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Operation of renewable-dominated power systems with a significant penetration of plug-in electric vehicles
Energy xxx (2015) 1e9
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Energy journal homepage: www.elsevier.com/locate/energy
Operation of renewable-dominated power systems with a significant penetration of plug-in electric vehicles n a, *, Rafael Za rate-Min ~ ano b Miguel Carrio a b
Department of Electrical Engineering, UCLM, Toledo, Spain Department of Electrical Engineering, UCLM, Almad en, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 2 July 2015 Accepted 25 July 2015 Available online xxx
This paper aims to study the operational consequences of the integration of a large number of plug-in electric vehicles in a renewable-dominated power system. The coordination between the power system operator and the charging process of plug-in electric vehicles under a smart-grid environment is modeled using several approaches. The operation of the power system is modeled by means of a network-constrained stochastic economic dispatch. This problem is formulated using a two-stage stochastic programming model in which the uncertainties associated with the charging process of plug-in electric vehicles and with the availability of the renewable sources are characterized as stochastic processes. Numerical results on a realistic case based on the Iberian Peninsula power system are provided and analyzed. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Plug-in electric vehicles Smart grid framework Stochastic economic dispatch Stochastic programming
1. Introduction PEVs (plug-in electric vehicles) are becoming an actual option to replace traditional combustion-engine cars. This fact is a consequence of several reasons; firstly, PEVs are widely considered as an effective means of reducing the carbon emissions resulting from the extensive usage of combustion-engine vehicles. The reduction of carbon emissions might result in a positive impact against the global climate change and an improvement of the air quality in our cities. Secondly, the usage of PEVs can be considered as a tool for reducing the dependency on fossil fuels and, therefore, for increasing energy supply security. This fact is particularly relevant for those countries without fossil fuel reserves. This argument is reinforced thanks to the high increase of the usage of renewable technologies for electric energy production that may be used to charge PEVs. In a scenario in which the general usage of PEVs is promoted, it is necessary to carefully analyze the impact caused by the additional demand which results from charging PEVs (hereinafter referred to as PEV demand) on the operation of power systems. That is, the operation of a power system could be at risk if an
* Corresponding author. Tel.: þ34 925268800 (5750). n), [email protected] E-mail addresses: [email protected] (M. Carrio rate-Min ~ ano). (R. Za
excessive demand is added in inadequate periods, especially during peak demand hours. In this situation, demand-side management actions could help to place this additional demand in more convenient periods. Special attention should be paid to renewable-dominated power systems, in which an important portion of the demand procurement is obtained by means of non-dispatchable generating units. For these power systems, an adequate selection of the energy and reserve schedules is vital for ensuring a safe procurement of the demand at a reasonable cost. The evolution of the communication capabilities between energy suppliers and domestic consumers will facilitate the incorporation of novel PEV charging control schemes. Moreover, the demand associated with the charging process of PEVs is suitable for demand-side management since the usage of PEVs does not coincide in time with the consumption of power from the electrical grid. In this regard, smart grids provide an adequate framework for implementing an effective communication between the ISO (Independent System Operator) and PEV users in order to manage PEV demand effectively [1]. Therefore, considering a smart grid environment, the ISO may control the charging process of PEVs to allocate the PEV demand in adequate periods from the standpoint of the system operation. The so-called G2V (Grid-to-Vehicle) and V2G (Vehicle-to-Grid) capabilities allow the ISO to exercise control over the charging process of PEVs. The G2V capability enables the ISO to decide in which periods PEVs are charged, whereas the V2G
http://dx.doi.org/10.1016/j.energy.2015.07.111 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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2
capability additionally allows the ISO to use the energy stored in the batteries of PEVs to supply part of the demand, if it is necessary. Since the publication of the pioneering work of Kempton and Letendre [2] in the late nineties analyzing the economical advantages of using vehicle-to-grid approaches, the study of the impact of PEVs and PHEVs in the power system operation has been an active research topic, especially in recent years. For example, reference [3] analyzes the usage of an electric-vehicle fleet for providing regulation services. The coordination of an electric vehicles aggregator with the system operator considering a tertiary regulation control is formulated in Ref. [4]. In Ref. [5], the usage of vehicle-to-grid approaches in power systems with high wind power penetration is studied. Ref. [6] proposes a probabilistic constrained load flow considering both wind power generation and electric vehicles. In Ref. [7] a demand side management procedure is applied to optimize the charging cycles of electric vehicles. In Ref. [8] the battery degradation is explicitly considered in the energy management performed by the grid operator. In Ref. [9], an algorithm is proposed to control the charge of electric vehicles in deregulated electricity markets, whereas the price-responsiveness of plug-in electric vehicles is considered in Ref. [10]. Reference [11] analyzes the cost savings obtained if smart charging of PEVs is implemented. In Ref. [12] the impact of charging electric vehicles in the distribution grid is analyzed. The power consumption of electric vehicles is estimated in Ref. [13]. A robust optimization model to analyze the effect of including vehicle-to-grid facilities in small electric energy systems is presented in Ref. [14]. Finally, Ref. [15] presents a mid-term operation model to analyze the impact of PEVs in the Spanish power system. For an extensive and detailed review concerning the integration of electric vehicles, power grids, and renewable energies, the reader is referred to Ref. [16]. The objective of this paper is to analyze the impact of the integration of a large number of plug-in electric vehicles on the operation of a renewable-dominated power system. For that, it is assumed that the ISO, as responsible for the system operation, solves a network-constrained stochastic economic dispatch problem that optimizes energy and reserve deployment simultaneously. This type of economic dispatch is especially tailored for power systems with significant renewable capacity. The stochastic economic dispatch is formulated as a two-stage stochastic programming problem [17]. The first stage represents the day-ahead scheduling whereas the second stage models the real-time dispatch for different realizations of the uncertain parameters. The transmission network is modeled using a dc model. The coordination between the ISO and the PEVs is characterized using three different approaches: i) the ISO does not have control over the charging process of PEVs, ii) the ISO decides the periods in which PEVs are charged, and iii) in addition to controlling the charging of PEVs, the ISO disposes of the energy stored in PEVs for supplying part of the demand if necessary. The last two approaches correspond to the so-called G2V (Grid-to-Vehicle) and V2G (Vehicle-toGrid) configurations, respectively [18]. The resulting problem is a linear programming problem that is solved by means of commercial software [19]. The structure of the rest of the paper is as follows. Section 2 describes the proposed decision-making process. Section 3 presents the modeling of the demand associated with the charging process of PEVs. The mathematical formulation of the problem is provided in Section 4. A realistic case study is discussed in detail in Section 5. Relevant conclusions are provided in Section 6. 2. Decision-making process The operation of a power system is a complex problem which is divided into several stages. Firstly, a market-clearing procedure is
performed. The market-clearing is usually a day-ahead market which is realized the day prior to the actual energy delivery on an hourly basis. The objective of the market-clearing is to determine for each hour of the next day: i) the energy produced by each power unit, ii) the energy consumed by each load and, iii) the marketclearing prices. Next, short-time markets (spanning from minutes to hours) as adjustment and ancillary service markets are cleared in order to adjust the power production to the actual consumption needs in each instant, while the technical constraints of the production units, loads and transmission lines are satisfied. These markets are of high interest in power systems with either numerous uncertain production units or with uncertain loads. Finally, when the energy delivery is physically provided, a real-time dispatch is performed to ensure the energy balance if fluctuations in demand and power outputs occur. However, it is important to note that the most part of traded energy is negotiated in the day-ahead market. The market-clearing procedure used in this paper to represent the day-ahead market corresponds to a network-constrained stochastic economic dispatch. The classical economic dispatch is a mathematical programming problem consisting in allocating the total demand among available generating units so that the production cost is minimized [20]. The network-constrained stochastic economic dispatch is an economic dispatch model that explicitly considers the transmission network and the uncertainty associated with both the power production and demand. This model is appropriate for those power systems with high penetration of non-dispatchable power units. These units are those whose power output depends on the randomness of the natural sources involved in their power production processes. For instance, the power outputs of solar PV (photovoltaic) and wind power plants are subjected to the randomness associated with the solar irradiation and the wind speed, respectively. Specifically, the uncertain parameters considered in this paper are twofold: a) the power production of non-dispatchable generation units, namely, photovoltaic and wind power plants, and b) the system demand, which is considered as a combination of PEVs demand and conventional demand. Observe that the demand associated with PEVs is uncertain for the ISO when the day-ahead market is cleared the day prior to the physical energy delivery. In order to explicitly consider the uncertainty faced in the operation of the power system, the network-constrained stochastic economic dispatch co-optimizes simultaneously energy and reserve deployment accounting for different realizations of the uncertain parameters, [17] and [21]. Traditionally, the reserve deployments are the changes over the energy scheduled in the dayahead market, which are performed by the dispatchable units (thermal and hydro units). These reserve deployments are made in order to maintain the energy balance in each bus of the system if a deviation between electricity production and consumption occurs. In this paper, it is considered an additional reserve deployment that is procured by those PEVs controlled by the ISO. Then, the ISO may use the energy stored in the PEV batteries to compensate generation deficits and it may also decide to charge the PEV batteries in those hours with generation surplus. The expected demand of those PEVs that are not controlled by the ISO is procured in the dayahead market, whereas its deviations with respect to the expected value are satisfied with the reserve deployments described above. If energy and reserve deployment are simultaneously optimized it is possible to determine a day-ahead schedule that is flexible enough to accommodate effectively the different realizations of the uncertain parameters. This problem is formulated as a classical two-stage stochastic programming problem in which the firststage represents the day-ahead market, while the second-stage represents the actual energy deployment in which uncertain parameters are revealed and reserves are deployed. This second stage is usually named as real-time dispatch.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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The uncertain parameters are characterized as stochastic processes which are discretized into a set of scenarios [22]. Each scenario is a plausible realization of the stochastic processes and it contains information of: power outputs of non-dispatchable units, demand of PEVs, and the rest of system demand. Different scenario generation procedures are provided in Ref. [23]. Taking into account this representation of the uncertain parameters, Fig. 1 represents graphically the decision-making process described above.
consumption among the hours in which PEVs are available to be charged:
3. PEV demand modeling
Observe that the proposed charging profiles represent two extreme cases. The first charging profile leads to peak demands in some specific hours, which is an unfavorable event for the power system operation. On the other hand, the aggregated demand of a PEV type in the second charging profile causes a smooth demand profile which is a desirable property from the power system point of view. These two charging profiles are benchmarks in order to analyze the advantages of including G2V and V2G capabilities in the charging process of PEVs.
