Optimal distribution feeder reconfiguration and generation scheduling for microgrid day-ahead operation in the presence of electric vehicles considering uncertainties

Journal of Energy Storage 21 (2019) 58–71

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Journal of Energy Storage journal homepage: www.elsevier.com/locate/est

Optimal distribution feeder reconfiguration and generation scheduling for microgrid day-ahead operation in the presence of electric vehicles considering uncertainties

T

Mostafa Sedighizadeha, , Gholamreza Shaghaghi-shahra, Masoud Esmailib, Mohammad Reza Aghamohammadia ⁎

a b

Faculty of Electrical Engineering, Shahid Beheshti University, Evin, Tehran, Iran Department of Electrical Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran

ARTICLE INFO

ABSTRACT

Keywords: Microgrid Optimal generation scheduling (OGS) Distributed generation (DG) Distribution feeder reconfiguration (DFR) Demand response (DR) Electric vehicles (EV)

Distribution Feeder Reconfiguration (DFR) and Optimal Generation Scheduling (OGS) are indispensable operation tasks that are used in Microgrids (MGs) to enhance efficiency as well as technical and economic features of MGs. The OGS problem usually minimizes the cost of energy assuming a fixed configuration of power systems. On the other hand, the DFR problem is done assuming a predefined generation of units. However, performing these two tasks separately may lose the optimal solution. In this paper, a framework is proposed to jointly perform OGS and optimal DFR on a day-ahead time frame. The total operation cost of MG is minimized subject to diverse technical and economic constraints. The Demand Response (DR) program offered by curtailable loads is considered as a Demand Side Management (DSM) tool. The Electric Vehicles (EVs) and non-dispatchable Distributed Generations (DGs) are modeled along with the uncertainty of MG components. The charging pattern of EVs is modeled in two ways including uncontrolled and controlled patterns. The objective function includes the cost of purchasing active/reactive power from the upstream grid as well as DGs, cost of switching in DFR, cost of DR, and cost of energy losses. MG profit from selling electric energy to the upstream grid is also incorporated in the objective function. The proposed model is formulated as a Mixed-Integer Second-Order Cone Programming (MISOCP) problem and solved by the GAMS software package. The efficacy of the proposed model is confirmed by examining it on the IEEE 33-bus distribution network.

1. Introduction Distribution networks including MGs are usually operated in a radial topology because of its simpler protection coordination and lower level of shortnetworks including MGs are usually operated in a radial topology because of its simpler protection coordination and lower level of short-circuit current. DFR is the task of changing the open/close status of sectionalizes and tie switches to improve the operational performance of electric distribution systems. Since there are numerous switching combinations, discovering the suitable configuration for the MG is a complicated optimization problem with various objectives and constraints.

Meanwhile, employing dispatchable/nonemploying dispatchable/ non-dispatchable DG units as well as EVs in MGs can economically improve the operation of MGs. Renewable DGs such as WTs and PV cells that are installed in an MG usually face with uncertainty, which should be accounted for energy management of MG and OGS of units. Moreover, consumers in the MG have a vital role in DSM by participating in DR programs. Also, EVs as emerging devices connected to MG can help the operator of MG with more economical utilization by charging and discharging electrical energy stored in their batteries in suitable times. In [1], EV energy storage availability is investigated by incorporating several random parameters into a stochastic dynamic programming management scheme of smart building energy

Abbreviations: ANN, artificial neural network; BM, biomass; DR, demand response; DFR, distribution feeder reconfiguration; DG, distributed generation; DSM, demand side management; EES, electrical energy storages; EMS, energy management system; FC, fuel cell; G2V, grid to vehicle; GAMS, general algebraic modelling system; GT, geothermal; MG, microgrid; MT, micro turbine; MICP, mixed integer conic programing; OGS, optimal generation scheduling; SCIP, solving constraint integer programs; SH, small hydro; SOC, state of charge; EV, electric vehicles; PHEV, plug-in hybrid electric vehicles; PV, photovoltaic; RES, renewable energy sources; V2G, vehicle-to-grid; WT, wind turbine ⁎ Corresponding author. E-mail address: [email protected] (M. Sedighizadeh). https://doi.org/10.1016/j.est.2018.11.009 Received 17 June 2018; Received in revised form 3 November 2018; Accepted 7 November 2018 2352-152X/ © 2018 Elsevier Ltd. All rights reserved.

Journal of Energy Storage 21 (2019) 58–71

M. Sedighizadeh et al. ¯

Nomenclature

Pch (e ) Maximum charge power of the eth EV (kW) Charge efficiency of the eth EV ch (e ) Discharge efficiency of the eth EV dch (e ) SOCMIN (e ) Minimum SOC of the battery of EV (kWh) SOCMAX (e ) Maximum SOC of the battery of EV (kWh) SOC 0 (e ) Initial SOC of the battery of EV (kWh) SOC f (e ) The SOC of the battery of EV at the final period (kWh) CchEV Cost of charging of EVs at hour t ($/kWh) CdchEV Cost of discharging of EVs at hour t ($/kWh) SB The main substation of the distribution grid t Time interval (hour)

Sets

S NDG NL NK I L T E

Set Set Set Set Set Set Set Set

of of of of of of of of

scenarios buses with DGs loads that contributes in DR program switches buses lines time EVs

Variables

Parameters

Total operation cost of the system ($) Cost PDG (i , t , s ) Active energy generated by ith DG unit at hour t and scenario s (kW) QDG (i, t , s ) Reactive energy generated by ith DG unit at hour t and scenario s (kVAr) Pgrid (t , s ) Active energy purchased from the upstream grid at hour t and scenario s (kW) Qgrid (t , s ) Reactive energy purchased from the upstream grid at hour t and scenario s (kVAr) PDR (j, t , s ) Value of reduced load by ith customer at hour t and scenario s (kW) Cond (k, t , s ) 1 if kth switch at hour t and scenario s is closed; otherwise 0 I (i , j, t , s ) Current magnitude of line between bus i and j in scenario s (A) INCM (s ) Income from selling power to the upstream grid at scenario s ($) DGCost (s ) Cost of purchasing power from DG units at scenario s ($) GCost (s ) Cost of purchasing power from the upstream grid at scenario s ($) DRCost (s ) Cost of DR program at scenario s ($) SWCost (s ) Cost of switching actions at scenario s ($) LCost (s ) Cost of active power losses at scenario s ($) Psell (t , s ) Active power sold to the upstream grid at hour t and scenario s (kW) Qsell (t , s ) Reactive power sold to the upstream grid at hour t and scenario s (kVAr) V (i, t , s ) Voltage magnitude of the ith bus at hour t and scenario s (V) EV Pdch (e, t , s ) Discharge power of the eth EV at hour t and scenario s (kW) EV Pch (e, t , s ) Charge power of the eth EV at hour t and scenario s (kW) EV PCostch (s ) Cost of charging EVs at scenario s ($) EV PCostdch (s ) Income from discharging EVs at scenario s ($) SOC (e , t , s ) SOC of the eth EV at hour t and scenario s (kWh) P (i , j, t , s ) Active power flowing through line between bus i and j at hour t and scenario s (kW) Q (i, j, t , s ) Reactive power flowing through line between bus i and j at hour t and scenario s (kVAr) (i , j ) 1 if the line between bus i and j at hour t and scenario s is connected; otherwise 0 (i , j, t , s ) 1 if bus j is the parent of bus i; otherwise 0 y (e , t , s ) 1 if the eth EV discharged at hour t and scenario s; otherwise 0

