Economic and technical analysis of reactive power provision from distributed energy resources in microgrids

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Economic and technical analysis of reactive power provision from distributed energy resources in microgrids ⁎

Oktoviano Gandhia,b, , Carlos D. Rodríguez-Gallegosb,c, Wenjie Zhangc, Dipti Srinivasanc, Thomas Reindlb a b c

Graduate School of Integrative Sciences and Engineering, National University of Singapore (NUS), Singapore 117456, Singapore Solar Energy Research Institute of Singapore (SERIS), National University of Singapore (NUS), Singapore 117574, Singapore Department of Electrical and Computer Engineering, National University of Singapore (NUS), Singapore 117576, Singapore

H I G H L I G H T S power costs for photovoltaic system and battery energy storage are proposed. • Reactive reactive power locally is not always economically or technically beneficial. • Providing power costs consideration is especially important in poorly distributed systems. • Reactive are found to be competitive with switched capacitors for reactive power provision. • DERs • Inverter efficiency is the most crucial factor affecting DERs’ reactive power provision.

A R T I C L E I N F O

A B S T R A C T

Keywords: Battery energy storage system Microgrid Photovoltaic system Power dispatch optimization Reactive power Scheduling Switched capacitors

This work analyses the economic and technical impact of local reactive power provision in grid-connected microgrids with distributed energy resources. Costs of reactive power provision by photovoltaic systems and battery energy storage systems are explicitly formulated and an objective function incorporating the costs is proposed. The advantage of the proposed objective function is validated by comparing it with other objective functions frequently employed in the literature. From various case studies, the extent of economic and technical benefits of local reactive power provision for the microgrid is established. Subsequently, the technical and economic competitiveness of reactive power provision using inverter-based distributed energy resources are compared against those using switched capacitors. Extensive sensitivity analyses are performed to determine the scenarios in which one technology is more competitive than the other. Inverter efficiency has been identified as the most important parameter for reactive power provision from distributed energy resources while electricity price is the most crucial factor for switched capacitors’ competitiveness in producing reactive power.

In this paper, all active, reactive and apparent power quantities have the units [kW], [kVA], and [kVAr] respectively. 1. Introduction Reactive power dispatch (RPD) is an integral part of power systems operations, especially to manage voltage stability and line losses [1]. In distribution systems and microgrids, where the ratio of resistance to reactance is higher than in transmission systems, local reactive power compensation can significantly reduce the power losses, and thereby the operational costs [2,3]. To provide reactive power locally, many researchers have analyzed the optimal allocation and operation of

⁎

reactive power compensation devices in distribution systems [4–7]. Recently, with the rise of inverter-based distributed energy resources (DERs) such as photovoltaic systems (PVs), many works have also proposed to use the inverters for local reactive power compensation [8–11], which have been shown to be capable in producing reactive power with little to even no additional costs [12,13]. Compared to traditional power factor correction devices that are used in distribution systems, i.e. capacitor banks, inverters have faster response time and therefore can regulate voltage more accurately, especially during transient disturbances [14]. Yet, despite the possibility to manage both active and reactive power of the DERs, most works have focused on one or the other.

Corresponding author at: Graduate School of Integrative Sciences and Engineering, National University of Singapore (NUS), Singapore 117456, Singapore. E-mail address: [email protected] (O. Gandhi).

http://dx.doi.org/10.1016/j.apenergy.2017.08.154 Received 31 March 2017; Received in revised form 25 July 2017; Accepted 13 August 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Gandhi, O., Applied Energy (2017), http://dx.doi.org/10.1016/j.apenergy.2017.08.154

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Nomenclature

δxDCH ,t Indices

j,k t x X

cxBESS,deg ,t ctPgrid

distribution network node indices. Node j and k are adjacent, where current flows from j to k index of time period (1 ⩽ t ⩽ T ) index of BESS, PV, and SC indicators of BESS, PV, and/or SC quantities

c PPV cQgrid cxQX ,t

Parameters

Gt I jk,t Imax

ηCH,ηDCH charging and discharging efficiency of BESS ηDOD battery degradation constant related to depth-of-discharge (DOD) [SGD] ηP battery degradation constant related to charging and discharging power [SGD/kW 2 ] ηSOC battery degradation constant related to state-of-charge (SOC) [SGD] ηT power temperature coefficient of solar cells [°C−1] cR current-dependent loss coefficient of an inverter [kW−1] standby loss coefficient of an inverter [kW] cself voltage-dependent loss coefficient of an inverter cV number of BESS, and PV in the system B,M ExBESS energy capacity of the xth BESS [kW h] H length of time period t [h] NOCT nominal operating temperature of solar cells [°C] PV rated power of the PV at standard test conditions Prated BESS BESS Pmax ,Pmin maximum charging and discharging power of BESS X X,invloss active power loss in BESS/PV inverter when Smax flows Pmax through the inverter apparent power demand at node j. Available from the Sjbus distribution system data X BESS/PV inverter rating Smax SOCmax upper limit of the SOC of the BESS [%] SOCmin lower limit of the SOC of the BESS [%] SOCref reference SOC of the BESS for the degradation cost [%]

P ave PxBESS ,t Ptgrid P jload ,t loss P jk ,t

PxPV ,t PxX,invloss ,t Qtgrid Qjload ,t loss Qjk ,t X Q lim, t

QxX,t Vj,t Sjload ,t loss Sjk ,t SxX,t SOCx ,t Tta,TtPV

and 0 otherwise discharging variable that takes the value of 1 when PxBESS < 0 and 0 otherwise ,t cost of battery degradation from xth BESS [SGD] price of active power from the grid (electricity price) at period t [SGD/kW h] payment for active power generated by PV [SGD/kW h] reactive power charge from the grid [SGD/kVArh] cost of producing reactive power using xth BESS/PV/SC at period t [SGD/kVArh] solar irradiance at period t [W/m2 ] current flowing from node i to j at period t [p.u.] upper limit of current flowing across the distribution lines [p.u.] average net load in the time periods considered charging or discharging power of xth BESS at period t active power taken from the grid at period t active power demand at node j at period t active power losses on the line connecting node j and k at period t active power injected to the grid by xth PV at period t active power loss in xth BESS/PV inverter at period t reactive power taken from the grid at period t reactive power demand at node j at period t reactive power losses on the line connecting node j and k at period t limit of reactive power generated by BESS/PV without reducing the BESS/PV active power output reactive power generated by xth BESS/PV/SC at period t voltage at node j at period t [p.u.] apparent power demand at node j at period t apparent power losses on the line connecting node j and k apparent power flowing through xth BESS/PV inverter at period t SOC of the xth BESS at period t [%] ambient and solar cells’ temperature at period t [°C]