The objective of this section is to characterize the demand associated with the charging process of PEVs. For this, it is assumed that each PEV is equipped with a large battery that is charged using the power grid. The electricity demand associated with the charge of these batteries is modeled as follows: The number of PEVs connected to each bus of the power system is assigned. PEVs are categorized in SK types, in such a way that PEVs with similar usage patterns are assigned to the same type. A PEV type is characterized by the daily driven distance and by the set of hours in which PEVs are available to be charged. In this way, all PEVs belonging to the same type are assumed to have similar charging profiles. The daily distance driven by PEVs is an uncertain parameter that is unknown when clearing the day-ahead market. This distance is characterized by a probability distribution, which is identified by analyzing historical data. The probability distribution is discretized into finite set of scenarios. Each scenario has information of daily distance driven and it has an occurrence probability [22]. Accounting for both the daily driven distance and the average electricity consumption per driven kilometer, the daily energy consumption of each PEV type is computed for each scenario. Using this information, the initial status of the batteries at the beginning of the charging period is straightforwardly derived. If the charge of PEVs is not controlled by the ISO, two different charging profiles are proposed to distribute the daily energy
Charging profile 1: The charge of PEVs starts at the first hour in which PEVs are available to be charged. Hence, the charge of all PEVs belonging to the same type begins simultaneously. Charging profile 2: The charge of PEVs is evenly distributed during all hours in which PEVs are available to be charged.
4. Mathematical formulation This section presents the mathematical formulation of the problem described in Section 2. The proposed formulation assumes that the aim of the ISO consists in maximizing the expected social welfare. In order to formulate the market-clearing model as a linear programming problem the following assumptions are made: 1. The demand is inelastic. The capacity of electricity users to respond to pricing in current power systems is very small and it can be neglected. 2. The minimum power output of generating units is assumed to be zero. If the minimum power output of generating units is different from zero it is necessary to include binary variables in the formulation of the technical constraints of the units, leading to a unit commitment problem [20] which is out of the scope of this paper. 3. Generation-side offer curves are linear. In general, marketclearing procedures consider step-wise linear offer curves [24]. 4. It is considered that only thermal and hydro units have the ability to provide reserve services because they are dispatchable units which are able to modify the energy previously scheduled in the day-ahead market. 5. As is customary for energy scheduling problems, the transmission network is represented by the dc approximation [20]. The exact representation of the network is afterwards used by the ISO for verifying that all the operational constraints of generators, lines and loads are satisfied, and for taking corrective actions if it is necessary. Observe that these assumptions are usually enforced in actual market-clearing models. As a consequence of considering the system demand inelastic, maximizing the expected social welfare is equivalent to minimizing the expected generating-side production cost. The full mathematical formulation of the problem is as follows:
X
X
t2ST
c2SC
MinimizeQ þ
X
X
t2ST
c2SC
X
C;Disp CcCO pct
þ
X h2SH
! H;Disp ChHO pht
þ
X
tu
u2SU
X CDu CDd HDu HDd þ CcCR rctu rctu ChHR rhtu rhtu !
h2SH
CnUD pUD ntu
n2SN
(1) Fig. 1. Decision framework.
Subject to:
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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4
(Relationship between the day-ahead market and the real-time dispatch)
cc2SC ; ct2ST ; cu2SU
CDu CDd pCctu ¼ pC;Disp þ rctu rctu ; ct
pH htu
¼
pH;Disp ht
þ
HDu rhtu
HDd rhtu ;
H
U
T
cc2S ; ct2S ; cu2S
(2) (3)
G2V V2G EV BPT 0 pBC Nkn Pmax ; kntu gkn þ gkn i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU 0
(22)
i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU
1 BD pkntu pBS kntu ; aBD k
(23)
(Technical constraints of generating units)
cc2SC ; ct2ST ; cu2SU
C 0 pCctu Pmax;c ;
cc2SC ; ct2ST ; cu2SU
C pCctu pCct1;u Pup;c ;
pCct1;u
pCctu
(4)
C Pdown;c ;
C
T
cc2S ; ct2S ; cu2S
i h V2G EV BPT K N O F U 0 pBD kntu gkn Nkn Pmax ; ck2S ; cn2S ; t2 tk ; tk ; cu2S (24)
(5) U
(6)
G2V V2G EV BS Nkn pBS Pmax;k ; ck2SK ;cn2SN ;t ¼ tkF ;cu2SU kntu ¼ gkn þ gkn (25)
0
pH htu
H Pmax;h ;
H
U
T
ch2S ; ct2S ; cu2S
(7)
(Power balance in the day-ahead market)
X pRrtu
þ
pRS rtu
¼
R R Urtu Pmax;r ;
pRrtu ; pRS rtu 0;
R
U
T
cr2S ; ct2S ; cu2S
cr2SR ; ct2ST ; cu2SU
(8) (9)
pC;Disp þ ct
c2SCn
L;Disp
[2SLF;n
p[t
X
pH;Disp þ ht
h2SH n
X
þ
X
[2SLO;n
r2SRn D;Exp
¼ Pnt
þ
X
pR;Disp rt
X
EV;Exp
þgNC kn Pknt
pL;Disp [t
; cn2SN ; ct2ST
k2SKn
(Reserve deployments)
(26)
cc2SC ; ct2ST ; cu2SU
CDu C 0 rctu Pmax;c ;
(10)
(Power balance in the real-time dispatch)
X 0
CDd rctu
0
HDu rhtu
0
HDd rhtu
C Pmax;c ;
H Pmax;h ;
H Pmax;h ;
C
T
cc2S ; ct2S ; cu2S
U
H
T
U
H
T
U
ch2S ; ct2S ; cu2S ch2S ; ct2S ; cu2S
(11) (12) (13)
L;Disp
¼
L Pmax;[
L Pmax;[ ;
p=2; p=2 qDisp nt
c[2SL ; ct2ST L
c[2S ; ct2S
T
cn2SN ; ct2ST
1 qOð[Þtu qFð[Þtu ; X[
L L pL[tu Pmax;[ ; Pmax;[
p=2 qntu p=2;
[2SLO;n
h2SH n
pL[tu
D;Exp Pnt þ
X
X
pL;Disp [t
þ
X [2SLF;n
r2SRn
pL[tu
pL;Disp [t
D þ pUD ntu ¼ Pntu
X EV;Exp EV þ gNC pBC kn Pkntu Pknt kntu
k2SKn
k2SKn
N T U pBD kntu ; cn2S ; ct2S ; cu2S ;
c[2SL ; ct2ST ; cu2SU
c[2SL ; ct2ST ; cu2SU
cn2SN ; ct2ST ; cu2SU
where Q ¼ fpBC ; pBD ; pBS ; pC ; pC;Disp ; pH ; pH;Disp ; pL[tu ; pL;Disp ; [t kntu kntu kntu ctu ct htu ht
(15) (16)
(17)
(18) (19)
(State-of-charge constraints)
G2V V2G EV BS;0 Nkn pBS Pknu ; kntu ¼ gkn þ gkn
ck2SK ; cn2SN ;
t ¼ tkO 1; cu2SU 1 BD pkntu ; aBD k i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU
BS BC BC pBS kntu ¼ pknt1;u þ ak pkntu
(27)
(14)
(Power flow constraints in the real-time dispatch)
pL[tu ¼
X
k2SKn
1 Disp Disp q qFð[Þt ; X[ Oð[Þt L;Disp p[t
(Power flow constraints in the day-ahead market)
p[t
c2SCn
X X CDu CDd HDu HDd rctu þ rhtu þ pRrtu pR;Disp rctu rhtu rt
R;Disp
Disp
UD CDu CDd HDu HDd pRrtu ; prt pRS rtu ; pntu ; rctu ; rctu ; rhtu ; rhtu ; qntu ; qnt g , is the set of optimization variables. The objective function (1) consists in minimizing the expected generation costs of dispatchable units (thermal and hydro), considering the scheduled energy in the day-ahead market and the deployment of reserves in the real-time dispatch, plus the cost of the unserved demand. Observe that the day-ahead scheduling is a first-stage decision which is considered to be made before knowing the actual realizations of the uncertain parameters. Only thermal and hydro units submit generation offer prices to the day-ahead market ðCcCO ; ChHO Þ and to the real-time dispatch ðCcCR ; ChHR Þ greater than or equal to zero. On the contrary, non-dispatchable units, such as PV or wind power plants, are assumed to bid at zero price. Constraints (2) and (3) establish the relationships among the power generated in each scenario ðpCctu ; pH Þ, the scheduled power htu C;Disp
(20)
(21)
in the day-ahead market ðpct
H;Disp
; pht
Þ, and up and down
CDu ; r CDd ) deployed reserves in the real-time dispatch for thermal (rctu ctu HDu , r HDd ), respectively. and hydro units (rhtu htu Constraints (4)e(6) limit the power output of thermal units by C C , PC ) and power ramps (Pup;c ). The their power limits (Pmax;c down;c H power limits of hydro units (Pmax;h ) are formulated by constraints
(7). Constraints (8)e(9) establish the power limits for renewable
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
rate-Min n, R. Za ~ ano / Energy xxx (2015) 1e9 M. Carrio R 2½0; 1 models the availability of generating units. Parameter Urtu renewable resources for unit r, hour t and scenario u. Therefore, if R is equal to 1, the full capacity of renewable unit r, ðP R Urtu max;r Þ, can be used. Constraints (10)e(11) and (12)e(13) limit the deployed reserves of thermal and hydro units, respectively. Constraints (14) determine the resulting power flow from the L;Disp
day-ahead schedule in each line (p[t ) as a function of the reactance of the line (X[) and the difference of voltage phase angles Disp
(qnt ) at buses O([) and F([) connected by line [. Constraints (15)
5
5. Numerical results The model proposed in Section 4 has been tested on a realistic case study based on the current configuration of the Iberian Peninsula power system. This power system comprises the mainland areas of Spain and Portugal, with an installed capacity over 100 GW. The numerical results are organized in two sections. First, a base case is solved, in which the model proposed in Section 4 is tested for different types of coordination between the ISO and PEVs. Secondly, a sensitivity analysis is performed.
