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inventions Article

An Improved Control Strategy for Three-Phase Power Inverters in Islanded AC Microgrids Muhammad Zahid Khan 1, * ID , Muhammad Mansoor Khan 1 , Huawei Jiang 2 , Khurram Hashmi 1 and Muhammad Umair Shahid 1 ID 1

2

*

School of Electronic, Information and Electrical Engineering (SEIEE), Shanghai Jiao Tong University, Shanghai 200240, China; [email protected] (M.M.K.); [email protected] (K.H.); [email protected] (M.U.S.) State Grid Wuxi Power Supply Company, Wuxi 214000, China; [email protected] Correspondence: [email protected]; Tel.: +86-132-6290-7535

Received: 7 June 2018; Accepted: 10 July 2018; Published: 11 July 2018

 

Abstract: Microgrids (MGs) are composed of multiple distributed generators (DGs) interfaced to micronetwork through paralleled connected power inverters (PIs). Load sharing among multiple DG units is an important task for autonomous operation of microgrids. In order to realize satisfactory power sharing and voltage regulation between DG units, different voltage droop control strategies have been reported in the literature. In the medium voltage (MV) microgrids, power sharing, and voltage regulation often deteriorate due to dependence on nontrivial feeder impedances. The conventional control strategies are subject to steady-state active and reactive power-sharing errors along with system voltage and frequency deviations. Furthermore, complex microgrid configurations either in looped or meshed networks often make power balancing and voltage regulations more challenging. This paper presents an improved control strategy that can be extended for radial networks in order to enhance the accuracy of power sharing and voltage regulation. The proposed control strategy considers load voltage magnitude regulation as opposed the voltage regulation at inverters terminals. At the same time, a supervisory control loop is added to observe and correct system frequency deviations. This proposed method is aimed at replacing paralleled inverter control methods hitherto used. Simulation studies of the proposed scheme in comparison with the conventional control strategy in MATLAB/Simulink validate the effectiveness of the proposed strategy. Keywords: AC microgrids; power-sharing; distributed generation (DG); smart grid; voltage regulation; frequency regulation; voltage source inverters

1. Introduction Microgrids are small-scale power systems that make possible the effective integration of distributed generators (DGs) [1]. A DG has advantages of high-energy utilization rate, pollution reduction, low power transmission losses, and flexible installation locations [2]. DG units present a higher degree of control and operation as compared to the conventional generators, which allows the microgrids to play a significant role in order to maintain the stability of electrical networks [3,4]. Furthermore, DG units provides the clean and renewable power to close consumer’s end. Therefore, it reduces the strain on conventional transmission and distribution infrastructures [5,6]. Power-electronics-based MGs are convenient when integrating renewable energy resources, active loads and DG units [1,7]. The DG units of a microgrid can be classified into grid-following and grid-forming DG units [6,8]. The DG units are controlled as grid following in grid-connected mode. Grid-following inverter’s control strategies are described in [9,10]. However, in islanding Inventions 2018, 3, 47; doi:10.3390/inventions3030047

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Inventions 2018, 3, 47

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mode, the distributed power inverters interfaces (DPIs) between load and microsource are governed by the droop control algorithm, which are responsible for the voltage regulation and power sharing in accordance with their ratings and corresponding energy source power. Hence, the control of paralleled connected power inverters has been investigated in recent years [11–13]. Conventionally, the frequency and voltage magnitude droop are used as decentralized control schemes among DG units [11,12]. It can be seen as primary control of a synchronous machine. With the help of droop control active power sharing can be achieved among these DGs units. However, reactive power sharing is highly dependent on a DG unit’s output filter and feeder impedances [11,14–16]. The identical feeder impedance could be unequal as various DG units and load are located at different distances to each other. The unequal LCL-filter’s impedance among various DGs units are due to different design considerations and system conditions [15]. In addition, configuration of microgrid network and existence of local loads often aggravate the power balancing problem. Therefore, power sharing of conventional droop control can be affected by mismatch of feeder impedances and make islanded microgrids less flexible and reliable [11,15]. To solve the power control issue, a considerable number of control schemes based on droop concept have been proposed, which are classified into four main categories: (1) virtual framework structure-based method [17,18]; (2) conventional and variants of the droop control [18,19]; (3) the hybrid droop/signal injection method [18,20]; and (4) “construct and compensate” based methods [20,21]. Furthermore, in [14] reactive power and the harmonic power, sharing errors were decreased by injecting noncharacteristic harmonic current. Although the power balancing issue was addressed, the power quality of the microgrid was degraded by steady state voltage distortions. The author proposed an Q-V dot droop in [14]. It can be observed that when local loads are added, then reactive power sharing improvement is not obvious. The virtual output impudence control in [11] is proposed to match the identical power line impedances. To decrease the droop control’s dependence on the DG’s output filter, Sao and Lehn [20] presented compensation of the voltage magnitude drop. Nevertheless, this scheme may still be affected by mismatched feeder impedances. Usually, in a grid-forming inverter’s control strategies [6], the loads are directly connected with DG units however, these loads can be connected with looped or mesh network type configuration [22,23]. These complex microgrid configurations either in looped or mesh networks often make power balancing and voltage regulations more challenging [7,23]. In response to a complex AC microgrid configuration, this paper presents an improved control strategy which is extended for multiple feeders with limited number of grid forming nodes in radial networks. This strategy considers the load voltage magnitude regulation rather than voltage regulation at inverter terminals. Furthermore, a supervisory loop also been added to restore the frequency deviations. The remainder of this paper is organized as follows. In Section 2 the network model is presented. In Section 3 proposed control strategy is discussed and then in Section 4 results and discussion has been demonstrated. Finally, Section 5 concludes this paper. 2. Network Model Figure 1 illustrates the configuration of a microgrid. As shown, microgrids are composed of multiple DG units and loads. Every DG unit is interfaced to the microgrid with distributed power inverters where these power inverters are connected to AC bus via their respective feeder. Secondary central controller controlled the status of main grid and microgrid [24]. MGs can be connected (grid-following mode) or disconnected (islanded mode) from the main grid by using static transfer switch (STS) at the point of common coupling (PCC). Active and reactive power references are usually assigned by the central controller in grid-following mode. In this mode of operation, power balancing is not the real concern. However, by switching the microgrid into islanded mode, the load demand must be properly shared by DG units.

Inventions 2018, 3, 47 Inventions 2018, 3, x FOR PEER REVIEW

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Microgrid Laods at PCC Main Grid

PCC

STS

DG1 Installation point

Central Controller

Load ith

Common AC Bus

DG 2 Installation point

DGn Installation point Load 1

Load 2

S1

S1

Feeder 1

Feeder 2

Controller

DG 1

Communication Bus

Vsource2

Controller

Vsource ith

DG 2

Feeder i

Receiver

Receiver

Receiver

Vsource1

S1

Controller

DG ith

Figure 1. Illustration of the microgrid configuration. Red arrow used as communication link. Figure 1. Illustration of the microgrid configuration. Red arrow used as communication link.

