research article synergetic control of grid-connected

Research ArticleSynergetic Control of Grid-Connected Photovoltaic Systems

Junjie Qian, Kaiting Li, Huaren Wu, Jianfei Yang, and Xiaohui Li

School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210042, China

Correspondence should be addressed to Xiaohui Li; [email protected]

Received 8 October 2016; Revised 26 November 2016; Accepted 16 January 2017; Published 29 March 2017

Academic Editor: Md. Rabiul Islam

Copyright © 2017 Junjie Qian et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

It is important to improve the dynamic performance and the low-voltage ride-through (LVRT) capability of a grid-connectedphotovoltaic (PV) system. This paper presents synergetic control for the control of a grid-connected PV system. Modeling of agrid-connected PV system is described, and differential-algebra equations are obtained. Two control strategies are used innormal operation and during LVRT of a PV system. Practical synergetic controllers with two control strategies are synthesized.The mathematical expressions are derived for computing control variables. The design of the synergetic controllers does notrequire the linearization of the grid-connected PV system. A grid-connected PV system with synergetic controllers is simulatedin Simulink surroundings. The control performance is studied in normal operation and during LVRT. Simulation results showthat the synergetic controllers are robust and have good dynamic characteristics under different operation states.

1. Introduction

The world is faced with serious problems of energy depletionand environmental pollution. The research and developmentof photovoltaic (PV) technologies have become a hot topic inthe world [1]. Solar PV is now used around the world as animportant technology for the conversion of solar energybecause of its cleanliness and security. The solar PV capacityincreased 25% over 2014 to a record 50GW, lifting the globaltotal to 227GW. The solar PV industry is one of the fastestgrowing high-tech industries [2].

The control of a PV system is an important and difficulttask. A grid-connected PV systemmainly includes maximumpower point tracking (MPPT) and the control of the DC-ACconverter. Much research onMPPT has been conducted, andvarious MPPT algorithms have been proposed. The maxi-mum power point (MPP) may be located by the perturbationand observation (P&O) algorithms [3], the incrementalconductance (InC) algorithm [4], and the artificial neuralnetwork algorithm [5].

Reference [6] proposes a modified InC algorithm. Thealgorithm eliminates the division calculations involved inits structure and improves the variable step size, whichonly depends on the PV power change. Reference [7]improves P&O algorithm. This approach combines ant

colony optimization with the traditional P&O method toyield faster and efficient convergence. This improved P&Oalgorithm can recognize global MPP under partially shadedconditions. A new MPPT algorithm is proposed in [8].This scheme uses a gray wolf optimization technique totrack the global peak of a PV array under partial shadingconditions. It can solve the problems such as lower track-ing efficiency, steady-state oscillations, and transients asencountered in P&O.

A two-stage three-phase grid-connected PV system in [9]contains a DC-DC boost converter and a DC-AC VSCconverter. Pulse width modulator (PWM) signals fire theconverters. The DC-AC VSC control system has an externalvoltage control loop and an internal current control loop.The external control loop regulates the DC link voltage,and the internal control loop regulates grid currents. The gridcurrents are transformed into d-axis and q-axis currents toaccomplish vector control. Two control loops adopt theproportional-integral (PI) algorithm. Reference [10] presentsa novel sliding-mode (SM) control for grid-connected PVsystems. A systematic adaptive procedure to calculate theband of the hysteresis comparators is developed to improvethe performance of the SM controller. A vector controllercan keep the maximum power delivery of the PV system.Reference [11] uses a probabilistic wavelet fuzzy neural

HindawiInternational Journal of PhotoenergyVolume 2017, Article ID 5051489, 11 pageshttps://doi.org/10.1155/2017/5051489

https://doi.org/10.1155/2017/5051489

network (PWFNN) to structure the reactive power controllerfor a grid-connected PV system. The balance of the activepower between the PV array and the DC-AC converterduring grid faults is controlled by the DC link voltage. Thecontroller can improve the operation of the grid-connectedPV system during LVRT. Reference [12] suggests injectingthe maximum rated current to maximize the inverter powercapability during LVRT. The strategy combines a properbalance between positive- and negative-current sequences.High- and low-power production scenarios limit the inverteroutput current to the maximum rated value and avoid activepower oscillations. Reference [13] presents a new adaptivePI controller using the continuous mixed p-norm (CMPN)algorithm for enhancing the LVRT capability of grid-connected PV systems. The adaptive PI controller is usedto control the DC-AC converter. The gains of the PIcontroller are changed by the CMPN algorithm onlinewithout the need to fine-tune or optimize.