Variables

δxCH ,t

>0 charging variable that takes the value of 1 when PxBESS ,t

with limited number of DERs. In addition, the coefficients in the payment functions are generated randomly and therefore it is not clear how economical it is to produce the reactive power. Furthermore, the optimization generally occurs for only one time step, which is not suitable for time-dependent DERs such as PV. Recently, there is more research considering the integrated optimization of active and reactive power. At the transmission level, [32] proposed the clearing of coupled of active and reactive power market, minimizing active and reactive power payment to the generators. Subsequently, [33] proposed multiobjective clearing of the coupled market. Meanwhile, at the distribution level, [11] controlled the active and reactive power schedule of the BESS, together with the curtailment of wind power, to minimize the losses and wind curtailment. The scheduling of PV, BESS, transformers’ settings, and controllable loads are optimized in [34] to minimize losses in distribution system. Liang et al. [6] proposed an enhanced firefly algorithm to solve multi-objective optimal active and reactive power dispatch, minimizing fuel costs, transmission losses, and voltage deviation. Sousa et al. [35] also minimized active power generation and voltage deviation, while considering various DERs, such as PV, wind, EV and biomass, in distribution system. Both [10,36] solved the optimization of active and reactive power

On the one hand, researchers have refined many optimization techniques to harness the potential of distributed active power generation, either to minimize power taken from the grid [15,16] or to minimize total costs of running a microgrid [17–21]. Nevertheless, many of them did not consider the test systems where the DERs are being implemented. Important indicators such as line losses and voltage variability were often ignored. On the other hand, many works have also explored the optimization of reactive power provision by the DERs to provide ancillary services such as voltage support [22–24] as well as to reduce the transmission losses [9,24,25]. However, most of them took the active power component of the DERs as constant and did not take the system’s economics or the reactive power costs into account. Reactive power payment functions have been formulated for conventional generators [26,27] and reactive power devices [28]. The reactive power payment includes the availability payment, operation payment, and lost of opportunity payment. Using the payment functions, the reactive power dispatch optimization has been explored using market-based approaches, with objective functions ranging from minimization of expected payment function [26,27,29], societal advantage function [30], as well as other objectives including maximizing voltage stability and minimizing transmission losses [31]. However, the market-based approaches are mainly explored in transmission systems 2

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2. Problem formulation

market clearing in distribution system in the presence of DERs (synchronous distributed generation and wind turbine in [10], and electric vehicles in [36]). The approaches have either been an integrated active-reactive power market-based approach [10,32,33,36] or day-ahead generation scheduling [6,11,34,35]. The market-based approach still suffers from most of the aforementioned drawbacks, which are the arbitrary reactive power costs and optimization of only one period. Although [10] considered active and reactive power markets in distribution systems with wind generation for 24 h, the authors have not taken into account the line losses and also use arbitrary values for the reactive power prices. Meanwhile, authors who employ the generation scheduling approach have optimized the integrated active and reactive power dispatch in distribution systems with DERs, but have not taken into account the costs of reactive power produced [6,11,34,35]. Nevertheless, reactive power can be a significant part of the costs and by ignoring them entirely, the optimization of power dispatch will not yield optimum economic results. This is particularly the case for microgrids connected to the main grid where there are reactive power charges when the reactive power taken from the main grid is above a certain value – 33% and 62% of active power taken from the grid for the case of United Kingdom [37] and Singapore [38], respectively. Thus, there needs to be a balance between the amount of reactive power produced by the DERs and the line losses in the distribution system to minimize the operational costs of running the system. It is also of utmost importance to explicitly calculate the cost of reactive power provision from DERs and assess their competitiveness before power system planners and operators can determine whether a shift from traditional reactive power devices towards inverters with reactive power capability is cost effective. Even though reactive power costs are much smaller than the active power costs, the investment involved is significant. This study has two main parts. Firstly, a practical objective function is proposed to achieve the balance between reactive power provision from the DERs and the line losses in distribution systems. To do so, reactive power costs from DERs are formulated and calculated using values from real systems to allow meaningful economic insights. The proposed objective function is then compared with other objective functions in the literature through multi-objective optimization. Secondly, the cost-competitiveness of the DERs in providing local reactive power provision is compared with switched capacitors (SCs), representing traditional reactive power devices. Thorough sensitivity analyses are conducted to determine the conditions in which DERs are preferred for reactive compensation or otherwise. The sensitivity analyses also allow planners to choose the parameters and results presented in this paper which are applicable to them based on their market situation. The main contributions of this paper are the following:

We want to minimize the total costs of running a grid-connected microgrid containing PV and BESS. An independent system operator (ISO) is assumed to have control over the BESS and has been authorized to utilize unused inverters’ capacity of the PV systems for reactive power provision. Charging the BESS represents a cost while discharging the BESS represents a benefit. The PV systems are still paid for the power they generate to recover the investment required. Each DER is compensated for the reactive power produced as explained in Section 3.1. The objective function is therefore to minimize Eq. (1): T

Cost =

M

grid grid PPV [  ctPgrid cQgrid ∑ PxPV,t t +  t + c P Q x

∑ t

cost of P from grid M

PV cxQPV ,t Q x ,t x   

∑

+

cost of Q from grid

+

B

cxQBESS QxBESS ,t ,t x    

∑

cost of Q from PV

cost of Q from BESS

cost of P from PV B BESS,deg + c x x ,t

∑

 

]H

cost of BESS degradation

(1) Eq. (1) represents the total payment made by the microgrid to the main grid as well as to the DERs’ owners. The first term, which is the payment for active power to the grid, already includes the net cost of B charging of BESS (ctPgrid ∑x PxBESS ,t ) as well as the active power losses N

