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Electrical Power and Energy Systems

journal homepage: www.elsevier.com/locate/ijepes

A novel quasi-master-slave control frame for PV-storage independentmicrogrid

Jian Yanga, Wenbin Yuana, Yao Suna,⁎, Hua Hana, Xiaochao Houa, Josep M. Guerrerob, Fellow,IEEEa Central South University, School of Information Science and Engineering, Changsha, ChinabAalborg University, Department of Energy Technology, Denmark

A R T I C L E I N F O

Keywords:PV-storage independent systemQuasi-master–slave control frameCCVSMPPT-based power droop control

A B S T R A C T

In microgrid, photovoltaic (PV) and storage are always combined as a droop-controlled ideal source, which is notvery practical. Alternatively, this paper introduces a PV-storage independent system via allocating the PV-sto-rage separately. For this structure, a novel quasi-master-slave control frame is proposed without communication.Storages work as master voltage sources, and PVs operate as current controlled voltage sources (CCVS). For theslave PVs, a MPPT-based power droop control and an adaptive reactive power control are proposed. Thus, PVscan simultaneously achieve maximum energy utilization in real-time and the voltage/frequency regulation.Compared with the conventional master-slave frame, this quasi-master-slave frame is more applicable for al-lowing a high PV penetration and for unifying islanded and grid-connected modes. Furthermore, the small signalstability of entire system is analyzed to design the physical and control parameters, such as, the minimumcapacitance value of DC side, droop coefficients. Finally, simulation and experimental results are presented toverify the system effectiveness.

1. Introduction

Renewable energy sources are drawing considerable attention be-cause of the cleanness, environmental protection and sustainability.Among the renewable sources, photovoltaic (PV) has emerged to be oneof the major distributed generators (DGs) due to the decreased in-stallation cost in recent years [1,2]. To integrate PV sources, the con-cept of PV-storage microgrid has been widely researched [3–5], andstorage is a supplementary component for the power supply-demandbalance. In islanded PV-storage microgrid, the coordination controlbetween PVs and storages and the system voltage/frequency stabilityare two major tasks. Hence, this paper would focus on the control frameof PV-storage system.

In PV-storage based microgrid, there are two typical configurationsshown in Fig. 1 [6–9]: (a) PV-storage integrated system; (b) PV-storageindependent system. In the former, storage units are integrated withPVs to form a micro-source which is independent on the power char-acteristics of solar panels. Due to the power fluctuations of PV, the unitswould charge or discharge frequently, resulting in low efficiency andshort lifespan. To overcome these drawbacks, a centralized storagesystem should be disposed. As a separate unit, storage is managed ac-cording to the voltage/frequency of AC bus. Therefore, the latter is

preferable to flexibly dispatch storage and easily optimize storage al-location. For the PV-storage independent system, the two generalstructures are shown in Fig. 1(b): (b.1) DC/AC coupled architecture.(b.2) AC coupled architecture. In the DC/AC coupled architecture, PVsand storages are connected to the DC bus. The AC bus is connected withthe DC bus via a DC/AC inverter. The benefit of this architecture is thatit can fed DC loads through the DC bus directly, which avoids the extrapower losses [8–10]. Since there is only one inverter, the system iseasier to be controlled. Meanwhile, the inverter must be highly reliablebecause almost all the power needed by ac loads flows through it [11].This architecture is more suitable for the local energy managementwhich has lots of DC loads, such as loads of the households. In the ACcoupled architecture, the loads are connected directly to the AC bus. Itwould cause the power loss and extra cost with a high proportion of DCload [11]. However, the system has a high flexibility to be controlledand optimized and it is easier to be modularized. It is convenient forutilizing the remote DGs. The investigation in this paper is focused onthe AC coupled architecture.

For the PV-storage integrated microgrid, peer-to-peer control frameis often applied to feature the plug-and-play capacity. As a typicalcontrol scheme, various droop control methods have been widelyadopted [12–16]. In [12], the basic concepts of frequency droop, angle

https://doi.org/10.1016/j.ijepes.2017.11.008Received 13 June 2017; Received in revised form 2 October 2017; Accepted 7 November 2017

⁎ Corresponding author.E-mail address: yaosuncsu@gmail.com (Y. Sun).

Electrical Power and Energy Systems 97 (2018) 262–274

0142-0615/ © 2017 Elsevier Ltd. All rights reserved.

T

droop and virtual impedance control are revealed. In [13], an adaptivedroop control is investigated for PV-storage hybrid units. The batterymay provide extra power when the available power of the integrated PVis insufficient. In [14], a V-I droop mechanism is utilized in the primarycontroller to share load power among DGs. These peer-to-peer strate-gies [12–16] do not require communication, which reduce the systemcost and improve the reliability. However, this peer-to-peer frame isonly applicable for the ideal sources [17,18]. It needs considerablestorages to fill the fluctuation of renewable energy generation, which isexpensive and impractical.

For the PV-storage independent system, the master-slave frame hasbeen a common control structure [19–23]. In [19], an auto-master-slave control technique is presented to ensure a fast dynamic responseand precise load power sharing. In [20], a utility interface (UI) installedat the PCC is controlled as the master source. The UI works in grid-supporting mode under grid-connected operation and grid-formingmode under islanded operation. To eliminate the limitation of physicalconnection among DGs, a master-slave control with analog wirelesscommunication is demonstrate in [21]. This master-slave frame in[19–23] enables PVs as slave current sources to inject maximum energyto Microgrid. Storages operate as master voltage sources to supportsystem voltage and frequency. However, there are some limitations: (a)Real-time communication reduces system reliability and increases cost;(b) It needs a considerable master source to avoid a single point offailure [24]; (c) High-output voltage/frequency overshoot may occurduring transients since only master sources support the system voltage.In a word, the existing master-slave frame is operational for the mi-crogrid with a low PV penetration. With the penetration level in-creasing, PVs should participate in the system voltage/frequency reg-ulation [25]. These challenges would be addressed in this paper.

