric vehicle v in time period t for scenario e (kW) charging power for electric vehicle v in time period t for scenario e (kW) optimal demand for bus n in time period t for scenario e (kW) optimal shiftable demand for bus n in time period t for scenario e (kW) amount of demand that goes from time period t to time period t 0 for bus n and scenario e (kW) state of charge for battery b in time period t for scenario e (kWh) state of charge for electric vehicle v in time period t for scenario e (kWh)
PG;e r j;t Pd;e b;t Pc;e b;t Pd;e v ;t Pc;e v ;t
Uen;t
Cen;t M en;t;t0 Seb;t Sev ;t
Binary variables bet binary variable that takes the value ‘‘1’’ if the agent is buying in time period t for scenario e, and ‘‘0’’ otherwise v G;e binary variable that takes the value ‘‘1’’ if generator j is t;j running in time period t for scenario e, and ‘‘0’’ otherwise yG;e binary variable that takes the value ‘‘1’’ if generator j t;j starts up in time period t for scenario e, and ‘‘0’’ otherwise sG;e binary variable that takes the value ‘‘1’’ if generator j t;j shuts down in time period t for scenario e, and ‘‘0’’ otherwise yd;e binary variable that takes the value ‘‘1’’ if electric vehiv ;t cle v is discharging in time period t for scenario e, and ‘‘0’’ otherwise yc;e binary variable that takes the value ‘‘1’’ if electric vehiv ;t cle v is charging in time period t for scenario e, and ‘‘0’’ otherwise
To make decisions each agent poses an optimization problem to maximize its profit over a set of periods, they can perform DSM strategies and Vehicle-to-Grid (V2G). As energy prices are usually higher for high demand periods, the optimization problems result in a flattened load curve. Following the regulatory trends in many countries, in particular in countries in Europe [16], the renewable generation in the model is also prioritized over the conventional generation. The framework considers market and technical
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operation of the grid, and it is illustrated in a case study modeling a SG based on IEEE 37-bus distribution grid. The rest of the paper is organized as follows: in Section 2, the related work and paper contributions are introduced. Then, Section 3 presents a proposal for the SG operation, referred as problem statement, including the description of the operational algorithm steps previously mentioned. Section 4 focuses on DSM strategies, describing the optimization problems in detail and providing models of the different elements included. The case study and results are presented in Section 5. Finally, conclusions are drawn in Section 6.
Related work and contributions Many works are found in the literature investigating DSM benefits and SG modeling. Some of them cover problems regarding scheduling appliances based on pricing models; for instance, in [17], a voluntary household load shedding model is studied in order to keep the system in secure conditions with respect to demand peaks. Using two different methodologies, the benefits of DSM for both the consumers and utilities are shown in [18,19], stressing the importance of identifying the flexible loads. In comparison to these works, in this paper, operation of appliances is not considered and, instead, a fraction of the initial demand is assumed to be shiftable. In addition, agents with generation or storage assets are included in our formulation, while the previous works only stress the role of consumers. Other authors study how the demand can be allocated through optimization problems based on utility functions and other specific constraints. In [20], the objective of the proposed model is to maximize the utility of a consumer subject to a minimum daily consumption level and restrictions over load levels including price uncertainty. Authors in [21] consider the problem of maximizing the social welfare expressed as the sum of utilities of consumers minus the energy provider costs. In [22], a similar approach is proposed but uncertainty in renewable power generation is addressed and supply and demand are coordinated in two different time scales. The extension to several energy providers and the joint consideration of distributed and renewable generation units, storage devices, active demand and EVs is studied in [23]. One common aspect in these works is that the demand is calculated depending on the constraints, while in our work the total demand over the time horizon is known and it is only arranged differently. Moreover, the proposed model considers the maximization of the agents profit, whereas the social welfare or the utility functions are considered in [21–23]. Finally, only in [23] several elements present in SGs are modeled in a similar way to our proposal and, although some aspects are similar the way the demand is allocated is completely different. Finally, DSM can also be applied to EVs and, for this reason, they may be also influenced by price signals changing their location or their consumption pattern if needed. We propose a optimizationbased model applicable to EVs considering that EV load can be shifted based on charging prices. V2G can be also performed to get additional profits. Some related papers are described next. The impact of EVs on the demand profile is analyzed in [24] and, in [25], the authors try to integrate EVs with demand response strategies involving the consumer. In these works, EVs contribution is included through simple policies with no formal mathematical modeling of EVs load management and without considering V2G. In [26], a game theoretic approach is proposed to schedule EVs charging for peak shaving and valley filling while, in [27], V2G is also considered for this purpose; developing an optimization problem that aims at getting a final load profile close to a target load curve. In [28], a coordination mechanism is proposed
691
to allocate EVs charging efficiently, stressing the role of renewable energy. EVs can also be managed to solve technical problems, like line congestion, through the change in the initial expected charging pattern [29]. Other authors consider a specific smart load management approach that can be applied to EVs but focusing on technical aspects like losses minimization or voltage limits without including market issues [30]. According to the ideas presented, the main contributions in this work are: The formulation of a particular DSM strategy based on optimization problems where the profit maximization of all the involved agents is pursued. An algorithm to optimize the hourly allocation of demand and generation, taking into account technical constraints and enabling the EVs and renewable resources integration.