N

loss (ctPgrid ∑ j ∑k P jk ,t ) , as can be inferred from the active power balance constraint in Eq. (7). The microgrid is assumed as a price taker and does not have influence on the electricity price from the grid, ctPgrid . The second term is the reactive power charge from the grid. The third and fourth terms are the payment to the PV owners for their active and reactive power output respectively. Lastly, the fifth and sixth term are the payment to the BESS owners for the reactive power output and for the BESS degradation. The payment to the DER owners can be settled on contractual basis (monthly or otherwise) based on the amount of active and reactive power the DERs are injecting to/absorbing from the grid (can be measured via net metering). A market structure has not been adopted in this work because real distribution systems typically still lack the necessary market infrastructure. One of the main contributions of this paper, which is the formulation and assessment of reactive power costs from DERs, is elaborated in Section 3. At the same time, the BESS have been employed to provide peak shaving service to smoothen the variability of the PV output and the net load of the microgrid. The objective of the peak shaving is to minimize the load variation throughout the day, and hence the power loss [34,39], as well as the equipment aging [40]. The load variation has been adapted from [41]:

T

Load Variation =

∑ ⎡⎢∑ j t

1. Formulate the costs of reactive power provision by DERs explicitly and analyse their competitiveness to grid reactive power charge and traditional reactive power device 2. Establish the extent of economic and technical benefits of local reactive power provision 3. Analyse extensively the impacts of changes in parameters on the techno-economic benefits of reactive power compensation from DERs and SCs

N

⎣

M

2

PV BESS ave⎤ P jload ,t − ∑ Px ,t + Ptotal,t −P ⎥ x ⎦

(2)

where P ave is the average net load of the system before the BESS’ charging and discharging:

P ave =

1 T

T

⎡

N

⎣

j

∑ ⎢∑

BESS Ptotal, t

t

M

PV⎤ P jload ,t − ∑ Px ,t ⎥ x ⎦

(3)

and is the total power of all the B BESS units, as explained in Section 4. However, it is not enough to analyse the RPD from DERs on its own. It is also necessary to compare the competitiveness of local reactive power provision using the DERs (cxQPV and cxQBESS in Eq. (1)) and SCs ,t ,t (cxQSC ) . Therefore, the RPD from the different sources are assessed ,t through economic and technical objectives. To evaluate the benefits of local reactive power provision with changing parameters, we adopt net monetary benefits and improvement in voltage stability as the economic and technical objectives, respectively.

The remaining part of the paper proceeds as follows: First, the problem is formulated and the objective function is proposed in Section 2. In Section 3, the reactive power costs for DERs are derived explicitly for grid-connected microgrid. The optimization algorithm is explained in Section 4. Section 5 describes the methods to analyse the technical and economic impact of local reactive power provision, as well as the test systems and parameters used. The results are presented and discussed in Section 6 and the work is concluded in Section 7. 3

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2.1. Economic objective – net monetary benefits

PxPV ,t =

The economic objective function is the net monetary benefits (NMB) of having either inverters or capacitors for RPD. It can be calculated as:

NMB = CostNoQ−Cost SC/DER

Gt PV Prated × (1−ηT (TtPV−25 [°C]))−PxPV,invloss ,t 1000 [W/m2]

TtPV = Tta +

(4)

Gt × (NOCT−20 [°C]) 800 [W/m2]

By replacing Gt and Tta can be obtained. Gt70,Tta70 ,

PV |QxPV ,t | ⩽ Q lim,t =

2.2. Technical objective – WVDI improvement

t

N

|QxPV ,t | ⩽

(Vj,t −Vref )2 (5)

j

(6)

2.3. Constraints from the power system The constraints of the power system are: N

N

Ptgrid− ∑ j

N

∑

M

∑

j

N

j

=

N loss load P jk ,t − ∑ P j,t +

k

Qtgrid− ∑ loss Sjk ,t

∑

N

loss 2 (P jk ,t )

j

+

loss 2 (Qjk ,t )

∑

B

QxPV ,t +

x

=

(7)

x

M

loss load Qjk ,t − ∑ Q j,t +

k

B BESS PxPV =0 ,t − ∑ Px ,t

x

(Vj,t −Vk,t ) I ∗jk,t

∑ x

(14) PV Q lim, t

PV 2 PV,invloss 2 (Smax ) −(Pmax )

(15)

In such cases, the ISO will have to compensate the PV owners for the lost opportunity cost (LOC) as will be explained in greater detail in Section 3.1. LOC may play an important role when the PV penetration becomes very high and there is excess generation in the middle of the day. At that time, it may be more desirable to produce reactive power rather than active power. The optimizations implemented in this work represent the dayahead scheduling and the values of the forecast can be updated accordingly. In this work, the PV inverter rating is taken to be the same as the rated power of the PV so that no extra investment cost is required to produce the reactive power [12].

WVDI improvement is therefore:

WVDI Improv.=Total WVDINoQ−Total WVDISC/DER

Tta70

is the rating of the PV inverter and is the limit of where reactive power that can be generated without reducing the active power output of the PV. The 70% confidence level has been used to ensure that the owner of the PV system is not forgoing the opportunity to produce active power because of the reactive power provision. The 70% confidence level has also been utilized by PJM – a regional transmission organization in the US – for unit commitment [46]. However, in cases where the ISO desires higher level of |QxPV ,t | than the limit outlined in Eq. (14), the limit can then be expressed as:

Voltage deviation has been used as a technical objective because voltage stability is one of the most important aspect in a microgrid with high DER penetration [29,42]. Large deviations in voltage may cause voltage collapse and power system failure [43]. Therefore, one of our objectives is to minimize the voltage deviation in the system. Weighted voltage deviation index (WVDI) penalizes higher voltage deviation more heavily and is therefore favoured over absolute voltage deviation. It takes the following form: T

Gt70

PV 2 2 (Smax ) −(PxPV70 ,t )

PV Smax

∑∑

(13)

to and in Eqs. (12) and (13), PtPV70 and PtPV70 are the upper limit of forecasted irradiance, ambient temperature, and PV power at 70% confidence level respectively. The values of PtPV70 are subsequently used to find the reactive power constraint for PV:

where the total cost is calculated from Eq. (1). NoQ refers to the system without local reactive power compensation while SC/DER refers to cases where the reactive power are provided by SCs or DERs respectively, as will be explained in greater detail in Sections 5 and 6.