There are some references about the voltage-controlled PV inverter.

Ref. [26] proposes a voltage-source control strategy based on droopcontrol concept for PV inverter. This controller can maintain the dc busstability even during load transient and automatically reduce genera-tion of PVs with low load demand. This controller is only applicable tosingle-stage inverter. Focusing on the specific characteristic of PV, theVdc/Vg-droop and P/Vg-droop are combined to obtain the proper powersharing in [27]. But each inverter requires a multistage controller toimplement this control strategy, which may reduce the system effi-ciency. In [28], a universal controller is proposed to combine themaximum power point tracking (MPPT), droop control and dc sidevoltage regulation. However, the range of load variation is limited bythe capacity of the storage in microgrid. In a word, each of [26–28] justproposes a single modified droop control for voltage-controlled PV in-verter, while they do not give a comprehensive point from a level of thesystem operation mode.

Considering the characteristics of PVs and storages, a novel controlframe should be developed, which can ensure the MPPT of PVs andefficient operation of storages. In this paper, a novel quasi-master-slavecontrol frame is proposed by combining features of peer-to-peer andmaster-slave frame. As shown in Fig. 2, the control frame is a com-promised choice, whose features are given as follows:

● Non-communication. This control frame allows DGs to regulate thevoltage and frequency without communication, so physical con-nection constraint and high cost are avoided. In addition, a highreliability and plug-and-play capability of the system are obtained.

● Multiple master and multiple CCVS-based slave sources. All of the dis-patchable energy sources are controlled as master sources to avoidthe single point of failure. The PV sources function as current con-trolled voltage sources (CCVS) to participate in the voltage/fre-quency regulation, especially for a high PV penetration.

Distributed Storage#1

PV-Storage Hybrid Ideal Unit#1

AC BUS

PV-Storage Hybrid Ideal Unit#N

(a) PV-storage integrated system

DC

DC

DC

DC

DC

AC

AC Load

DC Load

AC

DC

DC

AC

(b.1) DC/AC coupled architecture

DC Load

AC Load

Centralized Storage Unit

PV Unit#1

ESS

PV Unit#N

...

DC

DC

DC

DC

AC BUS

AC Load

DC Load

DC

AC

DC

AC

AC

DC

Centralized Storage Unit

PV Unit#1

ESS

PV Unit#N

...

DC

DC

DC

DC

DC BUS AC BUS

(b) PV-storage independent system(b.2) AC coupled architecture

Fig. 1. Architectures of PV-storage system.

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

263

● Considering source characteristic. The fluctuation of PVs is fully takeninto account. For PVs under CCVS mode, the power injected into thesystem is depended on the front-end MPPT algorithm. Thus, themaximum energy utilization is achieved at all times.

● Unified control structure for islanded and grid-connected modes. Sinceall the DGs behave as voltage sources, a unified controller can beadopted to ensure DGs working in both two modes without a controlmethods transforming.

It is noted that this quasi-master-slave control frame is very ap-propriate to the microgrid with dispatchable and non-dispatchablesources. In this frame, the dispatchable sources are controlled as mastervoltage sources to balance the supply-demand power. The non-dis-patchable sources behave as CCVS to inject the maximum power andprovide the auxiliary voltage/frequency regulation.

In order to test feasibility, a MPPT-based power droop controlscheme is introduced. In addition, an adaptive reactive power controlstrategy is proposed according to the stress for active power supplyingon the inverters. When microgrid works at the proposed quasi-master-slave control frame, PVs can achieve MPPT and voltage/frequencyregulation simultaneously without control scheme transforming.

2. Conventional control frames

2.1. Peer-to-peer control frame

In peer-to-peer control frame, each DG supports the system voltage/frequency regulation and shares the load demand. This frame has theplug-and-play capacity and the high system redundancy [12–15]. As atypical peer-to-peer control, the conventional droop control is com-monly used for the microgrid without any communication [29].

= − = −∗ω ω mP m ω ω P, ( )/ ratingmax min (1)

= − = −∗V V nQ n V V Q, ( )/ ratingmax min (2)

where ω, V are the angular frequency and voltage amplitude of an in-verter; P, Q, Prating, Qrating are output active/reactive power and ratedactive/reactive power; ω∗ and V∗ represent values of ω and V at no load;

m and n are droop coefficients of P-ω and Q-V, respectively. ωmax andωmin are maximum and minimum values of the allowable angular fre-quency; Vmax and Vmin are maximum and minimum values of the al-lowable voltage amplitude, respectively.

For a system with two DGs, since ω1=ω2 in steady state [24], Eq.(3) is obtained from (1)

≈ ≈P P m m P P/ / /rating rating1 2 2 1 1 2 (3)

Eq. (3) reveals that the conventional droop scheme ensures theproportional output power sharing based on the DG’s rating. However,since the droop coefficients are constants, it is not sensible to the powerfluctuation of PVs caused by irradiance level and temperature.