Problem statement The problem is posed on a SG that includes distributed generation (renewable and non-renewable), and EVs that can perform V2G operations. We study the operation in a typical day on a hourly basis, under the assumption that a similar operation could be done for each day. The problem is multi-period and thought to be applied for planning purposes, that is, not in real time. The agents in the considered SG can be of two types: (a) EVs, these agents can move among the nodes in the network, also one agent could aggregate several EVs and (b) agents that are always connected to the same node, these agents can be composed of a combination of: loads, renewable generators, non-renewable generators, and batteries. The SG architecture and examples of possible agents in the SG are illustrated in Fig. 1. The focus is on load shifting made by agents in the SG (rescheduling their loads) based on their profit maximization (generators) or cost minimization (pure loads). The number of periods that loads can be shifted, forward or backward, is referred to as ‘‘k’’, and it is an exogenous parameter in the proposed model. We study the results for different values of ‘‘k’’ because of two main reasons: (I) to evaluate the incentive (difference in profit or cost) that agents have to perform load shifting, and the resulting system performance (integration of renewable generation, losses, line apparent power flows, etc.) and (II) to evaluate the feasibility of the strategy, the higher the value of ‘‘k’’ the more difficult the strategy will be to apply for the agents in the real systems. In practice, it is interesting to understand what different values of parameter ‘‘k’’ mean for consumers and know other papers dealing with similar concepts. For instance, values of ‘‘k’’ below 3 h could be applied to cooling
Fig. 1. Agents considered in the smart grid.
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devices, through appropriate control signals, due to temperature restrictions [31]. In addition, air conditioning in commercial and residential areas has turned out to be the main responsible of demand peak in some countries and, thus, it is an ideal candidate for load shifting with higher values of this parameter [32,33]. Values between 2 h and 8 h have been considered by some authors as well to study reductions in distribution losses [34]. The agents can sell or buy energy, if it is technically feasible for them, (from/to) (other agents/the main grid). Each agent makes its own decisions, and there are not centralized decisions. The main grid is considered as a slack node with infinite capacity. The proposed model for the SG operation consists of two sequential stages, first a market based solution is calculated, and second the technical feasibility of the previous solution is checked in a technical operation stage. The SG operation along with these stages can be integrated in an specific operational algorithm, Fig. 2. In the first stage each agent makes decisions, for each period, about the quantities to generate, to buy from the main grid or the SG, its load shifting, and to sell its generation to the main grid or to the SG. Agents can choose between trade among them inside the SG, then the energy prices (selling and purchase) are determined by an internal auction based on the agents bids, or to trade with the main grid. The internal auction is ruled by the SG operator. Agents have to face two sets of parameters with uncertainty, on one hand the energy selling/purchase prices to/from the main grid, and on the other hand the available generation of the renewable resources. Both sets or parameters are modeled through scenario trees. They are also data, the initial energy demand for each agent (for each period) and the rate of that demand they can shift. To make their decisions, each agent poses an optimization problem. This problem is a mixed integer linear programming in the general case and a linear programming in some particular cases. We give a general description of these optimization problems in