In islanded operation of a microgrid, DG units as shown in Figure 1 can operate using the In islanded operation of a microgrid, DGreactive units aspower-voltage shown in Figure 1 can operate usingas:the conventional active power-frequency (P-f) and magnitude (Q-V) droop conventional active power-frequency (P-f ) and reactive power-voltage magnitude (Q-V) droop as:    *  DP . P (1) ω = ω ∗ − DP · P (1) V  V *  DQ . Q (2) V = V ∗ − DQ · Q (2) where, ω *, V *, DP and DQ are the nominal frequency, nominal voltage magnitude, active and reactive where, *, V *,respectively DP and DQ are the unit. nominal nominal magnitude, active and reactive power ω slopes, of DG Thefrequency, active power p andvoltage reactive power Q are measured after power slopes, respectively of DG unit. The active power p and reactive power Q are measured after the the low-pass filtration. Instantaneous voltage reference can be acquired with derived angular low-pass Instantaneous reference can (2). be acquired with derived angular frequency frequencyfiltration. and voltage magnitudevoltage in Equations (1) and and voltage magnitude in Equations (1) and (2). Mathematical Model Mathematical Model A simplified microgrid circuit is shown in Figure 2b with two DG units that are parallel A simplified circuit is the shown in Figure 2b withoftwo DG units thatrespectively. are parallel connected, connected, R1 andmicrogrid X1, R2 and X2 are feeder impedances DG1 and DG2, As shown Rin1 Figure and X1 ,2a, R2 the andcomplex X2 are the feeder impedances of DG1 and DG2, respectively. As shown in Figure 2a, power drawn to the kth ac bus can be written as: the complex power drawn to the kth ac bus can be written as: Si  Pi  jQi (3) Si = Pi + jQi (3) where, Pi and Qi are the active and reactive power injected at each node by DG inverters. Power flow through can be expressed where, P feeder and Q line are impedances the active and reactive power as: injected at each node by DG inverters. Power flow i

i

through feeder line impedances can Vbe expressed as: Pi  2 i 2 .[ Ri Vi  Ri Vk cos  ik  Xi Vk sin  ik ] (4) RV  xi i i ·[ Ri Vi − Ri Vk cos ∂ik + Xi Vk sin ∂ik ] (4) Pi = 2 2 Ri + Vi xi Qi  2 .[Ri Vk sin  ik  Xi Vi  Xi Vk cos  ik ] (5) RVi i  xi2 Qi = 2 ·[− Ri Vk sin ∂ik + Xi Vi − Xi Vk cos ∂ik ] (5) Ri + xi2 where, Vi and Vk are the magnitude of inverter output voltage and common bus voltage, respectively, where, andQVi kare arethe theactive magnitude of inverter output voltage and voltage, respectively, while PVi iand and reactive powers flowing from ithcommon inverterbus terminal to kth common while Pi and Q the active and reactive powers fromofith inverter to kth common bus voltage. represents the difference betweenflowing the phase the outputterminal impedance and power  iki are bus voltage. ∂ represents the difference between the phase of the output impedance and power angle. ik angle.

Inventions 2018, 3, 47 Inventions 2018, 3, x FOR PEER REVIEW

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P1 , Q1 Lf1 Vk Vi

i

R1

k

I

L1

Z1=R1+jX1

S=Pi+jQi

V1 DG ith

P2 , Q 2

1

VL

L2

L

Vload

Vt1

Z2=R2+jX2

Pload Qload

DG 1

Lf2

R2 Vt2

V2

2

DG 2

(b)

(a)

Figure 2. (a) An ith inverter connected with kth common ac bus; (b) configuration of the microgrid Figure 2. (a) An ith inverter connected with kth common ac bus; (b) configuration of the microgrid with two DG units. with two DG units.

The inductive components of higher voltage (HV) and medium (MV) network are typically The inductive components (HV) and MV medium (MV) network are typically higher higher then resistive as shownofinhigher Table voltage 1 [6], however, networks have inductive behaviour, then resistive as shown in Table 1 [6], however, MV networks have inductive behaviour, therefore, therefore, it can be assumed that: cos   1 and sin    , resulting power flow can be expressed as: it can be assumed that: cos ∂ ≈ 1 and sin ∂ ≈ ∂, resulting power flow can be expressed as: VV Pi , Rx  0  iV kV[ sin  ik ] (6) Pi,Rx =0 ≈ xi i k [sin ∂ik ] (6) xi 2 V V  V V cos  Qi , Rx 0  Vi 2 Vk k − iVi kVk cosik∂ik (7) xi (7) Qi,Rx =0 ≈ i xi  ∂k  P (8)(8) ∂ii − k ∝ Pi i Vii − V V Vkk  ∝Q Qi i

(9)(9)

where, according to toEquations Equations(8)(8) and active power depends on power while where, according and (9),(9), the the active power depends on power angle ∂angle  ik reactive ik while − power injected by each inverter depends on voltage difference V V . From Equation (6), if ∂ik if is i kVi − Vk. From Equation (6), reactive power injected by each inverter depends on voltage difference to be zero, proportional to angle ∂ik and can it becan expressed as: as: i willPbe is supposed to be then zero,Pthen i will be proportional to angle be expressed supposed  it and ik

ik

Z

∂ik = ∂i − ∂k = (∂i0 + ωi dt) − ∂k (V1 ∠∂1 , . . . , Vi ∠∂i , R1 + jX1 , . . . , Ri + jXi )  ik   i   k  ( i 0   i dt )   k (V11 ,..., Vi  i , R1  jX1 ,..., Ri  jXi )

(10) (10)

affectsthe the∂ik∂ikwhich whichis is calculated output voltage of DG units impedances. calculated byby output voltage of DG units andand line line impedances. By ∂∂kk affects By integrating ω i ,variations the variations ∂ik be canregulated. be regulated. integrating ωi, the in ∂ikincan 3. Proposed ProposedControl ControlStrategy Strategy 3. Aforementioned, in in aa grid-forming grid-forming inverter’s inverter’scontrol control strategies strategiesthe the loads loads are are usually usually directly directly Aforementioned, connectedwith withDG DG units. units. However, However,these theseloads loadscan canbe beconnected connectedwith withaaradial-type radial-typeconfiguration. configuration. connected In this section, a proposed control strategy is discussed for such type of microgrid configurations that In this section, a proposed control strategy is discussed for such type of microgrid configurations that can be be extended extended for for multiple multiple feeders feeders with with limited limited number number of of grid-forming grid-forming nodes. nodes. To To connect connect the the can secondary central controller with a DG unit’s local controllers, this strategy adopts a communication secondary central controller with a DG unit’s local controllers, this strategy adopts a communication link. The Theproposed proposedstrategy strategy considers considers the the load load voltage voltage magnitude magnitude regulations regulations rather rather than than voltage voltage link. regulation at atinverter inverterterminals. terminals. Furthermore, Furthermore, the theload loadvoltage voltagemagnitude magnitudeisismeasured measuredand andconverted converted regulation into dq-axis components using reference frame transformation. The inverter’s output active and reactive into dq-axis components using reference frame transformation. The inverter’s output active and powers are calculated based on these measurements and sent to droop controllers via low-pass filters. reactive powers are calculated based on these measurements and sent to droop controllers via lowDroop controllers voltages and frequency inner loops. The error is obtained pass filters. Droop send controllers send voltages andreferences frequencyto references to inner loops.signal The error signal after comparing the measured voltage and frequency values with reference values. These voltage and is obtained after comparing the measured voltage and frequency values with reference values. These frequency periodically corrected bycorrected the secondary loop.control loop. voltage anddeviations frequencyare deviations are periodically by thecontrol secondary 3.1. Power Flow Control The configuration of the microgrid with two DG units is shown in Figure 2b and its proposed control strategy block is illustrated in Figure 3. An inverter bridge is connected to dc power source and its output frequency and output voltages are adjusted by power, voltage and current controllers [12]. All DG units are individually formulated in its d-q frame which depends on their angular frequency