To explain the potential drawback of the conventional droop, a casefor the actual situation of two PVs is analyzed in different irradiancelevels. The active power droop curves of two PVs are shown in Fig. 3. Inthis case, assume that the available power of PV#1 is decreased from P1to ′P1 and the available power of PV#2 is not changed. When the irra-diance level of PV#1 is lower, the operation frequency increases toreduce the output power of PV#1. Because the PV#2 has to work at thesame frequency with PV#1, the output power of PV#2 is forced toreduce from P2 to ′P2. As a result, more energy would be supplied bystorage to balance the supply-demand power. That is to say, the con-ventional droop scheme is not an efficient operating frame, whichcannot ensure the maximum utilization of each PV with availablepower varying.

2.2. Master-slave control frame

In the master-slave control frame, there is one considerable DGacting as a master voltage source to support the system voltage. Theothers function as slave current sources to follow the active/reactivepower reference which is provided by the master source throughcommunication lines [24]. For the PV-storage based microgrid, storageserves as a V/f-controlled voltage source and PVs work as P/Q-con-trolled current sources normally [30]. Simplified control block of P/Qcontrol is shown in Fig. 4(b). For the single-phase system, the currentamplitude reference I and phase angle reference δ of a current-con-trolled inverter are given by

=+

IP Q

Vref ref

p

2 2

(4)

= −δ δQP

arctanpref

ref (5)

where Pref and Qref are the active and reactive power given by the front-end MPPT controller, respectively. Vp and δp are the voltage amplitudeand phase angle of the PCC obtained from a phase-locked loop (PLL). P/Q control enables each PV to output its maximum available power atthe price of abandoning the voltage/frequency support ability. There-fore, in the islanded mode, there should be at least one DG beingcontrolled as a master VSI to regulate voltage and frequency at the PCC.

In summary, master-slave control frame is very applicable for en-ergy management and generation maximum utilization. However, the

Master-Slave Control Frame

V/f + P/Q Control

Control Frame of PV-Storage System

VCVS CCCS...

Master DG Slave DGnSlave DG1

AC Bus

Peer-to-Peer Control Frame

Droop Control

CCCS

VCVS CCVS...

Master DG1 Slave DGnSlave DG1

AC Bus

CCVS

MPPT-Based Droop Control

Quasi-Master-Slave Control Frame

VCVS VCVS...

DG1

AC Bus

VCVS

DG2 DGn

VCVS

Master DGm

...

Communication Line

Fig. 2. A novel control frame combining with conventional droop control and master-slave control.

P0

Droop curve before shifting Droop curve after shifting

1b 2b2a

1c

*

2act

1act

1P 1P 2P 2P

1a

Fig. 3. P-ω curve of conventional droop and MPPT-based power droop control.

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

264

system is not redundant and has a high cost in communication links.Moreover, the existence of PLL has a serious effect on the dynamicstability of system [31].

3. Quasi-master-slave control frame

For the PV-storage independent microgrid in Fig. 1(b.1), a novelquasi-master-slave control frame is proposed by combining the peer-to-peer and master-slave control frame. Compared with the peer-to-peerframe, this frame takes the power fluctuation of PVs into account sothat the MPPT can be ensured. Compared with the master-slave frame,the slave sources serve as CCVS to participate in the voltage/frequencyregulation, and the communication links and PLLs are removed. Thus,the higher reliability, less cost and better dynamic response of systemare ensured.

To implement the proposed control frame, a MPPT-based powerdroop control and an adaptive reactive power control are proposed,whose principle is shown in Fig. 3. In the same case as described inSection 2.1, when the available output power of PV#1 reduces, thedroop curve of PV#1 is shifted down until the operating point c1. Due tothe same frequency in steady-state, the output power of PV#2 ismaintained at the available power. The power balance between gen-eration and demand is matched by storage. Similarly, when it is pos-sible to extract more power from PV#1, the controller should push thedroop curve upward to increase the output power. The key is to definethe shift angler frequency automatically.

In this paper, an adaptive droop is adopted to shift the droop curvevia holding the DC side capacitor voltage udci equal to udci

ref , which is aconstant value higher than the peak AC voltage to avoid over-mod-ulation. The MPPT-based power droop control is introduced as

= − − + ⎛⎝

+ ⎞⎠

−∗ω ω m P P K Ks

u u( ) ( )i i i i a PiIi

dci dciref

First termSecond term

(6)

⩽ ⩽ −m ω ωP

0 ii

max minmax (7)

where Pi_a is the available active power of the i-th PV given by the

feedforward controller. KPi and KIi are the proportional and integralcoefficients of the PI controller of the i-th PV, respectively. Comparedwith the conventional droop, =P v ii a dci dci is added in the first term,which is obtained from the front-end MPPT controller. By consideringthe fluctuation of PVs, the dynamic response is improved. The secondterm is the PI controller for DC bus voltage regulation. The PI controllerensures the balance between the power extracted by DC/AC inverterand the one supplied by DC/DC converter. Thus, the maximum utili-zation of energy is guaranteed. The block diagram is shown in Fig. 4(c).

The amount of reactive power supplied by inverter is an importantfactor that limits the active power capability of PV. Supplying reactivepower excessively would impose extra stress on the inverter, whichcould lead to the ripple in the dc bus voltage and affect the effectivenessof the MPPT. Therefore, an adaptive reactive power control strategy isproposed.