what follows, and they will be described in detail in the next section. These optimization problems consists of an objective function and a set of constraints. Agents make decisions based on their profit maximization, thus the objective function is the expectation on the set of scenarios of the agents profit. The agents profit is defined as the income from selling energy minus the costs from generation and/or energy purchase. The set of constraints is made up of the technical constraints for each particular component of the agent, for instance, the capacity bounds for generators, and the bounds for the energy flow from/to batteries or EVs. Finally, in the second stage, a load flow is used to check the technical feasibility of the previous solution. In this stage, the active losses in the network lines are calculated (we only consider the active losses) in the network lines and the technical constraints are checked, in particular the node voltage bounds and the apparent power in the lines. If some bounds are violated then a correction to the initial solution is applied, and the new result is again checked. We apply the correction algorithm described in [35], that minimizes the changes with respect to the initial solution. Description of the agent strategy In this section, the strategy followed by the agents to make their decisions regarding load shifting is described. In what follows, first the different SG elements of the agents and the main related parameters and variables are introduced. Then, the agent optimization problem, consisting of an objective function and a set of constraints, is presented. Smart grid elements The SG elements considered in this work are presented here. Each agent is considered to be formed of four possible components: loads, generators, batteries or EVs. Loads are characterized by a fraction of the total demand that can be shifted and they depend on the time period and the node in the more general case. Thus, the initial predicted demand Hn;t is defined as the sum of fixed demand /n;t and the shiftable component cn;t , expressed as a fraction f e of the total demand, in every node and time period; this can be written as:
Hn;t ¼ /n;t þ cn;t ¼ /n;t þ f e Hn;t
8t;
8n
ð1Þ
Once the agent makes the decision, based on the results from its optimization problem, the total demand changes to Uen;t and the optimal shiftable demand to Cen;t . Fig. 3 illustrates the limits for demand in the proposed load shifting mechanism. The maximum number of periods that loads can be shifted forward or backward is an exogenous parameter ‘‘k’’, explained in the previous section. It is assumed that part of the agent loads can be
Fig. 2. Flow chart of the operational algorithm.
Fig. 3. Parameters and variables related to the demand.
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shifted [36]. The agent can access to the necessary information, like hourly energy prices, generation costs or weather historical data, to decide how and when it is more favorable to satisfy its demand. Generators can be of two types: non-renewable and renewable. Non-renewable generator j is characterized by its operational cost, that is made up of the variable cost lj , fixed cost ij , start-up cost fj and shut-down cost 1j . Its operation is mainly conditioned on the relation between generation costs and energy prices. Techmax nical bounds for power output, P min g;j and P g;j , are also considered. The power supplied by renewable generators, namely photovoltaic panels and wind turbines, is modeled as a set of scenarios. The specific values are calculated using real generator models and real values of wind speed and solar radiation; these values are combined to get an overall number of different scenarios corresponding to representative situations that take place during the year. We follow the current regulatory trends, proposed in many countries, in particular in Europe [16], that prioritize the use of low emission renewable generators over the conventional generators, even if some subsidy is needed to make the operation feasible. In this regard in our model the renewable generation is prioritized over the conventional generators in the optimization problems assuming a zero generation cost for them (but we do not consider subsidies explicitly in the model). We consider the renewable generation as a parameter with values given by an scenario tree, and that all the available renewable generation is used in the system (no spillage). In case the renewable generation is greater than the demand in the SG, the excess of generation is transferred (sold) to the main grid through the connection node. Fixed storage devices are represented by bank of electric batteries in this work. Fixed batteries are modeled taking into account the following aspects: (i) A battery can charge (absorb energy from the grid) or discharge (inject energy to the grid) considering operational efficiencies gC and gD respectively, (ii) there is a limit for the power drawn