IET Generation, Transmission & Distribution

Research Article

Power factor angle consistency control fordecentralised power sharing in cascaded-typemicrogrid

ISSN 1751-8687Received on 1st November 2017Revised 23rd May 2018Accepted on 27th July 2018doi: 10.1049/iet-gtd.2018.5639www.ietdl.org

Lang Li1,2, Yao Sun1,2 , Hua Han1,2, Xiaochao Hou1,2, Mei Su1,2, Zhangjie Liu1,2

1School of Information Science and Engineering, Central South University, Changsha, People's Republic of China2Hunan Provincial Key Laboratory of Power Electronics Equipment and Grid, Changsha, People's Republic of China

E-mail: yaosuncsu@gmail.com

Abstract: The microgrid with cascaded H-bridge micro-converters (cascaded-type microgrid) is an effective way to integrate thedistributed generators (DGs) into medium/high-voltage distribution energy system. Just like the islanded microgrid composed ofparalleled inverters, achieving accuracy in power sharing and high voltage quality is a serious challenge in cascaded-typemicrogrid without communication. In this article, a decentralised control scheme is proposed to share the active and reactivepower accurately under the resistance-inductance and resistance-capacitance loads. The power factor angle of each DG isassigned to be consistent in the steady state via regulating both the frequency and voltage. The proposed scheme can be easilyimplemented only based on the local measured signals. Meanwhile, excellent load voltage quality is achieved. Small-signalanalysis method is performed to verify the effectiveness of the proposed scheme, and a guide for designing the power sharingcoefficient is given. The cascaded-type microgrid model is developed through simulations and experiments to verify theperformance of the proposed scheme.

1 IntroductionIntegrating distributed generators (DGs) into modern powerdistribution systems has drawn an increasing attention in recentyears [1, 2]. The microgrid concept is a quite appealing alternativeto account for this trend [3–5]. In microgrid, DGs are commonlyconnected by power electronic converters in paralleled or cascadedmanner [6, 7]. Accurate power sharing and system stability are thecore problems in microgrid research.

In islanded mode, the power sharing strategies have beendeeply studied for the microgrid composed of the paralleledinverters (paralleled-type microgrid), including the concentratedcontrol [8–10], the master/slave control [11–13], the distributedcontrol [14–17], and the decentralised control [18–23]. The firstthree control schemes can achieve excellent voltage regulation andaccurate power sharing. However, the high dependency oncommunications may bring about some problems such as lowerreliability and higher capital costs. Thus, as a typical decentralisedcontrol method, the droop control without any communicationsbecomes a most promising power sharing strategy [18–23].

The droop control strategies are based on the localmeasurements by emulating the droop characteristics ofsynchronous generators [7, 18]. The conventional P-ω/Q-V droopcontrol is developed by assuming highly inductive equivalentimpedance [18]. This technique may bring instable operation forlow-voltage microgrid, where the feeder impedance is usuallyresistive and mismatched [7]. To account for the low-voltagemicrogrid application, the P-V droop with Q-f boost (VPD/FQB)method [2, 19] is presented. However, this method stronglydepends on system parameters and is unable to share the activepower accurately. Virtual impedance method [20, 21] is introducedto change the output impedance characteristic, which can avoid theactive and reactive power coupling. In further investigation of thedroop concept, power-angle droop control [22, 23] is proposed toimprove load power sharing among DGs without a frequency drop.Nevertheless, if the local control broads are not synchronised witheach other, the crystal clock makes frequency of each DG slightlydifferent, which will lead to system instability. The detailedadvantages and disadvantages of these methods can be found in alatest review [2].

Compared to the paralleled configuration, the cascaded-typemicrogrid has the capability to develop a higher voltage level

power system. Inspired by the merits of cascaded H-bridge multi-level converters [24–26], it is applied to integrate the distributedenergy resources directly into a grid-connected [27–29] or islandedpower network [30]. For cascaded-type microgrid in grid-connected mode, only some concentrated power sharing strategiesdepending on high bandwidth communication network are studied[27, 28]. Excellent power sharing and voltage quality are obtainedat the expense of increasing the capital costs and reducing thereliability in case of communication failure. Thus, it is preferred toonly use the local measured signals to develop the control scheme.In addition, the droop schemes applied in paralleled-type microgridcannot be copied by cascaded-type microgrid. Therefore, it issignificant to do researches on decentralised power sharing controlof the islanded cascaded-type microgrid.