= −∗V V n Qi i i (8)

where ni is the adaptive droop coefficient

= − = −n V VQ

Q S P,ii a

i a rate imax min 2 2

(9a)

⩽ ⩽ −n V VQ

0 ii

max minmax (9b)

where Qi_a is the available reactive power of the i-th DG. It is calculatedaccording to the rated apparent power and available active power. Thedroop coefficient ni is inversely proportional to the Qi_a. The principle ofthe proposed reactive power control strategy is shown in Fig. 5. Whenthe available active power of PV#1 reduces, the Q-V curve would shiftto the right green one. It makes PV#1 supply more reactive power, andvice versa. Specially, the PV with a low ability of active power sup-plying can provide the reactive power for the system.

To match the power balance between generation and demand, theESS is controlled by conventional active power droop and proposedadaptive reactive power droop.

PIVoltage/Current

Loops

PWM

Common Load

AC BUS

(a) Peer-to-peer Frame in PV-Storage Integrated System

VSI

PWMCommon

Load

PV#i

AC BUS

P/Q Control

PWM

PLL

AC BUS

ESS

Master VSI

PWM

PV#iESS

PWM

Common Load

Master VSI

PV-Storage Hybrid Ideal Unit#i

DC

DC

DC

DC

(b) Master-Slave Frame in PV-Storage Independent System

DC

DCDC

DC

CC-VSIDC

DC

(c) Quasi-Master-Slave Frame in PV-Storage Independent System

DC

DC

V/f Control

Slave CSI

dciu

iu iiiu ii susi

PV

Pδ

Eq. (1)Eq. (8)

PVii dciiiC

fL

fC

+

−

ii

i i iu V δ= ∠

iu ii

P P Pu V δ= ∠

lineIZ

iP

iQ

im

refdciu

dciu

Pu

*ω

*V

−+

+

−+refiV

refiδ ref

iω

+ −

1s Average Power

Calculationref ref refi i iu V δ= ∠

lineSZ

Susi

fC

fL

Conventional Droop Control

+−_i aP

in

Fig. 4. Block diagram of three control frames. (a) Peer-to-peer frame, (b) master-slave frame, (c) quasi-master-slave frame.

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

265

4. Stability analysis

In this section, small signal stability is carried out to perform thesystem stability and sensibility analysis of control parameters. Theequivalent circuit of the microgrid is shown in Fig. 6, which consists ofm PV units and n-m separate storage units.

4.1. Small signal modeling

4.1.1. Network modelingThe power generation of the i-th DG is presented as

⎧⎨⎩

= − −= − − −

p G V V V δ B V V δq B V V V δ G V V δ

( cos ) sin( cos ) sin

i i i i P iP i i P iP

i i i i P iP i i P iP (10)

where δiP= δi-δP, Gi and Bi are the conductance and susceptance of lineadmittance, respectively. According to kirchhoff laws, the voltage ofPCC is obtained

∑= ′=

V e Y V ePjδ

i

n

i ijδ

1

P i

(11)

where

∑′ =

+= ′

=

′Y Y

Y YY e| |i

i

Lj

n

j

ijφ

1

i

(12)

Define = − = −∼δ δ δ ω ω i i s i s, where ωs is the frequency of steady state.Then, combining (10)–(12) yields

∑ ∑= − ′ − − ′ − ′ − − ′

= ⋯ ⋯

∼ ∼ ∼ ∼

∼ ∼ ∼= =

p G V G V V Y δ δ φ B V V Y δ δ φ

F V V V δ δ δ

| |cos( ) | |sin( )

( , , , , , , , )

i i i i ij

n

j j i j j i ij

n

j j i j j

n n

2

1 1

1 2 1 2 (13)

∑ ∑= − + ′ − − ′ − ′ − − ′

= ⋯ ⋯

∼ ∼ ∼ ∼

∼ ∼ ∼= =

q B V B V V Y δ δ φ G V V Y δ δ φ

G V V V δ δ δ

| |cos( ) | |sin( )

( , , , , , , , )

i i i i ij

n

j j i j j i ij

n

j j i j j

n n

2

1 1

1 2 1 2 (14)

Substituting (8) into (13), (14) and linearizing them around steadystate operating point yield

∑ ∑= − + ∼

= =

∼p n k Q k δΔ Δ Δij

n

j p V jj

n

p δ j1 1

i j i j(15)

∑ ∑= − + ∼

= =

∼q n k Q k δΔ Δ Δij

n

j q V jj

n

q δ j1 1

i j i j(16)

where

⎧

⎨⎪

⎩⎪

= =

= == ⋯ = ⋯

∂∂

∂

∂

∂∂

∂

∂

∼ ∼

∼ ∼

k k

k ki n j n

;

;( 1, , ; 1, , )

p VpV p δ

p

δ

q VqV q δ

q

δ

i jij i j

i

j

i jij i j

i

j (17)

Rewrite (15), (16) in matrix form as

= + ∼∼p K Q K δΔ Δ ΔpQ pδ (18)

= + ∼∼q K Q K δΔ Δ ΔqQ qδ (19)

where the variable vectors ( p q QΔ ,Δ ,Δ and∼δΔ ) and the parameter

matrices ( ∼ ∼K K K K, , ,pQ pδ qQ qδ ) are shown in the Appendix.

4.1.2. PV units modelingThe PV units with MPPT-based power droop control scheme are

modeled as

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

= −

= − += − +

= − + + −

= − = −

= ⋯

∼

u i p u

P ω P pQ ω Q q

ω m P K u K u u

δ δ δ ω ω

k m

( / )

( ) ( )

( )

( 1, , )

dck C PVk k dck

k c k k

k c k k

k k k Pk dck Ik dck dckref

k k s k s

1k

(20)

where Ck is the capacitance value of DC bus in Fig. 4(c), Pk and Qk areactive and reactive power of the k-th PV by a low-pass filter with cutofffrequency ωc.