L ) and voltage phase and (16) establish limits on power flows (Pmax;[
angles, respectively. Constraints (17)e(19) are equivalent to (14)e(16) and they are used to formulate the resulting power flows from the real-time dispatch. Constraints (20)e(25) formulate the state-of-charge of the PEV batteries controlled by the ISO. Variable pBS denotes the energy kntu BS;0 is a stored by type-k PEVs in hour t at bus n and scenario u, Pknu parameter modeling the energy stored by type-k PEVs at bus n and scenario u at the beginning of the first hour (tkO ) of the charging
represents the energy obtained from the period, variable pBC kntu power grid to charge the batteries of type-k PEVs in hour t at bus n denotes the power discharged from and scenario u, variable pBD kntu
=aBD are the eftype-k PEVs at bus n, hour t, and scenario u. aBC k k ficiency of charging/discharging type-k PEVs batteries from/into BPT and P BS are the peak the power grid respectively, and Pmax max;k
power transfer rate and the average capacity of the batteries of type-k PEVs, respectively. Constraints (20) establish the energy stored by those PEVs controlled by the ISO at the beginning of the charging period for each scenario. Constraints (21) compute the energy stored by PEVs in hour t as a function of the energy stored in the previous hour, t1, plus the energy charged from the power grid and minus the energy discharged from PEVs. Observe that the proposed model is based on one-hour periods, then power and energy units are equivalent. Constraints (22) bound the maximum amount of power that can be charged from the grid in a single hour. Constraints (23) and (24) formulate the upper bounds of the energy that can be discharged from the PEVs. Parameters gG2V and kt denote per unit number of vehicles controlled by G2V and gV2G kt V2G capabilities, respectively. These parameters, along with the in (26), per unit number of vehicles non controlled by the ISO, gNC kt þ gG2V þ gV2G ¼ 1. Completing this set, constraints satisfy that gNC kt kt kt (25) impose that all battery charging processes controlled by the system operator have to be completed at the end of the charge period (tkF ). Constraints (26) establish the power balance in the day-ahead
5.1. General input data A planning horizon of 31 h is analyzed. This planning horizon ranges from 0:00 h of a given day up to 7.00 h of the next day. The expected values of the electricity demand and the availability of wind and solar productions correspond to May 16th of 2011 in the Iberian Peninsula power system. The transmission network used to represent the Iberian Peninsula power system is based on the approximate model of the European Interconnected System reported in Ref. [25]. This model has been modified in order to include some recently built lines. The resulting transmission network is represented in Fig. 2. Light and dark lines represent 400 and 220 kV lines, respectively. The capacity of these lines is assumed to be 1350 and 450 MW, respectively [26]. The generating units have been located throughout the transmission network using the available information in the annual reports published by the ISOs of Spain [26] and Portugal [27]. Accordingly, the considered test system comprises 226 nodes, 390 transmission lines, 61 conventional thermal units, 77 hydro units and 90 wind farms. PV capacity is assigned to each node according to the local information provided in Refs. [26] and [27]. Table 1 provides the installed capacity for each generation technology. Four thermal technologies are considered: i) nuclear, ii) coal, iii) OCGT (open-cycle gas turbines) and CCGT (combined-cycle gas turbines). Moreover, three renewable technologies are also considered: hydro, wind and solar PV (photovoltaic). It is worth mentioning that the proposed formulation is general enough to straightforwardly include other renewable technologies such as biomass or CSP (Concentrating Solar Power) units. Observe that, in this study, the considered renewable sources constitute the 53.9% of the total installed capacity. The offering prices of nuclear, wind and PV units are assumed to be equal to zero. The load shed cost is fixed to 1000 V/MWh. Three PEV types based on the mobility study [28] are considered. The description of the charge period characterizing each PEV
EV;Exp represents the expected power demarket. Parameter Pknt mand of uncontrolled PEVs pertaining to type k in bus n and hour t.
The dual variable of this constraint ðlDA nt Þ represents the electricity price of the scheduled quantities in the day-ahead market. Therefore, all quantities traded in the day-ahead market are priced at lDA nt . Constraints (27) guaranty, for the realization of each considered scenario, the power balance for each bus and hour in the real-time dispatch. The deployments of reserves and the charge and discharge of PEVs have to meet the deviations on demand and on the production of non-dispatchable units. The probability-removed dual variable of this constraint represents the real-time price of the dispatched quantities in the real-time dispatch. All quantities traded in the real-time dispatch are priced at lRT ntu divided by the probability of the considered scenario tu.
Fig. 2. Iberian Peninsula transmission network.
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6
scenarios. Mathematically, the scenario generation of a stochastic process Xt can be formulated as follows:
Table 1 Installed capacity of generating technologies. Technology
Capacity (GW)
Average operating cost (V/MWh)
Nuclear Coal OCGT CCGT Hydro Wind PV Total
7.655 12.519 5.532 31.914 21.077 23.456 3.677 105.830
0.00 30.64 51.71 42.42 42.77 0.00 0.00 e
Table 2 PEV type characterization. Type
Beginning hour
Ending hour
Duration
Percentage of PEVs
1 2 3
16.00 21.00 2.00
7.00 (next day) 7.00 (next day) 21.00
16 h 11 h 19 h
45% 40% 15%
type is contained in Table 2. This table also provides the percentages of each PEV type considered in the study. For this study, each PEV has an actual energy consumption of 0.18 kW/km and is equipped with a 22 kWh battery. The efficiencies of the charger and the battery are 0.95 and 0.92, respectively. Thus, the efficiencies of charging and discharging processes (aBC and aBD ) k k are both considered to be 0.88. The parameters describing electrical vehicles are based on the characteristics of the Renault Zoe [29]. The charging voltage and the peak power transfer rate values depend on the technical characteristics of the charge coupler [30]. For simplicity, the study assumes that PEVs are charged under a charging voltage of 230 V and a peak power transfer rate of 7.2 kW. According to the PEV user patterns provided in Table 2, PEV demand scenarios have been obtained as established in Section 3. The daily distance driven by PEVs is characterized using the observed probability distribution of daily driven distance of Nissan Leaf vehicles described in Ref. [31] and the expected daily driving distance in Spain, [32]. Considering this information, the daily driven distance is described by using a normal distribution with mean and standard deviation equal to 35 and 9.6, respectively. This distribution is discretized using 5 scenarios, as represented in Fig. 3. For the uncontrolled PEV charge modeling, the charging profiles described in Section 3 are used to transform daily driving distances into hourly electric demand. The total number of private vehicles in the Iberian Peninsula considered in this study is 30 million, of which 30% are assumed to be PEVs. The uncertainties associated with solar and wind availabilities and with the system demand are also modeled by using a set of
Fig. 3. Scenario generation for daily distance driven.
Xtu ¼ Eu fXt g þ Nð0; st Þ;
ct2T; cu2U;
(28)
where Eu{$} refers to the expectation operator and N is the normal distribution. In (28), the standard deviation of the random term st is considered time-dependent, in such a way that it increases with the time period index. This scenario generation model has been previously used in Ref. [33]. The dependency between stochastic processes can be easily modeled considering the quasiecontemporaneous correlation of the series of errors. The reader is referred to [23] and [34] for further details. Observe that other scenario generation methods based on multi-variate time series models can also be used. An initial set of 1000 scenarios (5 PEV demand scenarios 200 demand/wind/PV scenarios) has been considered, which has been afterwards reduced to a final set of 15 scenarios by means of the scenario reduction algorithm presented in Ref. [35]. The resulting scenarios modeling the electricity demand, solar, and wind availabilities are represented in Fig. 4. The scenarios modeling charging profiles NC-1 and NC-2 are plotted in Fig. 5. All PEVs are forced to be totally charged at the end of the charging period defined for each PEVs type. As a consequence, the total demand corresponding to PEVs in both charging profiles is identical. The expected PEV demand is 68.3 GWh whereas the rest of system demand is 690.2 GWh. Therefore, the replacement of 30% of the combustion-engine cars by PEVs causes an increase of 9.9% in the total demand of the system. 5.2. Base case The base case includes the following situations: 1. Non-PEV: PEVs are not considered (gNC ¼ gG2V ¼ gV2G ¼ 0). kn kn kn 2. NC-1: The charge of PEVs is described according to the charging profile 1 proposed in Section 3 (gNC ¼ 1; gG2V ¼ gV2G ¼ 0). kn kn kn 3. NC-2: The charge of PEVs is described according to the charging profile 2 proposed in Section 3 (gNC ¼ 1; gG2V ¼ gV2G ¼ 0). kn kn kn 4. G2V: The ISO controls all PEVs using Grid-to-Vehicle capability (gNC ¼ 0; gG2V ¼ 1; gV2G ¼ 0). kn kn kn 5. V2G: The ISO controls all PEVs using Vehicle-to-Grid capability (gNC ¼ gG2V ¼ 0; gV2G ¼ 1). kn kn kn
Fig. 4. Scenarios for electricity demand, and wind and solar availabilities.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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Fig. 6. Expected generating mix.
Fig. 5. Scenarios for PEV demand.