Recently, Ali et al. [6] presented a multifunctional controlstrategy of the cascaded-type microgrid in both the grid-connectedmode and islanded mode. However, the implementation of thismethod requires communications. Furthermore, He et al. [30]studied the cascaded-type microgrid feeding the resistance-inductance load in islanded operation mode. Meanwhile, an inversepower factor droop control method is proposed to share active andreactive power accurately via the decentralised manner. Theproposed control strategy can guarantee the accuracy of powersharing even under the variations of feeder impedance parametersand non-linear loads. Meanwhile, the system shows an excellentanti-disturbance ability. However, this decentralised technique isunfeasible to supply resistance-capacitance loads.

In this article, a power factor angle consistency control schemeis proposed such as the one in [31], and it is presented in moredetail. The proposed scheme is to achieve active and reactivepower sharing accurately under both the resistance-inductance andresistance-capacitance loads. Meanwhile, excellent load voltagequality is retained. The implementation of this method is onlybased on the local information. It can ensure reliability in case ofcommunication failure and less capital costs. Furthermore, thestability of the proposed scheme is investigated based on the small-signal analysis method. The values of the power sharing coefficientare designed from the perspective of stability and allowablefrequency ranges. The effectiveness of the proposed scheme isverified through simulations and experiments.

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

1

The rest of this paper is organised as follows. Section 2 presentsthe power transmission characteristics of the cascaded-typemicrogrid. The power factor angle consistency control is proposedin Section 3. Then, the stability analysis of the proposed scheme isperformed in Section 4. Furthermore, simulation results in Section5 and experimental results in Section 6 are provided to verify theeffectiveness and performance of the proposed scheme. Finally, thepaper is concluded in Section 7.

2 Power transmission characteristics ofcascaded-type microgridThe studied microgrid structure is shown in Fig. 1a whichincorporates cascaded H-bridge micro-converters. The DC energysource is directly connected to a DC/AC low-voltage interfacingconverter with an output LC filter. All DGs are connected in seriesto supply electricity at the point of common coupling (PCC). Thecascaded-type microgrid can operate in grid-connected modethrough static switch based on a synchronous controller. When thisstring converter is switched to islanded operation mode, it cansupply electricity to the local loads at PCC [30]. This paper ismainly concentrated on the islanded operation mode.

Assume that the LC filter capacitor voltage is controlledproperly, the simplified equivalent circuit for the consideredmicrogrid is depicted in Fig. 1b. Vi ejδi is the output voltage of ithDG, VPCC ejδPCC is the voltage of the PCC, Vi and VPCC are theamplitudes of the corresponding voltages, δi and δPCC are the phaseangles of the corresponding voltages. zPCC, zi are load impedanceand line impedance, i ∈ {1, 2, …, n}. By the Kirchhoff voltagelaws, we can get

VPCC ejδPCC = y′zPCC∑i = 1

nVi ejδi (1)

y′ = 1zPCC + ∑i = 1

n zi(2)

where y′ is the equivalent admittance of the microgrid. Forconvenience, y′ is denoted as:

y′ = Y′ ejθ′ (3)

where Y′ and θ′ are the modulus and phase angle of y′. Afterobtaining the load voltage, the expressions of output active powerPi and reactive power Qi of ith DG are:

Pi = Vi Y′ ∑j = 1

nV jcos δi − δj − θ′ (4)

Qi = Vi Y′ ∑j = 1

nV jsin δi − δj − θ′ (5)

Therefore, the active power Pi and reactive power Qi of each DGcan be regulated by changing the output voltage Vi and the phaseangle difference between δi and δj.

3 Proposed power factor angle consistencycontrol3.1 Necessity for power factor angle consistency operation

With ∑ zi ≪ zPCC, the transmission line voltage loss is neglected.The sum of all output voltages of all DGs is the load voltage atPCC. Assume that the load current ILoad serves as the referencephasor in the steady state shown in Fig. 1c. When the multiplemicro-converters hold different voltage phase angles in the steadystate, the corresponding output voltage phasor diagram is shown inFig. 1c.1. Then, it can be easily obtained, VPCC < ∑ Vi .Obviously, it is difficult to control the amplitude of the load voltageat a certain value even in allowable ranges due to the uncertainoutput voltage phase angle.