Combining (18)–(20), the small signal models of PV units arewritten as

0

Droop curve before shifting Droop curve after shifting

V*V

PCCE

1Q 2Q1Q Q

1d

2d

1e

Fig. 5. Q-V curve of conventional droop and adaptive reactive power control.

AC BUS1 1 1u V

1 1,p q 1 1 1Y G jB

1R 1L

P P Pu VLY

DG#1

DG#m

m m mu V

,m mp q =m m mY G jB

. . . DG#m+1

mR mL

1mR1mL

1 1 1=m m mY G jB 1 1,m mp q

1 1 1m m mu V

DG#n

nRnL

=n n nY G jB ,n np q

n n nu V

. . .

Fig. 6. Equivalent circuit of the microgrid with n DGs.

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

266

⎧

⎨

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

= − −

= − + +

= − +

= + +− +

− +

=

∼

∼

∼

∼

∼

×

∼

∼

∼

∼

Δu K u K K Q K K δ

P ω P ω K Q ω K δ

Q ω K I Q ω K δ

ω K K K u ω m PK K ω m K Q

K K ω m K δ

δ ω

Δ Δ Δ

Δ Δ Δ Δ

Δ ( )Δ Δ

Δ ( )Δ Δ( ) Δ

( ) Δ

Δ Δ

dc dc pQPV

pδPV

PVc

PVc pQ

PVc pδ

PV

PVc qQ

PVm n c qδ

PV

PVP I dc c

PV PV

P cPV

pQPV

P cPV

qδPV

PVPV

1 2 2

1

2

2

(21)

where

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

= …= …= …

= =

= ==

{ } { }

Δu u u uP P P Pω ω ω ω

K diag K diag

K diag K K diag Km diag m

[Δ Δ Δ ]Δ [Δ Δ Δ ]Δ [Δ Δ Δ ]

;

{ }; { }{ }

dc dc dc dcmT

PVm

T

PVm

T

pC U C U

P Pk I IkPV

k

1 2

1 2

1 2

1 21k

k dck k dck02

(22)

where Udck and pk_0 are the stable state value of udci and pi respectively.

4.1.3. Storage units modelingCompared with the output power variation of PVs, the storage's

state of charge (SoC) varies in a larger time scale. Therefore, we assumethat the SoC of storage is not changed in our stability analysis. Thestorage units with conventional P-ω droop control and adaptive reactivepower control strategy are modeled as

⎧

⎨⎪

⎩⎪

= − += − +

= − = −

= + ⋯∼

P ω P pQ ω Q q

δ δ δ ω ω

h m n

( ) ( )

( 1, , )h c h h

h c h h

h h S h S (23)

where Ph and Qh are active and reactive power of the h-th storage.Linearizing (23) around the state of equilibrium and combining (18),(19), the small signal model of the storage unit is given by

⎧

⎨

⎪

⎩⎪

= − + +

= − +

= −

∼

∼

∼− ×

∼

∼

ΔP ω P ω K Q ω K δ

Q ω K I Q ω K δ

δ m P

Δ Δ Δ

Δ ( )Δ Δ

Δ Δ

Sc

Sc pQ

Sc pδ

S

Sc qQ

Sn m n c qδ

S

SS S

( )

(24)

where

⎧⎨⎩

= …=

+ +ΔP P P Pm diag m

[Δ Δ Δ ]{ }

Sm m n

T

Sh

1 2

(25)

4.1.4. Entire system modelingCombining the small signal models of PV part and storage part, the

small signal dynamic model of the entire system is constructed as fol-lows

=x A xΔ Δ (26)

where the state variable vector Δx and the system matrix A are shownin the Appendix.

4.2. Eigenvalue analysis

The eigenvalues of matrix A can be used to study the stability of thesystem around the operating point. According to the simulation de-scribed in Section V, the dominant poles of system (26) are analyzedwhile varying the capacitance Ci, control parameters mi, ni, KPi and KIi.The matrix A has one zero eigenvalue and twelve nonzero eigenvalues.The one zero eigenvalue is corresponding to rotational symmetry andonly the nonzero eigenvalues are valid for the system dynamic stability[32,33].

When the capacitance Ci changes from 2000 μF to 105 μF, the rootlocus of eigenvalues are shown in Fig. 7. When Ci is small, λ1∼λ4 lie onthe right half-plane, which means that system is unstable. These poleslie on the left of the imaginary axis when Ci increases to 3500 μF andmove away from it with further increasing Ci. Meanwhile, λ5∼λ8 be-come dominate poles while Ci increasing, and they always stay at theleft half-plane. In this case, the system is stable during Ci ∊ (3500 μF,+∞).

The droop coefficients mi and ni have a significant influence on thesystem stability. According to the requirement of steady state in (7) and(9), the range of mi and ni are (0, 4× 10−3) and (0, 6× 10−3), re-spectively. The root locus are shown in Figs. 8 and 9. In Fig. 8, λ1∼λ4move to the left of imaginary axis when mi increases to 2.8×10−4.With increasing mi, λ1∼λ4 move away from the imaginary axis keepingsystem stable. Meanwhile, λ5∼λ8 move close to the imaginary axisdecreasing the damping ratio of system. When mi is chosen in the rangeof (5× 10−5, 4× 10−3), the system is stable. Fig. 9 shows that ni haslittle influence on the system dynamic performance and the system keepstable during ni ∊ (0, 6× 10−3).