All cases are solved using CPLEX 12.2.0.1 [19] under GAMS [36] on a Linux-based server with four 2.9 GHz processors and 250 GB of RAM. Table 3 provides the observed results for each case. The total costs correspond to the objective function (1) for each case. As expected, the case with the smallest operation cost is the one in which there are no PEVs. Observe that the increment of the cost is relevant when PEVs are incorporated. Concretely, a 9.9% increment in the total demand, which is caused by charging PEVs, increases the expected cost a 14.0% in the most favorable case (G2V) and a 17.1% in the worst case (NC-1). In G2V and V2G cases the expected cost is reduced with respect to the best uncontrolled case (NC-2) in 2.1% and 2.2%, respectively. It is also worth mentioning that G2V and V2G obtain quite similar expected costs. This first result indicates that, in the analyzed case, V2G does not significantly outperforms G2V in terms of the expected cost. In the G2V case, it has also been observed that the expected energy cycled out from the batteries only represents 2.6% of the energy charged. Therefore, problems related to the premature aging of the batteries are not expected. With respect to the computional issues, the size of the solved models comprises up to millions of variables and constraints. As expected, the computing times of the optimization problems considering G2V and V2G capabilities are larger than those of the rest of cases. Fig. 6 represents the expected generating mix resulting from Non-PEV, NC-1 and G2V cases. It can be observed that hydro and CCGT units are used to satisfy the demand in peak hours, whereas nuclear and coal units are used as base units. It can be also observed that the thermal production is higher in NC-1 than in G2V case. The allocation of the expected PEV demand throughout the 31hour horizon planning is represented in Fig. 7. This figure shows that in G2V and V2G cases, the PEV demand is mainly located in the valley hours of the day and in those periods with high wind resources (see Fig. 4). Fig. 8 represents the wind spillage for different cases. The dark line represents the expected value, whereas the gray color
Fig. 7. PEV demand.
represents the area comprised within the maximum and minimum values. Observe that, if coordination is accounted for, the reduction of the expected and maximum wind spillage is apparent. The resulting average day-ahead market prices for NC-1, NC-2, G2V and V2G cases are represented in Fig. 9. These prices are computed as the dual variables of the day-ahead energy balance constraints (constraints (26)). In case NC-1, expected prices experiment a high variation between peak and valley hours. This case presents the smallest and highest prices in valley and peak hours, respectively. On the other hand, G2V and V2G present a small difference in price values between valley and peak hours. Fig. 10 depicts the average real-time prices for each case and scenario. Black circles represent the expected value of the prices whereas gray lines represent their values for each scenario. These prices correspond with the probability-removed dual variables of the real-time energy balance (constraints (27)) in each scenario divided by the probability of that scenario. It is observed that the
Table 3 Results. Total cost (millions V)
6
# Variables (10 ): # Constraints (106): Time (s):
Non-PEV
NC-1
NC-2
G2V
V2G
11.692
14.105
13.912
13.620
13.603
1.43 1.51 4061.0
1.43 1.51 3438.7
1.43 1.51 2862.7
1.58 1.81 11730.2
1.58 1.81 16872.4
Fig. 8. Wind spillage.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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Fig. 9. Day-ahead prices.
Fig. 10. Real-time prices.
volatility of balancing prices is highly reduced for G2V and V2G cases. 5.3. Sensitivity analysis In this section, a sensitivity test is performed to study the impact on the results of the variation of input data. For this purpose, the variation of the following four parameters is analyzed: the number EV ), the portion of PEVs controlled by the system operator of PEVs (Nkn R , gV2G ), the capacity of renewable resources (Pmax;r ), and the (gG2V kn kn
BPT ). In all cases, non-analyzed peak power transfer rate of PEVs (Pmax parameters are fixed to the values previously established in Subsection 5.1. This analysis focuses on the comparison of cases G2V and V2G with regard to NC-2, which represents the most favorable of all uncontrolled-charge cases. The obtained results are represented in Fig. 11. This figure provides, for each analyzed parameter, the variation of: a) the expected cost reduction obtained in G2V and V2G cases with respect to NC-2, b) the expected wind spillage, and c) the expected deployed reserve (summation of up and down deployed reserves by thermal and hydro units). Firstly, Fig. 11 shows that the reduction of the expected costs in G2V and V2G cases with respect to NC-2 has a maximum for an integration of PEVs around 40% over the total number of vehicles. For an integration of PEVs greater than that value, the expected deployment of reserves increases in the controlled cases, which causes an increment in the expected costs. This fact reduces the difference between the expected costs in controlled and uncontrolled cases. However, it should be emphasized that G2V and V2G cases outperform NC-2 case in all instances in terms of the expected cost. It is noticeable that only for a 10% of PEVs over all vehicles, the reduction of the cost in coordinated charge cases is significant. It can be also observed that G2V and V2G cases attain smaller expected costs with respect to NC-2 as the number of controlled PEVs increases. This fact is a consequence of the reduction of both the expected wind spillage and deployed reserves. It is remarkable that for 20% of controlled PEVs, the reduction of the expected cost in coordinated charge cases with respect to NC-2 case is equal to 39.5% of the reduction obtained with 100% of controlled PEVs. It is also interesting to study the case in which the installed capacity on wind and PV units is modified. It is observed a large reduction of the expected cost in the coordinated charge cases with respect to NC-2 case as the renewable capacity increases. This reduction is over 4.5% in the case in which the installed capacity reaches the double value of the considered one in the base case. As expected, both expected wind spillage and deployed reserves are higher if renewable capacity increases.
Fig. 11. Sensitivity analysis.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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Finally, it is observed that a large enough peak power transfer rate reduces the number of hours needed for the charging and discharging processes, which results in a better performance of V2G case with respect to G2V case in terms of the expected cost and wind spillage. 6. Conclusions This paper analyzes the integration of a high number of electrical vehicles in a renewable-dominated power system which is operated using a network-constrained stochastic economic dispatch. For this purpose, different coordination schemes between the ISO and PEV users have been modeled. Specifically, it has been considered that G2V and V2G capabilities are used in the real-time dispatch by the ISO to counter deviations in the energy demand and in the power outputs of non-dispatchable generating units. This has been mathematically modeled using a two-stage stochastic programming problem in which the day-ahead market is characterized in the first stage, whereas the second stage represents the real-time dispatch. The system conventional demand, the demand of charging PEVs, and the power outputs of non-dispatchable units have been characterized using a set of plausible scenarios. The proposed formulation has been successfully tested on a case study based on the Iberian Peninsula power system. The computational requirements are higher if G2V and V2G capabilities are taken into account, but they are kept under reasonable levels. The numerical results reveal that including coordination between the ISO and the charge of PEVs reduces the total expected operation cost. Additionally, this coordination allows taking advantage of renewable resources reducing the wind spillage and the usage of deployed reserves. The difference of prices between peak and valley hours in the day-ahead market is reduced if coordination is taken into account. Additionally, the volatility of the real-time prices is also reduced if coordination is implemented. The realization of a sensitivity analysis allows us to observe that, although the number of either total or controlled PEVs be small, the usage of coordinated charge reduces the expected costs with respect to uncontrolled cases. Finally, it is also concluded that the coordinated charge is specially tailored for those power systems with a significant amount of renewable (non-dispatchable) resources. References [1] Tuttle DP, Baldick R. The evolution of plug-in electric vehicle-grid interactions. Operat Res 2011;3(1):500e5. [2] Kempton W, Letendre S. Electric vehicles as a new power source for electric utilities. Transp Res Part D 1997;2:157e75. [3] Tomic J, Kempton W. Using fleets of electric-drive vehicles for grid support. J Power Sources 2007;168:459e68. zquez MA, Bouffard F, Silva V. Electric vehicle aggregator system [4] Ortega-Va operator coordination for charging scheduling and services procurement. IEEE Trans Power Syst 2013;28:1806e15. [5] Lund H, Kempton W. Integration of renewable energy into the transport and electricity sectors through V2G. Energy Policy 2008;36:3578e87. [6] Vlachogiannis JG. Probabilistic constrained load flow considering integration of wind power generation and electric vehicles. IEEE Trans Power Syst 2009;33(4):1808e17. [7] Finn P, Fitzpatrick C, Connolly D. Demand side management of electric car charging: benefits for consumer and grid. Energy 2012;42:358e63.