or supplied by a battery b; Pc;max and Pd;max , and b b (iii) the energy contained in the battery is tracked considering its State of Charge (SOC) Seb;t . Finally, mobile storage devices are represented by electric vehicles. Similar aspects enumerated for fixed batteries are applied for electric vehicles although some additional considerations are needed to define appropriately the mobility model. We consider two models for the EVs, the uncontrolled operation and the operation controlled by an aggregator [37], because they model two common situations in real systems, the individual user and a company fleet. In the uncontrolled situation we assume that EVs follows a fixed pattern, that is defined by three kinds of time periods: Transition, charging periods, and resting periods. During the transition periods the EVs move on the network and they consume the energy in their battery. In the charging periods the EVs consume energy from the network. And during the rest periods the EVs neither consume their own energy nor charge energy from the network. In this case the values of the energy flows in each periods are also fixed quantities. Two parameters are needed to determine the energy consumption (kWh) in transitions: (i) Parameter jtcm is the amount of kilometers covered in time period t m and (ii) parameter # that represents the energy consumption in kWh/km. In the case of operation controlled by an aggregator only the transition periods and their corresponding energy consumption are fixed. For the other periods, the aggregator makes the decision on when to charge and the quantity to consume from the network, they can perform V2G in these periods. Optimization problem description In this section, the mathematical relationships between the parameters and variables with respect to the elements of each
agent are developed in the form of an optimization problem, for the general case it is a mixed integer linear programming. First the objective function is described, and next the set of common constraints (balancing and DSM), and the set of constraints for each possible component of the agents (generators, batteries, EVs) according to the ideas described in Section 4.1 are presented. The number of equations, continuous variables, binary variables and execution time for the optimization problem of each agent, as described in Section 5.1, is given in Table 1. The corresponding values mainly depend on the SG elements of each agent and they can be calculated with the following equations: The number of equations is:
jTjjEj ð3 þ 2jGj þ 4jBj þ 3jHj þ 3jAjÞ þ jEj ðjBj þ jHj ð1 2jT M jÞÞ The number of continuous variables is:
jTjjEj ðjGj þ 3jBj þ 2jHj þ 2Þ þ jAjjEj ð2jTjk k ðk þ 1ÞÞ The number of binary variables is:
jTjjEj ð3jGj þ jBj þ 2jHj þ 1Þ The simulations were carried out in a computer Intel Core 2 Duo @ 3 GHz with 4 GB RAM. The software GAMS (using the CPLEX optimizer) was used to perform the optimization problems linked with MATLAB as a support to coordinate the execution of these problems, store data and make graphical representations. Regarding the objective function, the agents maximize their expected profit, that in the more general case is defined by: tf jEj jGj X X X ^kb PS;e ^ks P B;e We C G;e nmaximizeo t t t t t;j P S;e ;PB;e ;C G;e t t t;j
e¼1
t¼t 0
! ð2Þ
j¼1
where ^ kbt and ^ kst are the hourly forecasted buying and selling market prices (parameters), P B;e and P S;e are the hourly power bought and t t G;e sold (variables) and C t;j represents the function of generation costs for non-renewable generator j, defined in Section 4.2.2, t 0 is the initial time period and t f is the final time period. For a particular agent, some terms in Eq. (2) are fixed to zero depending on the agent composition, for instance if it contains only generators or only loads. From the historical data in real power systems, for instance in the Spanish system [38], we observe that average prices are higher for higher demand. Thus, the consequence of profit maximization for agents is that they try to shift their load to the periods with the lowest prices, and the demand curve is flattened. Common constraints (balancing and DSM) The constraints common to all the optimization problems include the energy balancing and DSM constraints. The balancing constraint relates PB;e and PS;e with the power t t supplied from generators, the bus load and the power drawn or
Table 1 Solving time and number of variables for agents optimization problems. Agent 1 2 3 4 5 6 7 8
Equations
Continuous
