Reliability improvement considering plug-in hybrid

IET Generation, Transmission & Distribution Research Article

Reliability improvement considering plug-in hybrid electric vehicles parking lots ancillary services: a stochastic multi-criteria approach

ISSN 1751-8687 Received on 27th April 2017 Revised 21st August 2017 Accepted on 27th September 2017 doi: 10.1049/iet-gtd.2017.0657 www.ietdl.org

Seyed Mohsen Mohammadi-Hosseininejad1, Alireza Fereidunian2 , Hamid Lesani1 1School

of Electrical and Computer Engineering, University of Tehran, Tehran, Iran of Electrical Engineering, K. N. Toosi University of Technology (KNTU), Tehran, Iran E-mail: [email protected]

2Faculty

Abstract: In this study, the electric vehicle parking lot (PL) allocation problem is solved through considering PLs ancillary services in both reliability-related and operational programmes. The reliability-related objective function aims to simultaneously minimise the total reliability cost and system average interruption duration index. The total cost of reliability includes: total customer interruption cost, total cost of PL installation, and PL incorporation costs. PLs can provide two ancillary services in the restoration process, including: acting as a backup unit for the interrupted zone and as a storage unit in the backup feeder, to reduce the interruption duration and congestion occurrence, respectively. Moreover, a stochastic formulation is introduced for the reliability-based PL allocation to consider the uncertainties of restoration problem including: distribution system conditions and the available power of the participating PLs during restoration process. These uncertainties are realised through several restoration scenarios, which are derived based on historical data of outage occurrence and PLs tendency to participate in restoration process. Furthermore, energy loss and voltage deviation costs are considered in the operational objective function. Thus, both reliability-based and operational objectives are considered in the collective objective function to optimally benefit from different PLs ancillary services. A standard test system (RBTS-4) is employed to evaluate the effectiveness of the proposed approach.

INC/PMC

Nomenclature Subscripts ch/dch/k

i/l j/s m opt t/t′

charge/discharge/available plug-in hybrid vehicles (PHEVs) load point number/branch number contingency/restoration scenario restoration strategies for each contingency optimal value time interval for restoration/operation

electric

Superscripts cap/ini/pen cs/pl/tr d/net ent/ext inco/ave max / min rel/res/opr

req vd/des

capacity/initial value/penalty charge charging station (CS)/parking lot (PL)/transformer demand/net value entering to/existing from a PL incorporated/available PEHVs. maximum/minimum reliability/restoration process/operational programmes number of required CSs should be installed voltage deviation/desired value

Variables and parameters AYCP Bdg DLF EBC ESAIDI ESOC ETCI ETRC ETPIC ETYC

average yearly cost of a PL available budget for the PL allocation distribution load flow matrix equivalent battery capacity for the installed PLs expected value of system average interruption duration index (hours per customer per year) equivalent state of charge (SOC) for the installed PLs expected total interruption cost ($/year) expected total reliability cost ($) expected total PL incorporation cost ($) expected total yearly cost ($)

IET Gener. Transm. Distrib. © The Institution of Engineering and Technology 2017

IP/EP ir/lt LRI nc/N NI OF/COF P/Q/S PF/Pen R/ X /M SAIDI SDLF SI SOC TOC TPIC TPIMC TPLC TVDC uv/ov V /VDV [ΔV]/[I] xhi / lo

λ η ω/ β π r

investment cost for constructing/maintenance cost of a CS incentive price/electricity price interest rate/life time of a PL load restoration indicator number of customers/number of electric vehicles integer decision variable which is equal to number of installed CSs objective function/collective OF active/reactive/apparent power power factor/penalty factor ($/V) resistance/reactance/big M system average interruption duration index (hours per customer per year) selected DLF matrix binary decision variable that is equal to 1 if restoration strategy applicable in contingency SOC of a PHEV total operation cost ($) total PL incorporation cost ($) total PL investment and maintenance cost ($) total power loss cost ($) total voltage deviation cost ($) amount of under/over voltage for each load point voltage level/voltage deviation value (kV) bus voltage matrix/bus current injection matrix binary variable which is equal to 1 if the voltage level becomes higher/lower than the acceptable level failure rate charging/ discharging efficiency weighting coefficients probability of a restoration scenario interruption duration

1 Introduction Electric vehicles (EVs) are highly considered as substantial opportunities to mitigate the global warming risk and utilise the 1