Reference [14] reviews the general synergetic controldesign procedure. Synergetic control is applied to a DC-DCboost converter, deriving a basic control law. An adaptivecontrol strategy gives better trade-off between large-signalstability and load step response time. Reference [15]introduces a practical synergetic controller to regulatethe buck converters that coordinate pulse current chargingof batteries. Simulation and experiment results show thatthe synergetic controller is robust for such nonlineardynamic systems and achieves better performance than thestandard PI controller.

This paper presents a design for the synergetic controllersfor an internal current control loop of a three-phase grid-connected PV system. The theory of synergetic control isfirst described. Modeling of a grid-connected PV system isintroduced, and differential-algebra equations are obtained.Synergetic controllers are derived in detail for normal opera-tion and during LVRT of a PV system. Two control strategiesare used during normal and LVRT operations of PV systems.The design of a synergetic controller does not require lin-earization of the PV system. The parameters T1 and T2 ofthe two synergetic controllers are the same, and T1 equalsT2. The parameters of the synergetic controllers are easyto determine, and the proposed control schemes are easyto achieve. An example given in Matlab is adapted accord-ing to the synergetic controllers for assessing the perfor-mance of synergetic control of the grid-connected PVsystem. The synergetic control is chatter-free, and the simu-lation results demonstrate the effectiveness of the proposedcontrol schemes.

2. Synergetic Control Theory

Synergetic control is a state space control method basedon modern mathematics. Synergetic control is applicable tothe control of nonlinear, dynamic, and high-dimensionalsystems. It can be perfectly analyzed by mathematicalexpressions.

The nonlinear state equation of a controlled system is

x• = f x,u,t , 1

where x is the state vector of the controlled systemRn, f ⋅ isa continuous nonlinear function, and u is the control vectorof Rm m ≤ n .

The macrovariables are defined for each input channel asa function of the state variables. The synergetic controllerdirects the system to move into the manifold from any initialmotion point

ψ x,t = 0, 2

where ψ is the macrovector of Rk 0 < k ≤m .The dynamic evolution of the macrovariable towards the

manifolds is defined as follows [14]:

T ψ• + ψ = 0, 3

where T defines the rate of convergence of the system.Substituting from (2) into (3) yields

T∂ψ∂x

x• + ψ = 0 4

The control vector u can be acquired by substituting(1) into (4). The system can be controlled to stay in thedesired manifold.

3. Modeling of the Grid-Connected PV System

The main circuit of the two-stage grid-connected PV systemis described in Figure 1. A PV array is connected to a power

MPPT

idc2idc1 uiaea

eb

ec

uib

ia

ib

ic

uic

upv

ipv

us udc C2

isiC1 iC2

C1

R1 L1 R3 L3

PV ar

ray

DC-

DC

DC-

AC

Figure 1: Main circuit of a grid-connected PV system.

C-axis

u𝛼

uq

u𝛽Uiq‒axis

B‒axis𝛽‒axis

𝛼‒axis

d‒axis

A‒axisωtud

Figure 2: Reference frames.

2 International Journal of Photoenergy

grid via a DC boost converter and a three-phase voltagesource converter (VSC) [9].

The differential equations (5), (6), (7), and (8) can bewritten according to Figure 1.

C1dupvdt

= ipv − is,

upv = R1is + L1disdt

+ us,

C2dudcdt

= idc1 − idc2,

Uiabc − Eabc = R3Iabc + L3dIabcdt

,

5

6

7

8

where

Uiabc =uiauibuic

,

Eabc =eaebec

,

Iabc =iaibic

9

Eabc is the grid voltage, Uiabc is the output voltage of the DC-AC VSC converter, and Iabc is the alternating current.

Equation (8) is based on a three-phase (abc) referenceframe. abc, αβ0, and dq0 reference frames are shown inFigure 2 [16].

Equation (8) is transformed into (10) from the abcreference frame to the dq0rotating reference frame usingthe sinus-based Park transformation.