Total WVDI =

(12)

2.5. Constraints from BESS

QxBESS =0 ,t (8)

The charging and discharging of a battery are limited by the maxBESS BESS imum charging (Pmax ) and discharging power (Pmin ). The BESS’ state of charge (SOC) must also lie within a certain range. The SOC of the battery is updated according to the following equations:

(9)

I jk,t ⩽ Imax

(10)

Vmin ⩽ |Vj,t | ⩽ Vmax

(11)

Eq. (7) is the active power balance constraint, where positive PxBESS ,t represents charging of BESS, and therefore is considered as load. The reactive power balance constraint is expressed in Eq. (8) where positive BESS QxPV represent reactive power provision from the DERs. Eq. ,t and Q x ,t (9) illustrates the line loss calculation from voltage and current as well as the relation between active and reactive power. The line losses are therefore linked to the power of the DERs via the voltage and current quantities. The current flowing through the distribution lines is limited according to Eq. (10). Lastly, the voltage at each node needs to lie within a certain range (Eq. (11)). The current and voltage for all the lines and nodes are obtained through the Backward Forward Sweep algorithm, an accurate load flow algorithm for radial distribution systems [44].

BESS BESS Pmin ⩽ PxBESS ⩽ Pmax ,t

(16)

SOCmin ⩽ SOCx ,t ⩽ SOCmax

(17)

CH BESS + δ DCH (ηDCH )−1P BESS ] SOCx ,t + 1 = SOCx ,t + [δxCH ,t η Px ,t x ,t x ,t

H ExBESS

(18)

Reactive power provision by BESS is also limited by the inverter rating and the charging or discharging power:

|QxBESS ,t | ⩽

BESS 2 2 (Smax ) −(PxBESS ,t )

(19)

In this work, the ISO is in control of both the active and reactive can be increased or decreased power output of the BESS, such that PxBESS ,t accordingly depending on the desired QxBESS ,t . 3. Cost functions

2.4. Constraints from the PV system

3.1. Reactive power cost

The forecasted active power injection from a PV system (PxPV ,t ) dePV pends mainly on the rating of the system (Prated ), the irradiance (Gt ), the temperature of the solar cells (TtPV ) and the power loss in the inverter (PxPV,invloss ). The temperature of the solar cells also depends on the solar ,t irradiance and the ambient temperature (Tta ). Their relations are expressed by the following equations [45]:

The inverters that connect PV and BESS to the system are assumed to have reactive power capability. The reactive power injection or abX sorption is limited by Eqs. (14) and (19), where Smax , is taken to be the BESS PV same as Prated and Pmax for PV and BESS respectively. Therefore, no additional investment is necessary to provide the reactive power management using the DERs. 4

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To solve the optimization problem in Eq. (1), we first need to formulate the costs of producing reactive power using PV, BESS, and EV charging stations. In [47], Braun showed that inverters suffer from power losses that are dependent on the apparent power flowing through the inverters. When the inverters inject reactive power, the apparent power flowing through them increases, inducing additional power loss in the inverters. The cost of reactive power is therefore the additional power loss multiplied by the cost of the electricity to fulfill the additional loss. The power loss in the inverter is approximated by [47]:

P invloss = cself + cV S + cR S 2

any charging of the BESS (even with PV) will cause the ISO to buy more power from the grid. Therefore cxQBESS is always associated with ctPgrid . If ,t total PV generation at period t goes above the total load and losses in the system, and PV is used to charge the BESS at that period, then cxQBESS ,t will be associated with c PPV . When the BESS’ SOC is at SOCmin and is not initially charging, the BESS will charge just enough to compensate for will also be proportional to ctPgrid . the losses, and therefore cxQBESS ,t QX The values of cx ,t for different PxX,t and QxX,t can be seen in Fig. 3 in Section 5.4. As can be seen from Eqs. (23) and (24), the cost of reactive power depends on QxX,t ,ctPgrid (known by the ISO), and ΔPxX,invloss , which ,t can be obtained from the inverters’ manufacturer [48]. This means that cxQX ,t can be easily calculated by the ISO.

(20)

where cself ,cV , and cR are constants determined experimentally that fit the efficiency curve of the inverter. The additional losses due to the reactive power injection are therefore [47]:

ΔPxX,invloss = ,t

X X X 2 X 2 X ⎧ cV (Sx ,t −Px ,t ) + cR ((Sx ,t ) −(Px ,t ) ) Px ,t ≠ 0 ⎨ cself + cV QxX,t + cR (QxX,t )2 PxX,t = 0 ⎩

3.2. Battery degradation cost Batteries’ lifetime diminishes when they continuously charge and discharge. As the parameters to calculate the battery degradation need to be obtained experimentally and are specific for each type of battery and manufacturer, we adopt the BESS and its degradation constants from [49]. The cost function of the battery degradation is [49]:

(21)

Even though the calculation of the additional power loss in the inverter is the same for PV and BESS, the calculation of their costs can be different because different sources of active power may be used to compensate for the additional losses. Additionally, when the system requires the DERs to curtail its active power generation to provide more reactive power support, there will be lost opportunity cost (LOC) incurred by the DERs’ owners. In such cases, the active power output of the DERs has to be reduced by ΔPxPV,oppcost , ,t which can be expressed as:

ΔPxX,oppcost = ,t

X X )2−(QxX,t )2 |QxX,t | > Q lim, ⎧ PxX,t − (Smax t X ⎨0 |QxX,t | ⩽ Q lim, t ⎩

cxBESS,deg = ηDOD (SOCx ,t + 1−SOCx ,t )2 ,t 2 2 + ηP (PxBESS ,t ) + ηSOC (SOC x ,t + 1−SOCref )