recent advancement on battery technology, promotion of EVs is expected to reduce the emissions produced in the transportation and power system sectors, simultaneously. Furthermore, other factors such as fossil fuel shortages and rising fuel price accelerate the EV deployment in developed cities in last decade [1, 2]. In spite of these benefits, poorly managed high penetration of EVs imposes peaks on the electric power distribution system (EDS) demand pattern, which causes problems such as feeder congestion and network losses. Thus, the uncontrolled promotion of these movable micro power plants jeopardises the power system physical security [3]. In this regard, several studies have been conducted to reduce these undesirable issues [3–11]. Sortomme et al. [3] proposed a control strategy for minimising the network losses via coordinating the plug-in hybrid EVs (PHEVs) charging pattern. In [4], voltage profile improvement and network losses reduction are two objectives of the PHEVs real-time coordination. Moreover, alleviating the congestion occurrence induced by uncontrolled charging of PHEVs is conducted in [5]. Besides, PHEVs parking lots (PLs) and distributed renewable resources are simultaneously allocated in EDS in [6]. Additionally, Amini and Islam [7] proposed a reliability-constraint optimum PLs allocation considering three significant EDS reliability indices. Also, optimal PLs placement with optimal power systems scheduling is studied in [8], aiming at maximising the benefit, considering various peak load and electricity prices states. In [9], the optimal placement of EVs charging stations (CSs) is formulated aiming at minimising the total cost of PLs placement. Again, the optimal CS placement is conducted through simultaneous consideration of electric and traffic networks in [10]. Further, an optimal planning framework for different CSs types of is presented in [11]. New applications have been proposed for PHEVs in the literature, following the introduction of the vehicle to grid concept [12–17]. In [12], PHEVs are incorporated in unit commitment, to reduce the operating cost of power system, and compensate the wind energy fluctuations. Moreover, peak shaving is proposed in [13] as one of the benefits of optimally coordinated PEVs charging pattern. Furthermore, Wu et al. [14] investigated PHEVs participation in frequency and voltage regulation programmes. In addition, the optimal power factor of PHEVs PLs is determined in [15], considering PHEVs participation in loss reduction programme. Although PHEVs are considered as a threat to the physical security of the EDS, they can be regarded as backup sources, in case of failure occurrence, to decrease the interruption duration for affected customers which leads to the reliability improvement [16, 17]. Sharma et al. [17] proposed a multi-agent system approach for incorporating the EVs in the restoration process. Furthermore, Rahmani-andalibi and Venayagamoorthy [18] investigated the effect of PHEV contribution on system adequacy, using Markov processes. Moreover, the role of PL as a storage system is investigated in enhancing the reliability level of a renewable-based EDSs in [19]. In [20], the effect of PHEV incorporation is examined in two possible failures. Nevertheless, the optimal evaluation of PHEV contribution, available for restoration processes, pertaining to all possible failures is not elaborated. As such, EVs PL allocation problem (EVPLAP) should be solved to improve the effects of the PHEV contribution in restoration process [18, 19]. In [18], the objective function of the EVPLAP is considered as improving the system reliability through cooperating with DSO. However, the PHEV owners’ comfort is not considered in the behavioural modelling. Moreover, restoration priority and technical reliability evaluation indices such as system average interruption duration index (SAIDI), and so on are not considered. Again, other effective facilities of PLs such as network loss reduction and voltage profile improvement are rarely considered in literature. In this regard, Neyestani et al. [19] proposed a multi-criteria EVPLAP through considering reliability, voltage deviation, and loss costs simultaneously. However, the impacts of available controllable devices are not considered in the reliability evaluation of this study. Further, restoration priority and technical reliability indices, as two determinant factors of reliability-based EVPLAP remain disregarded. Moreover, the optimal number of CSs is not 2

determined in [19]. Our past research conducts the EVPLAP to enhance the self-healing ability of smart EDS in case of the external fault occurrence [16]. However, there are certain differences between [16] and the present research, since, [16] deals with external contingencies, whereas this work proposes a contingency-based EVPLAP which aims to reinforce the healer system of distribution network against the internal faults. Moreover, the economics of PL allocation are not considered in [16], while this important factor is covered in this paper. In addition, the optimal sizes of the installed PLs are not determined in [16]. Moreover, deterministic EVPLAP is solved in [20] considering healer reinforcement approaches. However, the uncertainties of service restoration, including load profile, energy price, and available power of PLs are not covered in [20]. Further, PLs ancillary services in operational programmes which lead to quality of service improvement – i.e. voltage deviation and power loss costs reduction – are not considered in [20]. In this paper, a stochastic model is proposed to consider the existing uncertainties more accurately in contingency-based EVPLAP. These stochastic parameters during contingencies – including: EDS condition (such as load level, electricity price etc.) and the available power of the participating PLs [such as number of available PHEVs per system buses, state of charge (SOC) of PHEVs etc.] – are realised through considering prospective scenarios. Accordingly, the optimal PL locations and sizes are selected regarding the prospective scenarios for the EDS system and the available power of the PLs in case of contingencies. Moreover, the objective function of EVPLAP in this paper simultaneously minimises the total reliability cost (TRC) and SAIDI indices. The TRC composes of customers’ interruption costs, PLs installation cost, and PL incorporation costs. In addition, two types of PLs contribution in the service restoration process are considered in the submitted manuscript, including cooperating with the outage management system as a ‘backup unit’ and ‘storage unit’ to reduce the interruption duration for customers in the faulted zone and its downstream zone(s), respectively. Further, this paper explores the optimal number of CSs to be installed in the EDS. Moreover, network power loss cost and voltage deviation cost are considered in the proposed EVPLAP to deal with both operational and reliability-related issues. Herein, the collective case presents a comprehensive EVPLAP through considering various PLs ancillary services. The contributions can be summarised as follows: • Proposing a stochastic model to determine the effect of incorporating PL ancillary services on reliability improvement considering the uncertainties in the service restoration, • Considering PLs ancillary services in power loss reduction programmes including: injecting active and reactive powers, • Considering PLs ancillary services in voltage deviation reduction programmes, • Considering two types for PLs contribution in the service restoration part including acting as a backup unit for customers in the faulted zone and acting as a storage unit in the backup feeding path to preclude backup feeder congestion and restore load points in the downstream zones of the faulted section. The rest of the paper is organised as follows. The proposed scheme for PLs cooperation with the outage management system is introduced in Section 2. Afterwards, the EVPLAP is formulated in Section 3 considering all PLs available ancillary services. In Section 4, the salient attributes of the proposed formulation for EVPLAP are investigated through implementing on the standard reliability test system and finally the paper is concluded in Section 5.