Uidq0 − Edq0 = R3Idq0 + L3dIdq0dt

+ L3

−ω Iqω Id0

, 10

where Uidq0 = PUiabc, Edq0 = PEabc, Idq0 = PIabc, and P is thePark transformation matrix given in (11). Consider

P = 23

sin ω t sin ω t −2π3 sin ω t + 2π

3cos ω t cos ω t −

2π3 cos ω t + 2π

312

12

12

11

Equation (10) may be written in (12) and (13). Consider

L3dIddt

= −R3Id + ωL3Iq − Ed +Uid =U3d +Uid ,

L3dIqdt

= −R3Iq − ωL3Id − Eq +Uiq =U3q +Uiq,

12

13

where

U3d = −R3Id + ωL3Iq − Ed ,

U3q = −R3Iq − ωL3Id − Eq

14

15

Uid andUiq in (12) and (13) are control variables that controlthe DC-AC VSC converter.

The MPPT algorithm computes the duty cycle to controlthe DC boost converter. The relationship of inputs andoutputs of the DC boost converter is depicted by (16) and(17). Consider

idc1 = 1−D is,us = 1−D udc,

16

17

where D is the duty cycle of the DC boost converter.

EdEq

IqId

Iq

++

+––

–

Σ

ΣΣIq_refId_ref

udc_ref Id

udc

Uid Uiq

PI

Uabc_ref ωt

ωtωt

Synergeticcontrol

(26)–(28)

abcdq0

abcdq0

abcdq0PLLPWM

DC-

DC

DC-

ACFigure 3: Synergetic control scheme of the PV system in normal operation.

3International Journal of Photoenergy

The instantaneous active and reactive powers are definedby (18) and (19). Consider

p = EdId + EqIq,q = −EdIq + EqId

18

19

Selecting Eq = 0, (18) and (19) change into the twofollowing equations:

p = EdId ,

q = −EdIq

20

21

The model above can be used to design the synergeticcontrol of the grid-connected PV system.

4. Synergetic Control of a Grid-Connected PVSystem in Normal Operation

Control strategies of the DC boost converter and the DC-ACVSC converter in the grid-connected PV system must bemade. MPPT is implemented in the DC boost converter innormal operation. There are a number of MPPT algorithms;however, this paper does not analyze them.

The DC-AC VSC converter is controlled using thesynergetic control presented in this paper. The control vari-ables Uid and Uiq in (12) and (13) are derived by synergeticcontrol theory.

The reference value of Id may be obtained from theexternal voltage control loop.

Id re f = KP +Ki

sudc − udc re f = KP udc − udc re f + Iu,

22

where Iu = Ki s udc − udc re f that is,

dIudt

= Ki udc − udc re f , 23

where KP is the gain of the proportional term, Ki is thegain of the integral term, udc re f is the reference value of theDC voltage udc, and subscript re f denotes a reference value.

There are 2 control variables, and therefore, 2 macro-variables must be selected. The first macrovariable is

ψ1 = Id re f − Id = KP udc − udc re f + Iu − Id 24

Substituting (24) into (4), (25) is obtained:

T1 KPdudcdt

+ dIudt

−dIddt

+ ψ1 = 0 25

Substituting (12), (23), and (24) into (25), the first controlvariable is computed by (26) as follows:

Uid = KPL3dudcdt

+ KiL3 udc − udc re f

+ L3T1

Id re f − Id −U3d

26

The second macrovariable is selected

ψ2 = Iq re f − Iq, 27

where Iq re f is a constant.Substituting (27) into (4) and considering (13), the

second control variable is as follows:

Uiq =L3T2

Iq re f − Iq −U3q 28

The control variables Uid and Uiq are computed by(26) and (28), respectively, to guarantee system stabilityin normal operation. The synergetic control scheme of thegrid-connected PV system is shown in Figure 3.

5. Synergetic Control during LVRT

The PV system should stay connected and support the gridwith reactive power during the voltage dip. Therefore, thereference value of Iq is Iq re f = const , depending on thevoltage magnitude. Figure 4 depicts the principle of voltagesupport in the event of grid faults [17].

The abscissa in Figure 4 stands for ΔU/Un, and theordinate is ΔIB/In. ΔU =U −U0 and ΔIB = IB − IB0, where U

100%

Dead band

Overexcitedoperation

Underexcitedoperation50%

‒50% ‒30% ‒10% 0 10% 30% 50%Un

ΔU

ΔIBIn

‒50%

‒100%

Figure 4: Principle of voltage support in the event of grid faults.

Start

Calculate Id_ref from (22)

Id_limit = sqrt(1‒Iq_ref)

Id_ref = Id_limit

Calculate Iq_refaccording to Fig. 4.