3.1. Power Flow Control The configuration of the microgrid with two DG units is shown in Figure 2b and its proposed control strategy block is illustrated in Figure 3. An inverter bridge is connected to dc power source Inventions 2018, 3, 47 5 of 14 and its output frequency and output voltages are adjusted by power, voltage and current controllers [12]. All DG units are individually formulated in its d-q frame which depends on their angular frequency ωi and∂iangle ∂i. Each DG unit’s interfaced inverters transferred thed-q d-q frame by ω i and angle . Each DG unit’s interfaced inverters areare transferred totothe byusing using transformation transformationequation equation[25] [25]as: as: "

# " #" # (∂i − sin fd  fD  cos cos( i))  sin( i)(∂i )fd   =   sin(∂i )  ) f  , f q , cos i)(∂i  fQ   sin(i) cos(   q 

fD fQ

(11) (11)

The Theangle angleofofith ithDG DGunits’ units’d-q d-qfame famecan canbe bewritten writtenas: as:

 i  Z (i  i )dt ∂i = (ωi + δωi )dt

(12) (12)

δVi δωi

i

Vodi Voqi

i*ldqi Voltage Controller

Current Controller

Voi abc/dq

ioi

i

abc/dq

ildi ilqi

V*odi V*oqi

vodi voqi Power iodi Controller ioqi

i

Lf1

i

abc/dq

R1

L1

Voi

ili Load

DG 1

DG 2

Figure diagram of of proposed control strategy. Two upup right diagonal lines “//”“//” shows the two Figure3.3.Block Block diagram proposed control strategy. Two right diagonal lines shows the oi (Va, Vb, Vc) and ioi (ia, ib, ic) are the three phase voltage and references for their respective controllers. V two references for their respective controllers. Voi (Va , Vb , Vc ) and ioi (ia , ib , ic ) are the three phase current so these three up showslines these“///” three phase references voltagesignals, and current signals, so right thesediagonal three uplines right“///” diagonal showssignals these three phase tosignals transformation (abc/dq). referencesblock to transformation block (abc/dq).

Figure 4 shows the power controller block which follow the droop control strategy and it send Figure 4 shows the power controller block which follow the droop control strategy and it send voltage reference V*odi, and V*oqi, to inner loop. Average output active and reactive powers are voltage reference V*odi , and V*oqi , to inner loop. Average output active and reactive powers are obtained from instantaneous power passing low pass filters, can be denoted as: obtained from instantaneous power passing low pass filters, can be denoted as:

ciωci PP  p p i i = +ci ωcii i s s 

(13) (13)

 ωci q (14) QQi i= s ci+ ω q i (14) s  ci ici where, ωci the cutoff frequency of low pass filter. Instantaneous active and reactive power in d-q the can cutoff where, ci rotatingframe be frequency written as: of low pass filter. Instantaneous active and reactive power in d-q rotating frame can be written as: pi = Vodi ·iodi + Voqi ·ioqi (15) ·ioqi − V.oqi pqii =VVodiodi.iodi V i ·iodi oqi oqi

(16) (15) On individual frame d-q, vodi , voqi , iodi and ioqi are the load voltage and line current of an ith  Vodi .ioqi  Vbetween .i i oqi odi inverter. Droop technique shows the qrelationship the frequency and active power(16) p-ω, and between the voltage amplitude and reactive power Q-V can be represented as: ωi = ωi ∗ − m Pi Pi

(17)

V ∗ odi = Vi ∗ − nQi Qi

(18)

inverter. Droop technique shows the relationship between the frequency and active power p-ω, and between the voltage amplitude and reactive power Q-V can be represented as:

 i   i *  m Pi Pi

(17)

V * odi  Vi * nQi Qi

Inventions 2018, 3, 47

(18)

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where ωi*, V*i, mPi and nQi are nominal frequency, nominal voltage and droop coefficients, respectively, DG unit. V*odi is the reference voltage for inner voltage loop. Q-V droop control where ω i *, V i *,ofmith Pi and nQi are nominal frequency, nominal voltage and droop coefficients, respectively, strategy with consideration of voltage control can presented as Q-V Equation by Equation (18), of ith DG unit. V*odi is the reference voltage for inner voltage loop. droop(19) control strategy with illustrated in Figure 3. control can presented as Equation (19) by Equation (18), illustrated in Figure 3. consideration of voltage

V * odi  Vi * nQi Qi   Vi (19) V ∗ odi = Vi ∗ − nQi Qi + δVi (19) δVi can written as, shown in Figure 5b: δVi can written as, shown in Figure 5b:  Vi  Vi *  Vavg (20) δVi = Vi ∗ − Vavg (20) where Vi* and Vavg are the nominal voltage and average voltage (21) of all inverters. While δVi is where Vi * and Vavg are the nominal voltage and average voltage (21) of all inverters. While δVi responsible to regulate the load voltage which compensates the voltage deviation caused by droop is responsible to regulate the load voltage which compensates the voltage deviation caused by controller. droop controller. δωi

ωi*

voi ioi

abc to dq

vodi.iodi + voqi.ioqi

vodi.ioqi - v

pi Low-pass

Pi

filter

qi Low-pass Qi oqi.iodi filter

Power Calculation

Filter

ωi*- mPi Pi

ωi

Vi*

ʃ



δVi

Vi* - nQi Qi

V*odi

∑ 0

Droop Controller

i

V*oqi

Figure 4. 4. Power Power controller controller for for ith ith DG DG unit. unit. Figure Table1. 1. Typical Typicalline lineimpedance impedancevalues. values. Table

Types of Line R (Ω/km) X (Ω/km) R (Ω/km) X (Ω/km) Low voltage line 0.642 0.083 Low voltage line voltage line0.642 0.161 0.083 Medium 0.190 Medium voltage line 0.161 0.190 High voltage line 0.06 0.191 Types of Line