If all micro-converters have the same voltage phase angles inthe steady state, their output voltage phasor diagram is shown inFig. 1c.2. As seen, ∑ Vi = VPCC , that is the voltage at PCC is thescalar sum of all DGs’ output voltages. Compared to the former, itis easy to guarantee a certain load voltage and supply high-qualityelectricity.

3.2 Power factor angle consistency control

To ensure the reliability in case of communication failure, it ispreferred to only use the local measured signals to develop acontrol scheme. Assume Qi ≠ 0, in this paper, the power factorangle consistency control is proposed to ensure an accurate powersharing as:

Fig. 1  Cascaded-type microgrid(a) Diagram, (b) Equivalent circuit, (c) Phasor diagram of the load voltage: (1) different and (2) same voltage phase angles

2 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

f i = f ∗ + sgn QiPimi

(6)

Vi = mi

∑i = 1n mi

VPCC∗

(7)

where f i and f ∗ are nominal frequency and reference frequency,respectively. sgn( ⋅ ) is a signum function. mi is a positive powersharing coefficient, which will be given in Section 4. f max and f minare the maximum and minimum frequency allowed by themicrogrid, respectively. f ∗ = f max + f min /2 andPi/mi ∈ 0, f max − f min /2 . VPCC

∗ is the reference voltage at PCC.When the microgrid is connected by the resistance-inductanceloads (Qi > 0) or resistance-capacitance loads (Qi < 0), thecorresponding sgn Qi is 1 or −1, respectively. The P-fcharacteristics of the proposed scheme are shown in Fig. 2.

When the microgrid is in the steady state, f i = f j, then (6)becomes

1mi

Pi = 1mj

Pj (8)

Define that φi is the phase angle difference between the outputvoltage Vi and the output current Ii of the ith DG. WithPi = ViIicos φi, we can get

1mi

ViIicos φi = 1mj

V jI jcos φj (9)

Combine Ii = I j, substitute (7) into (9), we can get

cos φi = cos φj (10)

Usually, φi should lie in [ − π /2, π /2], φi = arcsin Qi /ViIi(feasible solution for resistance-inductance load, see Section 4) orφi = − arcsin Qi /ViIi (feasible solution for resistance-capacitanceload, see Section 4). As seen, the power factor angle consistencycontrol is realised.

Neglecting the line voltage loss, from (7), we can easily get∑i = 1

n Vi = VPCC . Therefore, the voltage amplitude at PCC can becontrolled as a constant.

With Qi = ViIisin φi, and yields,

QiQj

= PiPj

(11)

Therefore, the reactive power can be shared accurately with thesame ratio of the active power sharing. This characteristic isobviously different from the conventional droop scheme in themicrogrid with paralleled inverters. It shares the active poweraccurately, but the reactive power may be shared with somedeviates.

The proposed scheme can drive the power factor angle equal forthe cascaded-type microgrid. The active and reactive power sharingare always accurate in the steady state. Meanwhile, excellent loadvoltage quality is obtained by a sum of all output voltage scalarrather than its vector. Moreover, the implementation of theproposed scheme only needs the local measured signals; thus, thedecentralised manner is retained.

4 Stability analysisStability is a critical issue for the microgrid in which the sourcepower electronic interfaces are controlled in decentralised mannerbased on its local signals. The system stability is investigated inthis section, and the small-signal analysis method is applied [7, 18,32–35]. The cascaded-type microgrid in islanded mode shown inFig. 1a is studied.

Suppose that the output frequency reference is tracked by theith DG without the steady state error. Then, the proposed scheme in(6) can be written as follows:

ωi = ω∗ + 2πsgn QiPimi

(12)

where ωi is the output angular frequency of the ith DG, ω∗ = 2π f ∗.Assume that ωs is the microgrid synchronous angle frequency in

the steady state. Let δs = ∫ ωs dt, and denote δ~

i = δi − δs, then (12)is rewritten as:

δ~

i = ω∗ − ωs + 2πsgn QiPimi

(13)

Linearisation of (4) and (13) near the equilibrium point yields

ΔPi = − Vi Y′ ∑j = 1

nV jsin δi

o − δjo − θ′ Δδ

~i − Δδ

~j (14)

Δδ~

i = 2πsgn Qio 1

miΔPi (15)

where ‘o’ denotes the corresponding steady state values. Since theoutput voltage phase angle is controlled as the same in the steadystate, δi

o − δjo = 0. Substituting (14) into (15) yields

Δδ~

i = − 2πsgn Qio 1

miVi Y′ ∑

j = 1

nV jsin −θ′ Δδ

~i − Δδ

~j (16)

Express (16) in the matrix form:

X = AX (17)

where A = − ai j ,aii = 2πsgn Qi

o (1/mi)Vi Y′ ∑ j = 1, j ≠ in V jsin −θ′ ,

ai j = − 2πsgn Qio (1/mi)Vi Y′ V jsin −θ′ , X = Δδ

~1 ⋯ Δδ

~n

T.