2 PL participation in service restoration After fault detection and isolation, alarm messages are sent to PLs in the affected zones, asking for their available power from PHEVs. Hence, PLs declare their participation data, i.e. their calculated equivalent battery capacity and equivalent SOC, using (1) and (2), respectively. Herein, t0 denotes the initial equivalent IET Gener. Transm. Distrib. © The Institution of Engineering and Technology 2017

SOC. Then, the PLs send their participation data to outage management system. Afterwards, outage management system determines their optimal power exchange during restoration process, based on its objective function(s) EBCres i = ESOCitres0 =

∑ Pikcap

(1)

k

res ∑ SOCini ik ,

k

(2)

3 Problem formulation This section explains formulation of the EVPLAP, as well as optimisation constraints for distribution network and PL ones. 3.1 Reliability-related objective function for EVPLAP Service restoration might have objectives like minimising the interrupted loads [21]; however, in this paper the objective function is minimising the expected SAIDI (ESAIDI) and the expected TRC (ETRC), as two reliability-related objectives. Moreover, these should be normalised with the optimal ones because of distinct values of each index, to equalise the effect of each index in objective function, as follows: OFrel : ω1 .

ETRC − TRCopt ESAIDI − SAIDIopt + ω2 . TRCopt SAIDIopt

(3)

The optimal value of each index (TRCopt and SAIDIopt) is determined when one of the weighting coefficients is set to zero (and the other is one) [22]. The ETRC index consists of three parts including: expected total interruption cost (ETIC), total PL investment and maintenance cost (TPIMC), and the expected total PLs incorporation cost in service restoration (ETPICres) (4). In (5), ETIC is calculated for all possible contingencies, considering different customer types. According to this formula, the restoration priority might change for different load points based on their customer composition ETRC = ETIC + ETPICres + TPIMC ETIC =

∑ πs . ∑ s

i

ρispen .

∑∑ j

t

d λ j . Pits . ri jts

(4) (5)

Moreover, TPIMC consists of two different costs including investment and maintenance costs (6). AYCP is the average yearly cost of a PL, which has just one CS, that is calculated through annualising INC as present investment cost of the PL including: purchasing CS elements and land (7). Moreover, PMC pertains to yearly PL maintenance cost such as replacement and repair of the elements [23, 24]. Thus, TPIMC is obtained based on the number of CSs installed in PL located at load point i NIcs i , which is decision variable of the problem TPIMC =

∑ (AYCPi + PMC) . NIcsi i

AYCPi = ir . (1 + ir)lt /((1 + ir)lt − 1) . (INCi)

(6) (7)

In addition, the interrupted area extends, if the backup feeder becomes congested during service restoration process. Hence, in addition to the load points in the faulted zone, the downstream ones should tolerate interruption duration equal to the repairing time. Acting as backup units, PLs in the faulted zone could supply healthy load points in islanded mode. Also, acting as storage units, PLs in backup feeding path could prevent congestion occurrence in the backup feeding path through injecting their available power. This PL participation should be rewarded by the distribution system operator (DSO). This capacity payment is proportional to the PLs injected power. However, the PL participation leads to load IET Gener. Transm. Distrib. © The Institution of Engineering and Technology 2017

restoration, thus the customer returns a percentage of the incentive price, as their electricity bill. Accordingly, the overall cost of PLs contribution should be calculated as follows: ETPICres =

∑ πs . ∑ ∑ ∑ Pipljtsres . λ j . (IPitsres − EPts) ,

s

i

j

(8)

t

where the injected active power of PLs in each hour of restoration is determined through (9). Herein, the number of incorporated PHEVs might be lower than the number of available participating PHEVs in the restoration process. Thus, the exchangeable active power of each PL should be adjusted based on the PHEV incorporation to PHEV participation ratio Niinco, res /Niave, res . Further, the number of incorporated PHEVs should be limited to the number of available PHEVs (10), and also to the number of CSs installed at each load point (11) res Pipljts = Nisinco, res /Nisave, res . η . ESOCres i jts − ESOCi j(t − 1)s

(9)

Nisinco, res ≤ Nisave, res

(10)

Nisinco, res ≤ NIcs i

(11)

In addition, the SAIDI index should be evaluated in different manner rather prevalent ones because of considering the actual (variable) load in the restoration process (12). Herein, ri jts is a variable which is equals to one if all of customers connected to the ith load point are interrupted at hour t of the repair time of the contingency j occurrence in the restoration scenario s. Moreover, for each load point, ri jts is proportional to the number of customers interrupted in hour t of the j contingency repair time. This variable should be calculated for each contingency through load flow analysis which is explained in Section 3.5 ESAIDI =

∑ s

πs .