PI control coefficients of (6) should be designed properly to ensurethe system stable. The root locus with KPi and KIi varying are shown inFigs. 10 and 11. When KPi is small, the dominated poles λ5∼λ8 stay atthe right half-plane. As KPi increases, λ5∼λ8 move to the left half-planand λ1∼λ2 become the dominated poles. When KPi increases to 3.5, λ1and λ2 move to the unstable region. Moreover, Fig. 11 shows that in-creasing KIi attracts the conjugate polesλ1 and λ2 to the imaginary axis,which would make the system instable. The stable regions of KPi and KIi

are KPi ∊ (0.05, 3.5) and KIi ∊ (0, 18), respectively.When the ratio of line impedance r1= X1/R1 changes from 0.01 to

-120 -100 -80 -60 -40 -20 0 20-400

-300

-200

-100

0

100

200

300

400

Real Part

-10 -8 -6 -4 -2 0-6-4-20246

1

2

3

4

8

9

10 13

Ci=3500 F

Ci=2100 F

Ci=2100 F

Ci=3500 F

Ci increases

Imag

inar

y Pa

rt

Fig. 7. Eigenvalues of (26) for different capacitance Ci.

-120 -100 -80 -60 -40 -20 0 20

-300

-200

-100

0

100

300

Imag

inar

y Pa

rt

Real Part

10 13

1

2

3

4mi increases

200

-12 -6 -4 0

0-5

-10

510

5

69

8

7 mi=5×10-5

mi=2.7×10-5

mi=2.7×10-5

mi=5×10-5

Fig. 8. Eigenvalues of (26) for different droop coefficient mi.

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10, the root locus are shown in Fig. 12. When r1 increases to 0.08, allthe poles lie on the left of the imaginary axis and move away from itwith further increasing r1. It shows that the system is stable duringr1 ∊ (0.08, +∞), which means the adaptive droop control is robust.

5. Simulation results

To investigate the validity of the proposed quasi-master-slave con-trol frame, a single-phase AC microgrid with two PVs and one storage isbuilt. The simulation parameters are listed in Table 1 [34]. The normalvoltage reference is 50 Hz/311 V. The DC bus voltage is controlled at

350 V to avoid over-modulation.

5.1. Case I: Simulation with PV power fluctuation

In this case, a random disturbance is imposed on PV output currentiPVi to simulate the power fluctuation of PV. Fig. 13 shows the outputactive/reactive power and load demand, random PV output current, theDC bus voltage and the frequency of three DGs. FromFig. 13(a), (c) and (d), two PVs output their available power all the timeand the storage unit supplies power when load demand exceeds thetotal available power of PVs. The reactive power results are shown inFig. 13(b). The reactive power of PV is decreased/increased when theactive power is increased/decreased so that the burden of power supplyamong DGs are shared. The remaining reactive power is supplied by thestorage unit. Fig. 13(d) shows that DC bus voltages of two PVs aremostly kept at 350 V even with available power varying, which in-dicates the maximum utilization of renewable energy is alwaysachieved. Fig. 13(e) reveals the system frequency is approximated to50 Hz under the fluctuation of PVs.

5.2. Case II: Simulation with load change

To study the dynamic performance of the system, the load powerchanges at 0.6 s and recovers at 1.2 s. The available power of PVs are setas P1_a = 1.5 kW and P2_a= 1 kW. The results shown in Fig. 14 revealthat the system has a fast response for the load change. From Fig. 14(a),

-100 -80 -60 -40 -20 0-250-200

-150

-100

-50

0

50

100

150

200

250Im

agin

ary

Part

Real Part

10 13

1

3

4

5678

ni increases

2

9

Fig. 9. Eigenvalues of (26) for different droop coefficient ni.

-500-400

-300

-200

-100

0

100

200

300

400

500

-120 -100 -80 -60 -40 -20 0 20

1

2

3

4

KPi=3.5

KPi=3.5

3020100

-10-20-30

-30 -20 -10 0

KPi=0.01KPi=0.05

KPi=0.05KPi=0.01

5

69

8

7

10 13

Kpi increases

Real Part

Imag

inar

y Pa

rt

Fig. 10. Eigenvalues of (26) for different proportional parameter KPi.

-120 -100 -80 -60 -40 -20 0 20-250-200

-150

-100

-50

0

50

100

150

200

250

Imag

inar

y Pa

rt

Real Part

10 13

1

2

3

4

5

6

7

8

-3 -2 -1 0-4-2024

9

5

KIi increases

KIi=18

KIi=18

Fig. 11. Eigenvalues of (26) for different integral parameter KIi.

-100 -80 -60 -40 -20 0

-100

-50

0

50

Imag

inar

y Pa

rt

Real Part

10 ~ 13

1

2

3

4

r1 increases

100

9

5

68

7 r1=0.08

r1 0.08

2

-2

-2 -1 0 1 2-3

0

Fig. 12. Eigenvalues of (26) for different line impedance ratio r1.

Table 1System parameters.