Ceng (i, t ) Cost of purchasing one kWh energy from ith DG unit at hour t ($/kWh) CVAr (i, t ) Cost of purchasing one kVArh energy from ith DG unit at hour t ($/kVArh) grid Ceng (t ) Cost of purchasing one kWh energy from the upstream grid at hour t ($/kWh) grid CVAr (t ) Cost of purchasing one kVArh energy from the upstream grid at hour t ($/kVArh) CDR (j, t ) Cost of load reduction of the jth customer at hour t ($/kWh) CSwitching (k ) Cost of switching of the kth switch ($/action) R (i , j ) Resistance of line between bus i and j (Ω) X (i , j ) Reactance of line between bus i and j (Ω) Closs (t ) Cost of active power losses at hour t ($/kWh) (s ) The probability of scenario s P Csell (t ) Cost of selling active power to the upstream grid at hour t ($/kWh) Q Cost of selling reactive power to the upstream grid at hour Csell (t ) t ($/kVArh) PD (i, t , s ) Active power demand at bus i at hour t and scenario s (kWh) QD (i, t , s ) Reactive power demand at bus i at hour t and scenario s (kVAr) IMAX (i , j ) The maximum allowable current of the line between bus i and j (A) VMAX (i , j ) The maximum voltage of bus i (V) VMIN (i , j ) The minimum voltage of bus I (V) Minimum active power generation of ith DG unit (kW) _PDG (i) ¯

PDG (i ) Q _ DG (i )

Maximum active power generation of ith DG unit (kW) Minimum reactive power generation of ith DG unit (kVAr)

QDG (i)

Maximum reactive power generation of ith DG unit (kVAr)

PGrid

Maximum active power exchange between the distribution grid and the upstream network (kW) Minimum active power exchange between the distribution grid and the upstream network (kW)

¯

¯

_PGrid ¯

QGrid _Qgrid ¯

Maximum reactive power exchange between the distribution grid and upstream network (kVAr) Minimum reactive power exchange between the distribution grid and the upstream network (kVAr)

PDR (i, t , s ) The maximum active power which can be reduced by the customer at bus i in hour t and scenario s (kW) PDR _ (i, t , s ) The minimum active power which can be reduced by the customer at bus i at hour t and scenario s (kW) ¯

Pdch (e )

Maximum discharge power of the eth EV (kW)

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management. The smart grid is defined as an electric power system that can deliver power in a controlled, smart way from points of generation to active costumers. On the other hand, DR, by promoting the interaction and responsiveness of the customers, may offer a broad range of potential benefits on system operation and expansion as well as market efficiency [2]. An optimization scheme for efficient energy management and allocation of a smart home with home battery, PHEV, and PV arrays is presented in [3]. In [4], energy scheduling in microgrids is addressed considering the range anxiety of PHEVs and V2G features. In [5], the effects of energy storage technologies are investigated on power system operation and planning models when non-dispatchable renewable energy sources are integrated. There are numerous studies devoted to DFR in the distribution systems. Ref. [6] employs a Biased Randomare numerous studies devoted to DFR in the distribution systems. Ref. [6] employs a Biased Random-Key Genetic Algorithm to solve the problem of DFR. In [7], a new method is presented to reconfigure the MG coupled with the optimal placement of DGs by the Cuckoo Search Algorithm and graph theory. The objective function includes active power losses and voltage stability. A new hybrid optimization method is introduced in [8] which determines radial boundaries as nominated solutions for the DFR problem using a combination of the concept of fuzzy domination with Shuffled Frog Leaping Algorithm. In [9], a three-layer ANN optimized by a dynamic fuzzy clustering algorithm is introduced to carry out DFR to minimize active power losses. In [10], the maximization of a new voltage stability index is taken into account for optimal DFR. Ref. [11] presents a multi-objective optimization method to reconfigure the distribution system and to reduce the cost of active power losses and energy not supplied, as well as to increase voltage stability and DG penetration level. The uncertainties of electric demands and power generated by WTs are modeled based on a two-point estimation method. It analyzes the impact of DGs on the DFR problem to reduce the voltage drop and voltage collapse, based on a multi-objective optimization problem. On the other hand, there are several types of research dedicated to OGS and energy management in distribution networks and MGs. In [12], a new stochastic framework is introduced to study the impact of correlated wind generators on energy management in MGs. A stochastic framework is employed based on the improved point estimation method to model uncertainties of wind generation and electric demands. Ref [13] presents a method based on chancethe other hand, there are several types of research dedicated to OGS and energy management in distribution networks and MGs. In [12], a new stochastic framework is introduced to study the impact of correlated wind generators on energy management in MGs. A stochastic framework is employed based on the improved point estimation method to model uncertainties of wind generation and electric demands. Ref [13] presents a method based on chance-constrained second-order cone scheduling to control the risk in MG along with considering DG units and PHEVs which are randomly charged. It also incorporates the uncertainty of renewable wind and solar units into the problem. Ref. [14] presents two energy management strategies for optimum utilization of the V2G potential of PHEVs in the management of energy imbalance in MGs. Ref. [15] introduces a comprehensive framework for retail energy market based on a relaxation algorithm with considering DG resources and DSM. Ref. [16] proposes a state machine as the solution for EMS of an automated MG to improve transient performance during transition operations. Ref. [17] proposes a robust model combining particle swarm optimization algorithm and primal–dual interior point method for optimal energy management of the MG, considering VAR compensation mode of the PV inverters. Ref. [18] proposes an optimal management system of battery energy storage to improve the resilience of the MG while minimizing its operational cost.