∑ ∑ ∑ λ j . ri jts . nci ∑ nci i

j

t

(12)

i

3.2 Operational objective function for EVPLAP Network power loss reduction and voltage profile improvement can be accounted as two advantageous applications of PLs, due to their ability to inject active and reactive powers. Although the PLs contribution could lead to power loss reduction, this ancillary service should be paid by DSO. Thus, the operational objective function includes power loss, voltage regulation, and PLs participation costs TOC = TPLC + TVDC + TPICopr

(13)

3.2.1 Network loss cost: The total network power loss cost is determined via considering transformer and line losses (14) [25]. The net demanded apparent power of each load point is equal to the demanded apparent power of its connected loads minus the injected apparent power of its connected PLs (15). The exchangeable active power of each PL is determined through (16). Similar to (9), the exchangeable active power of PLs should be normalised with ratio of the number of incorporated PHEVs to the number of participating PHEV in operational programme. Also, PHEV owners’ participation in the power loss and voltage deviation reduction programmes is different from that of the restoration process. Thus, the number of available PHEVs in the ave, opr operational programme Nit′ is different from that of the restoration process Niave, res . It is assumed that, the number of participating PHEVs remains unchanged during the restoration process, due to the short repair time of network faults (usually 2–3 h). However, in the operational programmes, the number of participating PHEVs and their available power change during the operation period (24 h). Hence, the arrival and departure of PHEVs opr, ent opr, ext and ESOCit′ ) are considered for calculation of the (ESOCit′ 3

exchangeable power of each PL in (16). Further, the number of PHEVs that could be incorporated in each load point for the operational programme should be restricted to the number of participating PHEVs (17) and the number of installed CSs in that load point (18). The PLs could inject both active and reactive powers [17]. In this paper, it is assumed that the power factor of the injected power of PLs is fixed at 0.85 (i.e. PFpl = 0.85). The injected apparent power of PLs should be restricted due to the maximum apparent power of chargers (19) TPLC = 365 × ∑ EPt′ . Pt′loss, tr + Pt′loss, l

(14)

t′

pl

net d Sit′ = Sit′ − Sit′ pl

inco, opr

ave, opr

Pit′ = Nit′

/Nit′

+ ESOCit′

− ESOCit′

opr, ent

(15)

inco, opr

ave, opr

≤ Nit′

inco, opr

Nit′

ETYC = (ETRC + TOC) (16) (17)

≤ NIcs i

(18)

pl

Pit′ ≤ Smax, cs . PF pl . NIcs i

(19)

3.2.2 Voltage deviation cost: The DSO regulates the voltage level through incorporating capacitor banks to reduce the reactive power flows in the network. In this regard, PLs could inject both active and reactive powers, thus reduce the DSO necessity for installing capacitor banks. In this study, it is assumed that there exists a contract between customers and DSO which determines the customers’ desired voltage quality. Therefore, total voltage deviation cost is formulated in (20) where the first part refers to the cost of installing capacitor banks and the second one pertains to the penalty cost should be paid by DSO based on the signed contract TVDC = 365 × ∑ ∑ Penvd it′ . VDVit′ i

The EVPLAP should be solved via considering both operational and reliability-related objective functions to optimally benefit from various PLs ancillary services. Similar to ETRC, the operational objectives are parts of yearly costs associated with network operation. Therefore, expected total yearly cost ETYC imposed on the network operator includes: ETRC and TOC (28). The collective objective function is formulated in (29) to simultaneously consider both reliability-related and operational issues. Herein, both components of the collective objective function (ESAIDI and ETYC) possess dissimilar dimensions. In order to deal with this issue, both components are normalised by minimum (optimum) values as presented in (29), and as follows:

opr

opr

. η . ESOCit′ − ESOCi(t′ − 1)

opr, ext

Nit′

3.3 Collective objective function for the EVPLAP

t′

(20)

ESAIDI − SAIDIopt SAIDIopt

hi 0 ≤ ovit′ ≤ M × xit′

(21)

hi 0 ≤ ovit′ − V it′ − V ides ≤ M × 1 − xit′

(22)

lo 0 ≤ uvit′ ≤ M × xit′

(23)

3.4.1 PLs constraints: There exist charging/discharging rate constraints for PLs (30). Also, this constraint should be adjusted based on the number of installed CSs in each load point. Moreover, it is assumed that the maximum allowable number of installed CSs is different for the network load points due to the existing municipal limitations, which is considered in (31). In addition, the total number of CSs should be greater than the number of incumbent CSs to satisfy the existing demand of the PHEV owners (32). Furthermore, the SOC of PHEVs should be restricted to prevent battery degradation. Consequently, the equivalent SOC of PLs during restoration process should be bounded, proportional to the ratio of the number of incorporated PHEVs to the number of participating ones (33). The same equation could be written for operational case (34). Moreover, the total PLs allocation cost must be limited to the available budget for PL allocation (35)

(24)

lo hi xit′ + xit′ ≤1

(25)

VDVit′ = ovit′ + uvit′

(26)

3.2.3 PLs participation cost for operational programmes: Although PLs could cooperate with DSO to simultaneously reduce network power loss and improve voltage profile, there exists an additional cost which should be paid to PHEV owners. Thus, the participation cost paid for incorporating PLs could be obtained from TPICopr = 365 × ∑ ∑ Pit′

pl, opr

t′

. EPit′

max, cs max, cs Pdch × NIcs × NIcs i ≤ Pi jts, it′ ≤ Pch i

(30)

max, cs NIcs i ≤ NIi

(31)

∑ NIcsi ≥ NIcs nec ,

(27)

(32)

i

max inco, res SOCLmin . EBCres /Nisave, res ≤ ESOCres i . N is i jts ≤ SOCL (33) inco, res . EBCres /Nisave, res i . N is

opt

lo 0 ≤ uvit′ + V it′ − V ides ≤ M × 1 − xit′

(29)

3.4 Constraints

pl

The voltage deviation penalty is extracted from [26]. Also, the voltage deviation is linearly calculated from (21)–(26), where M is a big number (e.g. 1,000,000) and x is a binary variable which is equal to one if the load voltage deviates from the acceptable level. For instance, if the voltage level of a load point becomes lower than the desired value, xhi equals to one and the amount of under voltage is calculated, i.e. uvit′ = V ides − V it′