Fig. 2  P-f characteristics of proposed power factor angle consistencycontrol

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

3

Clearly, aii + ∑i ≠ j, j = 1n ai j = 0, ai j = aji. If aii > 0, then − A is a

Laplacian matrix [36], and the eigenvalues of A are non-positive.There is a simple eigenvalue at zero corresponding to rotationalsymmetry, which has been proven in [37]. Then, the system isstable. In order to ensure aii > 0, the following condition must bemet

2πsgn Qio 1

miVi Y′ ∑

j = 1, j ≠ i

nV jsin −θ′ > 0 (18)

In the case of resistance-inductance loads, Qio > 0, φi ∈ (0, π /2],

that is φi = φj, sgn Qio = 1, and θ′ < 0, sin −θ′ > 0, mi > 0, then

(18) is satisfied. While in the case of resistance-capacitance loads,Qi

o < 0, φi ∈ [ − π /2, 0), φi = φj, then sgn Qio = − 1, and θ′ > 0,

sin −θ′ < 0, mi > 0, then (18) also holds. When Qio = 0, (18) is

undermined; the system is unstable. Therefore, the proposedscheme can maintain the system stable operation.

Define that PRated is the rated active power of DGs. In order tocontrol f i within its allowable ranges, then mio should meet thefollowing equation

0 < mi ≤ 2PRatedf max − f min

(19)

5 Simulation resultsThe proposed power factor angle consistency control scheme isverified through MATLAB/Simulink, the considered cascaded-typemicrogrid consists of two DGs (see Fig. 1a). The associatedparameters are listed in Table 1. LLinei and RLinei are the linecoupling inductance and resistance, i = 1, 2. The detailedconfiguration of the local controller is depicted in Fig. 3.

5.1 Case 1: performance of the proposed scheme under theresistance-inductance load

In this case, the power factor consistency control and excellent loadvoltage quality are verified. The active power load demands PLoadare scheduled as 1200 W in the interval [0 s, 4 s]. The reactive

power load demands QLoad are scheduled as 300 and 600 Var in theinterval [0 s, 2 s] and [2 s, 4 s], respectively.

In terms of the proposed scheme, variations of the frequency areshown in Fig. 4a, which converge to a certain constant quickly asload changes. It exceeds the reference frequency 50 Hz. Thischaracteristic is obviously different from the traditional droopscheme in the microgrid with paralleled inverters, where thefrequency of system decreases with active power increasing. Thepower factors of DGs shown in Fig. 4b tend to be consistent in thesteady state via regulating both frequency and voltage. Therefore,the proposed scheme can realise the power factor consistencycontrol as load changes.

The output voltages of DG1 and DG2 are shown in Fig. 4c, inwhich the phase-angle of each DG is the same but the amplitude isdifferent. As seen, the load voltage at PCC is the scalar sum of alloutput voltages, and it is shown in Fig. 4d. The load voltage can becontrolled at a certain constant when the line voltage loss isneglected. Therefore, the advantage of excellent load voltagequality for the proposed scheme has been verified.

5.2 Case 2: power sharing with a ratio of 1:1 under theresistance-inductance and resistance-capacitance load

In this case, the accurate power sharing of the proposed scheme isverified under the resistance-inductance and resistance-capacitanceload. The load demands are shown in Fig. 5a, in which theresistance-inductance and resistance-capacitance load arescheduled in the interval [0 s, 2 s] and [2 s, 4 s], respectively. Thevariations of frequency are shown in Fig. 5b, which are alwayscontrolled within the allowable ranges [49 Hz, 51 Hz] [38, 39]. Inaddition, the frequency of the system exceeds 50 Hz in the interval[0 s, 2 s] and is lower than 50 Hz in the interval [2 s, 4 s]. It can beconcluded that the proposed scheme can maintain the stableoperation under the resistance-inductance and resistance-capacitance load.