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ndez IJ, Calvillo CF, Sa nchez-Millares A, Boal J. Capacity fade and aging [8] Ferna models for electric batteries and optimal charging strategy for electric vehicles. Energy 2013;60:35e43. [9] Kristofferson T, Capion K, Meibom P. Optimal charging of electric drive vehicles in a market environment. Appl Energy 2011;88:1940e8. [10] Dallinger D, Wietschel M. Grid integration of intermittent renewable energy sources using price-responsive plug-in electric vehicles. Renew Sustain Energy Rev 2012;16:3370e82. [11] Kiviluoma J, Meibom P. Methodology for modelling plug-in electric vehicles in the power system and cost estimates for a system with either smart or dumb electric vehicles. Energy 2011;36:1758e67. [12] Clement-Nyns K, Haesen E, Driesen J. The impact of charging plug-in hybrid electric vehicles on a residential distribution grid. IEEE Trans Power Syst 2010;25(1):371e9. [13] Wu D, Aliprantis DC, Gkritza K. Electric energy and power consumption by light-duty plug-in electric vehicles. IEEE Trans Power Syst 2011;26(2): 738e46. [14] Battistelly C, Baringo L, Conejo AJ. Optimal energy management of small electric energy systems including V2G facilities and renewable energy sources. Electr Power Syst Res 2012;92:50e9. [15] Fernandes C, Frías P, Latorre JM. Impact of vehicle-to-grid on power system operation costs: the Spanish case study. Appl Energy 2012;96: 194e202. [16] Richardson DB. Electric vehicles and the electric grid: a review of modeling approaches, impacts, and renewable energy integration. Renew Sustain Energy Rev 2013;19:247e54. [17] Pritchard G, Zakeri G, Philpott A. A single-settlement, energy-only electric power market for unpredictable and intermittent participants. Operat Res 2010;58(4):1210e9. [18] Modeling load shifting using electric vehicles in a smart grid environment. OECD/IEA; 2010. working paper. Available from: http://www.oecd-ilibrary. org. [19] The IBM CPLEX. Available from: http://www-01.ibm.com/software/ commerce/optimization/cplex-optimizer/. mez-Expo sito A, Conejo AJ, Can ~ izares C. Electric energy systems: analysis [20] Go and operation. Boca Raton: CRC Press; 2008. [21] Morales JM, Conejo AJ, Liu K, Zhong J. Pricing electricity in pools with wind producers. IEEE Trans Power Syst 2012;27(3):1366e76. [22] Birge JR, Louveaux F. Introduction to stochastic programming. New York, NY: Springer-Verlag; 1997. n M, Morales JM. Decision making under uncertainty in [23] Conejo AJ, Carrio electricity markets. New York, NY: Springer; 2010. [24] Ott A. Experience with PJM market operation, system design, and implementation. IEEE Trans Power Syst 2003;18:528e34. [25] Zhou Q, Bialek JW. Approximate model of European interconnected system as a benchmark system to study effects of cross-border trades. IEEE Trans Power Syst 2005;20(2):782e8. ctrica de Espan ~ a). Available from: http:// [26] Spanish Network Operator (Red Ele www.ree.es. ticas Nacionais). Available from: [27] Portuguese Network Operator (Redes Energe http://www.ren.pt. [28] Mobility report for residents in Spain (MOVILIA). Available from: http://www. fomento.es. [29] Renault Zoe. Available from: http://group.renault.com/en/company-vehicles/ discover/renault-electric-vehicles/. [30] SAE International. SAE standard on EV charging connector approved. Available from: http://www.sae.org/mags/AEI/7479. [31] Nicholas M, Tal G, Davies J, Wookjack J. Charging behaviour impacts on electric vehicle miles traveled: who is not plugging in?. Tech. rep. University of California, Davis. Institute of Transportation Studies; Nov. 2014. Available from: http://www.its.ucdavis.edu/wp-content/themes/ucdavis/pubs/ download_pdf.php?id¼2098. [32] National Institute of Statistics of Spain. Available from: http://www.ine.es. n M, Conejo AJ, Arroyo JM. Forward contracting and selling price [33] Carrio determination for a retailer. IEEE Trans Power Syst 2007;22(4):2105e14. [34] Morales JM, Mínguez R, Conejo AJ. A methodology to generate statistically dependent wind speed scenarios. Appl Energy 2010;87(3):843e55. n M. Scenario reduction for futures [35] Morales JM, Pineda S, Conejo AJ, Carrio market trading in electricity markets. IEEE Trans Power Syst 2009;24(2): 878e88. [36] Rosenthal RE. GAMS, a user's guide. Washington, DC: GAMS Development Corp; 2008.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Operation of renewable-dominated power systems with a significant penetration of plug-in electric vehicles n a, *, Rafael Za rate-Min ~ ano b Miguel Carrio a b
Department of Electrical Engineering, UCLM, Toledo, Spain Department of Electrical Engineering, UCLM, Almad en, Spain
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 2 July 2015 Accepted 25 July 2015 Available online xxx
This paper aims to study the operational consequences of the integration of a large number of plug-in electric vehicles in a renewable-dominated power system. The coordination between the power system operator and the charging process of plug-in electric vehicles under a smart-grid environment is modeled using several approaches. The operation of the power system is modeled by means of a network-constrained stochastic economic dispatch. This problem is formulated using a two-stage stochastic programming model in which the uncertainties associated with the charging process of plug-in electric vehicles and with the availability of the renewable sources are characterized as stochastic processes. Numerical results on a realistic case based on the Iberian Peninsula power system are provided and analyzed. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Plug-in electric vehicles Smart grid framework Stochastic economic dispatch Stochastic programming
1. Introduction PEVs (plug-in electric vehicles) are becoming an actual option to replace traditional combustion-engine cars. This fact is a consequence of several reasons; firstly, PEVs are widely considered as an effective means of reducing the carbon emissions resulting from the extensive usage of combustion-engine vehicles. The reduction of carbon emissions might result in a positive impact against the global climate change and an improvement of the air quality in our cities. Secondly, the usage of PEVs can be considered as a tool for reducing the dependency on fossil fuels and, therefore, for increasing energy supply security. This fact is particularly relevant for those countries without fossil fuel reserves. This argument is reinforced thanks to the high increase of the usage of renewable technologies for electric energy production that may be used to charge PEVs. In a scenario in which the general usage of PEVs is promoted, it is necessary to carefully analyze the impact caused by the additional demand which results from charging PEVs (hereinafter referred to as PEV demand) on the operation of power systems. That is, the operation of a power system could be at risk if an
* Corresponding author. Tel.: þ34 925268800 (5750). n), [email protected] E-mail addresses: [email protected] (M. Carrio rate-Min ~ ano). (R. Za
excessive demand is added in inadequate periods, especially during peak demand hours. In this situation, demand-side management actions could help to place this additional demand in more convenient periods. Special attention should be paid to renewable-dominated power systems, in which an important portion of the demand procurement is obtained by means of non-dispatchable generating units. For these power systems, an adequate selection of the energy and reserve schedules is vital for ensuring a safe procurement of the demand at a reasonable cost. The evolution of the communication capabilities between energy suppliers and domestic consumers will facilitate the incorporation of novel PEV charging control schemes. Moreover, the demand associated with the charging process of PEVs is suitable for demand-side management since the usage of PEVs does not coincide in time with the consumption of power from the electrical grid. In this regard, smart grids provide an adequate framework for implementing an effective communication between the ISO (Independent System Operator) and PEV users in order to manage PEV demand effectively [1]. Therefore, considering a smart grid environment, the ISO may control the charging process of PEVs to allocate the PEV demand in adequate periods from the standpoint of the system operation. The so-called G2V (Grid-to-Vehicle) and V2G (Vehicle-to-Grid) capabilities allow the ISO to exercise control over the charging process of PEVs. The G2V capability enables the ISO to decide in which periods PEVs are charged, whereas the V2G
http://dx.doi.org/10.1016/j.energy.2015.07.111 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
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capability additionally allows the ISO to use the energy stored in the batteries of PEVs to supply part of the demand, if it is necessary. Since the publication of the pioneering work of Kempton and Letendre [2] in the late nineties analyzing the economical advantages of using vehicle-to-grid approaches, the study of the impact of PEVs and PHEVs in the power system operation has been an active research topic, especially in recent years. For example, reference [3] analyzes the usage of an electric-vehicle fleet for providing regulation services. The coordination of an electric vehicles aggregator with the system operator considering a tertiary regulation control is formulated in Ref. [4]. In Ref. [5], the usage of vehicle-to-grid approaches in power systems with high wind power penetration is studied. Ref. [6] proposes a probabilistic constrained load flow considering both wind power generation and electric vehicles. In Ref. [7] a demand side management procedure is applied to optimize the charging cycles of electric vehicles. In Ref. [8] the battery degradation is explicitly considered in the energy management performed by the grid operator. In Ref. [9], an algorithm is proposed to control the charge of electric vehicles in deregulated electricity markets, whereas the price-responsiveness of plug-in electric vehicles is considered in Ref. [10]. Reference [11] analyzes the cost savings obtained if smart charging of PEVs is implemented. In Ref. [12] the impact of charging electric vehicles in the distribution grid is analyzed. The power consumption of electric vehicles is estimated in Ref. [13]. A robust optimization model to analyze the effect of including vehicle-to-grid facilities in small electric energy systems is presented in Ref. [14]. Finally, Ref. [15] presents a mid-term operation model to analyze the impact of PEVs in the Spanish power system. For an extensive and detailed review concerning the integration of electric vehicles, power grids, and renewable energies, the reader is referred to Ref. [16]. The objective of this paper is to analyze the impact of the integration of a large number of plug-in electric vehicles on the operation of a renewable-dominated power system. For that, it is assumed that the ISO, as responsible for the system operation, solves a network-constrained stochastic economic dispatch problem that optimizes energy and reserve deployment simultaneously. This type of economic dispatch is especially tailored for power systems with significant renewable capacity. The stochastic economic dispatch is formulated as a two-stage stochastic programming problem [17]. The first stage represents the day-ahead scheduling whereas the second stage models the real-time dispatch for different realizations of the uncertain parameters. The transmission network is modeled using a dc model. The coordination between the ISO and the PEVs is characterized using three different approaches: i) the ISO does not have control over the charging process of PEVs, ii) the ISO decides the periods in which PEVs are charged, and iii) in addition to controlling the charging of PEVs, the ISO disposes of the energy stored in PEVs for supplying part of the demand if necessary. The last two approaches correspond to the so-called G2V (Grid-to-Vehicle) and V2G (Vehicle-toGrid) configurations, respectively [18]. The resulting problem is a linear programming problem that is solved by means of commercial software [19]. The structure of the rest of the paper is as follows. Section 2 describes the proposed decision-making process. Section 3 presents the modeling of the demand associated with the charging process of PEVs. The mathematical formulation of the problem is provided in Section 4. A realistic case study is discussed in detail in Section 5. Relevant conclusions are provided in Section 6. 2. Decision-making process The operation of a power system is a complex problem which is divided into several stages. Firstly, a market-clearing procedure is
performed. The market-clearing is usually a day-ahead market which is realized the day prior to the actual energy delivery on an hourly basis. The objective of the market-clearing is to determine for each hour of the next day: i) the energy produced by each power unit, ii) the energy consumed by each load and, iii) the marketclearing prices. Next, short-time markets (spanning from minutes to hours) as adjustment and ancillary service markets are cleared in order to adjust the power production to the actual consumption needs in each instant, while the technical constraints of the production units, loads and transmission lines are satisfied. These markets are of high interest in power systems with either numerous uncertain production units or with uncertain loads. Finally, when the energy delivery is physically provided, a real-time dispatch is performed to ensure the energy balance if fluctuations in demand and power outputs occur. However, it is important to note that the most part of traded energy is negotiated in the day-ahead market. The market-clearing procedure used in this paper to represent the day-ahead market corresponds to a network-constrained stochastic economic dispatch. The classical economic dispatch is a mathematical programming problem consisting in allocating the total demand among available generating units so that the production cost is minimized [20]. The network-constrained stochastic economic dispatch is an economic dispatch model that explicitly considers the transmission network and the uncertainty associated with both the power production and demand. This model is appropriate for those power systems with high penetration of non-dispatchable power units. These units are those whose power output depends on the randomness of the natural sources involved in their power production processes. For instance, the power outputs of solar PV (photovoltaic) and wind power plants are subjected to the randomness associated with the solar irradiation and the wind speed, respectively. Specifically, the uncertain parameters considered in this paper are twofold: a) the power production of non-dispatchable generation units, namely, photovoltaic and wind power plants, and b) the system demand, which is considered as a combination of PEVs demand and conventional demand. Observe that the demand associated with PEVs is uncertain for the ISO when the day-ahead market is cleared the day prior to the physical energy delivery. In order to explicitly consider the uncertainty faced in the operation of the power system, the network-constrained stochastic economic dispatch co-optimizes simultaneously energy and reserve deployment accounting for different realizations of the uncertain parameters, [17] and [21]. Traditionally, the reserve deployments are the changes over the energy scheduled in the dayahead market, which are performed by the dispatchable units (thermal and hydro units). These reserve deployments are made in order to maintain the energy balance in each bus of the system if a deviation between electricity production and consumption occurs. In this paper, it is considered an additional reserve deployment that is procured by those PEVs controlled by the ISO. Then, the ISO may use the energy stored in the PEV batteries to compensate generation deficits and it may also decide to charge the PEV batteries in those hours with generation surplus. The expected demand of those PEVs that are not controlled by the ISO is procured in the dayahead market, whereas its deviations with respect to the expected value are satisfied with the reserve deployments described above. If energy and reserve deployment are simultaneously optimized it is possible to determine a day-ahead schedule that is flexible enough to accommodate effectively the different realizations of the uncertain parameters. This problem is formulated as a classical two-stage stochastic programming problem in which the firststage represents the day-ahead market, while the second-stage represents the actual energy deployment in which uncertain parameters are revealed and reserves are deployed. This second stage is usually named as real-time dispatch.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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The uncertain parameters are characterized as stochastic processes which are discretized into a set of scenarios [22]. Each scenario is a plausible realization of the stochastic processes and it contains information of: power outputs of non-dispatchable units, demand of PEVs, and the rest of system demand. Different scenario generation procedures are provided in Ref. [23]. Taking into account this representation of the uncertain parameters, Fig. 1 represents graphically the decision-making process described above.