4

ETYC − TYCopt + β2 TYCopt

Minimise: ⋅ COF = β1

Penvd it′

i

(28)

inco, opr

SOCLmin . EBCit′ . Nit′ opt . EBCit′ .

inco, opr ave, opr Nit′ /Nit′

ave, opr

/Nit′

opr

≤ ESOCi jt′ ≤ SOCLmax

∑ INCi . NIcsi ≤ Bdg

max

i

(34)

(35)

3.5 Network constraints For each contingency, the load flow equations should be solved to select the most efficient restoration strategy (36) and (37). Thus, in the Teng's load flow method [27], the appropriate distribution load flow matrix should be selected for each contingency (38). Herein, it is assumed that one restoration strategy can be selected in each hour of restoration (39). The selected restoration strategy leads to switching manoeuvre for restoring the interrupted customers. Hence, restoration possibility for load points in the downstream zones of the faulted section is determined according to the selected restoration strategy (40). Herein, if one of the downstream zones cannot be transferred to the backup feeder in the selected restoration strategy, the load restoration indicator (LRI) for load points in this zone equals to zero. Subsequently, their demanded IET Gener. Transm. Distrib. © The Institution of Engineering and Technology 2017

Fig. 1 Test system schematics (modified RBTS-4) [28]

current and power (both active and reactive) will equal to zero, based on (40) and (37), respectively. Thus, customers in these load points should tolerate the outage time; however, if PLs are installed in these load points, the demanded power of them could be provided by these PLs, fully or partially. Therefore, the outage time for these load points decreases based on the exchangeable power of the installed PLs (40)–(43). Moreover, the operational objective function should be calculated in the normal operation of the EDS through load flow analysis. In this regard, expressions (14)–(26), (36), (37), and (44)–(48) are considered for the load flow analysis where t′ refers to the normal operation period of the EDS, e.g. 24 h of a day. Accordingly, two groups of subscripts are defined in these expressions for each parameters/variables which denote the load flow equations for the restoration process and operational programme ΔV jts, t′ = SDLF jts, t′ . [I djts, t′] net Pinet jts, it′ + jQi jts, it′ V i jts, it′

Iidjts, it′ =

∗

∑ DLF jm . SI jmts

SDLF jts =

m

∑ SI jmts = 1 m

Iidjts ≤ I d, max .

∑ LRIi jmts . SI jmts . m

pl d Pinet jts = Pi jts . 1 − ri jts − Pi jts d Qinet jts = Qi jts . 1 − ri jts

0 ≤ ri jts ≤

∑ m

(36)

1 − LRIi jmts . SI jmts

(37)

(38) (39)

(40) (41) (42) (43)

net d Pit′ = Pit′ − Pit′

pl

(44)

pl

(45)

net d Qit′ = Qit′ − Qit′

Moreover, network load points must be fed within the acceptable voltage range (46). Furthermore, thermal limits of feeders are the most restrictive constraint of the EDSs. Hence, the feeders should not be overloaded during the restoration process (47)–(48). The lines current is calculated in (47) using bus injected to branch current matrix [27]. Thus, ri jts is calculated through (36)–(43) and (46)–(48). Accordingly, the mentioned reliability indices – i.e. ETCI and ESAIDI – are derived using (5) and (12), respectively V imin ≤ V i jts, it′ ≤ V imax

(46)

Il jts, lt′ = BIBC jt, t′ . [I djts, t′]

(47)


Il jts, lt′ ≤ Ilmax

(48)

4 Simulation results 4.1 Test system The proposed methodology for EVPLAP is implemented to bus number four of the standard Roy Billiton test system (RBTS 4), which includes seven radial feeders, five tie switches, and 4779 customers including residential, industrial, and commercial customers [28]. The test system is assumed to be reinforced with 11 remotely controlled switches to accurately accomplish the contingency-based PL allocation, as shown in Fig. 1. In addition, failure rates for lines, busbars, and transformers are set same as given in [28]. Also, it is assumed that the defected transformer could be replaced via a reserve one in 5 h. Moreover, the load behaviour pattern during restoration is considered different for various load types and contingency occurrence hours [29]. Further, the number of CSs that could be installed in each load point is assumed to be restricted, due to some reasons such as physical limits. This limitation is randomly considered for different load points. Moreover, it is assumed that, the battery capacities of PHEVs are 24 or 16 kWh [30]. In addition, the SOCs of the PHEVs are circumscribed to maximum and minimum allowable SOC, 90 and 20%, respectively [31]. Also, PL chargers are supposed to be capable of fast battery charging/discharging. Further, the charging/ discharging capacity of a CS is restricted to 22 kWh [31]. In addition, the uncertainties of the restoration problem are realised, using a number of restoration scenarios which are generated as follows. 4.2 Uncertainty characterisation Restoration problem deals with uncertainties caused by distribution system and available power of the participating PLs, due to the unpredictable nature of fault occurrence time. In this study, these uncertainties are considered, using historical data, as follows. 4.2.1 Distribution system uncertainties: Network average load has been considered in most of prevalent reliability evaluation methods. However, due to the time-dependent PHEV owners’ behaviour, when investigating the effect of PHEVs participation in service restoration, the reliability evaluation indices should be considered as time dependent. In this paper, using historical data [29], the outage occurrence probability is derived for each hour of the day. For instance, probability of failure occurrence for lines is depicted in Fig. 2. Then, an electricity price is assigned to each restoration scenario, respecting their failure occurrence hour. Moreover, the system load profile is also assigned to each prospective outage occurrence scenario, considering different customer types (residential, commercial, and industrial). Finally, a number of valid scenarios are generated for distribution system conditions during restoration process, as illustrated in Fig. 3. 4.2.2 Available power of the participating PLs: The PHEVs availability to participate in service restoration might change for 5