Binary
Execution time (s)
36,960 19,584 28,800 23,040 19,584 20,736 17,280 3144
150,336 84,096 125,568 104,256 84,096 103,104 82,944 2160
3456 4608 8064 4608 4608 1152 1152 2088
1.155 0.577 0.796 0.671 0.592 0.827 0.561 0.032
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delivered from batteries for each agent. According to Eqs. (3)–(5), variables P S;e and PB;e cannot be different from zero at the same t t time period, that is, whenever one of them is different from zero, the other one must equal zero. Thus, an agent is not allowed to buy and sell simultaneously: B;e PS;e t Pt ¼
jRj jGj jBj jAj X X X X c;e P R;e PG;e ðP d;e Uen;t i;t þ j;t þ b;t P b;t Þ i¼1
j¼1
8t; 8e:
n¼1
b¼1
ð3Þ e 0 6 PB;e t 6 bt X 8t; 8e
ð4Þ
e 0 6 PS;e t 6 ð1 bt Þ X; 8t; 8e
ð5Þ
G;e d;e where PR;e i;t ; P j;t and P b;t are the hourly power supplied for renewable generator i, non-renewable generator j and battery b; Pc;e b;t is the hourly power absorbed by battery b and Uen;t is the total demand in node n. Note that terms for batteries are extensible for EVs. Eqs. (4) and (5), which constitute an application of the Big-M method [39], assure that an agent cannot buy and sell at the same time through binary variable bet . Finally, X is a large enough parameter that can be fixed taken into account the capacity constraints for a particular agent, for instance the capacity of the lines feeding the agent. The DSM constraints for each agent, which regulate how the loads can be shifted between periods, are expressed in the following way:
Uen;t ¼ /n;t þ Cen;t Uen;t
8t; 8n; 8e
X e X e ¼ Hn;t þ M n;t0 ;t M n;t;t0 t0
Cen;t ¼ cn;t þ
t0
t0
(
M en;t;t0 ¼ 0 if
8t; 8n; 8e 8t; 8n; 8e
kd 6 C
ð8Þ
t0
8t; 8n; 8e 0
t¼t; t þ k < t 0 or t 0 þ k < t
0 6 Cen;t 6 k /n;t 8t; 8n; 8e e n;tþ1
ð7Þ
t0
X e X e M n;t0 ;t M n;t;t0
X e M n;t;t0 6 cn;t
ð6Þ
C
e n;t
6 kd 8t; 8n; 8e
ð9Þ ðaÞ
8n; 8e ðbÞ
ð10Þ ð11Þ ð12Þ
In Eq. (6), the optimal demand Uen;t (variable) that is really consumed in time period t, is expressed as the sum of fixed demand /n;t (parameter) and Cen;t (variable) which represents the optimal shiftable for node n in time period t. Total demand for node n and period t is written in (7) in terms of the amount of energy that is shifted from other periods t 0 to the current period t; M en;t0 ;t , minus the amount of energy that leaves period t to other period t 0 ; M en;t;t0 , for each node n and scenario e. Eq. (8) defines a similar relation compared to (7) but in terms of the optimal shiftable demand. In practice, either (7) or (8) should be used. Eq. (9) expresses the limit for the total amount of energy that can be shifted to other time periods. The variable Men;t;t0 also has to satisfy logical relationships needed to model load shifting through parameter ‘‘k’’. Condition (10a) assures that the demand cannot be shifted to the same time period; condition (10b) sets that demand cannot be shifted more than k periods forward and backward and it has to stand true 8t and 8t0 . Finally, to allow for a smooth transition for the final demand curve, some conditions are applied. These conditions are represented by a bound in the demand that can be shifted and bounds for the slope of the curve expressed by Eqs. (11) and (12) respectively. Parameter k is set depending on the willingness of the agent to shift the loads conditioned by the activities it develops
in its area. Parameter kd can be chosen taking into account operational constraints in the grid, like the capability of supporting sharp demand changes between two consecutive time periods. Generators modeling The constraints and equations taken into consideration for agents with non-renewable generators are given next: G;e G;e G;e G;e C G;e 8t; 8j; 8e t;j ¼ lj P t;j þ ij v t;j þ fj yt;j þ 1j st;j
v
G;e t;j
Pmin g;j
6
PG;e t;j
6v
G;e t;j
Pmax g;j
8t; 8j; 8e
G;e G;e G;e yG;e t;j st;j ¼ v t;j v t1;j 8t; 8j; 8e
ð13Þ ð14Þ ð15Þ
Eq. (13) defines the generation cost for a non-renewable generator based on the operational costs defined previously. Binary variables G;e G;e v G;e t;j =yt;j =st;j are equal to 1 in case that during the current time period, the generator: Is already running/starts-up/shuts-down, and 0 in any other case. Eq. (14) establishes the power output technical bounds, and (15) sets the relation among the binary variables which represent start-up, shut-down and generator operation. Renewable generators are modeled following the ideas presented in Section 4.1. Fixed batteries modeling For electric fixed batteries the following constraints are included in the optimization problem: d;max d;e 0 6 P d;e 8t; 8b; 8e b;t 6 yb;t P b