High voltage line

0.06

0.191

R/X R/X 7.7 0.85 7.7 0.85 0.31

0.31

3.2. Frequency & Voltage Regulation 3.2. Frequency & Voltage Regulation The frequency regulation strategy restores the frequency deviation of the DGs to the nominal The frequency regulation strategy restores the frequency deviation of the DGs to the nominal value. Frequency restoration method is given in (23) and elaborated in Figure 5a. value. Frequency restoration method is given in (23) and elaborated in Figure 5a. N N

∑ ωk  k =1 k

ω = avg avg

k 1

N N

ω ωavg) ) i =((ω i ∗* − i

i

avg

Z

δω k pkf ωi + i =  kkifi f iω dti dt i pf i

(21) (21) (22) (22) (23) (23)

ω frequency, ωk is theismeasured system frequency that is being ωii** is is the thenominal nominalreference reference frequency, the measured system frequency that issensed being k at all nodes of inverters in the neighborhood of the node i being considered. δωi is the frequency sensed at all nodes of inverters in the neighborhood of the node i being considered.  is the correction which is sent to frequency reference of the ith inverter node as shown in Figure 5a. Ki p1 and Ki1 are proportional and integral gains for controllers. Load node voltage regulation method is shown in Figure 5b and can be expressed as: N

∑ Vk

Vavg =

k =1

N

(24)

5a. Kp1 and Ki1 are proportional and integral gains for controllers. Load node voltage regulation method is shown in Figure 5b and can be expressed as: N

Inventions 2018, 3, 47

Vavg 

V

k

7 (24) of 14

k 1

N

ViV= ((VVi i ∗* − V Vavg )) i avg

(25)

Z

δVi V=i k pkfpfVVi i+kkiiff VV  i dti dt

(26) (26)

where, VkVis the system voltage in in d-axis that is thenominal nominalreference referencevoltage voltageinind-axis, d-axis, k is themeasured measured system voltage d-axis that where,VVi *i*isisthe sensed at each DG’s interface inverters nodes in communication neighborhood of the node i. K and p1 is sensed at each DG’s interface inverters nodes in communication neighborhood of the node i. Kp1 Kand and integral gains for controllers as shown in Figure Here, δVHere, voltage i1 are i is the Ki1proportional are proportional and integral gains for controllers as shown in 5b. Figure 5b. δV i is the correction command applied to voltage of the ithof inverter voltage correction command applied toreference voltage reference the ith node. inverter node.



V1



V2



kp1+ ksi1

i

kp1+ ksi1

Vk

ωi*

vi

Vi* (b)

Figure5.5. (a) (a) Frequency Frequencyregulation; regulation;(b) (b)voltage voltageregulation. regulation. Figure

4. Results Results and and Discussion Discussion 4.

Inthis this section, section, the the results results obtained obtained from from conventional conventionaland and proposed proposedcontrol controlstrategies strategiesfor forpower power In sharing, inverter inverter terminal, frequency regulation areare compared andand discussed. The sharing, terminal, load loadvoltage, voltage,and and frequency regulation compared discussed. simulations on MATLAB/Simulink are conducted on circuit configuration given in Figure 2a for three The simulations on MATLAB/Simulink are conducted on circuit configuration given in Figure 2a phase 50phase Hz islanded microgridmicrogrid wherein the two paralleled connectedconnected DG1 and DG for three 50 Hz islanded wherein the two paralleled DG21 are andconnected DG2 are to the shared load via feeder impedance X 1–R1 and X2–R2. Same system and controller parameters connected to the shared load via feeder impedance X1 –R1 and X2 –R2 . Same system and controller have been used shown in as Table 2 [26] both2 conventional proposed and control schemes but in parameters haveasbeen used shown infor Table [26] for both and conventional proposed control conventional strategy the inverter terminal voltage are measured for regulation while in proposed schemes but in conventional strategy the inverter terminal voltage are measured for regulation while control strategy the strategy load voltage magnitude measuredisfor load voltage regulation. sake of in proposed control the load voltage ismagnitude measured for load voltage For regulation. comparison, active power p and reactive power Q are measured on inverter terminals and at Vloadand for For sake of comparison, active power p and reactive power Q are measured on inverter terminals equal unequal impedances. However, However, system parameters are given follows: at V and for equal andline unequal line impedances. system parameters are given follows: load

 The system voltage is 230 V, 50 Hz. • The system voltage is 230 V, 50 Hz.  Two 60-KVA DG units are applied with output filter inductor Lf = 250 μF is to reduce ripples. • Two 60-KVA DG units are applied with output filter inductor Lf = 250 µF is to reduce ripples.  A three-phase RL & C load is applied of value 0.8 Ω, 0.15 mH and 120 μF, respectively. • A three-phase RL & C load is applied of value 0.8 Ω, 0.15 mH and 120 µF, respectively. The droop controller and other parameters are given in Table 2. The droop controller and other parameters are given in Table 2. Table 2. System and controller parameters. Table 2. System and controller parameters.

Parameter Nominal frequency Parameter Nominal voltage Nominal frequency Switching frequency Nominal voltage Ratings of each DG unit Switching frequency Ratings of each unit dc DG voltage dc voltage Voltage loop Current loop Frequency droop Voltage droop Equal line impedances Unequal line impedance

Symbol f* Symbol V* f* fs V* VA fs VA Vdc

Vdc Kpv , Kiv KpI , KiI mP1 , mP2 nQ1 , nQ2 Line 1, Line 2 Line 1, Line 2

Value 50 Hz Value 230 V 50 Hz 16 KHz230 V 60 KVA 16 KHz 700 V60 KVA

700 V 20, 50 40, 100 0.0034 rad/w 0.001 rad/w 0.05 + j1.099 Ω 0.05 + j1.099 Ω, 0.05 + j1.3 Ω

Voltage loop Current Current loop loop Frequency Frequency droop droop Voltage Voltage droop droop Equal Equal line line impedances impedances Inventions 2018, 3, 47 Unequal Unequal line line impedance impedance

Kpv, Kiv K KpIpI,, K KiIiI m P 1 , m mP1, mPP22 n nQQ11,, n nQQ22 Line 1, Line Line 1, Line 22 Line Line 1, 1, Line Line 22

20, 50 40, 40, 100 100 0.0034 0.0034 rad/w rad/w 0.001 0.001 rad/w rad/w 0.05 0.05 ++ j1.099 j1.099 Ω Ω 0.05 + j1.099 Ω, 0.05 + j1.099 Ω, 0.05 0.05 ++ j1.3 j1.3 Ω Ω