different outage occurrence times. Moreover, the available power from the PHEVs alters for different network load points, based on failure occurrence time and their customer type. Thus, the available power of the participating PLs is estimated for the generated scenarios (outputs of step 1 in Fig. 3) based on the national household travel data [32]. In order to generate the scenarios of PHEVs behaviour, expressions (49)–(53) are employed. Truncated Gaussian distribution is widely employed for modelling the uncertainties in PHEVs arrival and departure times [33–35]. Expression (49) is defined to generate scenarios for the SOC of the arrived PHEV. Herein, f TG refers to the truncated Gaussian distribution. μ and σ2 are mean value and variance of the initial max SOC of the arrived PHEVs, respectively. Further, SOCmin ik , SOCik denotes the truncation region for SOC. The parameters of PHEV's probability distributions are reported in Table 1. As shown, three different fleets are assumed to consider various customer types, namely industrial, commercial, and residential customers 2 min , res = f (x) = f TG x; μSOC, σSOC SOCini , SOCik , SOCikmax ik

(49)

Moreover, expression (50) is used to generate scenarios for PHEVs arrival time. Expression (51) should be considered to guarantee the rationality of the generated scenarios 2 tikarv = f (x) = f TG x; μarv, σarv , tikarv, min, tikarv, max

(50)

tikdep ≥ tikarv

(51)

Accordingly, expression (52) is employed for modelling the truncation region of PHEVs departure time 2 tikdep = f (x) = f TG x; μdep, σdep , tikdep, min, tikdep, max

(52)

Moreover, the number of PHEVs connected to the PL, Nitava, are formulated as Nitava = Nitava − Nitdep + Niava t−1

(53)

Therefore, prospective scenarios are generated for realising the overall situation of various uncertain parameters of restoration problem. However, these numerous scenarios may lead to a nontractable EVPLAP; thus, the generated scenarios should be reduced. Herein, the generated scenarios are reduced to nine of them, as reported in Table 2. Herein, the ninth scenario (S9) has the highest occurrence probability among all scenarios. Moreover, equivalent SOCs of the network load points in the restoration scenarios are sketched in Fig. 4. According to foregoing remarks, the EVPLAP is a comprehensive constrained optimisation which is formulated as a mixed-integer non-linear programming. All simulations are implemented on a PC equipped with Intel 2.67 GB CPU and 4 GB RAM using Simple Branch & Bound method solver in GAMS environment [36]. The practical application of the proposed methodology implies the use of the emergent concepts of microgrids and smart grids. Actually, managing a large number of EVs needs distribution automation. Without distribution automation, PHEVs charge/discharge management is not possible. Moreover, it is assumed that, the installed sectionaliser switches can be controlled from a remote control centre, which is another capability of an automated (smart) distribution network. 4.3 Reliability-related objective function

Fig. 2 Probability of line failure occurrence during day, based on historical data [29]

II), the EVPLAP is solved through assuming the nine extracted scenarios which are generated for the system conditions and the available power of the participating PLs during the service restoration. In the other words, the first case explores a deterministic EVPLAP; while, in the second one this problem is formulated as a stochastic optimisation problem. The objective function of the proposed approach is minimising (3). Also, using analytic hierarchy process (AHP) method, weighting coefficients are obtained equal to 0.67 and 0.33 for ω1 and ω2, respectively. The results for ‘case I’ and ‘case II’ are presented in Table 3. The optimal PLs locations are presented in the second column of this table, where the number of PL-located load points in ‘case II’ is greater than ‘case I’. As shown this table, the number of installed CSs is equal to 694 for ‘case II’, while 520 CSs are decided to install in ‘case I’. Hence, regarding all probable costs for different scenarios changes (increases) the economic justifiability of PLs installation. Therefore, TPIMC for the second case is higher than the first one. In addition, in the first case, 520 CSs are installed in

Fig. 3 Scenario generation for service restoration process

Table 1 Parameters of PHEVs’ probability distributions Fleet 1 µ σ min max ini

SOC , % arv

50

25

20

The reliability-related objective function aims to simultaneously reduce the economic and technical detriments caused by network contingencies. The EVPLAP is solved for two cases to illustrate the effectiveness of this healer reinforcement approach. In the first case (case I), the EVPLAP is formulated as a deterministic EVPLAP. Herein, the input data of the EVPLAP, including the load, SOC, and battery capacity profiles of the network during restoration, are considered same as the most probable scenario –i.e. the ninth restoration scenario. However, in the second case (case