4. Optimization algorithm Genetic Algorithm (GA) has been used to minimize Eqs. (1) and (2). A heuristic optimization approach is employed instead of exact optimization methods because the backward forward sweep used in calculating the voltage at and current across the nodes is non-exact. In particular, GA is employed because of the wide use in power dispatch optimization [50–52] and for its flexibility and scalability [52]. Other algorithms such as Particle Swarm Optimizations (PSO) [53] and Interior Programming Method (IPM) [54] have also been employed in the simulations, but it was found that GA yield the best results. BESS First, the peak shaving is carried out by aggregating PxBESS into Ptotal, ,t t and minimizing Eq. (2). The optimization is done over 48 half-hour BESS periods, giving us 48 variables for Ptotal, t . Next, the active and reactive power dispatch is optimized for each time period, the individual PxBESS is ,t B BESS allowed to vary, but ∑x PxBESS = Ptotal, ,t t , such that a finer optimization to reduce the line losses and to suit the optimal value of QxBESS can be ,t carried out. To compare the performance of the proposed objective function and those in the literature, a multi-objective optimization incorporating the technical (Eq. (5)) and economic (Eq. (1)) objective was performed. As the total costs and voltage stability of the system are not always aligned, there will be pareto optimal solutions where the solutions are non-dominated with respect to other solutions. Non-dominated Sorting Genetic Algorithm-II (NSGA-II) [55] has been adopted as the multi-objective optimization algorithm as it has been found to perform better than other multi-objective algorithms [4,56]. Moreover, GA handles both binary and real-number coding well, and is therefore suitable for both DERs’ and SCs’ reactive power output. Subsequently, NSGA-II was also employed to compare the competitiveness of local reactive power provision using DERs and SCs. Continuous [57] and binary values were adopted for DER and SC cases respectively. All NSGA-II parameters are the same for the DER and SC cases. The parameters for GA and NSGA-II, such as the crossover and mutation probability, have been determined following the suggestions from [57,55] respectively. The number of chromosomes and generations have been determined empirically to balance the quality of the results and the computational burden. Each case considered is run five

(22)

X Q lim, t

is the reactive power limit that can be generated by the where DERs without reducing their active power output. Note that X X ΔPxX,oppcost = 0 when |QxX,t | ⩽ Q lim, ,t t because Px ,t is not reduced. PV,invloss PV is compensated by P during the daytime and by For PV, ΔP P grid in the dawn and at night. However, from the perspective of the ISO, any active power loss must be compensated by taking more power from the grid (because the PV generation is always less than the total load in the microgrid in the current study). Therefore, the cost of reactive power generation for PV is: Pgrid PV cxQPV × (ΔPxPV,invloss + ΔPxPV,oppcost ) ,t ,t Q x ,t = ct ,t

(23)

PBESS

≠ 0 , the additional power loss reduces the For BESS, when BESS’ charging or discharging power, i.e. ΔPBESS,invloss reduces the power bought from the grid or decreases the power that can be sold to the grid. Therefore cxQBESS is associated with the electricity price at that ,t period. When PBESS = 0 , the power loss from the reactive power injection decreases the SOC of the BESS. The associated costs are then the average cost of electricity that has been purchased to charge the battery. Hence, they take the form of:

cxQBESS QxBESS ,t ,t

Pgrid × ΔPxBESS,invloss ⎧ ct ,t ⎪ Pgrid = ∑tt′= 1 δxCH × ct′ PxBESS ′ ′ t t , , ⎨ × ΔPxBESS,invloss ,t BESS ⎪ ∑tt′= 1 δxCH P ,t ′ x ,t ′ ⎩

PxBESS ≠ 0 ,t PxBESS =0 ,t

(25)

(24)

where t ′ indicates the periods from the beginning of the day until period t. The discharging power is not taken into account as it does not contribute towards the SOC at time t. In this work, as the ISO determines both the active and reactive power of the BESS, there is no lost opportunity cost involved. In cases where lost opportunity cost for BESS needs to be included, it will depend on the use of the BESS, i.e. the opportunity cost when BESS is utilized for frequency regulation will be different from when it is employed for energy arbitrage. The PV systems can technically also charge the BESS, but since the PV generation considered in this work is always below the total load, 5

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also calculated based on the NoQ cases with the respective parameters changed (i.e. NMB of DER case with 110% PV LCOE are calculated by subtracting Total Cost of the DER case from the NoQ case with 110% PV −Cost110%PVLCOE LCOE, i.e. NMB110%PVLCOE = Cost110%PVLCOE ). NoQ SC/DER Analysis on the cost-competitiveness of reactive power provision using the DERs is deliberated in Section 6.2.

times with 150 chromosomes and 60 generations for the 37 and 69-bus system. For the 119-bus system, the cases are run with 250 chromosomes and 100 generations each. The best results out of the five runs are shown for all the cases. 4.1. Decision variables The decision variables considered in the GA for objective function BESS BESS comparison are QxPV ,t , Px ,t ,Q x ,t . The PV are assumed to always operate at maximum power point and produce maximum PxPV ,t given the rating of the PV, solar irradiance and ambient temperature, unless when PxPV ,t needs to be reduced because of QxPV ,t . When comparing the RPD of DERs and SCs using NSGA-II, PxBESS is fixed such that any difference will be ,t from the differences in the RPD.

5.3. Test system To test the validity of the proposed objective functions and reactive power cost formulations, radial 37-bus [59], 69-bus [60], and 119-bus [61] test systems have been employed as the test microgrids. The power factor (PF) of the original load demand (without any DERs added), measured by dividing the total active power demand by the total apparent power demand, is 0.850, 0.816, and 0.800 for the 37-bus, 69bus, and 119-bus system respectively. The layout of the microgrids as well as the placement of the DERs can be seen in Fig. 1. For the 37-bus system, the load at each node in the microgrid is classified into either commercial, industrial, or residential load. For the 69-bus and 119-bus test system, the type of load at each bus is not available. Therefore, without loss of generality, all the nodes in 69-bus and 119-bus system have been assumed to have industrial load profile. Theload profile for each type of load [62] can be seen in Fig. 2. PV Prated of each PV system is 300 kWp in the 37 and 69-bus system, and 500 kWp in the 119-bus system. The BESS in all the test systems are Lithium ion batteries with 500 kW h capacity and 500 kW power [49]. For the SC cases, the capacitor banks’ rating are therefore 100/ 166.7 kVAr each, forming switched capacitors of 300/500 kVAr to replace the DERs. The PV and BESS penetration2 in the systems are approximately 80% and 40% respectively. The placement of the DERs in the systems are completely arbitrary. The load data for each bus in the test systems at each time period are generated using the following equation:

5. Implementation The study is divided into two main parts. The first part is the analysis of the economic and technical impact of reactive power provision using the DERs, along with their associated costs, through the proposed objective function as explained in Section 5.1. In the second part of the study, the competitiveness of reactive power compensation using inverter-based DERs is assessed and compared with SCs, as outlined in Section 5.2. The configuration of the microgrid, cost parameters, and weather parameters are laid out in Sections 5.3, 5.4, and 5.5 respectively. 5.1. Analysis of economic and technical impact To analyse the economic and technical impact of reactive power provision using the DERs, we use our proposed objective function (Eq. (1)), called Integrated Optimization (IO), and compare it with two other objective functions that have been used in the literature for different scenarios of local reactive power provision. The first one is the cost minimization without considering the reactive power costs [6,11,35], termed Loss Minimization (LM) for brevity. The second objective function is the market-based minimization of payment function, considering the reactive power costs, but without considering the losses in the system [10,18,19,58], termed Payment Minimization (PM) for brevity. GA has been used to optimize the test system mentioned in Section 5.3 according to the three objective functions. At the end of the optimization the total operating costs (Eq. (1)) are calculated regardless of the objective function. The results of power dispatch for the original test systems without the DERs are also presented for comparison. Analysis of reactive power provision from DERs through the different objective functions is elaborated in Section 6.1.