8 of 14

4.1. 4.1. Case Case 1: P, Q Measured Measured at at Inverters Inverters Terminals Terminals Case 1: 1: P, P, Q Terminals In In this case, both conventional and proposed control strategies are applied for equal and unequal In this this case, case, both bothconventional conventional and and proposed proposed control control strategies strategies are are applied applied for for equal equal and and unequal unequal line impedances. The active and reactive powers are measured at inverter terminals V t 1 and V for line inverter terminals Vt1Vand Vtt22 V for line impedances. impedances. The Theactive activeand andreactive reactivepowers powersare aremeasured measuredatat inverter terminals t1 and t2 both schemes, as shown in Figure 2b. Conventional strategy considers the voltage regulations at both schemes, as shown in Figure 2b. Conventional strategy considers the voltage regulations at for both schemes, as shown in Figure 2b. Conventional strategy considers the voltage regulations inverter terminal while in proposed scheme load voltage inverter terminal while in in proposed scheme load voltage isismeasured measured and restored atatload load node. at inverter terminal while proposed scheme load voltageis measuredand andrestored restoredat loadnode. node. Results obtained for this case are discussed below. Results obtained for this case are discussed below. below. 4.1.1. Equal Line Line Impedance Impedance 4.1.1. Equal Equal Line Impedance In In this this case, case, the system is considered symmetrical symmetrical as as the the distance distance is is the the same same from from each each DG DG to In this case, the system system is considered considered symmetrical as the distance is the same from each DG to load. To verify the effectiveness of the proposed strategy, the power-sharing and voltages results are load. To verify the effectiveness of the proposed strategy, and voltages results are load. To the effectiveness of the proposed strategy, the power-sharing results are obtained obtained from from simulations simulations as as shown shown in in Figures Figures 6–8. 6–8.

250 250 245 245 240 240 235 235 230 230 225 225 220 220 215 215 210 210 205 205 200 200 0 0

Voltage(V) (V) Voltage

Voltage(V) (V) Voltage

VV −  desired measured V VVmeasured desired Verror (%(%) ) =  V × 100 desired measured  100 V Verror (%)  100 V error desired V Vdesired desired

V1-DG-1 V1-DG-1 V2-DG-2 V2-DG-2 Vload Vload

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4 0.5 0.5 0.6 0.6 (a) Time(s) (a) Time(s)

0.7 0.7

0.8 0.8

0.9 0.9

11

250 250 245 245 240 240 235 235 230 230 225 225 220 220 215 215 210 210 205 205 200 200 00

(27) (27) (27)

V1-DG-1 V1-DG-1 V2-DG-2 V2-DG-2 Vload Vload

0.5 0.5

11

1.5 1.5

22 2.5 2.5 33 (b) (b) Time(s) Time(s)

3.5 3.5

44

4.5 4.5

55

48 48 47.5 47.5 47 47 46.5 46.5 46 46 45.5 45.5 45 45 44.5 44.5 44 44

ActivePower Power(KW) (KW) Active

ActivePower Power(KW) (KW) Active

Figure Figure 6. (a) Inverter Inverter terminal terminal and and load load voltages voltages for for the conventional control control scheme; scheme; (b) (b) inverter inverter Figure 6. (a) (a) Inverter terminal and load voltages for the conventional conventional control scheme; (b) inverter terminal and load voltages for proposed control scheme. terminal and load voltages terminal for proposed control scheme.

P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2

00

0.1 0.1

0.2 0.2

0.3 0.3 0.4 0.4 0.5 0.5 0.6 0.6 (a) (a) Time(s) Time(s)

0.7 0.7

0.8 0.8

0.9 0.9

11

55 55 54.5 54.5 54 54 53.5 53.5 53 53 52.5 52.5 52 52 51.5 51.5 51 51 50.5 50.5 55 0 0

P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2

0.5 0.5

11

1.5 22 2.5 1.5 2.5 (b) (b) Time(s) Time(s)

33

3.5 3.5

44

2500 2400 2300 2200 2100 2000 1900 1800 1700 1600 1500

Reactive Power (W)

Reactive Power (W)

Figure Active power for the control strategy; (b) power for control Figure 7. Active power the conventional control strategy; (b) active for proposed Figure 7.7.(a) (a)(a) Active power for for the conventional conventional control strategy; (b) active active power power for proposed proposed control strategy. control strategy. Inventions 2018,strategy. 3, x FOR PEER REVIEW 9 of 14

Q1-DG-1 Q2-DG-2

0

0.1

0.2

0.3

0.4 0.5 0.6 (a) Time(s)

0.7

0.8

0.9

1

2500 2450 2400 2350 2300 2250 2200 2150 2100 2050 2000

Q1-DG-1 Q2-DG-2

0

0.5

1

1.5

2 2.5 3 (b) Time(s)

3.5

4

4.5

5

Figure Figure 8. 8. (a) (a) Reactive Reactive power power for for the the conventional conventional control control strategy; strategy; (b) (b) reactive reactive power power for for proposed proposed control control strategy. strategy.

Figure 6 shows the results obtained for load and inverter terminal voltages from both the conventional and proposed control scheme. In the conventional scheme, the inverter terminal voltages after regulation are stabled at 230 (phase to ground) volts as illustrated in Figure 6a while the load voltage is held stable at 215 volts with an error of 6.52% Equation (27), which shows the drawback of the conventional control scheme. This error has been compensated in a proposed scheme

Inventions 2018, 3, 47

9 of 14

Figure 6 shows the results obtained for load and inverter terminal voltages from both the conventional and proposed control scheme. In the conventional scheme, the inverter terminal voltages after regulation are stabled at 230 (phase to ground) volts as illustrated in Figure 6a while the load voltage is held stable at 215 volts with an error of 6.52% Equation (27), which shows the drawback of the conventional control scheme. This error has been compensated in a proposed scheme that stabilizes load voltage at its nominal value of 230 volts as shown in Figure 6b, which shows the effectiveness of the proposed strategy. In addition, for the powering sharing case, since the distance is equal from distribution generation DG to load. As such, identical transient trends are observed for P1 , P2 and Q1 , Q2 for both conventional and proposed control scheme as well as comparing results of both schemes to each other they share divergent power sharing. In the conventional scheme, power-sharing for each inverter is investigated with load Pload = P1 + P2 = 94.6 kw, Qload = Q1 + Q2 = 4.2 kvar while in proposed scheme each inverter share power with load Pload = 106.2 kw, Qload = 4760 var as illustrated in Figures 7 and 8. 4.1.2. Unequal Line Impedance The results acquired for unequal line impedances are shown in Figures 9–11. It is assumed that load is located on distances with respect to DG units. The conventional and proposed control strategy has been applied on unequal line impedances set as R1 + jX1 = 0.05 + j1.099 Ω and R2 + jX2 = 0.05 + j1.3 Ω. In the conventional strategy, the load voltage error with a value of 7.82% is spotted as shown in Figure 9a this error can be compensated by the proposed scheme. As proposed strategy regulate this load voltage error and restore it by nominal load voltage value of 230 volts as shown in Figure 9b. Q − Qmeasured Qerror (%) = desired × 100 (28) Qdesired

250 245 240 235 230 225 220 215 210 205 200

270 260

Voltage (V)

Voltage (V)