ð16Þ
c;max d;e 8t; 8b; 8e 0 6 P c;e b;t 6 ð1 yb;t Þ P b
ð17Þ
06
Seb;t
6
Smax b
8t; 8b; 8e
ð18Þ
d;e Seb;t Seb;t1 ¼ gC Pc;e b;t ð1=gD Þ P b;t 8t; 8b; 8e
ð19Þ
Seb;t0
ð20Þ
¼
Seb;tf
8b; 8e
Eqs. (16) and (17) models the bounds for the hourly maximum and minimum power supplied and drawn from battery b; Pd;e b;t and d;max Pc;e and Pc;max . Binary variable yd;e b;t , through P b b b;t ensures that the battery is not charging and discharging at the same time. The battery SOC Seb;t has to lie between 0 and a maximum value Smax b expressed in (18). Eq. (19) represents the energy balance for the battery through charging and discharging efficiencies. Finally, Eq. (20) guarantees that the initial and final SOCs, Seb;t0 and Seb;tf respectively, must be identical in order to avoid non-realistic solutions. Electric vehicles modeling The constraints that a controlled EV adds to the optimization problem are similar to the constraints modeled by Eqs. (16)–(20) described in Section 4.2.3. However, to comply with the standard IEC 61851, charging and discharging power are modeled as semicontinuous variables: min d;e max d;e yd;e 8t; 8v ; 8e v ;t P v 6 P v ;t 6 yv ;t P v
ð21Þ
min c;e max c;e yc;e 8t; 8v ; 8e v ;t P v 6 P v ;t 6 yv ;t P v c;e d;e yv ;t þ yv ;t 6 1 8t; 8v ; 8e
ð22Þ ð23Þ
d;e where binary variables yc;e v ;t and yv ;t define if EV v is charging or discharging. According to Eqs. (21)–(23) an EV is not allowed to charge and discharge at the same time period, that is, if the variable representing charging power P c;e v ;t is positive and different from zero then the variable representing discharging power Pd;e v ;t is zero and vice versa. In addition, charging and discharging power can take values max within the minimum and maximum power bounds, Pmin v and P v respectively.
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In addition, two constraints are included representing the mobility model adopted:
Sev ;te ¼ Smax 8v ; 8e v Sev ;tm þ1 ¼ Sev ;tm jtcm #
ð24Þ t m 2 T M ; 8v ; 8e
ð25Þ
e
Eq. (24) states that EV SOC Sv ;t has to be maximum in period t e . The EV SOC is reduced according to (25) when it is moving during time period t m , that is, in transition between two connections to the grid [37,40]. Case study and results To illustrate how the proposed method works, it is applied to a case study for the SG depicted in Fig. 5. Different operating conditions characterized by the number of periods that loads can be shifted, parameter ‘‘k’’, are studied. The SG consist of 8 agents, with 2 renewable generators, 5 non-renewable generators, 2 batteries and 14 EVs on a network based on the IEEE-37 bus distribution grid [41]. In what follows, first the data for the case study are described and second the main results regarding the questions posed in Section 3 are presented and discussed. Case study data The data for the case study are: (i) the initial demand curve of the agents, (ii) the scenario tree for energy prices and renewable generation, and (iii) the parameters for the DSM constraints and the models for the technical operation of the agents. A typical demand curve from a real distribution grid is assumed and selling/purchase prices are set to represent three different scenarios; hourly average historical values for prices [38] are defined along with a high prices scenario, defined by the extreme value of the blue bar, and a low prices scenario, defined by the extreme value of the orange bar, and corresponding to the 110% and 90% of the average prices respectively, Fig. 4. The sum of the hourly demand along the 24 h of the day is constant although DSM operations can change the hourly values, that is, the demand is rearranged. Load buses, generators, batteries and EVs considered in the case study are represented in Fig. 5, where grid areas belonging to the seven defined SG agents are labeled with circled numbers. Another agent, an EV aggregator, is responsible for providing the energy needed by EV owners to perform their daily trips. In relation to renewable generators, Fig. 6 shows the hourly power output for the wind and the photovoltaic plants considered. Note that 4 scenarios are used for each renewable source. Combining them, 16 scenarios are obtained, representing typical situations. The values of f e ¼ 0:15 and k ¼ 2:5 are relatively small and have been considered in order to limit the load shifted without
Fig. 4. Demand curve and price scenarios.
Fig. 5. IEEE 37-bus distribution case study.