bus Sjload × ratiot × rand (0.9, 1.1) ,t = Sj

(26)

where ratiot is the normalized load variation over 24 h from [62] at period t (Fig. 2), representing commercial, industrial, or residential load demand, depending on the node. rand (0.9,1.1) is a random number in the range of [0.9, 1.1]. The PF of the load is constant throughout the day, assuming that the resistance and inductance of the load do not change with voltage or current. Vmin and Vmax are 0.90 p.u. and 1.05 p.u. respectively, while Imax is set at 1 p.u. 5.4. Cost parameters

Meanwhile, to compare the competitiveness of DERs and SCs in generating reactive power for the microgrid, the following base cases are considered: DER Base Case: The PV and BESS inverters in the systems are able to generate reactive power according to Eqs. (15) and (19). SC Base Case: The PV and BESS inverters are not able to generate reactive power. In their place, a switched capacitor consisting of 3 capacitor banks1 each are available for reactive power provision. Based on the two cases, we conducted thorough sensitivity analyses by varying electricity price, levelised cost of electricity (LCOE) of PV (c PPV ), SC cost (cQSC ), inverter efficiency, as well as DER/SC penetration. The two objective functions, WVDI Improvement and NMB are

ctPgrid is the wholesale electricity price plus grid charge in Singapore on 26 February 2015 [63]. cQgrid is the reactive power charge in Singapore for consumers taking supplies at 22 kV or 6.6 kV [38]. The consumers are charged for reactive power at 0.63 cents SGD/kVArh if their reactive power consumption is higher than 62% of their active power consumption. c PPV is taken to be the average of ctPgrid , which is 10.97 cents SGD/kW h, similar to the current levelised cost of electricity (LCOE) of PV in Singapore. c PPV is constant throughout the lifetime of the PV. cQSC has been adopted from [2] due to its suitability for short term case study. To obtain the values of cself ,cV ,cR of the different inverters – 300 kVA for PV in 37-bus and 69-bus systems, as well as 500 kVA for BESS and PV in 119-bus system – empirical values of cself ,cV ,cR for a 208 kVA inverter are first obtained from [47]. Next, the efficiency curve for the whole range of apparent power rating of the 208 kVA is obtained. The 300, 500 kVA inverters are assumed to have the same efficiency curve

1 Each SC therefore has four operating points, corresponding to 0, 1, 2, and 3 capacitor banks providing reactive power support.

2 PV and P BESS to The PV and BESS penetration are also defined as the ratio of total Prated max the average load demand respectively.

5.2. Analysis of competitiveness of local reactive power provision

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Fig. 1. The layout of the test systems and location of the DERs.

Fig. 2. The normalized commercial, industrial, and residential load profile.

The battery degradation constants, ηDOD,ηP , and ηSOC are obtained experimentally from a 500 kW h BESS [49].

as the 208 kVA inverter. From the efficiency curves, the values of cself ,cV ,cR for the different inverters are obtained. Fig. 3 shows the unit reactive power cost (both provision and absorption), cxQX ,t , assuming electricity price of 10.91 cents SGD/kW h (the average of ctPgrid ). The area at the top right of the figure is unfeasible as it lies outside of the inverters’ capacity.

5.5. Weather parameters Forecast method adapted from [64,65] has been utilized to generate 7

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Fig. 3. Unit reactive power cost for inverter-based DERs as a function of active and reactive power flowing through the inverter. The cost has not taken LOC into account.

presented for brevity, as the insights across the test systems are the same. There are five main insights based on the simulated cases. They are:

solar irradiance data on 26th February 2015 (Fig. 4). Real irradiance and temperature data are obtained from Solar Energy Research Institute of Singapore (SERIS) at latitude 1.3026° and longitude 103.7729° , with tilted angle and azimuth angle of 10° and 180° respectively. All the PV systems in this work use the same weather data. Ambient temperatures are taken from the same location at the same time. The irradiance forecast are used in Eq. (12) while the upper limits of 70% confidence level are used in Eq. (14) [46]. The real irradiance data are not used in the simulations, but serve as an illustration that the even for day-ahead forecast, the real data would broadly be within the 70% confidence level. The forecast can be updated accordingly for hour-ahead scheduling.

1. After the costs of reactive power exceed the costs of system losses that RPD reduces, it is no longer economically beneficial to produce reactive power locally 2. Reactive power provision using the DERs has diminishing technical benefits 3. Reactive power costs consideration becomes more important in poorly distributed system 4. DERs’ reactive power capability is already significant. Moreover, producing reactive power using DERs are cost-competitive with the charge from the grid and with SCs as long as the active power output of the DERs need not be reduced 5. The most important parameters affecting the benefits of reactive power provision from DERs and SCs are inverter efficiency and electricity price respectively

6. Results and discussion This section is divided into two main parts, namely (1) economic and technical analysis of local reactive power provision (Section 6.1), as well as (2) cost competitiveness of reactive power provision using DERs (Section 6.1). In Section 6.1, the results from the three test systems are presented, to show the impacts of local reactive power provision and consideration of reactive power costs across different configurations. However, in Section 6.1, only the results from 37-bus system are

6.1. Economic and technical analysis of local reactive power provision For IO, LM and PM cases in 37-bus system, the peak shaving has Fig. 4. Forecast and real solar irradiance data.