Because of unequal line impedances, the total reactive power is not evenly shared to load. Start-up reactive power transient error has been noticed in Figure 10a. It is observed that system stabilizes to active and reactive power within 1 s as shown in Figures 10a and 11a. The slight reactive power sharing error is noticed in Figure 10b and it can be calculated with Equation (28) as the ratio of the differential of desired and measured reactive power to desired reactive power. In addition, each inverter shares Pload = 92.2 kw and Qload = 7150 var for the conventional scheme while Pload = 105 kw, and Qload = 8175 var in the2018, proposed as shown in Figures 10 and 11. Inventions 3, x FORscheme PEER REVIEW 10 of 14

V1-DG-1 V2-DG-2 Vload

250 240 230 220

V1-DG-1 V2-DG-2 Vload

210 0

0.5

1

1.5

2 2.5 3 (a) Time(s)

3.5

4

4.5

200

5

0

0.5

1

1.5 2 2.5 (b) Time(s)

3

3.5

4

50 49 48 47 46 45 44 43 42 41 40

Active Power (KW)

Active Power (KW)

Figure 9.9. (a) (a) Inverter Inverter terminal terminal and and load load voltages voltages for for the the conventional conventional control control strategy; strategy; (b) (b) inverter inverter Figure terminaland andload loadvoltages voltagesfor forproposed proposedcontrol controlstrategy. strategy. terminal

P1-DG-1 P2-DG-2

0

0.5

1

1.5

2 2.5 3 (a) Time(s)

3.5

4

4.5

5

60 58 56 54 52 50 48 46 44 42 40

P1-DG-1 P2-DG-2

0

0.5

1

2 2.5 1.5 (b) Time(s)

3

3.5

4500

)

Figure 10. (a) Active power for the conventional control strategy; (b) active power for proposed control strategy. 7000

4

215 210 205 200

0

0.5

1

1.5

2 2.5 3 (a) Time(s)

3.5

4

4.5

220 210 200

5

V1-DG-1 V2-DG-2 V2-DG-2 Vload Vload

0

0.5

1

1.5 2 2.5 (b) Time(s)

3

3.5

4

Figure 9.3,(a) Inventions 2018, 47 Inverter terminal and load voltages for the conventional control strategy; (b) inverter 10 of 14

50 49 48 47 46 45 44 43 42 41 40

Active ActivePower Power (KW) (KW)

Active ActivePower Power (KW) (KW)

terminal and load voltages for proposed control strategy.

P1-DG-1 P2-DG-2

0

0.5

1

1.5

2 2.5 3 (a) Time(s)

3.5

4

4.5

5

60 58 56 54 52 50 48 46 44 42 40

P1-DG-1 P2-DG-2

0.5

0

2 2.5 1.5 (b) Time(s)

1

3

4

3.5

4500

Reactive Reactive Power Power (VAR) (VAR)

Reactive Reactive Power Power (VAR) (VAR)

Figure 10. (a) (a) Active Active power power for for the the conventional conventional control control strategy; strategy; (b) (b) active active power power for for proposed proposed Figure control strategy. control

4000 3500 3000

Q1-DG-1 Q2-DG-2

2500 2000 1500

0

0.5

1

1.5

2 2.5 3 (a) Time(s)

3.5

4

4.5

7000 6000 5000 4000

Q1-DG-1 Q2-DG-2

3000 2000 1000

5

0

0.5

1

1.5 2 2.5 (b) Time(s)

3

3.5

4

Figure Figure 11. 11. (a) (a) Reactive Reactive power power for for the the conventional conventional control control strategy; strategy; (b) (b) reactive reactive power power for for proposed proposed control control strategy. load 4.2. Vload load 4.2. Case Case 2: 2: P, P, Q Q Measured Measured at at Terminal Terminal V load as shown in Figure 2a. Results are obtained and In In this this case, case, p,p,QQisismeasured measuredatatnode nodeVload Vload as shown in Figure 2a. Results are obtained discussed below for equal and unequal line impedances for both conventional and proposed control and discussed below for equal and unequal line impedances for both conventional and proposed strategies. control strategies.

4.2.1. 4.2.1. Equal Equal Line Line Impedance Impedance

240 235 230 225 220 215 210 205 200 195 190

260 250

Voltage (V)

Voltage (V)

Figure 12shows showsthe the results obtained for voltages from conventional and proposed control Figure 12 results obtained for voltages from conventional and proposed control schemes. schemes. The load voltage error caused by droop in islanded microgrid is compensated in the The load voltage error caused by droop in islanded microgrid is compensated in the proposed strategy, proposed strategy, stabled at theits load voltagevalue at its of nominal value 230 volts as shown in Figure which stabled the which load voltage nominal 230 volts asofshown in Figure 12b. In the load =Q89.2 = load load 12b. In the conventional scheme, power sharing load kw, Q load = 2550 var injected towards Vload conventional scheme, power sharing Pload = 89.2Pkw, 2550 var injected towards V node by load load node by each inverters is slightly lesser as proposed scheme shared P load = 101 kw, Q load = 2900 var as load Qload = 2900 var load as illustrated each inverters is slightly lesser as proposed scheme shared Pload = 101 kw, illustrated in 3, Figures 13 and 14. in Figures 13 and 14.PEER Inventions 2018, x FOR REVIEW 11 of 14

V1-DG-1 V2-DG-2 Vload

0

0.05 0.1

0.15

0.2 0.25 0.3 (a) Time(s)

0.35 0.4

240 230 V1-DG-1 V2-DG-2 Vload

220 210 200

0.45 0.5

0

0.1

0.2

0.3

0.4 0.5 0.6 (b) Time(s)

0.7

0.8

0.9

1

Figure 12. (a) Inverter terminal and load voltages for the conventional conventional control strategy; (b) inverter proposed control control strategy. strategy. terminal and load voltages for the proposed

Active Power (KW)

Active Power (KW)

45 44.6 44.2 43.8 P1-DG-1 P2-DG-2

43.4 43

0

0.1

0.2

0.3 0.4 0.5 (a) Time(s)

0.6

0.7

0.8

0.9

1

51 50.9 50.8 50.7 50.6 50.5 50.4 50.3 50.2 50.1 50

P1-DG-1 P2-DG-2 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

205 205 200 200 195 195 190 190

220 210 210

V2-DG-2 Vload Vload

00

0.05 0.1 0.1 0.05

0.15 0.2 0.2 0.25 0.25 0.3 0.3 0.15 (a) Time(s) Time(s) (a)

0.35 0.4 0.4 0.35

200 200

0.45 0.5 0.5 0.45

V2-DG-2 V2-DG-2 Vload Vload

00

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.4 (b) (b)

0.5 0.6 0.6 0.5 Time(s) Time(s)

0.7 0.7

0.8 0.8

0.9 0.9

11

Figure 12.3, (a) (a) Inverter terminal terminal and and load load voltages voltages for for the the conventional conventional control control strategy; strategy; (b) (b) inverter inverter Inventions 2018, 47 Inverter 11 of 14 Figure 12. terminal and and load load voltages voltages for for the the proposed proposed control control strategy. strategy. terminal