The problem of joint DFR and OGS can be a sophisticated optimization problem especially when different features are included such as dispatchable/nonproblem of joint DFR and OGS can be a sophisticated optimization problem especially when different features are included such as dispatchable/non-dispatchable generation units, upstream electricity market, the role of PHEVs as interactive loads, and uncertainties of renewable DGs. Recently, considering the optimal DFR simultaneously with energy management for MG day-ahead operation is a subject that has received attention by researchers. Ref. [19] proposes a stochastic model in day-ahead MG management for optimal reconfiguration and power scheduling of units considering the upstream grid market. It takes into account load demand and wind power generation uncertainties modeled by Monte-Carlo Simulation. However, it does not address EESs such as battery and PHEV. Ref. [20] proposes a two-stage approach for real-time OGS coordination with hourly network reconfiguration considering non-dispatchable DGs in an MG. The stochastic behavior of electrical demands and EESs are not modeled. Ref. [21] introduces a multi-objective energy management based on DFR at the same time with renewable DGs allocation and sizing. The goals are the minimization of active power losses, annual operation costs, and pollutant gas emissions. However, the variation in wind speed, solar irradiation, and load are modeled as deterministic using a time sequence. References [22] and [23] present a joint problem of DFR and OGS without considering the stochastic behavior of WT and PV units. They take into account a multi-objective framework for minimization of electrical power losses, operation cost, and pollutant gas emissions as well as maximization of the voltage stability index in MG. Ref. [24] simultaneously performs DFR and OGS with considering DR program by the Hong’s 2 m point estimate method. The objective functions are to minimize operating costs as well as to enhance the reliability and resiliency of MGs when faced by uncertainties. Ref. [25] proposes a multi-objective problem based on the optimal DFR, by simultaneously re-phasing and optimal DG sizing, to minimize active power losses and phase unbalancing and improve voltage profile. Ref. [26] performs optimal DFR with taking into consideration of uncertainties related to load demand and output power of DGs. The aims of optimization are the minimization of active power loss and the number of switching operations as well as maximization of the voltage stability margin. In the present paper, the DFR problem is addressed in an integrated framework coupled with OGS. It aims to minimize overall costs which are composed of different items as the cost of purchasing active and reactive power from the upstream grid and DGs, cost of switching operations in the DFR, load reduction cost related to DR program, cost of active power losses, as well as to maximize profit made from selling power to the upstream grid. The proposed problem is solved for day the present paper, the DFR problem is addressed in an integrated framework coupled with OGS. It aims to minimize overall costs which are composed of different items as the cost of purchasing active and reactive power from the upstream grid and DGs, cost of switching operations in the DFR, load reduction cost related to DR program, cost of active power losses, as well as to maximize profit made from selling power to the upstream grid. The proposed problem is solved for dayahead operation in which energy management and DFR are conducted hourly. The switching cost is incorporated into the objective function to reduce frequent switching which deteriorates the lifetime of switches. Also, renewable energy units including WT and PV systems considering the uncertainty of their power generations are also included in this study as different scenarios. EVs are also included and their charge/ discharge status in different hours of the day-ahead model are considered as control variables. It also takes into account costumers’ DR programs, as one of the tools in energy management of MGs. Since the proposed study is to schedule day-ahead energy, the solution to the

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problem should be so formulated that exceeding solution times and voluminous calculations are avoided. It should also offer a high chance of convergence. The proposed formulation is modeled as a conic problem implemented in GAMS 24.1 software aided by its SCIP solver. The main contributions provided by this paper include:

2. Problem formulation This section deals with the formulation of the problem. The objective function, constraints, and their conversion into a conic problem are formulated. Our optimization model includes (1) as the objective function that is minimized subject to (2)-(11), and (15)-(35) as follows.

• Proposing a new model for distribution network operation with integrated coupled DFR and OGS for MG day-ahead operation. • Modeling the uncertainty of renewable energy units including WT • • • •

2.1. Objective function

and PV in the proposed approach. These uncertainties are related to their nature which is not predictable accurately. Modeling EVs as electrical energy storages in the suggested framework to reduce the total cost by employing their charge and discharge ability. This makes it possible to use EVs as distributed energy storage units to enhance the efficiency of microgrid operation. Considering the DR program and the participation of customers in the operation of MG to enhance flexibility and to reduce the total cost. Modeling the charging pattern of EVs in two ways of controlled and uncontrolled patterns. Proposing a convex optimization model with considering constraints of different devices.

As mentioned before, the objective function includes different items including the cost of purchasing active and reactive power from DG units and upstream grid, DR cost, switching cost, cost of active power losses, and revenue earned from selling active and reactive power to the upstream grid, as elaborated below:

Cost =

(s ) s S

DGCost (s ) + GCost (s ) + DRCost (s )+ × SWCost (s ) + LCost (s )

EV INCM (s ) + PCostch (s )

EV PCostdch (s )

(1)

The rest of this paper is organized as follows. In Section 2, the proposed method and problem formulation for OGS and optimal DFR are presented. The simulation results are analyzed in Section 3 to evaluate the benefits of this work. Finally, the conclusions are outlined in Section 4.

DGCost (s ) =

t × (Ceng (i , t ) × PDG (i , t , s )

s

S

t T i NDG

+ CVAr (i, t ) × QDG (i , t , s ) )

Fig. 1. Single diagram of IEEE 33-bus network.

61

(2)

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Table 1 Characteristics of dispatchable and non-dispatchable DG units. ¯

PDG (kW ) 500 250 500 280 500 150 150 150 250

Q _ DG (kVAr ) −50 −25 −50 −28 −50 −15 −15 – –

¯

QDG (kVAr ) 50 25 50 28 50 15 15 – –

Bus no.

Type

Technology

DG no

17 28 29 21 32 14 24 17 31

Dispatchable Dispatchable Dispatchable Dispatchable Dispatchable Dispatchable Dispatchable Non-dispatchable Non-dispatchable

Microturbine-1 Microturbine -2 Microturbine -3 Biomass Fuel cell Small hydro Geothermal Photovoltaic Wind turbine

1 2 3 4 5 6 7 8 9

Fig. 2. Proposed energy prices for generation of active power by dispatchable DGs. Table 2 Types of demands.

Fig. 4. The bid of customers for their load reduction through DR program.

Type

Bus numbers

Residential Commercial Industrial

1, 4, 11, 13, 18, 21, 30, 31 3, 6, 7, 9, 10, 12, 14, 16, 19, 21, 23, 24, 25, 27, 28, 29, 32 2, 5, 8, 15, 17, 20, 26

Table 3 Different parameters considered in simulations. parameter

Value

parameter

Value

CSwitching (

80

VMIN

(pu)

0.95

Closs

80

VMax

(pu)

1.05

PGrid_(kW )

−4000 4000

_Qgrid (kVAr )

¯ PGrid

$ ) action $ ( ) kWh

(kW )

¯ QGrid

(kVAr )

−3000 3000

Fig. 3. (Up): Demand profile of test network for 24 h of the next day; (Down): Hourly energy price of purchasing electrical power form an upstream grid.

Fig. 5. Generated power by the wind unit in different scenarios.