The active power sharing is shown in Fig. 5c, in which it sharesloads accurately with the ratio of 1:1 under the two loads.Meanwhile, the reactive power sharing is also accurate with thesame ratio of active power sharing without any errors shown inFig. 5d. This characteristic is obviously better than theconventional droop scheme in the microgrid with paralleledinverters, where the reactive power may share with some errors.

Table 1 Parameters for simulationsparameters values parameters valuesf / f ∗, Hz [49, 51]/50 LLine1, H 0.6 × 10−3

VPCC∗ , V 60 RLine1, Ω 0.2

C f , μF 20 LLine2, H 0.3 × 10−3

L f , H 1.5 × 10−3 RLine2, Ω 0.3

Fig. 3  Configuration of the local controller

4 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

From the simulation result, it is verified that the proposedscheme can maintain the stable operation under the resistance-inductance and resistance-capacitance load. In addition, the activeand reactive power can be shared accurately with the same ratio.

5.3 Case 3: power sharing with a ratio of 2:1 under theresistance-inductance and resistance-capacitance load

In this case, the accurate power sharing of the proposed scheme isverified with the ratio of 2:1. The load demands shown in Fig. 6aare scheduled as the resistance-inductance and resistance-capacitance load in the interval [0 s, 2 s] and [2 s, 4 s], respectively.The variations of frequency are shown in Fig. 6b. The active andreactive power sharing are shown in Figs. 6c and d, in which theload demands are shared accurately with the ratio of 2:1.

Based on these simulation results, it is verified that theproposed scheme can share the active power accurately with thedifferent ratio among DGs. Meanwhile, the reactive power isshared with the same ratio as the active power sharing.

6 Experimental resultsA cascaded-type microgrid prototype shown in Fig. 7 is built in thelab to verify the effectiveness and performance of the proposedmethod. It comprises two DGs based on the single-phase voltagesource inverters which are controlled by digital single processors(TMS320f28335) and the sampling rate is 12.8 kHz. Theexperimental parameters are shown in Table 2. R f and Rd are the

series resistance of the filter capacitance and inductance,respectively.

6.1 Case 1: performance of the proposed scheme under theresistance-inductance and resistance-capacitance load

In this experimental case, the performance of proposed scheme isverified to switch steadily between the resistance-inductance andresistance-capacitance load. The load demand is scheduled asresistance-inductance load in the first interval and fed byresistance-capacitance load in the second interval. Theexperimental waveforms are shown in Fig. 8a. From theexperimental result, the load voltage VPCC can maintain at 60 Veven as load changes, which holds the same phase angle as V1 andV2. Therefore, a high-quality load voltage is retained in terms of theproposed scheme. In Fig. 8a, a temporary zero-current is caused bythe nature switching time of the physical switch during the loadchanging.

The waveforms of power sharing, frequency and power factorbased on the proposed scheme are illustrated in Fig. 8b. The activepower and reactive power are shared accurately under theresistance-inductance and resistance-capacitance loads shown inFig. 8b.1. The waveform of frequency is shown in Fig. 8b.2, whichexceeds 50 Hz in the first interval (sgn Qi = 1) due to using theinverse droop characteristic. In the second interval, the frequency islower than 50 Hz due to using the droop characteristic(sgn Qi = − 1). The power factor of DGs is calculated in Fig.8b.3, which always tends to be consistent as load changes.

Fig. 4  Simulation results under the resistance-inductance load(a) Frequency, (b) Power factor, (c) Output voltage of DG1 and DG2, (d) Load voltageat PCC

Fig. 5  Power sharing results with the ratio of 1:1(a) Load demands, (b) Frequency, (c) Active power, (d) Reactive power

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

5

This experimental result verified that the proposed schememaintains the stabilisation during switching the resistance-inductance and resistance-capacitance load. Meanwhile, excellentload voltage quality is achieved.

6.2 Case 2: power sharing with a ratio of 1:1 under theresistance-inductance load

In this test, the accurate power sharing among DGs with a ratio of1:1 is verified under the resistance-inductance load. Theexperimental waveforms in terms of the proposed scheme for 1:1power sharing are shown in Fig. 9a. The frequency of system isshown in Fig. 9b.1, which is always within the allowable ranges[49 Hz, 51 Hz]. From Fig. 9b.2, the active power is always sharedaccurately with the ratio of 1:1 regardless of the load increasingand decreasing. The reactive power sharing among DGs is shownin Fig. 9b.3, which also shares accurately with the same ratio asactive power sharing. Based on this experimental result, it can beconcluded that the proposed scheme can always share the activeand reactive power accurately with the ratio of 1:1 as the loadchanges.