Active ActivePower Power(KW) (KW)

Active ActivePower Power(KW) (KW)

45 45 44.6 44.6 44.2 44.2 43.8 43.8

P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2

43.4 43.4 43 43 00

0.1 0.1

0.2 0.2

0.3 0.4 0.4 0.5 0.5 0.3 (a) Time(s) Time(s) (a)

0.6 0.6

0.7 0.7

0.8 0.8

0.9 0.9

11

51 51 50.9 50.9 50.8 50.8 50.7 50.7 50.6 50.6 50.5 50.5 50.4 50.4 50.3 50.3 50.2 50.2 50.1 50.1 50 50

P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2 00

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.5 0.5 0.6 0.6 0.4 (b) Time(s) Time(s) (b)

0.7 0.7

0.8 0.8

0.9 0.9

11

1400 1400 1350 1350 1300 1300 1250 1250 1200 1200 1150 1150 1100 1100 1050 1050 1000 1000

Reactive ReactivePower Power(VAR) (VAR)

Reactive ReactivePower Power(VAR) (VAR)

Figure 13. (a) (a) Active power for the conventional control strategy; (b) active power for proposed Figure 13. (a) Active Active power power for for the the conventional conventional control control strategy; strategy; (b) (b) active active power power for for proposed proposed Figure control strategy. control control strategy.

Q1-DG-1 Q1-DG-1 Q2-DG-2 Q2-DG-2 00

0.1 0.1

0.2 0.2

0.3 0.3 (a) (a)

0.4 0.5 0.5 0.4 Time(s) Time(s)

0.6 0.6

0.7 0.7

0.8 0.8

0.9 0.9

11

1600 1600 1550 1550 1500 1500 1450 1450 1400 1400 1350 1350 1300 1300 1250 1250 1200 1200

Q1-DG-1 Q1-DG-1 Q2-DG-2 Q2-DG-2 00

0.1 0.1

0.2 0.2

0.3 0.3

0.4 0.5 0.5 0.6 0.6 0.4 (b) Time(s) Time(s) (b)

0.7 0.7

0.8 0.8

0.9 0.9

11

Figure 14. (a) (a) Reactive power for the conventional control strategy; (b) reactive power for proposed Figure Figure 14. (a) Reactive Reactive power power for for the the conventional conventional control control strategy; strategy; (b) (b) reactive reactive power power for for proposed proposed control strategy. control strategy. control strategy.

250 245 240 235 230 225 220 215 210 205 200

270 Voltage (V)

Voltage (V)

4.2.2. Unequal Unequal Line Impedance Impedance 4.2.2. 4.2.2. Unequal Line Line Impedance In this this case, line line impedances set set as R R1 + jX11 == 0.05 0.05 + j1.099 Ω Ω and R R2 + jX22 == 0.05 0.05 ++ j1.3 j1.3 Ω. Ω. In In In this case, case, line impedances impedances set as as R11++jX jX1 = 0.05+ +j1.099 j1.099 Ωand and 2R+2 jX + jX2 = 0.05 + j1.3 In Ω. conventional control scheme, the slightly higher load voltage error is noticed with value of 7.82% as conventional control scheme, the slightly higher load voltage error is noticed with value of 7.82% as In conventional control scheme, the slightly higher load voltage error is noticed with value of 7.82% shown in in Figure 15a 15a this this error error is is eliminated eliminated by proposed scheme scheme and restored restored the load load voltage at at shown as shown Figure in Figure 15a this error is eliminatedbybyproposed proposed schemeand and restoredthe the load voltage voltage at nominal value as depicted in Figure 15b. nominal nominal value value as as depicted depicted in in Figure Figure 15b. 15b. In conventional conventional control control scheme, scheme, the the startup divergent divergent trend has has been spotted spotted for active active power In In conventional control scheme, the startup startup divergent trend trend has been been spotted for for active power power and it it stabilizes within within 0.5 ss as as shown in in Figure 16a 16a while in in proposed scheme scheme the active active power is is and and it stabilizes stabilizes within 0.5 0.5 s as shown shown in Figure Figure 16a while while in proposed proposed scheme the the active power power is proportionally shared with a value of 99.7 kw. Slightly higher reactive power sharing error is proportionally sharedwith witha value a value of 99.7 kw. Slightly reactive power sharing error is proportionally shared of 99.7 kw. Slightly higherhigher reactive power sharing error is observed observed for the conventional control scheme as shown in Figure 17a. Reactive power of inverter1 is observed for the conventional control in Figure 17a.power Reactive power of is inverter1 is for the conventional control scheme asscheme shown as in shown Figure 17a. Reactive of inverter1 gradually gradually increased increased and and stabilizes stabilizes within 0.7 0.7 s to to values values of of +3400 +3400 var var while while inverter2 inverter2 shares shares −850 −850 var. var. gradually increased and stabilizes within 0.7 within s to valuessof +3400 var while inverter2 shares −850 var. However, However, in proposed control scheme reactive power is proportionally shared after a small start-up However, in proposed control schemepower reactive power is proportionally shared afterstart-up a smalltransient start-up in proposed control scheme reactive is proportionally shared after a small transient trend trend as as depicted depicted in in Figure Figure 17b. 17b. transient trend as 2018, depicted in PEER Figure 17b. Inventions 3, x FOR REVIEW 12 of 14

V1-DG-1 V2-DG-2 Vload

260 250 240 230 V1-DG-1 V2-DG-2 Vload

220 210

0

0.2

0.4

0.6

0.8 1 1.2 (a) Time(s)

1.4

1.6

1.8

200

2

0

0.5

1

1.5

2 2.5 3 (b) Time(s)

3.5

4

4.5

5

44 43.5 43 42.5 42 41.5 41 40.5 40 39.5 39

Active Power (KW)

Active Power (KW)

Figure 15. (a) Inverter terminal voltages for the conventional conventional control control scheme; scheme; (b) inverter Figure 15. (a) Inverter terminal and and load load voltages for the (b) inverter terminal and load voltages for proposed control scheme. scheme.

P1-DG-1 P2-DG-2 0

0.2

0.4

0.6

0.8 1 1.2 (a) Time(s)

1.4

1.6

1.8

2

50.2 50.1 50 49.9 49.8 49.7 49.6 49.5 49.4

P1-DG-1 P2-DG-2 0

0.5

1

1.5

2 2.5 (b) Time(s)

3

3.5

4

220 215 215 210 215 210 210 205 205 205 200 200 0 200 0 0

V2-DG-2 Vload Vload

0.2 1.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 11 1.2 1.4 1.4 1.6 1.6 1.8 1.8 22 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 (a) (a) Time(s) Time(s) (a) Time(s)

220 220 220 210 210 210 200 200 0 200 0 0

V2-DG-2 V1-DG-1 V2-DG-2 Vload V2-DG-2 Vload Vload

0.5 0.5 0.5

11 1

1.5 1.5 1.5

22 2.5 2.5 33 2 2.5 3 (b) (b) Time(s) Time(s) (b) Time(s)

3.5 3.5 3.5

44 4

4.5 4.5 4.5

55 5

Figure 15. Inventions 2018, 3, (a) 47 12 of 14 Figure 15. (a) Inverter Inverter terminal terminal and and load load voltages voltages for for the the conventional conventional control control scheme; scheme; (b) (b) inverter inverter Figure 15. (a) Inverter terminal and load voltages for the conventional control scheme; (b) inverter terminal terminal and and load load voltages voltages for for proposed proposed control control scheme. scheme. terminal and load voltages for proposed control scheme.