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M. Sedighizadeh et al.

grid grid t × (Ceng (t ) × Pgrid (t , s ) + CVAr (t )

GCost (s ) =

s

S

t T

(3)

× Qgrid (t , s ))

DRCost (s ) =

t × (CDR (j, t ) × PDR (j, t , s )) t T

s

S

(4)

j NL

SWCost (s ) =

CSwitching (k )

s

S

t T k NK

× [abs (Cond (k, t , s ) Cond (k , t Fig. 6. Generated power by the solar unit in different scenarios. Table 4 Characteristic of EVs battery [38]. Value

¯ ¯ Pch (kW), Pdch (kW)

25

ch

0.90

48

dch

0.95

Battery consumption during each journey (kWh) (kWh)

23

Parameters

SOCMAX

2 j I R (i, j ) × I (i, j, t , s )

i I

)

× Closs (t )

s

S

Q P t × (Csell (t ) × Psell (t , s ) + Csell (t ) × Qsell (t , s ))

(6)

s

S

t T

Value

(kWh)

(

1000

INCM (s ) =

Parameters

SOCMIN

t T

LCost (s ) = t ×

(5)

1, s )) ]

(7) EV PCostch (s ) =

EV t × (CchEV (t ) × Pch (e , t , s ) )

s

S

t T e NEV

119

EV PCostdch (s ) =

EV t × (CdchEV (t ) × Pdch (e, t , s ))

s

S

t T e NEV

Table 5 EV connection pattern for uncontrolled charging [36].

(8) (9)

2.2. Constraints of the problem

EVs

Transitions

Charging periods

EV1-EV4 EV5-EV6 EV7 EV8-EV9 EV10-EV11 EV12 EV13-EV14

t7, t8, t8, t8, t9, t9, t9,

t20, t20, t19, t16, t21, t20, t19,

t19 t19 t18 t15 t20 t19 t18

t21, t21, t20, t17, t22, t21, t20,

t22, t22, t21, t18, t23, t22, t21,

The integrated problem of DFR and OGS has a set of constraints that should be met. These constraints are formulated as follows.

t23 t23 t22 t19 t24 t23 t22

2.2.1. Load flow and radiality constraints Load flow equations should be met at each time of system operation. For a distribution system, by excluding the phase angles of voltages and currents from the classical load flow equations, the angle-relaxed formulation of the branch flow model is obtained as (10)-(13). The unit of quantities should be properly adjusted in these equations. The constraints (10) and (11) presents the active and reactive power balance at all buses. The relation of squared voltages magnitude between any two connected buses can be expressed by (12), and (13) shows the squared current magnitude of each line. This classical formulation is known as DistFlow equations [27].

Table 6 The results of the proposed model for the case study I. Time

Electrical power provided by the grid (kW)

The demand of EVs (kW)

The demand of MG (kW)

Power losses (kW)

Open switches

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

2195.48 1790.55 1666.11 1612.63 1626.58 1598.44 1654.03 1579.51 1835.50 1970.3 2096.02 2160.76 2248.92 2170.72 2133.12 2221.43 2315.81 2672.09 3759.03 4167.55 4111.01 3781.00 3474.14 2915.65

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 48 48 48 144 288 336 336 240 48

2119.2 1730.0 1609.8 1558.1 1571.6 1544.4 1598.1 1526.1 1773.0 1903.7 2023.2 2085.7 2170.8 2095.3 2059.0 2091.1 2182.2 2526.1 3465.5 3700.0 3560.2 3274.1 3084.5 2761.2

76.28 60.55 56.31 54.53 54.98 54.04 55.93 53.41 62.05 66.60 72.82 75.06 78.12 75.42 74.12 77.00 80.28 92.66 133.53 147.55 144.15 133.57 122.98 101.12

s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s6, s7, s 7, s 7, s 7, s 7, s 7, s6, s 7, s 7,

s10, s14, s31, s37 s9, s14, s32, s37 s10, s14, s31, s37 s10, s14, s31, s37 s10, s14, s31, s37 s10, s14, s30, s37 s10, s31, s34, s37 s10, s13, s31, s37 s10, s13, s31, s37 s10, s13, s30, s37 s10, s13, s30, s37 s10, s14, s30, s37 s11, s14, s30, s37 s11, s14, s28, s36 s11, s14, s36, s37 s8, s14, s28, s36 s 8, s14, s 28, s36 s 8, s14, s 28, s36 s 8, s14, s 28, s36 s 8, s14, s 28, s36 s 8, s14, s 28, s36 s11, s14, s30, s37 s11, s14, s30, s37 s10, s14, s31, s37

i

I

sS

t

T

(10)

i

I

sS

t

T

(11)

(i , j )

L

I 2 (i , j , t , s ) =

s

S

t

(12)

T

P 2 (i, j, t , s ) + Q2 (i, j, t , s )

(i , j )

V 2 (i, t , s )

L

s

S

t

T

(13)

The nonlinear Eq. (13) will make the problem non-convex. To provide a convex model, (13) is substituted with:

I 2 (i , j , t , s )

P 2 (i , j , t , s ) + Q 2 (i , j , t , s ) V 2 (i , t , s ) L

s

S

t

T

(i , j ) (14)

If (14) is used instead of (13), the formulation of distribution power flow is conic. One of the most important features of the conic formulations is their convexity which guarantees the global optimal solution. Ref. [28] proves that the solution of optimal power flow with angle relaxation (OPF-ar) is always precise for radial distribution networks and the solution of optimal power flow with conic relaxation (OPF-cr) is exact if all inequality constraints (14) are converged to the equality ones (13). In this study, the reconfiguration problem is modeled as a MICP formulation based on OPF-cr. However, to model the DFR problem, (12) and (13) of classical load flow are extended as follows: 63

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M. Sedighizadeh et al.

T V 2 (j, t , s )

(i, j )) + V 2 (i, t , s )

M × (1

2 × [R (i, j ) × P (i, j , t , s ) + X (i, j ) × Q (i, j, t , s )] + [R2 (i, j ) + X 2 (i, j )] × I 2 (i, j, t , s )

(i , j )

L

s

S

t

(15) T V 2 (j, t , s )

(i, j )) + V 2 (i, t , s )

M × (1

2 × [R (i, j ) × P (i, j, t , s ) + X (i, j ) × Q (i, j , t , s )] + [R2 (i, j ) + X 2 (i, j )] × I 2 (i, j , t , s )

(i , j )

L

s

S

t

(16)

(i , j , t , s ) = n

1

s

S

t

T

(17)

(i, j) L

( i , j , t , s ) + ( j , i , t , s ) = (i , j , t , s )

(i , j )

L

s

S

t

2.2.3. Operational constraints of upstream grid The MG is connected to the upstream grid through one transformer in the main substation. Active and reactive power exchanged with the MG, and the power should be limited to a definite value based on the capacity of the transformer installed on the main substation, as expressed in (27) and (28).