consumption among the hours in which PEVs are available to be charged:
3. PEV demand modeling
Observe that the proposed charging profiles represent two extreme cases. The first charging profile leads to peak demands in some specific hours, which is an unfavorable event for the power system operation. On the other hand, the aggregated demand of a PEV type in the second charging profile causes a smooth demand profile which is a desirable property from the power system point of view. These two charging profiles are benchmarks in order to analyze the advantages of including G2V and V2G capabilities in the charging process of PEVs.
The objective of this section is to characterize the demand associated with the charging process of PEVs. For this, it is assumed that each PEV is equipped with a large battery that is charged using the power grid. The electricity demand associated with the charge of these batteries is modeled as follows: The number of PEVs connected to each bus of the power system is assigned. PEVs are categorized in SK types, in such a way that PEVs with similar usage patterns are assigned to the same type. A PEV type is characterized by the daily driven distance and by the set of hours in which PEVs are available to be charged. In this way, all PEVs belonging to the same type are assumed to have similar charging profiles. The daily distance driven by PEVs is an uncertain parameter that is unknown when clearing the day-ahead market. This distance is characterized by a probability distribution, which is identified by analyzing historical data. The probability distribution is discretized into finite set of scenarios. Each scenario has information of daily distance driven and it has an occurrence probability [22]. Accounting for both the daily driven distance and the average electricity consumption per driven kilometer, the daily energy consumption of each PEV type is computed for each scenario. Using this information, the initial status of the batteries at the beginning of the charging period is straightforwardly derived. If the charge of PEVs is not controlled by the ISO, two different charging profiles are proposed to distribute the daily energy
Charging profile 1: The charge of PEVs starts at the first hour in which PEVs are available to be charged. Hence, the charge of all PEVs belonging to the same type begins simultaneously. Charging profile 2: The charge of PEVs is evenly distributed during all hours in which PEVs are available to be charged.
4. Mathematical formulation This section presents the mathematical formulation of the problem described in Section 2. The proposed formulation assumes that the aim of the ISO consists in maximizing the expected social welfare. In order to formulate the market-clearing model as a linear programming problem the following assumptions are made: 1. The demand is inelastic. The capacity of electricity users to respond to pricing in current power systems is very small and it can be neglected. 2. The minimum power output of generating units is assumed to be zero. If the minimum power output of generating units is different from zero it is necessary to include binary variables in the formulation of the technical constraints of the units, leading to a unit commitment problem [20] which is out of the scope of this paper. 3. Generation-side offer curves are linear. In general, marketclearing procedures consider step-wise linear offer curves [24]. 4. It is considered that only thermal and hydro units have the ability to provide reserve services because they are dispatchable units which are able to modify the energy previously scheduled in the day-ahead market. 5. As is customary for energy scheduling problems, the transmission network is represented by the dc approximation [20]. The exact representation of the network is afterwards used by the ISO for verifying that all the operational constraints of generators, lines and loads are satisfied, and for taking corrective actions if it is necessary. Observe that these assumptions are usually enforced in actual market-clearing models. As a consequence of considering the system demand inelastic, maximizing the expected social welfare is equivalent to minimizing the expected generating-side production cost. The full mathematical formulation of the problem is as follows:
X
X
t2ST
c2SC
MinimizeQ þ
X
X
t2ST
c2SC
X
C;Disp CcCO pct
þ
X h2SH
! H;Disp ChHO pht
þ
X
tu
u2SU
X CDu CDd HDu HDd þ CcCR rctu rctu ChHR rhtu rhtu !
h2SH
CnUD pUD ntu
n2SN
(1) Fig. 1. Decision framework.
Subject to:
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rate-Min n, R. Za ~ano / Energy xxx (2015) 1e9 M. Carrio
4
(Relationship between the day-ahead market and the real-time dispatch)
cc2SC ; ct2ST ; cu2SU
CDu CDd pCctu ¼ pC;Disp þ rctu rctu ; ct
pH htu
¼
pH;Disp ht
þ
HDu rhtu
HDd rhtu ;
H
U
T
cc2S ; ct2S ; cu2S
(2) (3)
G2V V2G EV BPT 0 pBC Nkn Pmax ; kntu gkn þ gkn i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU 0
(22)
i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU
1 BD pkntu pBS kntu ; aBD k
(23)
(Technical constraints of generating units)
cc2SC ; ct2ST ; cu2SU
C 0 pCctu Pmax;c ;
cc2SC ; ct2ST ; cu2SU
C pCctu pCct1;u Pup;c ;
pCct1;u
pCctu
(4)
C Pdown;c ;
C
T
cc2S ; ct2S ; cu2S
i h V2G EV BPT K N O F U 0 pBD kntu gkn Nkn Pmax ; ck2S ; cn2S ; t2 tk ; tk ; cu2S (24)
(5) U
(6)
G2V V2G EV BS Nkn pBS Pmax;k ; ck2SK ;cn2SN ;t ¼ tkF ;cu2SU kntu ¼ gkn þ gkn (25)
0
pH htu
H Pmax;h ;
H
U
T
ch2S ; ct2S ; cu2S
(7)
(Power balance in the day-ahead market)
X pRrtu
þ
pRS rtu
¼
R R Urtu Pmax;r ;
pRrtu ; pRS rtu 0;
R
U
T
cr2S ; ct2S ; cu2S
cr2SR ; ct2ST ; cu2SU
(8) (9)
pC;Disp þ ct
c2SCn
L;Disp
[2SLF;n
p[t
X
pH;Disp þ ht
h2SH n
X
þ
X
[2SLO;n
r2SRn D;Exp
¼ Pnt
þ
X
pR;Disp rt
X
EV;Exp
þgNC kn Pknt
pL;Disp [t
; cn2SN ; ct2ST
k2SKn
(Reserve deployments)
(26)
cc2SC ; ct2ST ; cu2SU
CDu C 0 rctu Pmax;c ;
(10)
(Power balance in the real-time dispatch)
X 0
CDd rctu
0
HDu rhtu
0
HDd rhtu
C Pmax;c ;
H Pmax;h ;
H Pmax;h ;
C
T
cc2S ; ct2S ; cu2S
U
H
T
U
H
T
U
ch2S ; ct2S ; cu2S ch2S ; ct2S ; cu2S
(11) (12) (13)
L;Disp
¼
L Pmax;[
L Pmax;[ ;
p=2; p=2 qDisp nt
c[2SL ; ct2ST L
c[2S ; ct2S
T
cn2SN ; ct2ST
1 qOð[Þtu qFð[Þtu ; X[
L L pL[tu Pmax;[ ; Pmax;[
p=2 qntu p=2;
[2SLO;n
h2SH n
pL[tu
D;Exp Pnt þ
X
X
pL;Disp [t
þ
X [2SLF;n
r2SRn
pL[tu
pL;Disp [t
D þ pUD ntu ¼ Pntu
X EV;Exp EV þ gNC pBC kn Pkntu Pknt kntu
k2SKn
k2SKn
N T U pBD kntu ; cn2S ; ct2S ; cu2S ;
c[2SL ; ct2ST ; cu2SU
c[2SL ; ct2ST ; cu2SU
cn2SN ; ct2ST ; cu2SU
where Q ¼ fpBC ; pBD ; pBS ; pC ; pC;Disp ; pH ; pH;Disp ; pL[tu ; pL;Disp ; [t kntu kntu kntu ctu ct htu ht
(15) (16)
(17)
(18) (19)
(State-of-charge constraints)
G2V V2G EV BS;0 Nkn pBS Pknu ; kntu ¼ gkn þ gkn
ck2SK ; cn2SN ;
t ¼ tkO 1; cu2SU 1 BD pkntu ; aBD k i h ck2SK ; cn2SN ; t2 tkO ; tkF ; cu2SU
BS BC BC pBS kntu ¼ pknt1;u þ ak pkntu
(27)
(14)
(Power flow constraints in the real-time dispatch)
pL[tu ¼
X
k2SKn
1 Disp Disp q qFð[Þt ; X[ Oð[Þt L;Disp p[t
(Power flow constraints in the day-ahead market)
p[t
c2SCn
X X CDu CDd HDu HDd rctu þ rhtu þ pRrtu pR;Disp rctu rhtu rt
R;Disp
Disp
UD CDu CDd HDu HDd pRrtu ; prt pRS rtu ; pntu ; rctu ; rctu ; rhtu ; rhtu ; qntu ; qnt g , is the set of optimization variables. The objective function (1) consists in minimizing the expected generation costs of dispatchable units (thermal and hydro), considering the scheduled energy in the day-ahead market and the deployment of reserves in the real-time dispatch, plus the cost of the unserved demand. Observe that the day-ahead scheduling is a first-stage decision which is considered to be made before knowing the actual realizations of the uncertain parameters. Only thermal and hydro units submit generation offer prices to the day-ahead market ðCcCO ; ChHO Þ and to the real-time dispatch ðCcCR ; ChHR Þ greater than or equal to zero. On the contrary, non-dispatchable units, such as PV or wind power plants, are assumed to bid at zero price. Constraints (2) and (3) establish the relationships among the power generated in each scenario ðpCctu ; pH Þ, the scheduled power htu C;Disp
(20)
(21)
in the day-ahead market ðpct
H;Disp
; pht
Þ, and up and down
CDu ; r CDd ) deployed reserves in the real-time dispatch for thermal (rctu ctu HDu , r HDd ), respectively. and hydro units (rhtu htu Constraints (4)e(6) limit the power output of thermal units by C C , PC ) and power ramps (Pup;c ). The their power limits (Pmax;c down;c H power limits of hydro units (Pmax;h ) are formulated by constraints
(7). Constraints (8)e(9) establish the power limits for renewable
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
rate-Min n, R. Za ~ ano / Energy xxx (2015) 1e9 M. Carrio R 2½0; 1 models the availability of generating units. Parameter Urtu renewable resources for unit r, hour t and scenario u. Therefore, if R is equal to 1, the full capacity of renewable unit r, ðP R Urtu max;r Þ, can be used. Constraints (10)e(11) and (12)e(13) limit the deployed reserves of thermal and hydro units, respectively. Constraints (14) determine the resulting power flow from the L;Disp
day-ahead schedule in each line (p[t ) as a function of the reactance of the line (X[) and the difference of voltage phase angles Disp
(qnt ) at buses O([) and F([) connected by line [. Constraints (15)
5
5. Numerical results The model proposed in Section 4 has been tested on a realistic case study based on the current configuration of the Iberian Peninsula power system. This power system comprises the mainland areas of Spain and Portugal, with an installed capacity over 100 GW. The numerical results are organized in two sections. First, a base case is solved, in which the model proposed in Section 4 is tested for different types of coordination between the ISO and PEVs. Secondly, a sensitivity analysis is performed.