Calculate Uid from (26)Calculate Uiq from (28)

Calculate Uid from (30)Calculate Uiq from (28)

Calculate ΔD from (31)MPPT

Y

N

N

Y MP⩽ EdId_limit

ǀΔUǀ ⩽ 0.1Un

Iq_ref =02

Figure 5: Synergetic control strategies of the PV system.


is the present voltage during the fault,Un is the rated voltage,U0 is voltage before the fault, IB is the reactive current, In isthe rated current, and IB0 is the reactive current before thefault. If a voltage dip is more than 10% of the rated voltage,the generator should provide a reactive current amountingto at least 2% of the rated current for each percent of thevoltage dip within 20ms after fault recognition [17]. If avoltage dip is more than 50% of the rated voltage, thegenerator must inject the grid with a reactive power of100% of the rated current.

The limitation of Id is Id limit = 1− I2q re f pu, so the

current will not be greater than the rated current.If the maximum power of the PV array at MPP is less

than the power EdId limit, the maximum power can beinjected into the grid with Id < Id limit. A MPPT is usedduring LVRT to obtain the maximum power and economicbenefits, and the control strategies are the same as those innormal operation.

If the maximum power of the PV array at MPP is morethan the power EdId limit, Id re f = Id limit is set, and the poweroutput of the PV array equalsEdId limit for the power balance.The following control strategies are used:

The first macrovariable is selected as

ψ1 = Id re f − Id 29

Substituting (29) into (4) and considering (12), the firstcontrol variable is computed as follows:

Uid =L3T1

Id re f − Id −U3d 30

Equation (28) is also used for the second control variableduring LVRT.

A MPPT is not used, and the duty cycle D is determinedby a PI controller to regulate the DC link voltage.

ΔD = KPD + KiD

sudc re f − udc ,

D =D0 + ΔD,

31

32

where D0 is the initial value of D.The duty cycle of the DC boost converter is determined

by (31) and (32) during LVRT. The DC-AC VSC converteris controlled on the basis of (28) and (30).

The control strategies described above are shown inFigure 5.

Equations (26) and (30) are derived according to thesynergetic control algorithm. Id re f is variable and is com-puted by (22) in normal operation. Consequently, (26) isobtained for the control of the PV system in normal opera-tion. Id re f is a constant, and (30) is derived for the secondcontrol strategy during LVRT. Equations (26) and (30) areused under different operating conditions of the grid-connected PV system.

The DC link voltage udc should remain stable to maintaingood operation of the PV system. This requires a powerbalance in the PV system. If the power injected into the gridby the DC-AC converter is less than the output power of thePV array, udc will increase. If the output power of theconverter is the same as the output power of the PV array,udc will not change. The two control strategies can satisfy

Vabc_prim

Iabc_prim

Vabc_primωt

VdVq_prim

IdIq_primIabc_prim2

11

PLL & measurements

3Vdc

du/dt

Derivative Mean

500

VDC regulator

Vdc_mes

Vdc_ref

Id_ref

Vd_mes

Vq_mes

Id_mes

Iq_mes

Vdc

dVdc

Id_ref

Vd_conv

Vq_conv

fcn2

Synergetic control

x

Figure 6: VSC main controller.


the power balance in the PV system in normal operation andduring a LVRT.

The PV array works at the MPP because of the MPPT innormal operation. If the output power of the converter is lessthan the output power of the PV array and udc increases, theDC voltage regulator will generate greater Id re f on the basisof (22). The synergetic control will result in more outputpower of the converter and achieve a power balance in thePV system after the regulation process.

The synergetic control maintains the output powerEdId limit of the converter for the second control strategyduring LVRT. If the output power of the PV array isgreater than EdId limit and udc increases, the DC voltageregulator will give a smaller D according to (31) and(32). The voltage of the PV array will increase accordingto (17), and its output power will decrease due to thepower-voltage characteristics of the PV array. The powerbalance in the PV system will be achieved once more,and udc will return to its reference value.

The DC-AC converter may be damaged due to the largecurrent that passes through it. The two control strategiescan prevent the converter from overcurrent in normaloperation and during LVRT.

6. Case Studies

Matlab software provides an example titledDetailed Model ofa 100-kW Grid-Connected PV Array [9]. The controllers ofthe example are adapted to assess the performance of syn-ergetic control of the grid-connected PV system.

The example includes a PV array with an open-circuitvoltage of 321V. udc re f is 500V, and the rated AC voltageis 260V. A distribution transformer has a voltage ratio of25 kV/260V.