T (18)

(i , j , t , s ) = 1

i

(SB, j, t , s ) = 0 j

I

I and i

SB

s

S

t

T

(19)

j I

I 2 (i , j, t , s ) I 2 (i , j, t , s )

s

S

t

P 2 (i, j , t , s ) + Q 2 (i, j, t , s )

T

(i , j )

V 2 (i, t , s )

2 (i, j, t , s ) × IMAX (i , j )

L

s

S

(i , j )

L

s

t

T

S

t

(20)

_PGrid

PGrid (t , s )

(21)

_Qgrid

QGrid (t , s )

T

2 VMAX

(23)

(i )

V 2 (i , t , s )

2 VMIN

(i )

i

I and i

SB

s

S

t

T (24)

PDR (i, t , s )

The connection of buses has not been known before DFR, consequently, (12) is substituted by two inequality constraints (15) and (16). (i , j ) represents the status of the line that connects buses i and j : (i , j ) = 1 shows that the line is connected and constraints (15) and (16) are squeezed to the equality constraint (12). However, when the line is disconnected ( (i , j ) = 0 ), the upper and lower limits on V 2 (j, t , s ) are relaxed by adding and subtracting a large positive number (M ) to the upper bound and from the lower bound. At each hour of MG operation, the radial constraint should be met. This is guaranteed by the constraints (17)-(20) [29]. Regarding the following constraints, it can be seen that all buses expect the main substation bus have precisely one parent. In these equations, (i , j ) denotes the status of the line; however, (i , j ) shows parent buses: (i , j ) equals to 1 if bus i is parent of bus j and 0 otherwise. The cone constraints are exemplified by (21). The limits of I 2 (i , j, t , s ) and V 2 (i, t , s ) are expressed in (22) and (24), respectively. Constraint (22) shows that the current flowing through each line of MG should not exceed its maximum allowable value. Eq. (24) also indicates that voltage of other buses should be between the minimum and maximum values. Eq. (23) shows that voltage of the main substation bus equals to 1.

Q _ DG (i )

PDG (i , t , s ) QDG (i , t , s )

¯

PDG (i) ¯

QDG (i)

i

NDG i

NDG

s

S s

t S

t

T

s

t S

(27)

T t

(28)

T

PDR (i , t , s )

PDR (i, t , s )

j

I

s

S

t

T

2.2.5. EVs constraints EVs have charge and discharge capabilities due to their V2G and G2V possibilities. Each EV at an individual hour can only act in the charge or discharge mode. The constraints of EVs can be expressed as follows [30]:

0

EV Pdch (e , t , s )

¯

y (e , t , s ) × Pdch (e)

e

E

s

S

t

T (30)

0

EV Pch (e , t , s )

(1

¯

y (e , t , s )) × Pch (e)

e

E

s

S

t

T (31)

SOC (e, t , s )

SOC (e, t

EV (e , t , s ) 1, s ) = ch (e) × Pch 1 dch (e )

SOCMIN (e)

SOC (e, t , s )

e

E

s

S

t

T

EV (e , t , s ) Pdch

(32)

SOCMAX (e )

e

E

s

S

t

T (33)

SOC (e, t0, s ) = SOC 0 (e )

e

E

s

S

t = t0

(34)

SOC (e, t f , s ) = SOC f (e )

e

E

s

S

t = tf

(35)

Eqs. (30) and (31) express that charge and discharge powers of each EV should not exceed the maximum charge and discharge power of the vehicle. According to the binary variable y (e , t , s ), each EV can only act in either the charge or discharge mode. The SOC of a battery gives its stored energy level in kWh. Eq. (32) reflects that the SOC for each EV depends on charge or discharge power in that specific hour [30]. The (33) indicates the upper and lower limitations of EV battery [30]. The SOC level of EVs at the initial and final time periods are constrained by (34) and (35), respectively. Several literature works have investigated the determination of battery SOC based on different approaches [31]. Also, the condition monitoring of the battery is another issue that can be found in some papers [32]. In the proposed method, input parameters are the consumption load pattern, number of switches, network data including the resistance and

(25)

T

¯

QGrid

S

(29)

2.2.2. Operational constraints of DGs The amount of active and reactive power in each DG unit should be within their allowed limits that is expressed by (25)-(26). It is noted that these equations are applicable to all technologies of DG units, which can be generally classified into synchronous generator-based and inverter-based DGs. The synchronous generator-based DGs (such as MT, BM, SH, and GT) are composed of a prime-mover (thermal or hydro turbine) and a synchronous generator. In contrast, the inverter-based DGs (such as FC, PV, and WT) are composed of a generation unit to provide ac or dc power and converters. Both types of DG units have limitations on their active power generation constrained by (25). Also, both types of DG units can exchange reactive power with the MG as constrained by (26).

_PDG (i)

s

2.2.4. Constraints of DR program The DR value for each customer is also based on predetermined values. They should also range in the allowed limits, as expressed by (29). For loads that do not participate in the DR program, lower and upper values in (29) are set to zero.

(22)

V 2 (SB, t , s ) = 1

¯

PGrid

(26) 64

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Table 7 The results of the proposed model for the case study II. Time

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

Electrical power generated by dispatchable units (kW) MT-1

MT-2

MT-3

BM

FC

SH

GT

Grid

0 0 0 0 0 0 0 0 0 0 0 0 0 169.27 168.39 169.17 0 0 121.04 196.02 161.79 84.04 15.19 0

0 0 0 0 0 0 0 0 0 0 0 0 0 250.00 177.82 187.89 250.00 250.00 0 0 0 0 0 0

500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00

169.83 100.86 97.81 96.52 96.86 96.17 157.17 95.71 101.95 164.33 167.31 169.03 170.98 169.10 168.20 169.00 171.26 179.70 202.55 208.26 208.46 201.54 196.93 189.02

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 33.24 149.11 91.24 0 0 0

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

1185.19 851.72 730.29 679.53 693.00 665.86 659.82 647.57 894.93 967.30 1088.03 1151.22 1237.80 731.89 768.49 809.63 1011.28 1359.63 2463.02 2570.05 2537.60 2417.43 2252.79 1859.63

Demand of EVs (kW)

Open switches

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 48 48 48 144 288 336 336 240 48

s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33, s33,

s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34, s34,

s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35, s35,

s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36, s36,

s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37 s37

Table 8 The results of the proposed model for case study III. Time

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

Electrical power generated by dispatchable units (kW) MT-1

MT-2

MT-3

BM

FC

SH

GT

Grid

0 0 0 0 0 0 0 0 0 0 0 0 0 289.86 244.93 246.23 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 250.00 250.00 250.00 250.00 250.00 0 0 0 0 0 0

500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00

280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 37.34 155.12 98.34 0 0 0

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

1063.39 665.37 542.00 490.54 504.29 476.58 531.14 458.02 709.23 842.54 964.87 1028.99 1116.42 492.87 501.12 551.92 892.58 1245.56 2528.37 2842.16 2713.51 2407.91 2166.91 1747.48

reactance of lines, the output power of RESs, and DG characteristics. The variables are the power output of DGs in each hour, status of switches, power reduction of consumers in the DR program, and charge/discharge powers of EVs. The output of the method is the total cost and the value of variables.