P1-DG-1 P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2 P2-DG-2 0.2 1.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 11 1.2 1.4 1.4 1.6 1.6 1.8 1.8 (a) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (a) Time(s) Time(s) (a) Time(s)

50.2 50.2 50.2 50.1 50.1 50.1 50 50 50 49.9 49.9 49.9 49.8 49.8 49.8 49.7 49.7 49.7 49.6 49.6 49.6 49.5 49.5 49.5 49.4 49.4 0 49.4 0 0

ActivePower Power(KW) (KW) Active Active Power (KW)

ActivePower Power(KW) (KW) Active Active Power (KW)

44 44 43.5 44 43.5 43.5 43 43 42.5 43 42.5 42.5 42 42 41.5 42 41.5 41.5 41 41 41 40.5 40.5 40 40.5 40 40 39.5 39.5 39 39.5 39 0 39 0 0

22 2

P1-DG-1 P1-DG-1 P1-DG-1 P2-DG-2 P2-DG-2 P2-DG-2 0.5 0.5 0.5

11 1

1.5 22 2.5 1.5 2.5 1.5(b) 2 2.5 (b) Time(s) Time(s) (b) Time(s)

33 3

3.5 3.5 3.5

44 4

Figure Active power for the control scheme; (b) for control Figure 16. 16.(a) Active power the conventional control scheme; (b) power active for proposed 16. (a)(a) Active power for for the conventional conventional control scheme; (b) active active power power for proposed proposed control Figure 16. (a) Active power for the conventional control scheme; (b) active power for proposed control scheme. control scheme. scheme. scheme.

Q1-DG-1 Q1-DG-1 Q1-DG-1 Q2-DG-2 Q2-DG-2 Q2-DG-2 0.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 0.2 0.4 0.6 (a) 0.8 (a) (a)

11 1.2 1.2 1.4 1.4 1.6 1.6 1.8 1.8 Time(s) 1 1.2 1.4 1.6 1.8 Time(s) Time(s)

22 2

1600 1600 1600 1550 1550 1550 1500 1500 1500 1450 1450 1450 1400 1400 1400 1350 1350 1350 1300 1300 1300 1250 1250 1250 1200 1200 1200 1150 1150 0 1150 0 0

ReactivePower Power(VAR) (VAR) Reactive Reactive Power (VAR)

ReactivePower Power(VAR) (VAR) Reactive Reactive Power (VAR)

3500 3500 3500 3000 3000 3000 2500 2500 2500 2000 2000 2000 1500 1500 1500 1000 1000 1000 500 500 500 00 0 -500 -500 -500 -1000 -1000 -100000 0

Q1-DG-1 Q1-DG-1 Q1-DG-1 Q2-DG-2 Q2-DG-2 Q2-DG-2 0.2 11 1.2 0.2 0.4 0.4 0.6 0.6 0.8 0.8 1.2 1.4 1.4 1.6 1.6 1.8 1.8 (b) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 (b) Time(s) Time(s) (b) Time(s)

22 2

Figure Reactive power for control scheme; (b) for proposed Figure 17. 17. (a) (a) Reactive power for the the conventional controlcontrol scheme;scheme; (b) reactive reactive power forpower proposed 17.(a) Reactive power forconventional the conventional (b) power reactive for Figure 17. (a) Reactive power for the conventional control scheme; (b) reactive power for proposed control. control. proposed control. control.

Frequency regulation Frequency regulation results results are are presented presented in in Figure Figure 18. 18. Frequency Frequency is is gradually gradually restored restored to to the the Frequency Frequency regulation regulation results results are are presented presented in in Figure Figure18. 18. Frequency Frequency is is gradually gradually restored restored to to the the nominal value and remains within nominal frequency value of ±0.5 Hz. nominal value and remains within nominal frequency value of ±0.5 Hz. nominal value and remains within nominal frequency value of ± 0.5 Hz. nominal value and remains within nominal frequency value of ±0.5 Frequency (Hz) Frequency (Hz) Frequency (Hz)

50.1 50.1 50.1 50.05 50.05 50.05 50 50 50 49.95 49.95 49.95 49.9 49.9 49.9 49.85 49.85 49.85 49.8 49.8 49.811 1

Frequency Frequency Frequency

55 5

10 (s) 10 Time 15 (s) 15 10 Time Time (s) 15 (a) (a) (a)

20 20 20

25 25 25

Figure Figure 18. 18. Frequency Frequency regulation. regulation. Figure 18. 18. Frequency Frequency regulation. regulation. Figure

5. 5. Conclusions Conclusions 5. Conclusions 5. Conclusions In In order order to to improve improve the the overall overall performance performance of of aa droop droop controlled controlled microgrid, microgrid, an an improved improved In order to improve the overall performance of a droop controlled microgrid, an improved control strategy is and It that the strategy In order to improve the overall performance a droop controlled an improved control control strategy is proposed proposed and analyzed. analyzed. It is isofdemonstrated demonstrated that microgrid, the proposed proposed strategy can can be be control strategy is proposed and analyzed. It is demonstrated that the proposed strategy can be extended for radial configurations. Load voltage deviations have been eliminated and load power strategy is proposed and analyzed. It is demonstrated that the proposed strategy can be extended extended for radial configurations. Load voltage deviations have been eliminated and load power extended for radial configurations. Load voltage deviations have been eliminated and load power for radial configurations. Load voltage deviations have been eliminated and load power sharing accuracy has been enhanced along with frequency restoration. The proposed control strategy consists of two decoupled methods. The Q-V loops control the sharing of reactive power and load voltage restoration while P-f control loops address active power sharing and frequency restoration. Both sets of control loops have been implemented in a centralized manner. The validity of the proposed scheme has been tested through simulation studies on an islanded ring-feeder network. The results of the simulation study in MATLAB’s Simpower systems in comparison to the conventional strategy verify the effectiveness of the proposed methodology.

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Author Contributions: M.Z.K. proposed the idea for writing the manuscript. M.M.K. and K.H. suggested the literature and supervised in writing the manuscript. K.H. helped M.Z.K. in writing and formatting. M.U.S. helped in modifying the figures and shared the summary of various credible articles to be included in this manuscript. J.H. helped in system parameters to make the simulation test possible. Conflicts of Interest: The authors declare no conflict of interest.

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