90

µ

σ

55

20

Fleet 2 min 20

Fleet 3 min

Max

µ

σ

90

35

25

20

max 90

t ,h

8

3

5

17

16

3

13

1

20

3

18

4

tdep, h

16

3

11

24

24

3

19

8

7

3

5

9

6


seven PLs, which is about 74 CSs per PL. However, 694 CSs are installed in 13 PLs in the second case, which is about 53 CSs per PL. Thus, in ‘case II’, CSs are allocated in the network more evenly distributed than in ‘case II’, since the problem is solved considering nine probable restoration scenarios in the second case. Thus, PLs are allocated to be efficient in more restoration scenarios. For instance, the ETIC is equal to 109.532 k$ for the first case; while, this index is reduced to 104.809 k$ in the second case. Furthermore, the ESAIDI is equal to 0.838 hours per customer per year and 0.779 hours per customer per year for ‘case I’ and ‘case II’, respectively. Moreover, effects of optimal PLs incorporation in the ninth restoration scenario (the most probable restoration scenario) for both cases are shown in Table 4. As shown in this table, the number of incorporated CSs in the ninth restoration scenario equals to 630 for the second case; however, the first case utilises 520 CSs. Therefore, the number of incorporated PHEVs in the ninth restoration scenario for ‘case II’ is higher than that of ‘case I’. Hence, TPICres for the ninth restoration scenario in ‘case II’ is

higher than ‘case I’. Consequently, for the ninth restoration scenario, the total cost of reliability TRC in the second case is higher than the first case, while the TIC index for the first case is higher than the second one. Further, in ‘case I’, 7 PLs are installed and 12 PLs incorporations in all restoration scenarios are economically unjustifiable, which are almost 19% of all PLs incorporation possibilities (7 × 9 = 63), as shown in Table 5. However, in ‘case II’ this factor increases to almost 23%, as reported in Table 6. Indeed, 27 PLs incorporations in all prospective restoration scenarios are economically unjustifiable. Hereupon, the percentage of installed PLs utilisations for ‘case I’ is higher than that of ‘case II’. However, in the second case, the expected number of incorporated PLs for restoration process equals to 584, while about 441 CSs are expected to contribute in restoration process for the first case. Thus, the PHEVs incorporation is more affordable in the second case. In addition, the SAIDI and TCI indices for all restoration scenarios are depicted in Figs. 5 and 6, respectively. For all

Fig. 4 Initial equivalent SOC for each load point at the beginning of the restoration process ESOCitres 0s

Table 2 Probability of restoration condition scenarios Scenarios S1 S2 S3 Probability

0.024

0.118

0.151

Table 3 Reliability evaluation for different cases Case PL-located load points

S4

S5

S6

S7

S8

S9

0.034

0.044

0.013

0.029

0.057

0.53

ESAIDI, hours per customer per year ETIC, k$ Number of installed CSs

existing network − case I 8, 9, 14, 28, 30, 31, 36 case II 3, 4, 5, 8, 9, 14, 19, 20, 27, 28, 30,31, 36

1.318 0.838 0.779

196.542 109.532 104.809

0 520 694

Table 4 Reliability evaluation for the ninth restoration scenario in different cases Case Incorporated PLs SAIDI, hours per customer per year

TRC, k$ TIC, k$ Number of incorporated. CSs

case I PL8, PL9, PL14, PL28, PL30, PL31, PL36 case II PL3, PL4, PL5, PL8, PL14, PL19, PL20, PL30, PL31, PL36

102.978 91.242 104.387 88.327

0.824 0.803

520 630

Table 5 PLs participation for various scenarios in case I (I: incorporated, NI: not incorporated) PL locations S1 S2 S3 S4 S5

S6

S7

S8

S9

LP14, LP30, LP31, LP36 LP8 LP9 LP28

I NI NI NI

I I NI NI

I I NI NI

I I I I

Table 6 PLs participation for various scenarios in case II (I: incorporated, NI: not incorporated) PL-located load points S1 S2 S3 S4 S5

S6

S7

S8

S9

8 9 27 3, 4, 5, 19, 20 28 14, 30, 31, 36

NI NI NI NI NI I

I NI NI I NI I

I NI I I I I

I NI NI I NI I


I I I I

I I NI NI NI I

I I NI NI

I NI NI I NI I

I I I I

I I I I I I

I I NI NI

I NI NI I I I

I I I NI

I I I I NI I

7

4.5 Collective objective function

Fig. 5 SAIDI index for each service restoration scenarios

Both operational and reliability-based objective functions are simultaneously considered, to perform a comprehensive EVPLAP. The selected buses for PL installation are reported in the second column of Table 8. As presented, the number of installed PLs is less than the reliability-based EVPLAP and greater than operational EVPLAP. However, the number of installed PLs is equal to 750 for this case, while this parameter is equal to 694 and 538 CSs for reliability-based and operational EVPLAPs, respectively. Moreover, both reliability-related indices (TIC and SAIDI) and operational costs (voltage deviation and power loss costs) for the collective case are lower than reliability-based and operational studies. As a result, the economic justifiability of PL deployment is increased in collective case, since more revenue obtained from the PL incorporation in the collective case. Also, in comparison with operational costs, reliability-related costs are more affected (reduced) by the PL incorporation. Further, the cosine similarity of the reliability-based and collective cases is equal to 0.7396, while this measure is equal to 0.2265 for the operational case. Hence, the optimal location of PLs in the collective case is more similar to the reliability-related study. However, to validate this elicitation, a sensitivity analysis is performed on the effect of weighting coefficients definition on outcomes of the collective objective function, as reported in Table 9. As a result, the stated corollary is valid for different weighting coefficient definition manners, since the cosine similarity measure is >0.2265 (cosine similarity of operational and collective cases) for all cases. 4.6 Computational complexity