Demand of EVs (kW)

Open switches

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 48 48 48 144 288 336 336 240 48

s7, s7, s7, s7, s6, s6, s6, s6, s7, s7, s6, s7, s7, s6, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7,

s10, s14, s 28, s31 s9, s14, s 28, s32 s10, s14, s32, s37 s10, s14, s30, s37 s10, s31, s34, s37 s11, s14, s36, s37 s11, s31, s34, s37 s11, s30, s34, s37 s10, s30, s34, s37 s10, s12, s30, s37 s10, s30, s34, s37 s10, s14, s30, s37 s10, s14, s30, s37 s8, s13, s36, s37 s8, s14, s28, s36 s8, s13, s28, s36 s8, s14, s28, s36 s8, s14, s28, s36 s8, s14, s17, s 28 s8, s14, s17, s 28 s8, s14, s17, s 28 s9, s14, s 28, s36 s11, s14, s 28, s36 s11, s14, s 28, s36

tie switches. Fig. 1 shows that the sectionalizing switches (normally closed) are numbered from 1 to 32 (specified by solid lines) and tie switches (normally open) are numbered from 33 to 37 (specified by dashed lines). It can be observed that bus 0 represents the connection point of the system to the upstream grid. The total active and reactive power loads of this system are 3715 kW and 2300 kVAr, respectively, at peak hour. Total power loss in the original configuration of the network is 202.67 kW. Nine dispatchable/non-dispatchable DG units are taken into account in this study, and their characteristics are presented in Table 1. Fig. 2 shows the energy prices proposed by dispatchable DG units for generation of electrical power in each hour [33]. Table 2

3. Simulation results The proposed method is tested on the Baran and Wu 33-bus system [23], the single diagram of which is depicted in Fig. 1. This 12.66 kV radial distribution system consists of 32 sectionalizing switches and five 65

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Table 9 The results of the proposed model for case study IV. Time

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

Electrical power generated by dispatchable units (kW) MT-1

MT-2

MT-3

BM

FC

SH

GT

Grid

0 0 0 0 0 0 0 0 0 0 0 0 0 271.86 101.62 49.25 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 250.00 112.25 159.50 199.52 250.00 0 0 0 0 0 0

500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00 500.00

280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00 280.00

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35.27 152.36 95.65 0 0 0

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00 150.00

1037.74 705.2 643.90 632.55 667.81 666.64 663.55 659.91 720.15 751.99 868.53 929.37 1012.55 203.7 327.98 382.72 391.68 656.89 2208.60 2385.46 2377.46 2192.60 2002.34 1671.18

purchasing by EVs (kW)

Open switches

0 52.40 113.00 152.80 174.39 200.26 143.35 211.91 23.85 0 0 0 0 −208.65 −356.20 −337.45 −374.49 −384 −2.37 −57.22 −16.24 0 0 0

s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s7, s6, s7, s7, s7, s6, s7, s7, s7, s7,

s10, s14, s 28, s31 s9, s14, s 28, s32 s10, s14, s31, s37 s9, s14, s32, s37 s8, s14, s28, s36 s8, s14, s28, s36 s8, s14, s17, s 28 s8, s14, s17, s 28 s8, s14, s17, s 28 s10, s14, s31, s37 s10, s14, s31, s37 s10, s14, s31, s37 s10, s14, s30, s37 s8, s14, s28, s36 s8, s14, s28, s36 s11, s14, s30, s37 s11, s14, s30, s37 s10, s14, s31, s37 s11, s14, s28, s36 s11, s14, s36, s37 s8, s14, s28, s36 s8, s14, s28, s36 s8, s14, s28, s36 s8, s14, s28, s36

Fig. 7. The demand of EVs in different case studies.

indicates the types of electrical demands taken from [34]. Fig. 3 illustrates the daily load curves for the electrical demand of the MG and the energy prices of power purchased from the upstream grid [35]. The maximum amount of reducible load by customers at different hours for the DR program are considered as 10% of the hourly load. In a dayahead electricity market, the consumption of demands is set for the next day. When customers contribute in the energy management problem of a MG, they submit their proposal (bid) to reduce their consumption if accepted by the MG operator. The operator should pay customers for the reduction in their load. On the other hand, if their proposal is not accepted by the operator, they should consume their specified load without being paid. The outcome of the operator decision about the demand bids is specified by the result of the optimization problem. The bids of customers due to their load reduction through the DR program is shown in Fig. 4. Table 3 presents different parameters used in simulations. Four scenarios are considered to model the uncertainty of non-dispatchable units of WT and PV, as depicted in Figs. 5 and 6, respectively [36]. Consequently, we have 16 scenarios for each hour and 16 × 24 = 384 scenarios in total. This number of scenarios is usually

enough for operational problems such as the DFR and OGS of our problem. It is worthwhile to note that it is possible to use a higher number of stochastic scenarios at the cost of higher computational burden. However, since the problem is operational, the problem should be solved in a reasonable time. To use a higher number of scenarios, it is enough to increase the number of elements in set S in Eq. (1) without any change in the formulation. The proposed optimization problem can be solved using evolutionary or mathematical-based algorithms. We have used the Lagrange algorithm in this paper as one of mathematical-based ones. In the Lagrange method, the objective function is augmented by constraints (equality and inequality) multiplied by Lagrange multipliers to form the Lagrange function. Afterwards, the optimization problem is constructed in order to minimize the Lagrange function subject to its associated constraints. We here used the GAMS software to solve the problem. Regarding the settings of the employed solution algorithm in the simulations, we used the MICP as the problem model with the solver SCIP and the relative optimality criterion of 0.1 [37]. The solution optimality is ensured since the model is formulated as a conic problem. After solving the problem, its convergence is checked by the flags that are 66

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Fig. 8. The demand of the MG in different case studies.

Fig. 11. Cost of active power generated by DGs at different hours for various case studies.

Fig. 9. Cost of active power losses at different hours for various case studies.

reported by GAMS. Four case studies are taken into account to evaluate the proposed model in diverse situations:

• Case study I: Considering DFR without OGS and DR program. • Case study II: Considering OGS without DFR and DR program. • Case study III: Considering DFR and OGS as a joint problem without considering the DR program. • Case study IV: Considering DFR and OGS as a joint problem with considering DR program.

The four case studies take into account the EVs. We have considered 14 EVs to be placed at buses 2, 5, 8, 11, 14, 17, 19, 21, 24, 27, 28, 29, 31, and 32. Table 4 shows the characteristics of EVs battery. It is noted that the SOC of EVs at the initial and final time periods is considered as the maximum SOC of the EVs. In the case studies I to III, EVs are modeled using uncontrolled charging without considering V2G operation mode. All the same, the controlled charging is considered to model EVs in the case study IV with considering V2G operation mode. The uncontrolled charging shows a charging pattern when the EVs do not receive any control or price

Fig. 10. Cost of DR program at different hours for case study IV.