Fig. 6. Renewable generators scenarios.
implying non-realistic activities re-scheduling of the agents. Also, we consider a maximum value of k = 12, because a larger value implies in practical terms a great re-scheduling effort for agents, and the solutions would have to be defined over intervals of more than 24 periods (several days). The parameter kd is fixed to a value of 0.75 kW considering the average amount of energy trade in the system and the power capacity installed. A total number of 14 EVs is considered here. For the EVs uncontrolled charging pattern, EVs charge at a rate of 3.7 kW [42,43] during four time periods at the end of the day, as soon as they arrive from the last journey of the day; then the EVs idle for the remaining time periods. It is also considered that each EV performs two journeys, called transitions, and each one is attached to a particular time period. The assumption of two journeys per day and the charging timing preference is a reasonable assumption as shown for example in surveys like [44]. During transitions, EVs consume a certain amount of energy equal to half the total EV individual charging and they commute between the initial node represented
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in Fig. 5 and the closest node, assumed for the purpose of this work. Specifically, the battery consumption during journeys is taken as 6.66 kWh for uncontrolled and controlled charging while 3.33 kWh is chosen for controlled charging with V2G allowed, as described in next section. For an average energy consumption of 0.18 kWh/km, these values provide common daily travelled distances in European countries [37,40]. Maximum battery energy level is 16.5 kWh [45] for each EV and charging and discharging efficiencies are assumed to be 0.90 and 0.95 respectively. Table 2 shows the time periods for which either a transition or a charging operation takes place as explained in Section 4.2.4. Uncontrolled charging represents a probable charging pattern that EVs could follow in absence of control or price signals and it constitutes a reference to compare with other operation strategies. Similar approaches are found in [44,46]. In addition, a controlled operation where EVs respond to prices is considered. The performed journeys, and battery energy consumption, are the same as stated in Table 2 for uncontrolled charging, although the hourly charging power, and consequently the SOC, will be different because they are variables in the corresponding optimization procedure.
Fig. 7. Daily electricity load curves for several values of k.
Table 3 Standard deviation and demand range for different values of k. k
rk (kW) Drk (kW)
0
3
6
9
12
264.99 769.69
203.40 556.58
144.93 414.40
94.74 324.40
74.81 241.56
Case study results and discussion In order to illustrate the performance of the proposed model, some results referred to the final electricity load curve and EVs charging with DSM strategies are presented. According to the ideas presented in Section 3, the influence of parameter ‘‘k’’ on the agents profits and costs is studied and the system performance is analyzed in terms of active power losses and line apparent power flows. Firstly, the effect of the number of periods ‘‘k’’ that loads can be shifted on flattening the demand curve is shown in Fig. 7. For four different values of ‘‘k’’, the final electricity load curve is represented; obtained once the corresponding optimization problems are performed for each agent according to the ideas presented in Section 3. Results reveal that higher values of this parameter allocate the demand more efficiently, in other words, the total grid load is more uniformly distributed along time periods. Note that the load is shifted from time periods when higher prices are expected, for instance the end of the day, to time periods with lower expected prices, e.g. night and some afternoon time periods. To compare the final demand curve for different values of parameter ‘‘k’’, the standard deviation rk and demand range Drk , defined as the difference between the hourly maximum and minimum values of the demand, are given in Table 3. It is demonstrated that as the value of ‘‘k’’ is increased the standard deviation and demand range are reduced and, on that account, the load curve is flatter. The combined impact of EVs and DSM strategies on the load curve is analyzed next. For EVs operating under uncontrolled charging, considering the charging pattern given in Table 2, the demand peak is increased with respect to the initial load curve when DSM is not applied, Fig. 8. When EVs are charged responding to hourly prices, and DSM is performed at the same time, the load
Table 2 Electric vehicle connection pattern for uncontrolled charging. EVs EV1–EV4 EV5–EV6 EV7 EV8–EV9 EV10–EV11 EV12 EV13–EV14
Transitions
Charging periods
t7 ; t 19 t8 ; t 19 t8 ; t 18 t8 ; t 15 t9 ; t20 t9 ; t 19 t9 ; t 18
t 20 ; t21 ; t 22 ; t 23 t 20 ; t21 ; t 22 ; t 23 t 19 ; t 20 ; t 21 ; t 22 t16 ; t17 ; t18 ; t19 t21 ; t22 ; t23 ; t24 t 20 ; t21 ; t 22 ; t 23 t 19 ; t 20 ; t 21 ; t 22
Fig. 8. Daily electricity load curves with EVs charging.