Fig. 6 TIC for each service restoration scenarios

scenarios, both SAIDI and TIC indices in ‘case I’ are greater than ‘case II’, except the sixth scenario. Indeed, this scenario represents contingency occurrence in the off-peak hours. Accordingly, backup feeders are not congested in this scenario. Thus, PLs are incorporated in the service restoration only as backup units. However, in the other scenarios PLs are incorporated as both backup units and storage units. Thus, in the stochastic model, PLs are sited to be operated as backup and storage units, which lead to lower efficacy of the sixth scenario in ‘case II’ rather than ‘case I’. As reported in Tables 5 and 6, about 57% of installed PLs in first case are incorporated in the sixth scenario while the second case utilises from about 31% of installed PLs in the sixth service restoration scenario. 4.4 Operational objective function Although the roles of PLs as both backup sources and storage units are very profitable in the service restoration process, the impact of PLs on reducing the operational cost of network is unarguable. Hence, voltage deviation and energy loss costs are considered in the operational objective function as two conflicting objectives. Herein, the voltage deviation penalty is computed based on [37]. Furthermore, the daily electricity price is extracted from [38]. Further, the arrival and departure of PHEVs in PLs are estimated based on [15]. As presented in Table 7, when the loss reduction is considered as objective function of EVPLAP, most of PLs are located at the end of feeders. This is due to vehicle to grid capability of PLs, which could reduce current flow, hence the total loss of related feeder. Also, when the voltage deviation is selected as the objective function, most of PLs are located based on the importance of voltage profile of the network load points. Moreover, while both power loss and voltage deviation costs are considered in the objective function of EVPLAP, the obtained results are closer to the power loss based operational objective function, since PLs participation could possess more impact on power loss reduction.

8

The proposed methodology is implemented in GAMS software on a PC with an Intel 2.67 GB CPU and 4 GB RAM. Note that, for each contingency, the load flow analysis is performed just for the faulted and backup feeder not the entire system, which significantly reduces the computation time. The proposed methodology is presented for offline use. Therefore, the execution time is an inconsequential parameter for the PL allocation problem. In addition, the characteristics of the EVPLAP differ from other network allocation problems, e.g. distributed generator allocation and switch allocation problems. Indeed, the number of required CSs which should be installed for each urban area is different. Thus, in a large real-life network, the distribution network should be partitioned to several clusters based on their requirement of each area for PL allocation. Afterwards, PL allocation problem is solved for each cluster separately. Hence, the computational complexity factor of the PL allocation problem in a large real-life network may be equal to the employed test system. The total execution time for ‘existing network’, ‘case I’, and ‘case II’ is about 0.05, 0.25, and 5 h, respectively. Nevertheless, parallel computing can be employed to precipitate the computation to eschew inadequately long computational time, particularly for large EDSs with several feeders and critical loads, based on the fact that each restoration scenario can be solved separately, based on the number of allocated CSs, i.e. NIcs i .

5 Conclusions In this paper, EVPLAP was comprehensively solved through considering PLs ancillary services in both reliability-related and operational programmes. The reliability-related objective function aimed at reducing TRC and SAIDI indices. Furthermore, the existing uncertainties in the electric distribution network condition and available power of the participating PLs during service restoration were considered through employing a stochastic model for EVPLAP. PLs could contribute in the service restoration as backup units for faulted zone re-energising or as storage unit to prevent backup feeder congestion. As a result, stochastic EVPLAP might lead to more realistic conduction of PL allocation, rather than the deterministic one. Moreover, the operational objective function aimed at minimising energy loss and voltage deviation costs. Results show that, the operational EVPLAP is less economically justifiable than reliability-based one. Next, collective IET Gener. Transm. Distrib. © The Institution of Engineering and Technology 2017

Table 7 PLs allocation aiming at minimising operational costs OF Optimal PLs locations

CLossk$

CVDk$

NIcs

loss VD loss andVD

262.76 283.03 268.08

142.92 137.1 142.61

548 500 538

LP7, LP16, LP24, LP25, LP31, LP38 LP6, LP7, LP16, LP17, LP24 LP1, LP2, LP3, LP7, LP11, LP31

Table 8 Multi-criteria PLs allocation OF reliability-based operational collective

PL-installed load points

CLoss

CVD

ETIC

ESAIDI

3, 4, 5, 8, 9, 14, 19, 20, 27, 28, 30, 31, 36 1, 2, 3, 7, 11, 31 8, 9, 10, 14, 19, 20, 30, 31, 36

269.7 268.1 262.9

143.3 142.6 141.8

104.81 121.04 98.54

0.779 0.875 0.748

ESAIDI

ETCI

CLoss

CVD

0.851 0.827 0.755 0.696 0.642 0.639

101.8 101.2 98.3 98.9 105.4 106.5

259.7 261.4 263.1 267.6 274.4 275.2

143.3 143.4 141.6 140.8 139.4 140.4

Table 9 Sensitivity analysis on weighting coefficients of collective objective function Case PL-installed load points Cosine similarity β1 β2 1 0.9 0.75 0.5 0.25 0

0 0.1 0.25 0.5 0.75 1

8, 9, 14, 19, 20, 27, 28, 30, 31, 36 8, 9, 14, 19, 20, 27, 28, 30, 31, 36 3, 4, 5, 8, 9, 14, 19, 20, 30, 31,36 3, 4, 5, 8, 14, 15, 19, 20, 21, 22, 30, 31,32, 36 3, 4, 5, 14, 15, 18, 19, 20, 21, 22, 32, 34, 35, 36 3, 4, 5, 12, 14, 15, 18, 19, 20, 21, 22, 34, 35, 36

EVPLAP was solved through simultaneously considering both reliability-related and operational objective functions. The results depicted that the collective EVPLAP outputs including the optimal PL locations, and so on are more similar to the reliability-related one.

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