Fig. 6  Power sharing results with the ratio of 2:1(a) Load demands, (b) Frequency, (c) Active power, (d) Reactive power

Fig. 7  Prototype setup of the cascaded-type microgrid with two DGs

Table 2 parameters for experimentsparameters values parameters valuesf / f ∗, Hz [49, 51]/50 Rd, Ω 5

VPCC∗ , V 60 LLine1, H 0.3 × 10−3

C f , μF 20 RLine1, Ω 0.5R f , Ω 0.5 LLine2, H 0.6 × 10−3

L f , H 1.5 × 10−3 RLine2, Ω 0.5

Fig. 8  Experimental results(a) Experimental waveforms switching from resistance-inductance load to resistance-capacitance load, (b) Experimental results: (1) Power sharing, (2) Frequency, (3)Power factor

6 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

6.3 Case 3: power sharing with a ratio of 1:2 under theresistance-inductance load

In this experimental case, the proposed scheme is verified to shareactive and reactive power accurately with the ratio of 1:2 amongDGs. The experimental waveforms based on the proposed schemeare shown in Fig. 10a. The waveforms of frequency, active powersharing, and reactive power sharing are shown in Fig. 10b. FromFig. 10b.1, the frequency converges to a constant quickly.Therefore, the proposed scheme can maintain the system stableoperation in the presence of load changing. The active power isshared accurately with the ratio of 1:2 without any errors shown inFig. 10b.2. The reactive power is shared as the same ratio of theactive power sharing shown in Fig. 10b.3. Based on thisexperimental result, the proposed scheme can control the activeand reactive power accurately for 1:2 power sharing as loadincreases and decreases.

7 ConclusionIn this paper, a power factor angle consistency control has beenproposed to share load accurately via decentralised manner for theislanded cascaded-type microgrid. The power factor angle of eachDG has been driven to be consistent through regulating both the

frequency and voltage. The active power and reactive power can beshared accurately with the same ratio, and excellent load voltagequality has been achieved. The proposed scheme is easilyperformed only with the local information of each DG. Theeffectiveness of the proposed scheme has been verified through thesmall-signal stability analysis. Furthermore, the design of areasonable power sharing coefficient mi has been given. When theload is highly resistive ( Qi is nearly close to 0), the frequencychattering of system may occur. In fact, this situation may be quiterare in practice. For this limitation, it will be studied in the future.

For the readers, this main research explores the possibilities ofinspiring new control methods in grid-connected operation mode orin a hybrid power network with series-parallel connected inverters.

8 AcknowledgmentsThis work was supported by the National Natural ScienceFoundation of China under Grants nos. 61622311, and the JointResearch Fund of Chinese Ministry of Education under Grant no.6141A02033514, and the Natural Science Foundation of HunanProvince of China under Grant no. 2016JJ1019.

Fig. 9  Experimental results for 1:1 power sharing(a) Experimental waveforms, (b) Experimental results: (1) Frequency, (2) Activepower sharing, (3) Reactive power sharing

Fig. 10  Experimental results for 1:2 power sharing(a) Experimental waveforms, (b) Experimental results: (1) Frequency, (2) Activepower sharing, (3) Reactive power sharing

IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018

7

9 References[1] Jie, Y., Xinmin, J., Xuezhi, W., et al.: ‘Decentralised control method for DC

microgrids with improved current sharing accuracy’, IET Gener. Transm.Distrib., 2017, 11, (3), pp. 696–706

[2] Li, L., Ye, H., Sun, Y., et al.: ‘A communication-free economical-sharingscheme for cascaded-type microgrids’, Int. J. Electr. Power Energy Syst.,2019, 104, pp. 1–9. Available at https://doi.org/10.1016/j.ijepes.2018.06. 006

[3] Liu, Z., Su, M., Sun, Y., et al.: ‘Existence and stability of equilibrium of DCmicrogrid with constant power loads’, IEEE Trans. Power Syst., 2018, pp. 1–1, doi: 10.1109/TPWRS.2018.2849974