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produced the net load profile as shown in Fig. 5. It is clear that before the addition of BESS and the peak shaving service, the grid needs to ramp up and ramp down the generation drastically to fulfill the net load of the microgrid with large amount of PV. Peak shaving reduces the variability of the net load as well as the maximum power that needs to be taken from the main grid. However, the service requires the BESS to buy electricity when the price is high because that is when the net load is low due to the high PV penetration. From Table 1, it can be noted that the proposed objective function, IO, performs better than LM and PM economically, while LM performs better technically. However, from Fig. 6, we can see that while Case IO lies on the pareto optimal front, Case LM and PM do not. Case LM’s WVDI is slightly higher than the lowest WVDI in the pareto optimal front, but with much higher cost, whereas Case PM is located far away from the front.

bus system. Therefore, the local provision of reactive power is shared more equally among the DERs. Case IO balances the payment for the power losses and the costs of reactive power provision using the DERs and therefore achieves the best economic performance. There is no LOC involved in the IO cases. The findings from this work therefore highlight the increasing importance of reactive power cost consideration in system that are not designed optimally or whose load/DERs are poorly distributed.

6.1.1. Economic analysis Case PM only takes into account the payment for the active and reactive power produced according to the loads and did not take into account the line losses in the system. The DERs in this case only produce enough reactive power to avoid the grid charges as long as the reactive power generation from the DERs remains cost-competitive. As a result, Case PM produces the least reactive power using the DERs and rely on the grid for most of its reactive power consumption, as seen in Fig. 7(a), (d), (g). However, this leads to larger amount of current flowing from the grid through the lines in the system, which induces more line losses compared to Case LM and Case IO. The line losses are compensated by the grid and contribute to higher operational costs. There is no loss opportunity cost (LOC) involved in PM cases as the payment is always minimized. Meanwhile, Case LM produces the most reactive power using the DERs to reduce the losses in the systems as much as possible, fulfilling almost all the microgrid’s reactive power demand (Fig. 7(b), (e), (h)). The reactive power produced is more than necessary to avoid the reactive power charge as it does not consider the charge from the grid or the reactive power costs from the DERs. Consequently, the active power losses in the DERs’ inverters and the LOC caused by the reactive power provision increase the costs of running the systems. In particular, for the 69-bus system, the PV at node 61 and 64 (see X Fig. 1) are generating reactive power significantly beyond Q lim, t, causing the active power output to be reduced and incurring large LOC (530 SGD out of 654 SGD reactive power payment). Nevertheless, the PV systems at node 38 and 43 generated almost no reactive power at all. This is because the lateral containing node 38 and 43 is very lightly loaded, whereas the heavily loaded laterals are node 47–50 and 53–65. Therefore, only the PV in heavily loaded laterals are generating significant reactive power to minimize the losses in the system. The LOC incurred in the 119-bus system is not as significant, while there is no LOC incurred in 37-bus system. The load and the PV are more evenly distributed in 37 and 119-bus system compared to the 69-

TotalSloss [%] =

6.1.2. Technical analysis DERs and their reactive power capability have reduced the line losses in the systems significantly, as observed in Table 1. The total apparent power loss, Sloss , shown in Table 1 is calculated based on the following formula:

Total energy loss [kVAh] Total energy input [kVAh]

(27)

Case LM achieves the lowest losses (Table 1), followed by Case IO and Case PM. For the 37-bus system, Case LM produces about twice as much reactive power as Case IO, which in turn produces about twice as much reactive power as Case PM. Nevertheless, although Case IO has 22% lower losses than Case PM, Case LM’ line losses are only 11% lower than Case IO. Similar results were also observed for the 69 and 119-bus systems. This suggests the diminishing technical benefits of reactive power provision and that it is important to take into account the losses and reactive power costs to reach an optimum compromise. The lower losses not only translate to economic benefits, but they also decrease the line loading in the system, which increases the security of the systems and may delay the need to upgrade the distribution lines. As the power factor (PF) of the systems decreases, the difference between the PM and IO cases also diminishes. At a lower PF, Case PM produces more reactive power than at a higher PF to avoid the reactive power charge, nearing the level that Case IO produces to balance the losses and the costs. This finding is confirmed in Fig. 7, where the difference in reactive power profile is greatest for 37-bus system ((a) vs. (c)), and smallest for 119-bus system ((g) vs. (i)). From Table 1, we can observe that the optimizations have satisfied the minimum voltage constraints even when the original system does not. Vmax was never violated as the PV generation never exceeded the total load of the microgrids and there was no reverse power flow. From the technical perspective, Case LM has the best performance among the three objective functions considered as it employs the most local reactive power provision, which increases the voltage of the nodes in the systems and reduces its variability. Nevertheless, as indicated in Fig. 6, a system operator would benefit from choosing dispatch schedule using IO or other solutions from the pareto optimal front, if the goal is to minimize the operating cost and voltage deviation in the system. The line limit (Eq. (10)) is also satisfied in all cases. Fig. 5. Load profile of the 37-bus microgrid.

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Table 1 Results comparison for five runs of the algorithms for all test systems. 37-bus system

Total cost [SGD] WVDI

Sloss [%] max(std(|Vi,t|)) [p.u.] min(|Vi,t|) [p.u.] Power factor

69-bus system

119-bus system

Original

PM

LM

IO

Original

PM

LM

IO

Original

PM

LM

IO

10,267 1.437 4.10

10,195 1.161 3.70

10,224 0.941 2.58

10,149 1.014 2.90

10,723 0.891 5.00

10,517 0.7613 3.72

11,059 0.6389 2.70

10,463 0.6840 2.99

64,008 1.4325 5.73

62,441 1.1283 3.90

67,107 0.9474 2.78

62,169 1.0245 3.23

0.0366 0.892 0.850

0.0283 0.917 0.869

0.0200 0.941 1.000

0.0229 0.931 0.928

0.0324 0.8908 0.816

0.0261 0.9099 0.863

0.0213 0.9264 0.984

0.0235 0.9196 0.896

0.0415 0.8458 0.800

0.0301 0.9000 0.861

0.0225 0.9087 1.000

0.0263 0.9000 0.890

Fig. 6. NSGA results showing pareto optimal front and the optimization results using the three objective functions across the test systems.

between the DER and SC case arises from the fact that the DERs are able to provide any value of reactive power to minimize the total operating costs, compared to the discrete values of SCs’ reactive power output. In fact, it is noteworthy that the pareto optimal solutions of SC base case are significantly fewer than the those of DER base case. This is because the number of combinations of SCs’ settings is far lower than the number of combinations of inverters’ values. As the cost of reactive power for both technologies are similar, the differences in total costs are largely explained by the difference in power losses.