Item Symbol Quantity Unit

Capacitance C1= C2 8000 μFLine impedance (PV#1

Side)Z1 0.1+ j0.63 Ω

Line impedance (PV#2Side)

Z2 0.15+ j0.63 Ω

Line impedance (ESS Side) Z3 0.15+ j0.94 ΩLoad impedance ZL 12.5+ j9.7→

8.5+ j9.7Ω

Peak load demand PL_max 4.5 kWMaximum output power

of PVsP1_max = P2_max 2.5 kW

Storage system capacity CS 12.5 kW hStorage peak-power

capabilityPS_max 2.5 kW

Droop coefficients m1=m2=m3 1× 10−4 rad/(W s)n1= n2= n3 1× 10−5 V/Var

PI control coefficients KP1=KP2 0.5 rad/(V s)KI1 =KI2 2.1 rad/(V s2)

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

268

the output active power of two PVs are remained to the availablepower. When the load power is changed, the supply-demand powerbalance is maintained by storage unit. Fig. 14(a) and (c) show that theMPPT of PVs are achieved within 0.2 s when the load is changed.Fig. 14(d) shows the system has a fast response with the load changedue to an auxiliary service for frequency regulation of PVs.

5.3. Case III: Simulation with line impedance ratio change

To verify the system stability with the line impedance ratio change,

the ratio of line impedance r1 is changed from 2 to 1 at 1 s and to 1/2 at2 s. The available power of PVs are still set as P1_a= 1.5 kW andP2_a= 1kW. The results in Fig. 15 shows that the system remains stablewhen the ratio of line impedance changes in a certain region. FromFig. 15, though the system needs longer time to go to steady state whenthe line impedance ratio is equal to 2, the microgrid remains stable withline impedance ratio variations within a large region.

6. Experimental results

A laboratory microgrid prototype is built as shown in Fig. 16. Themicrogrid consists of two micro-sources based on the single-phase in-verters. One is supplied by photovoltaic simulator to simulate the PVsource and the other is supplied by storage. The main circuit of thesetup is shown in Fig. 17, which includes the experiment parameters ofoutput filter, line, and load. The sample frequency is 12.8 kHz. Thereferent voltage frequency ∗f and amplitude ∗V are 50 Hz and 48 V,respectively. The DC bus voltage is controlled at 60 V to avoid over-modulation.

0 0.5 1 1.5 2 2.5 3

-0.50

2.5A

ctiv

e Po

wer

(kW

)

(a)

21.51

0.5

P2P3PL

P1

PV#1PV#2

Storage

0 0.5 1 1.5 2 2.5 30R

eact

ive

Pow

er (k

Var

)

(b)

2

1.5

1

0.5

Q2Q3QL

Q1PV#1PV#2

Storage

0 0.5 1 1.5 2 2.5 3

Cur

rent

(A)

(c)

7 iPV1iPV2

0123456

0 0.5 1 1.5 2 2.5 3

Vol

tage

(V)

(d)

355

350

345

udc1udc2

Time (s)

Freq

uenc

y (H

z)

(e)

50.1

50.250.3

50

49.949.849.7

0 0.5 1 1.5 2 2.5 3f2

f3f1

Fig. 13. Simulation results of case I. (a) Active power of three DGs and load, (b) reactivepower of three DGs and load, (c) PV output currents, (d) DC bus voltages, (e) frequency ofthree DGs.

0 0.4 2

0Act

ive

Pow

er (k

W)

(a)

4

3

2

1

P2P3PL

P1

0.8 1.2 1.6

Load change

PV#1

PV#2

Storage

0 0.4 2

0

(b)

2

1.5

1

0.5

0.8 1.2 1.6

Rea

ctiv

e Po

wer

(kV

ar)

Q2Q3QL

Q1

Load changeStorage

PV#1

PV#2

0 0.4 2(c) 0.8 1.2 1.6

udc1udc2

Vol

tage

(V)

355

350

345Load change

Time (s)(d)

Load change

0 0.4 20.8 1.2 1.6

Freq

uenc

y (H

z)

50.1

50.250.3

50

49.9

49.849.7 f2

f3f1

Fig. 14. Simulation results of case II. (a) Active power of three DGs and load, (b) reactivepower of three DGs and load, (c) DC bus voltages, (d) frequency of three DGs.

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

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6.1. Case I: Experiment with PV power fluctuation

To simulate the power fluctuation of PV caused by atmosphericconditions, the output current of PV simulator at maximum power pointis set as iPV=0.27A during 0–0.25 s, 0.4 A during 0.25–0.7 s, 0.47 Aduring 0.7–1 s. Fig. 18 shows the measured waveforms with the MPPT-based power droop control and the adaptive reactive power controlstrategy. The waveforms from top to down are the output voltage ofinverter#1 (u1) and inverter#2 (u2), the output current of inverter#1(i1) and inverter#2 (i2), respectively. The voltage amplitudes of in-verter#1 and inverter#2 are 45.3 V and 45.8 V, respectively. The cur-rent amplitudes of inverter#1 are 1.2 A during 0–0.25 s, 1.05 A during0.25–0.7 s, 1.25 A during 0.7–1 s. The current amplitudes of inverter#2are 1.18 A during 0–0.25 s, 1.48 A during 0.25–0.7 s, 1.61 A during0.7–1 s. Fig. 16 shows that the system is always stable despite thefluctuation of available power of PV.

The steady-state output active and reactive power of each inverterare shown in Fig. 19. At first, the active power of two inverters are 16W

and 22W, respectively. Then, the active power of inverter#1 increasesto 24W at 0.27 s and to 28W at 0.72 s due to the rise of output currentfrom PV simulator. Correspondingly, its reactive power is decreasedfrom 20 Var to 7.6 Var at 0.27 s then to 2.5 Var at 0.72 s. The rest ofrequired active and reactive power are supplied by the storage. FromFig. 19, the MPPT of PV simulator is achieved quickly and exactly withthe MPPT-based power droop control. Meanwhile, the output reactivepower of each inverter is inversely correlated with the active powersupply ability to balance the energy supply burden.