[4] Chen, C., Duan, S., Cai, T., et al.: ‘Smart energy management system foroptimal microgrid economic operation’, IET Renew. Power Gener., 2011, 5,(3), pp. 258–267

[5] Iasonas, K., Nikos, H.: ‘Fully distributed economic dispatch of distributedgenerators in active distribution networks considering losses’, IET Gener.Transm. Distrib., 2017, 11, (3), pp. 627–636

[6] Hou, X., Sun, Y., Han, H., et al.: ‘A fully decentralized control of grid-connected cascaded inverters’, IEEE Trans. Power Deliv., 2017, 53, (2), pp.1538–1551

[7] Hou, X., Sun, Y., Yuan, W., et al.: ‘Conventional P-ω/Q-V droop control inhighly resistive line of low-voltage converter-based AC microgrid’, Energies,2016, 9, (11), pp. 1–19

[8] Shanxu, D., Yu, M., Jian, X., et al.: ‘Parallel operation control technique ofvoltage source inverters in UPS’. Proc. IEEE Int. Conf., Hong Kong, 1999,pp. 883–887

[9] Abdelaziz, M.M.A., Shaaban, M.F., Farag, H.E., et al.: ‘A multistagecentralized control scheme for islanded microgrids with PEV’, IEEE Trans.Sustain. Energy, 2014, 5, (3), pp. 927–937

[10] Brandao, D.I., Caldognetto, T., Marafão, F.P., et al.: ‘Centralized control ofdistributed single-phase inverters arbitrarily connected to three-phase four-wire microgrids’, IEEE Trans. Smart Grid, 2017, 8, (1), pp. 437–446

[11] Chen, J.F., Chu, C.L.: ‘Combination voltage-controlled and current controlledPWM inverters for UPS parallel operation’, IEEE Trans. Power Electron.,1995, 10, (5), pp. 547–558

[12] Caldognetto, T., Tenti, P.: ‘Microgrids operation based on master-slavecooperative control’, IEEE J. Emerg. Sel. Top. Power Electron., 2014, 2, (4),pp. 1081–1088

[13] Buticchi, G., Carne, G.D., Barater, D., et al.: ‘Analysis of the frequency-basedcontrol of a master/slave micro-grid’, IET Renew. Power Gener., 2016, 10,(10), pp. 1570–1576

[14] Xin, H., Zhang, L., Wang, Z., et al.: ‘Control of island AC microgrids using afully distributed approach’, IEEE Trans. Smart Grid, 2015, 6, (2), pp. 943–945

[15] Mahmud, M.A., Hossain, M.J., Pota, H.R., et al.: ‘Robust nonlineardistributed controller design for active and reactive power sharing in islandedmicrogrids’, IEEE Trans. Energy Convers., 2014, 29, (4), pp. 893–903

[16] Shafiee, Q., Guerrero, J.M., Juan, V.C., et al.: ‘Distributed secondary controlfor islanded microgrids – a novel approach’, IEEE Trans. Power Electron.,2014, 29, (2), pp. 1018–1031

[17] Kim, Y., Kim, E., Moon, S., et al.: ‘Distributed generation control method foractive power sharing and self-frequency recovery in an islanded microgrid’,IEEE Trans. Power Syst., 2017, 32, (1), pp. 544–551

[18] Han, H., Li, L., Wang, L., et al.: ‘A novel decentralized economic operation inislanded AC microgrid’, Energies, 2017, 10, (6), pp. 1–18

[19] Zhong, Q.: ‘Robust droop controller for accurate proportional load sharingamong inverters operated in parallel’, IEEE Trans. Ind. Electron., 2013, 60,(4), pp. 1281–1290

[20] Guerrero, J.M., De Vicuna, L.G., Matas, J., et al.: ‘Output impedance designof parallel-connected UPS inverters with wireless load-sharing control’, IEEETrans. Ind. Electron., 2005, 52, (4), pp. 1126–1135

[21] Liu, Z., Su, M., Sun, Y., et al.: ‘Optimal criterion and global/sub-optimalcontrol schemes of decentralized economical dispatch for AC microgrid’, Int.J. Electr. Power Energy Syst., 2019, 104, pp. 38–42. Available at https://doi.org/10.1016/j.ijepes.2018.06.045