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signals from the operator of MG and EVs are charged at four time periods at the end of the day, once they arrive from the last trip of the day, and they operate in an idle state for the rest of time periods. It is also taken into account that each EV carries out two trips per day, named transitions, and each one is attached to a particular period [36]. It is also assumed that the EVs individually consume half of the total stored electrical energy during the transition periods and they only travel between their host node displayed in Fig. 1 and its closest node. The time periods that represent transition and charging operations are exemplified by Table 5. The controlled charging pattern happens when the EVs respond to price signals transmitted by the MG operator. In the controlled charging pattern in Case IV, the journey length of EVs is different from that of Case I-III. Also, Case IV has EV discharging as V2G, which is not considered in Case I-III. 3.1. Case study I: DFR without OGS and DR program This case study only performs optimal DFR without considering OGS and DR program. On the other hand, there is no DG in this case study and the upstream grid provides the total demand, the demand of EVs, and electrical power losses. Table 6 shows the open switches, electrical power generated by the main grid, power losses, demand of MG, and demand of EVs at each hour. According to Table 5, the EVs has no connection with MG from hours 1 to 15; consequently, the EVs do not add to the additional demand during the mentioned hours as reported in Table 6. Nonetheless, the EVs are connected to MG for charging from hours 16 to 24 when the MG is already under stress with its peak demand. Hence, the power losses and cost of operation increase dramatically during these hours. Since the minimization of switching cost is one of the objective functions in the proposed model, changing the status of switches are kept at a minimum during a day.

Fig. 12. Cost of reactive power generated by DGs at different hours for various case studies.

3.2. Case study II: OGS without DFR and DR program This case study performs OGS without considering optimal DFR and DR program. It carries out OGS in the base configuration of MG. This study does not take into account DR; nonetheless, it considers EVs in an uncontrolled charging pattern similar to Case 1. In this case study, the demand of MG is similar to the previous case. Table 7 shows electrical power generated by DGs, main grid, and demand of EVs at each hour. The open switches are the same in all hours similar to the base configuration. As Table 7 implies, MT-3, SH, GT, and BM have high participation to supply electrical power demand during off-peak and peak periods due to having lower generation cost. In spite of that, the expensive generation units such as MT-1 and MT-2 contribute to providing the electrical power demand during peak periods when the cost of purchasing electrical power from the upstream grid is high. The FC generates electrical power in time periods when EVs are connected to MG and charged in uncontrolled pattern during peak hours. It is because that it is an expensive generation unit. Of course, the non-dispatchable generation units of PV and WT supply the electrical demand in a stochastic way in the periods when their generations are available.

Fig. 13. Cost of active power purchased from upstream grid at different hours for various case studies.

3.3. Case study III: DFR and OGS as a joint problem without considering the DR program This case study accomplishes OGS and optimal DFR as a joint problem without considering the DR program. It takes into account EVs in an uncontrolled charging pattern similar to Case study I. The demand of MG is similar to Case study I. Table 8 shows electrical power generated by all DGs, main grid, and demand of EVs, as well as open switches at each hour in a day-ahead scheduling. By comparing the results of this case study with previous ones, it can be observed that the power generation of MT-1 increases during hours 14–16, but it decreases to zero during hours 19–23. Also, the MT-2 raises its power generation during

Fig. 14. Cost of reactive power purchased from upstream grid at different hours for various case studies.

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Fig. 15. Total operation cost at different hours for various cases. Table 10 Different costs of system operation for various cases. Case study

Total operation cost ($)

Cost of power losses ($)

Cost of electrical power generated by DGs ($)

Cost of electrical power purchased from the main grid ($)

Cost of executing DR program ($)

I II III IV

9505 7696 7384 6792

64 31 23 19

0 2684 2818 2646

9440 4980 4541 3893

0 0 0 232

Fig. 16. Voltage profile of the test system for case study I at different time.

Fig. 17. Voltage profile of the test system for case study II at different time.

hours 15–16. Moreover, the BM increases its power generation to the rated capacity during the day. Above all, the FC increases its power generation during its working hours. This growth in the electrical power generated by DGs is related to optimal DFR. It is because that the DFR makes the optimal routes to deliver electrical power from DG units to electrical demands and EVs. Consequently, power losses also are reduced in the MG and the MG operator prefers to purchase less electrical power from the upstream grid. By the way, the PV and WT stochastically contribute to generating electrical power when they are available.

3.4. Case study IV: DFR and OGS as a joint problem with considering DR program This case study performs OGS and optimal DFR as a joint problem with considering DR program. It takes into account EVs in a controlled charging pattern according to the signals received from the MG operator. In this case study, the MG operator owns EVs which contribute in the electricity market by changing the time of charging and selling electrical power to MG in the V2G mode. Table 9 shows the electrical 69

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EVs present interactive loads that can be dischrged into the microgrid in some time slots. As seen in the blue curve of Fig. 7, EVs are discharged in hours 13–19 into the microgrid resulting in a negative loads (the area under the blue curve in these hours is negative). Fig. 8 shows the total electrical demand that is supplied by DGs and upstream grid in different case studies. In this figure, the network demand is affected by the base load, DR, and EVs. In case studies I-III, the demand of MG (base load) is supplied and the EVs charging times are fixed. Consequently, the overall load profile is the same for case studies I-III. However, these case studies lead to different results since the generation of DGs and the status of switches in the DFR are different for each case study. On the other hand, in case study IV, the EV time slots are optimized and also the DR affects the overall load profile. Therefore, the resulted load profile in case study IV is different from that of case studies I-III. It is clear that the demand is high during peak hours due to the uncontrolled charging of EVs at peak hours. However, in the case study IV, the demand curve is smoother than previous case studies due to executing the DR program and shifting charging time of EVs from peak hours to off-peak hours 2–9 hours. Moreover, the EVs contribute to supply electrical demand as V2G operating mode during peak hours 14-21. Fig. 9 shows the cost of active power losses in different case studies. As it is evident, active power losses are very high in case study I with only optimal DFR without DGs. It is due to the fact that the upstream main grid should supply the whole electrical demand of MG and EVs. It increases the amount of current flowing through the lines, and as a result, it increases active power losses. Nonetheless, in other case studies, there is a reduction in electrical power losses due to applying optimal DFR along with OSG and other ways for DSM that are DR and V2G program. Consequently, there is no need to purchase all of the required electrical power from the upstream grid. Fig. 10 displays the cost of the DR program for case study IV. It can be seen that the consumers have a high contribution in the DR program to reduce demand level during peak hours. It is because that the MG operator pays higher to consumers at this period. Figs. 11 and 12 illustrate the cost of active and reactive power, respectively, generated by DGs at different hours for case studies II-IV. It is previously expressed that the DGs are not considered in case study I. Therefore, the comparison is presented only for other case studies. Figs. 13 and 14 exemplifies the cost of active and reactive power, respectively, purchased from the upstream grid at different hours for various case studies. As the figures imply, the maximum electrical power purchased from the main grid is related to the case study I due to lack of DG generations. Fig. 15 depicts total operation cost at different hours for various case studies. It can be seen that the total operation costs increase during peak hours due to an increase in energy consumed by customers. It is more prominent in case I that is only the optimal DFR. Case study IV incurred the least operation cost due to using the DR program as curtailable loads. The difference between the total operation costs of different case studies is bolder during hours 14–20 when owners of EVs charge their vehicles despite the peak period in case studies I to III. Nevertheless, in case study IV, charge/discharge of EVs is controlled by the operator of MG based on minimization of operation cost. Table 10 presents total operation cost and its different components for various case studies. As seen, case study I incurred the highest operation cost ($9505), followed by case study II ($7696), and case study III ($7384). The lowest total operation cost is related to case study IV with $6792. The highest cost of purchasing power from the main grid happens in case study I, since there are no DG units on the MG, and the total required electrical power is purchased from the main grid. One of the most important constraints for operation of MG is the voltage profile. Therefore, Figs. 16–19 show the voltage profile at each hour for the case study I to IV, respectively. By comparing these figures, it can be observed that in case study I, the minimum voltage is 0.915 (pu) that is less than allowable value for long-term operation that is 0.95 (pu). However, these voltage drops happen in a few buses during