L ) and voltage phase and (16) establish limits on power flows (Pmax;[
angles, respectively. Constraints (17)e(19) are equivalent to (14)e(16) and they are used to formulate the resulting power flows from the real-time dispatch. Constraints (20)e(25) formulate the state-of-charge of the PEV batteries controlled by the ISO. Variable pBS denotes the energy kntu BS;0 is a stored by type-k PEVs in hour t at bus n and scenario u, Pknu parameter modeling the energy stored by type-k PEVs at bus n and scenario u at the beginning of the first hour (tkO ) of the charging
represents the energy obtained from the period, variable pBC kntu power grid to charge the batteries of type-k PEVs in hour t at bus n denotes the power discharged from and scenario u, variable pBD kntu
=aBD are the eftype-k PEVs at bus n, hour t, and scenario u. aBC k k ficiency of charging/discharging type-k PEVs batteries from/into BPT and P BS are the peak the power grid respectively, and Pmax max;k
power transfer rate and the average capacity of the batteries of type-k PEVs, respectively. Constraints (20) establish the energy stored by those PEVs controlled by the ISO at the beginning of the charging period for each scenario. Constraints (21) compute the energy stored by PEVs in hour t as a function of the energy stored in the previous hour, t1, plus the energy charged from the power grid and minus the energy discharged from PEVs. Observe that the proposed model is based on one-hour periods, then power and energy units are equivalent. Constraints (22) bound the maximum amount of power that can be charged from the grid in a single hour. Constraints (23) and (24) formulate the upper bounds of the energy that can be discharged from the PEVs. Parameters gG2V and kt denote per unit number of vehicles controlled by G2V and gV2G kt V2G capabilities, respectively. These parameters, along with the in (26), per unit number of vehicles non controlled by the ISO, gNC kt þ gG2V þ gV2G ¼ 1. Completing this set, constraints satisfy that gNC kt kt kt (25) impose that all battery charging processes controlled by the system operator have to be completed at the end of the charge period (tkF ). Constraints (26) establish the power balance in the day-ahead
5.1. General input data A planning horizon of 31 h is analyzed. This planning horizon ranges from 0:00 h of a given day up to 7.00 h of the next day. The expected values of the electricity demand and the availability of wind and solar productions correspond to May 16th of 2011 in the Iberian Peninsula power system. The transmission network used to represent the Iberian Peninsula power system is based on the approximate model of the European Interconnected System reported in Ref. [25]. This model has been modified in order to include some recently built lines. The resulting transmission network is represented in Fig. 2. Light and dark lines represent 400 and 220 kV lines, respectively. The capacity of these lines is assumed to be 1350 and 450 MW, respectively [26]. The generating units have been located throughout the transmission network using the available information in the annual reports published by the ISOs of Spain [26] and Portugal [27]. Accordingly, the considered test system comprises 226 nodes, 390 transmission lines, 61 conventional thermal units, 77 hydro units and 90 wind farms. PV capacity is assigned to each node according to the local information provided in Refs. [26] and [27]. Table 1 provides the installed capacity for each generation technology. Four thermal technologies are considered: i) nuclear, ii) coal, iii) OCGT (open-cycle gas turbines) and CCGT (combined-cycle gas turbines). Moreover, three renewable technologies are also considered: hydro, wind and solar PV (photovoltaic). It is worth mentioning that the proposed formulation is general enough to straightforwardly include other renewable technologies such as biomass or CSP (Concentrating Solar Power) units. Observe that, in this study, the considered renewable sources constitute the 53.9% of the total installed capacity. The offering prices of nuclear, wind and PV units are assumed to be equal to zero. The load shed cost is fixed to 1000 V/MWh. Three PEV types based on the mobility study [28] are considered. The description of the charge period characterizing each PEV
EV;Exp represents the expected power demarket. Parameter Pknt mand of uncontrolled PEVs pertaining to type k in bus n and hour t.
The dual variable of this constraint ðlDA nt Þ represents the electricity price of the scheduled quantities in the day-ahead market. Therefore, all quantities traded in the day-ahead market are priced at lDA nt . Constraints (27) guaranty, for the realization of each considered scenario, the power balance for each bus and hour in the real-time dispatch. The deployments of reserves and the charge and discharge of PEVs have to meet the deviations on demand and on the production of non-dispatchable units. The probability-removed dual variable of this constraint represents the real-time price of the dispatched quantities in the real-time dispatch. All quantities traded in the real-time dispatch are priced at lRT ntu divided by the probability of the considered scenario tu.
Fig. 2. Iberian Peninsula transmission network.
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scenarios. Mathematically, the scenario generation of a stochastic process Xt can be formulated as follows:
Table 1 Installed capacity of generating technologies. Technology
Capacity (GW)
Average operating cost (V/MWh)
Nuclear Coal OCGT CCGT Hydro Wind PV Total
7.655 12.519 5.532 31.914 21.077 23.456 3.677 105.830
0.00 30.64 51.71 42.42 42.77 0.00 0.00 e
Table 2 PEV type characterization. Type
Beginning hour
Ending hour
Duration
Percentage of PEVs
1 2 3
16.00 21.00 2.00
7.00 (next day) 7.00 (next day) 21.00
16 h 11 h 19 h
45% 40% 15%
type is contained in Table 2. This table also provides the percentages of each PEV type considered in the study. For this study, each PEV has an actual energy consumption of 0.18 kW/km and is equipped with a 22 kWh battery. The efficiencies of the charger and the battery are 0.95 and 0.92, respectively. Thus, the efficiencies of charging and discharging processes (aBC and aBD ) k k are both considered to be 0.88. The parameters describing electrical vehicles are based on the characteristics of the Renault Zoe [29]. The charging voltage and the peak power transfer rate values depend on the technical characteristics of the charge coupler [30]. For simplicity, the study assumes that PEVs are charged under a charging voltage of 230 V and a peak power transfer rate of 7.2 kW. According to the PEV user patterns provided in Table 2, PEV demand scenarios have been obtained as established in Section 3. The daily distance driven by PEVs is characterized using the observed probability distribution of daily driven distance of Nissan Leaf vehicles described in Ref. [31] and the expected daily driving distance in Spain, [32]. Considering this information, the daily driven distance is described by using a normal distribution with mean and standard deviation equal to 35 and 9.6, respectively. This distribution is discretized using 5 scenarios, as represented in Fig. 3. For the uncontrolled PEV charge modeling, the charging profiles described in Section 3 are used to transform daily driving distances into hourly electric demand. The total number of private vehicles in the Iberian Peninsula considered in this study is 30 million, of which 30% are assumed to be PEVs. The uncertainties associated with solar and wind availabilities and with the system demand are also modeled by using a set of
Fig. 3. Scenario generation for daily distance driven.