shifting makes it possible to reduce the demand peak and flatten the final load curve; shifting the charging to the night hours where prices are more favorable. If V2G is allowed, i.e. EVs discharge is permitted in the optimization problem, for a battery energy consumption in transitions according to Table 2, no V2G is finally carried out. This result can be justified taking into account that the particular EV constraints are satisfied if the SOC of the EVs is high enough to perform the arranged journeys and V2G. In other words, if consumption in transitions and the maximum SOC for EVs are of similar magnitude, there is no flexibility for allowing V2G in a economical way. If consumption in transitions is reduced to one half of the initial considered amount, V2G takes place in the most favorable time periods, Fig. 9. Similar results could have been obtained increasing the capacity of the battery of the EVs and keeping the previous battery energy consumption in journeys. Regarding EVs behavior, the SOC for EV1 vehicle, when different strategies are applied, is depicted in Fig. 10. For uncontrolled charging, the EV charges at the end of the day until maximum battery energy level. In case controlled charging is considered, the EV charges during night hours taking advantage of better buying prices. Additionally, if V2G is available, the EVs discharges at time periods t 20 and t21 when higher selling prices are expected providing additional profits. Finally, some economical and technical aspects of the proposed approach, profits/costs of the agents and system performance, are presented. For different values of the parameter ‘‘k’’, total income,
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Fig. 12. Total losses and maximum power.
Fig. 9. Daily electricity load curves with V2G allowed.
Fig. 13. Income and costs.
Fig. 10. State of charge for different strategies EV 1.
costs of non-renewable generation and costs of the energy bought, considering all the involved agents, are represented in Fig. 11. Although non-renewable generation cost increase as ‘‘k’’ grows, the income and costs of the energy bought increase and decrease respectively at a higher peace. Hence, the overall agents profit is improved through DSM utilization. From the technical point of view, total active losses slightly decrease as parameter ‘‘k’’ gets higher while average maximum line apparent power is reduced up to a certain limit, Fig. 12. The effect of DSM in losses is important at first but the variation is not very clear based on the value of ‘‘k’’ so that the power flow in lines is of similar magnitude in the different cases. However, the grid is less stressed during the last hours of the day when DSM is applied but high values of ‘‘k’’ can provoke the opposite behavior.
Fig. 11. Total income and costs.
In regard to EVs, in Fig. 13, total EVs charging costs and EVs discharging income are represented for the different cases considered. When EVs charge under the uncontrolled approach the average costs for an EV full charge can be estimated in 22.30 € while in controlled charging with and without V2G are roughly 9.90 € and 9.25 € respectively. Thus, DSM offers clear benefits to owners of EVs although the V2G use deserves a deeper consideration due to the small difference in charging prices. Conclusion A SG model relying on DSM strategies has been proposed. In this model, agents are modeled through optimization problems, with the possibility of flattening of the daily electricity load curve, shifting the demand from one time period to other time periods in response to hourly prices. It has been shown that it can be applied to common grid loads and EVs charging, helping to allocate the demand more efficiently. The particular characteristics of the load curve, the requirements for EVs mobility, as well as the hourly prices configuration, have been taken into account. Some input data of the model have to be chosen to allow for a suitable management of load shifting and EVs charging from each agent’s point of view, achieving a better use of the existing infrastructure through a reduction in losses and line power flows. For instance, small values of parameter ‘‘k’’, around 3 or 4 time periods, allow to maximize the expected profits or to minimize the costs of the agents and to improve the shape of the load curve. Results have shown that the deviations with respect to the mean for the final load curve can be decreased more than 70% with a significant reduction between the hourly maximum and minimum values of the demand. V2G capabilities have been also considered, thus including the possibility of obtaining additional profits for EVs owners and reducing the demand in time periods with high demand. The effect
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of the EVs on the load curve for the case study presented is small and bigger fleets of EVs have to be considered to improve the flattening of the load curve. Acknowledgment
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The authors would like to acknowledge the financial support from the Ministerio de Economía y Competitividad through Project ENE-2011-27495 and from the Junta de Andalucía through Proyecto de Excelencia with Ref. 2011-TIC7070.
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