Fig. 18. Voltage profile of the test system for case study III at different time.

Fig. 19. Voltage profile of the test system for case study IV at different time.

power generated by all DGs, main grid, selling/purchasing electrical power by EV owners, and open switches at each hour in the day-ahead scheduling. By comparing results of this case study with Case study III, it can be seen that by executing DR program and shifting the charging times of EVs to off-peak hours, the power generation of expensive DG units such as MT-1, MT-2, and FC is reduced during peak hours. Furthermore, the EVs discharge the electrical power to MG during peak hours to minimize the operation cost of MG. 3.5. Comparison of case studies Fig. 7 presents hourly charge/discharge of EVs in different case studies. It can be seen that EVs are charged with an uncontrolled pattern, and they do not play a role in DSM in the case studies I to III, so that they are charged at peak periods of MG and the operation cost of MG increases by this pattern. All the same, in the case study IV, charging periods of EVs shift from peak to off-peak hours so that it reduces electricity bill of EV owners for charging and harvest the benefits of selling electrical power at peak periods. As seen in Fig. 7, the EVs are positive loads in case studies I-III (the red curve). In this case studies, the EVs are only charged and it is impossible to discharge them into the microgrid in some time slots (V2G). As a result, the area under the red curve in Fig. 7 is always positive. On the other hand, in case study IV, 70

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peak periods (for a few hours) and are venial for the operator. This unacceptable voltage drop is due to this fact that demand of active and reactive power is supplied by the upstream grid in the case study I, and the DG units cannot help the operator of MG to keep voltage within allowed limits. In spite of that, in other case studies, all voltages are in a specified range especially in case study IV.

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4. Conclusions This paper proposes a new optimization model as a joint optimal DRF and OGS problem with considering the stochastic behavior of WT and PV units, DR program, and different charging patterns for EVs in an MG. Main objective of optimization are the minimization of different operation cost terms. The four case studies are simulated on the IEEE 33-bus distribution network to evaluate the proposed model. To begin, the case study that only involves the optimal DFR is evaluated. In the second place, the case study that only deals with OGS is assessed. Afterward, the case study that the takes into account the optimal DFR and OGS as a joint problem is simulated, and finally the case study that repeats the third case study with considering DR program is evaluated as the proposed model in this paper. Of course, the first to third case studies consider EVs with an uncontrolled charging pattern, whereas the fourth case study takes into account EVs with a controlled charging pattern and V2G capability. The simulation results show that the electrical power purchased from the upstream grid is reduced by 58.76%, 51.89%, and 47.24% for case studies IV, III, and II, respectively, in comparison to case study I. In addition, the cost of power losses is alleviated by 70%, 64.06%, and 51.56% for case studies IV, III, and II, respectively, compared to the first case study. Above all, the total operation cost of MG is decreased by 28.54%, 22.31%, and 19.03% for case studies IV, III, and II, respectively, compared to the first case study. Some suggestions for future works can be expressed as 1) adding reliability indices and their cost to the problem, 2) considering environmental issues and their costs in the proposed problem, and 3) adding reserve costs to the proposed method by formulating the joint reserve and energy model. References [1] X. Wu, X. Hu, X. Yin, et al., Stochastic optimal energy management of smart home with PEV energy storage, IEEE Trans. Smart Grid 9 (3) (2018) 2065–2075. [2] P. Siano, Demand response and smart grids—a survey, Renewable Sustainable Energy Rev. 30 (2014) 461–478 2014/02/01/. [3] X. Wu, X. Hu, Y. Teng, et al., Optimal integration of a hybrid solar-battery power source into smart home nanogrid with plug-in electric vehicle, J. Power Sources 363 (2017) 277–283 2017/09/30/. [4] M. Esmaili, H. Shafiee, J. Aghaei, Range anxiety of electric vehicles in energy management of microgrids with controllable loads, J. Energy Storage 20 (2018) 57–66 2018/12/01/. [5] A. van Stiphout, T. Brijs, R. Belmans, et al., Quantifying the importance of power system operation constraints in power system planning models: a case study for electricity storage, J. Energy Storage 13 (2017) 344–358 2017/10/01/. [6] H. de Faria, M. Resende, D. Ernst, A biased random key genetic algorithm applied to the electric distribution network reconfiguration problem, J. Heuristics 23 (6) (2017) 533–550. [7] T.T. Nguyen, A.V. Truong, T.A. Phung, A novel method based on adaptive cuckoo search for optimal network reconfiguration and distributed generation allocation in distribution network, Int. J. Electr. Power Energy Syst. 78 (2016) 801–815 2016/ 06/01/. [8] A. Asrari, S. Lotfifard, M.S. Payam, Pareto dominance-based multiobjective optimization method for distribution network reconfiguration, IEEE Trans. Smart Grid 7 (3) (2016) 1401–1410. [9] H. Fathabadi, Power distribution network reconfiguration for power loss minimization using novel dynamic fuzzy c-means (dFCM) clustering based ANN approach, Int. J. Electr. Power Energy Syst. 78 (2016) 96–107 2016/06/01/. [10] R.T.F. Ah King, S. Marappa Naiken, Voltage Stability Maximization by Distribution Network Reconfiguration Using a Hybrid Algorithm, (2016), pp. 144–153.

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