6.2. Cost-competitiveness of producing reactive power using DERs After determining that local reactive power provision using DERs is beneficial and that it is important to consider its costs, the next step is to compare the benefits brought about by the DERs’ RPD with those from traditional reactive power device. Results of the DER and SC base cases are illustrated in Fig. 8. It is clear that inverter-based DERs perform better than SCs in the economic objective. With high penetration of DERs (80% for PV and 40% for BESS, andtherefore 120% for SCs), both the DERs and SCs are able to satisfy the reactive power demand of the QBESS microgrid. The cost of reactive power from the DERs (cxQPV ) and ,t ,c x ,t ) are on the same order of magnitude and are lower than the SCs (cxQSC ,t reactive power charge (cQgrid ) as seen in Fig. 9. The difference in NMB

6.2.1. Effect of electricity price As can be seen from Fig. 10, higher c Pgrid increases the NMB of both SC and DER cases because the value of the power loss increases as

Fig. 7. Reactive power profile for the microgrids. (a)–(c) are the results for the 37-bus system; (d)–(f) 69-bus system; (g)–(i) 119-bus system. Each test system is run with three objective functions, PM, LM, and IO.

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Fig. 9. Reactive power cost and electricity prices for Case 37IO.

electricity price rises. The increase of NMB in DER cases are not as considerable (6% for every 10% increase in c Pgrid , compared to 12% for SC cases) as ctQPV and ctQBESS also depend on electricity price, and therefore increase when c Pgrid rises. At lower electricity price, the benefits from local reactive power provision is not as significant economically. Consequently, there are more technical and economic tradeoff in producing reactive power using SCs at lower c Pgrid , producing a larger pareto front. Regardless of the electricity price considered, DER inverters perform better than SCs, although the difference is lower at higher electricity price.

inverter losses (Eq. (14), (23), and (24)). With only 2% increase in inverter efficiency, compensating reactive power with DER already yields a significant reduction on the total cost as ctQPV drops by 36.7% and the total reactive power costs from DER decreases by 24 SGD. The 2% increase in efficiency translates to an inverter with peak efficiency of 98.2%,3 achievable standard even with current inverter topologies [66]. Comparing Figs. 12 and 14, it is important to note that a 3% increase of inverter efficiency in DER case yields higher NMB than a 30% decrease of SC cost in SC case. (see Fig. 15).

6.2.2. Effect of PV LCOE Varying PV LCOE (c PPV ) has no observable impact on the SC and DER cases (Fig. 11). Since the power generated by PV never exceeded Pgrid the total load in the microgrid, cxQPV (Eq. (23)), ,t always depends on ct and changes in c PPV do not affect the RPD of the PV systems.

6.2.5. Effect of DER/SC penetration The WVDI improvement in DER(SC) cases decreases with lower penetration of DER(SC). This is due to lower reactive capability at lower penetration of DERs and SCs. At lower penetration of DERs, the inverters are not able to fulfill the RPD of IO case, because of the limited reactive power capacity (Eqs. (14) and (19)). Therefore, by increasing the penetration of DERs, more optimal reactive power dispatches can be obtained to minimize both the total cost and WVDI. However, for SC cases, the NMB decreases with increasing SC penetration because of the assumption made in the simulation. It is assumed that even at higher SC penetration, there are only three capacitor banks per SC. As such, the discrete step size of SC reactive power output increases with the penetration, making optimal solutions more difficult to be obtained. Should the step size remains the same, the NMB will improve with higher SC penetration. At 20% and 40% penetration, SCs are more economically and technically valuable than DERs for local reactive power provision, but DERs are more competitive from 60% penetration onwards.

6.2.3. Effect of SC cost Fig. 12 shows that for every 10% change in ctQSC , the NMB of SCs changes by approximately 11% in the opposite direction. The different sizes of the pareto fronts at different ctQSC can be explained using the same arguments as in Section 6.2.1 regarding effect of electricity price. At 30% reduction in SC cost, the NMB and WVDI improvement of the SC case is comparable to that of DER base case. 6.2.4. Effect of inverter efficiency Higher inverter efficiency means that the DER systems are able to generate more active power (Eq. (12)). More local DER generation leads to higher voltages (closer to Vref ), leading to lower WVDI. Even though changes in inverter efficiency does not have any significant effect on SC cases (Fig. 13), higher inverter efficiency boost the competitiveness of local reactive power provision using DERs enormously (Fig. 14). For the DER cases, higher inverter efficiency allows the DER to generate more reactive power at a lower cost because of the lower

3 The peak inverter efficiency of the cases InvEff97%, InvEff98%, InvEff99%, DER Base, InvEff101%, InvEff102%, and InvEff103% are 93.4%, 94.3%, 95.3%, 96.3%, 97.2%, 98.2% and 99.1%, respectively.

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Fig. 10. Impact of changes in electricity price.

Fig. 11. Impact of changes in PV LCOE.

Fig. 12. Impact of changes in Switched Capacitor’s cost.

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Fig. 13. Impact of changes in inverter efficiency on SC cases.

Fig. 14. Impact of changes in inverter efficiency on DER cases.

Fig. 15. Impacts of DER/SC penetration on (a) SC cases and (b) DER cases. The number 20% to 100% refers to the PV penetration, with the base case having 80% PV penetration. The corresponding BESS penetration varies from 10% to 50% whereas the corresponding SC penetration varies from 30% to 150%.

7. Conclusion and future work

proposed objective function. It has also been shown that reactive power costs consideration becomes increasingly important in system that are not optimally designed. Reactive power provision using the DERs is also shown to be costcompetitive with the reactive power charge from the grid and with producing reactive power using switched capacitors (SCs). Among the considered parameters, inverter efficiency has been identified as the most important factor affecting the benefits derived from reactive power provision using the DERs, whereas electricity price is the most important factor for SCs. Therefore, as inverter efficiencies are expected to increase in the future, investment in reactive power capable DERs will be even more beneficial.

This work has analyzed the economic and technical impact of local reactive power provision using distributed energy resources (DERs) in a grid-connected microgrid. The costs of reactive power provision using two types of DERs, namely photovoltaic system (PV) and battery energy storage system (BESS), have been explicitly formulated and incorporated into a practical objective function of minimizing the total cost of operating the system. Through various case studies, the extent of economic and technical benefits of reactive power provision from DERs for the microgrid has been analyzed. The balance to minimize both line losses and reactive power costs from the DERs is achieved using the 13

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