[22] Majumder, R., Chaudhuri, B., Ghosh, A., et al.: ‘Improvement of stability andload sharing in an autonomous microgrid using supplementary droop controlloop’, IEEE Trans. Power Syst., 2010, 25, (2), pp. 796–808

[23] Majumder, R., Ledwich, G., Ghosh, A., et al.: ‘Droop control of converterinterfaced microsources in rural distributed generation’, IEEE Trans. PowerDeliv., 2010, 25, (4), pp. 2768–2778

[24] Yu, Y., Konstantinou, G., Hredzak, B., et al.: ‘Power balance of cascaded H-bridge multilevel converters for large-scale photovoltaic integration’, IEEETrans. Power Electron., 2016, 31, (1), pp. 292–303

[25] Zhang, L., Sun, K., Xing, Y., et al.: ‘A modular grid-tied connectedphotovoltaic generation system based on dc bus’, IEEE Trans. PowerElectron., 2011, 26, (2), pp. 523–531

[26] Xiao, B., Hang, L., Wei, J., et al.: ‘Modular cascaded H-bridge multilevel PVinverter with distributed MPPT for grid-connected applications’, IEEE Trans.Ind. Appl., 2015, 51, (2), pp. 1722–1731

[27] Malinowski, M., Gopakumar, K., Rodriguez, J., et al.: ‘A survey on cascadedmultilevel inverters’, IEEE Trans. Ind. Electron., 2010, 57, (7), pp. 2197–2206

[28] Chatzinikolaou, E., Rogers, D.J.: ‘A comparison of grid-connected batteryenergy storage system designs’, IEEE Trans. Power Electron., 2017, 32, (9),pp. 6913–6923

[29] He, J., Li, Y.W., Wang, C., et al.: ‘A hybrid microgrid with parallel and seriesconnected micro-converters’, IEEE Trans. Power Electron., 2017, 33, (6), pp.4817–4831

[30] He, J., Li, Y., Liang, B., et al.: ‘Inverse power factor droop control fordecentralized power sharing in series-connected micro-converters basedislanding microgrids’, IEEE Trans. Ind. Electron., 2017, 64, (9), pp. 7444–7454

[31] Li, L., Sun, Y., Liu, Y., et al.: ‘Power factor consistency control fordecentralized power sharing in islanded AC microgrids with cascadedinverters’. IECON 2017 – Conf. of the IEEE Industrial Electronics Society,Beijing, China, 29 October–1 November 2017, pp. 1435–1440

[32] Wu, X., Shen, C.: ‘Distributed optimal control for stability enhancement ofmicrogrids with multiple distributed generators’, IEEE Trans. Power Syst.,2017, 32, (5), pp. 4045–4059

[33] Mohamed, Y.A.-R.I., El-Saadanym, E.F.: ‘Adaptive decentralized droopcontroller to preserve power sharing stability of paralleled inverters indistributed generation microgrids’, IEEE Trans. Power Electron., 2008, 23,(6), pp. 2806–2816

[34] Guo, X.Q., Lu, Z.G., Wang, B.C., et al.: ‘Dynamic phasors-based modelingand stability analysis of droop-controlled inverters for microgridapplications’, IEEE Trans. Smart Grid, 2014, 5, (6), pp. 2980–2987

[35] Chandorkar, M.C.: ‘Distributed uninterruptible power supply systems’. Ph.D.dissertation, Univ. Wisconsin-Madison, Madison, WI, 1995

[36] Reza, O.S., Richard, M.M.: ‘Consensus problems in networks of agents withswitching topology and time-delays’, IEEE Trans. Autom.Control, 2004, 49,(9), pp. 1520–1533

[37] Simpson-Porco, J.W., Dörfler, F., Bullo, F.: ‘Synchronization and powersharing for droop-controlled inverters in islanded microgrids’, Automatica,2013, 49, (9), pp. 2603–2611

[38] Nutkani, I.U., Loh, P.C., Wang, P.: ‘Linear decentralized power sharingschemes for economic operation of AC microgrids’, IEEE Trans. Ind.Electron., 2016, 63, (1), pp. 225–234

[39] Xin, H., Zhao, R., Zhang, L., et al.: ‘A decentralized hierarchical controlstructure and self-optimizing control strategy for F-P type DGs in islandedmicrogrids’, IEEE Trans. Smart Grid, 2016, 7, (1), pp. 3–5

8 IET Gener. Transm. Distrib.© The Institution of Engineering and Technology 2018