6.2. Case II: Experiment with load change

To investigate the dynamic response of the system with load change,a 25Ω resistance is switched on at 1.3 s and is shed at 2.7 s. The outputcurrent of PV simulator at maximum power point is set as iPV=0.5 A.Figs. 20 and 21 show the measured waveforms and output power, re-spectively. The voltage amplitudes of inverter#1 and inverter#2 are45.1 V and 46.2 V, respectively. The current amplitudes of inverter#1are 1.28 A during 0–1.3 s, 1.72 A during 1.3–2.7 s, 1.28 A during2.7–4 s. The current amplitudes of inverter#2 are 1.66 A during 0–1.3 s,2.15 A during 1.3–2.7 s, 1.66 A during 2.7–4 s.

From Fig. 21, the steady-state output active power of inverter#1 iskept at 30W, which means the maximum energy utilization of PV isachieved all the time. The increased power caused by load change issupplied by the inverter#2. Although there is a rush to the output activepower of inverter#1 with load change, it is recovered to 30W within0.2 s, which indicates that the system has a fast response for the loadchange.

7. Conclusions

Taking the characteristic of PVs into account, the PV-storage in-dependent system is adopted to improve system efficiency. Beyond thepeer-to-peer frame and master-slave frame, a novel quasi-master-slavecontrol frame is proposed. PVs operate as slave CCVS and Storages actas master sources. A MPPT-based power droop control and an adaptivereactive power control is proposed to implement this control frame.Compared with the peer-to-peer control, this frame enables PVs to in-ject the maximum energy to the microgrid. Compared with the master-slave control, the slave sources behave as voltage sources to provide the

0 0.5 3

Act

ive

Pow

er (k

W)

(a)

2.5

1

1 1.5 2.5

Line Impedance Ratio changePV#1

PV#2

Storage

P2P3PL

P1

2

2

1.5

0

0.5

-0.5

0(b)

2

1.5

1

0.5

Rea

ctiv

e Po

wer

(kV

ar)

Storage

PV#1

PV#2

Line Impedance Ratio change Q2

Q3QL

Q1

0 0.5 31 1.5 2.52

(c)

udc1udc2

Vol

tage

(V)

355

350

3450 0.5 31 1.5 2.52

Line Impedance Ratio change

Time (s)(d)

Freq

uenc

y (H

z)

50.1

50.250.3

50

49.9

49.849.7 f2

f3f1

Line Impedance Ratio change

0 0.5 31 1.5 2.52

Fig. 15. Simulation results of case III. (a) Active power of three DGs and load, (b) reactivepower of three DGs and load, (c) DC bus voltages, (d) frequency of three DGs.

Driver

LC Filter + Line Impedance

RL Load

Controller

Inverters

PV Simulator

Storage

Fig. 16. Prototype of parallel inverters system setup.

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auxiliary voltage/frequency regulation, which improves the systemreliability and dynamic response. No-communication feature makessystem more flexible and ensures the plug-and-play capability of DGs.According to the small signal stability of entire system, the minimumcapacitance Ci of system critical stability is given, and the feasible re-gions of control parameters (mi, ni, KPi, KIi) are provided. Finally, si-mulation and experimental results have verified that PVs can achieve

the maximum energy utilization in real-time and the satisfied dynamicperformance with load change.

Acknowledgement

This work was supported by the National Natural ScienceFoundation of China under Grants 51777217, 61573384 and61622311, and the Project of Innovation-driven Plan in Central SouthUniversity.

fL

fC60V

1mH

22 Fμ

PV Simulator

Storage

CC-VSI#1

dcuPVi 1lineZ

2lineZ

0.1 0.63j+ Ω

0.15 0.94j+ Ω

12.5 Ω

31 mH 25 ΩCC-VSI#2 fL

1mH

1i

1i

1u

fC22 Fμ 2u

Fig. 17. Main circuit of the experiment system.

u1

u2

i1

i2

(50V/div)

(50V/div)

(2A/div)

(2A/div)

Fig. 18. Steady state experimental waveforms of case I.

0 0.2 10

Act

ive

Pow

er (W

)

(a)

5

0.4 0.6 0.8

10

15

20

25

30

iPV changeP1

P2

0 0.2 1

0

(b)

5

0.4 0.6 0.8

1015202530

iPV changeRea

ctiv

e Po

wer

(Var

) 35

Time (s)

Q2

Q1

Fig. 19. Steady-state power of case I. (a) Active power, (b) reactive power.

u1

u2

i1

i2

(50V/div)

(50V/div)

(2.5A/div)

(2.5A/div)

Fig. 20. Steady state experimental waveforms of case II.

0 0.5 40

Act

ive

Pow

er (W

)

(a)

10

1.5 2.5 3.5

20

30

40

50

Load change

1 2 3

P1

P2

0 5 4

0

10

1.5 2.5 3.5

20

30

40

Load change

1 2 3(b)

Rea

ctiv

e Po

wer

(Var

)

Q2

Q1

Time (s)

Fig. 21. Steady-state power of case II. (a) Active power, (b) reactive power.

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Appendix A

The variable vectors ( p q QΔ ,Δ ,Δ and∼δΔ ) and the parameter matrices ( ∼ ∼K K K K, , ,pQ pδ qQ qδ ) in (18) and (19) are shown as

(A.1)

The state variable vector Δx and the system matrix A in (26) are shown as

J. Yang et al. Electrical Power and Energy Systems 97 (2018) 262–274

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(A.2)

where In is the n-th order identity matrix and Im is the m-th order identity matrix.

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