Xtu ¼ Eu fXt g þ Nð0; st Þ;
ct2T; cu2U;
(28)
where Eu{$} refers to the expectation operator and N is the normal distribution. In (28), the standard deviation of the random term st is considered time-dependent, in such a way that it increases with the time period index. This scenario generation model has been previously used in Ref. [33]. The dependency between stochastic processes can be easily modeled considering the quasiecontemporaneous correlation of the series of errors. The reader is referred to [23] and [34] for further details. Observe that other scenario generation methods based on multi-variate time series models can also be used. An initial set of 1000 scenarios (5 PEV demand scenarios 200 demand/wind/PV scenarios) has been considered, which has been afterwards reduced to a final set of 15 scenarios by means of the scenario reduction algorithm presented in Ref. [35]. The resulting scenarios modeling the electricity demand, solar, and wind availabilities are represented in Fig. 4. The scenarios modeling charging profiles NC-1 and NC-2 are plotted in Fig. 5. All PEVs are forced to be totally charged at the end of the charging period defined for each PEVs type. As a consequence, the total demand corresponding to PEVs in both charging profiles is identical. The expected PEV demand is 68.3 GWh whereas the rest of system demand is 690.2 GWh. Therefore, the replacement of 30% of the combustion-engine cars by PEVs causes an increase of 9.9% in the total demand of the system. 5.2. Base case The base case includes the following situations: 1. Non-PEV: PEVs are not considered (gNC ¼ gG2V ¼ gV2G ¼ 0). kn kn kn 2. NC-1: The charge of PEVs is described according to the charging profile 1 proposed in Section 3 (gNC ¼ 1; gG2V ¼ gV2G ¼ 0). kn kn kn 3. NC-2: The charge of PEVs is described according to the charging profile 2 proposed in Section 3 (gNC ¼ 1; gG2V ¼ gV2G ¼ 0). kn kn kn 4. G2V: The ISO controls all PEVs using Grid-to-Vehicle capability (gNC ¼ 0; gG2V ¼ 1; gV2G ¼ 0). kn kn kn 5. V2G: The ISO controls all PEVs using Vehicle-to-Grid capability (gNC ¼ gG2V ¼ 0; gV2G ¼ 1). kn kn kn
Fig. 4. Scenarios for electricity demand, and wind and solar availabilities.
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Fig. 6. Expected generating mix.
Fig. 5. Scenarios for PEV demand.
All cases are solved using CPLEX 12.2.0.1 [19] under GAMS [36] on a Linux-based server with four 2.9 GHz processors and 250 GB of RAM. Table 3 provides the observed results for each case. The total costs correspond to the objective function (1) for each case. As expected, the case with the smallest operation cost is the one in which there are no PEVs. Observe that the increment of the cost is relevant when PEVs are incorporated. Concretely, a 9.9% increment in the total demand, which is caused by charging PEVs, increases the expected cost a 14.0% in the most favorable case (G2V) and a 17.1% in the worst case (NC-1). In G2V and V2G cases the expected cost is reduced with respect to the best uncontrolled case (NC-2) in 2.1% and 2.2%, respectively. It is also worth mentioning that G2V and V2G obtain quite similar expected costs. This first result indicates that, in the analyzed case, V2G does not significantly outperforms G2V in terms of the expected cost. In the G2V case, it has also been observed that the expected energy cycled out from the batteries only represents 2.6% of the energy charged. Therefore, problems related to the premature aging of the batteries are not expected. With respect to the computional issues, the size of the solved models comprises up to millions of variables and constraints. As expected, the computing times of the optimization problems considering G2V and V2G capabilities are larger than those of the rest of cases. Fig. 6 represents the expected generating mix resulting from Non-PEV, NC-1 and G2V cases. It can be observed that hydro and CCGT units are used to satisfy the demand in peak hours, whereas nuclear and coal units are used as base units. It can be also observed that the thermal production is higher in NC-1 than in G2V case. The allocation of the expected PEV demand throughout the 31hour horizon planning is represented in Fig. 7. This figure shows that in G2V and V2G cases, the PEV demand is mainly located in the valley hours of the day and in those periods with high wind resources (see Fig. 4). Fig. 8 represents the wind spillage for different cases. The dark line represents the expected value, whereas the gray color
Fig. 7. PEV demand.
represents the area comprised within the maximum and minimum values. Observe that, if coordination is accounted for, the reduction of the expected and maximum wind spillage is apparent. The resulting average day-ahead market prices for NC-1, NC-2, G2V and V2G cases are represented in Fig. 9. These prices are computed as the dual variables of the day-ahead energy balance constraints (constraints (26)). In case NC-1, expected prices experiment a high variation between peak and valley hours. This case presents the smallest and highest prices in valley and peak hours, respectively. On the other hand, G2V and V2G present a small difference in price values between valley and peak hours. Fig. 10 depicts the average real-time prices for each case and scenario. Black circles represent the expected value of the prices whereas gray lines represent their values for each scenario. These prices correspond with the probability-removed dual variables of the real-time energy balance (constraints (27)) in each scenario divided by the probability of that scenario. It is observed that the
Table 3 Results. Total cost (millions V)
6
# Variables (10 ): # Constraints (106): Time (s):
Non-PEV
NC-1
NC-2
G2V
V2G
11.692
14.105
13.912
13.620
13.603
1.43 1.51 4061.0
1.43 1.51 3438.7
1.43 1.51 2862.7
1.58 1.81 11730.2
1.58 1.81 16872.4
Fig. 8. Wind spillage.
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8
Fig. 9. Day-ahead prices.
Fig. 10. Real-time prices.
volatility of balancing prices is highly reduced for G2V and V2G cases. 5.3. Sensitivity analysis In this section, a sensitivity test is performed to study the impact on the results of the variation of input data. For this purpose, the variation of the following four parameters is analyzed: the number EV ), the portion of PEVs controlled by the system operator of PEVs (Nkn R , gV2G ), the capacity of renewable resources (Pmax;r ), and the (gG2V kn kn
BPT ). In all cases, non-analyzed peak power transfer rate of PEVs (Pmax parameters are fixed to the values previously established in Subsection 5.1. This analysis focuses on the comparison of cases G2V and V2G with regard to NC-2, which represents the most favorable of all uncontrolled-charge cases. The obtained results are represented in Fig. 11. This figure provides, for each analyzed parameter, the variation of: a) the expected cost reduction obtained in G2V and V2G cases with respect to NC-2, b) the expected wind spillage, and c) the expected deployed reserve (summation of up and down deployed reserves by thermal and hydro units). Firstly, Fig. 11 shows that the reduction of the expected costs in G2V and V2G cases with respect to NC-2 has a maximum for an integration of PEVs around 40% over the total number of vehicles. For an integration of PEVs greater than that value, the expected deployment of reserves increases in the controlled cases, which causes an increment in the expected costs. This fact reduces the difference between the expected costs in controlled and uncontrolled cases. However, it should be emphasized that G2V and V2G cases outperform NC-2 case in all instances in terms of the expected cost. It is noticeable that only for a 10% of PEVs over all vehicles, the reduction of the cost in coordinated charge cases is significant. It can be also observed that G2V and V2G cases attain smaller expected costs with respect to NC-2 as the number of controlled PEVs increases. This fact is a consequence of the reduction of both the expected wind spillage and deployed reserves. It is remarkable that for 20% of controlled PEVs, the reduction of the expected cost in coordinated charge cases with respect to NC-2 case is equal to 39.5% of the reduction obtained with 100% of controlled PEVs. It is also interesting to study the case in which the installed capacity on wind and PV units is modified. It is observed a large reduction of the expected cost in the coordinated charge cases with respect to NC-2 case as the renewable capacity increases. This reduction is over 4.5% in the case in which the installed capacity reaches the double value of the considered one in the base case. As expected, both expected wind spillage and deployed reserves are higher if renewable capacity increases.
Fig. 11. Sensitivity analysis.
n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111
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Finally, it is observed that a large enough peak power transfer rate reduces the number of hours needed for the charging and discharging processes, which results in a better performance of V2G case with respect to G2V case in terms of the expected cost and wind spillage. 6. Conclusions This paper analyzes the integration of a high number of electrical vehicles in a renewable-dominated power system which is operated using a network-constrained stochastic economic dispatch. For this purpose, different coordination schemes between the ISO and PEV users have been modeled. Specifically, it has been considered that G2V and V2G capabilities are used in the real-time dispatch by the ISO to counter deviations in the energy demand and in the power outputs of non-dispatchable generating units. This has been mathematically modeled using a two-stage stochastic programming problem in which the day-ahead market is characterized in the first stage, whereas the second stage represents the real-time dispatch. The system conventional demand, the demand of charging PEVs, and the power outputs of non-dispatchable units have been characterized using a set of plausible scenarios. The proposed formulation has been successfully tested on a case study based on the Iberian Peninsula power system. The computational requirements are higher if G2V and V2G capabilities are taken into account, but they are kept under reasonable levels. The numerical results reveal that including coordination between the ISO and the charge of PEVs reduces the total expected operation cost. Additionally, this coordination allows taking advantage of renewable resources reducing the wind spillage and the usage of deployed reserves. The difference of prices between peak and valley hours in the day-ahead market is reduced if coordination is taken into account. Additionally, the volatility of the real-time prices is also reduced if coordination is implemented. The realization of a sensitivity analysis allows us to observe that, although the number of either total or controlled PEVs be small, the usage of coordinated charge reduces the expected costs with respect to uncontrolled cases. Finally, it is also concluded that the coordinated charge is specially tailored for those power systems with a significant amount of renewable (non-dispatchable) resources. References [1] Tuttle DP, Baldick R. The evolution of plug-in electric vehicle-grid interactions. Operat Res 2011;3(1):500e5. [2] Kempton W, Letendre S. Electric vehicles as a new power source for electric utilities. Transp Res Part D 1997;2:157e75. [3] Tomic J, Kempton W. Using fleets of electric-drive vehicles for grid support. J Power Sources 2007;168:459e68. zquez MA, Bouffard F, Silva V. Electric vehicle aggregator system [4] Ortega-Va operator coordination for charging scheduling and services procurement. IEEE Trans Power Syst 2013;28:1806e15. [5] Lund H, Kempton W. Integration of renewable energy into the transport and electricity sectors through V2G. Energy Policy 2008;36:3578e87. [6] Vlachogiannis JG. Probabilistic constrained load flow considering integration of wind power generation and electric vehicles. IEEE Trans Power Syst 2009;33(4):1808e17. [7] Finn P, Fitzpatrick C, Connolly D. Demand side management of electric car charging: benefits for consumer and grid. Energy 2012;42:358e63.
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n M, Za rate-Min ~ ano R, Operation of renewable-dominated power systems with a significant penetration Please cite this article in press as: Carrio of plug-in electric vehicles, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.07.111