6.1. Normal Operation Simulation. MPPT used in the casestudy is based on incremental conductance with an integralcontroller that can ensure that the system operates in MPPwhen the radiation intensity and temperature change rapidly.

The DC-AC converter is controlled using a synergeticcontrol scheme. Equations (26) and (28) are rewrittenaccording to the symbols in the Matlab example [9]:

Vd conv = KPL3dVdcdt

+ KiL3 Vdc −Vdc re f

+ L3T1

Id re f − Id + R3Id re f − ωL3Iq re f +Vd mes,

Vq conv =L3T2

Iq re f − Iq + R3Iq re f + ωL3Id re f + Vq mes

33

34Figure 6 shows the VSC main controller containing

synergetic control.The VDC regulator in Figure 6 is constructed on the basis

of (22). The inputs of the PLL and measurements blockare primary voltages Vabc prim and currents Iabc prim of thedistribution transformer. This block tracks the frequency

and phase of a sinusoidal three-phase signal and performsPark transformation from a three-phase (abc) referenceframe to a dq0 reference frame. The synergetic control blockin Figure 6 is a Matlab function block. It includes Matlabcode. The code computes 2 control variables, Vd conv andVq conv , with (33) and (34). The control variables are trans-formed into the reference values of three-phase voltages togenerate PWM and control the VSC converters.

The parameters KP = 0 2, Ki = 150, T1 = 0 01, andT2 = 0 01 are selected and applied in (22), (33), and (34).The settings are Vd re f = 500V and Iq re f = 0 for the simula-tion in normal operation. The standard test conditions are1000W/m2 irradiance and 25°C temperature. The changeof sun irradiance is shown in Figure 7. Figure 8 describesthe change of temperature for the simulation.

The MPPT regulator changes the duty cycle to regulatethe PV voltage for tracking maximum power. At t = 0 1 sec,

Time (s)1 2 3

80

60

40

20

0Te

mpe

ratu

re (°

C)

Figure 8: Temperature.

1 2 3Time (s)

1200

800

400

0

Irra

dian

ce (W

/m2 )

Figure 7: Sun irradiance.

1 2 30

40

80

120

Time (s)

Pow

er (k

W)

Figure 9: PV array output power.


the MPPT is enabled, and Figure 9 shows the PV arrayoutput power. Maximum power is 100.4 kW at the standardtest conditions. VSC converters deliver the power to the gridby synergetic control.

The root mean square (RMS) of the primary voltageva prim of the distribution transformer is constant. TheRMS of the current ia prim is directly proportional to thepower. Figure 10 shows the primary current ia prim of thedistribution transformer.

Figures 9 and 10 indicate that the grid-connected PVsystem can track maximum power and deliver the power tothe grid when the radiation and temperature change rapidly.The system operates stably.

The bus voltage may change in normal operation. Simu-lation of voltage fluctuation is performed at the standard testconditions. Figure 11 depicts a 25 kV bus voltage va prim. TheRMS of va prim decreases by 10% at t = 1 sec.

The current ia prim is shown in Figure 12. ia prim increaseswhen the bus voltage decreases.

The maximum power does not change because sunirradiance and temperature are constant at the standardtest conditions. Figure 13 demonstrates that the powerinjected into the grid is almost constant during the gridvoltage fluctuation. This means that the synergetic controlperforms well in normal operation.

6.2. LVRT Simulation. LVRT is the capability of electricgenerators to stay connected to the grid during short periodsof voltage dip. LVRT is an important feature of the gener-ator control system. There are several standards for LVRTrequirements [17, 18]. Figure 14 shows the LVRT require-ment in [19]. These requirements may be used for largesolar power installations.

1 2 30

40

80

120

Time (s)

Pow

er (k

W)

Figure 13: Power invariance.

No trip

0 0.5 1 1.5 2 2.5 3Time (s)

0

0.2

0.4

0.6

0.8

1.0

1.2

Volta

ge (p

u)

‒0.5

Figure 14: LVRT requirement.

0 1 2 3

0

2

4

Time (s)

Curr

ent i

a_pr

im (A

)

‒2

‒4

Figure 12: Current increase.

0 1 2 3

0

10

20

Time (s)

Vol

tage

ua_

prim

(kV

)

‒10

‒20

Figure 11: Bus voltage decrease.

0 1 2 3

0

2

4

Time (s)

Curr

ent i

a_pr

im (A

)

‒2

‒4

Figure 10: Primary current ia prim.


Three cases are used to test the performances of thesynergetic control during a LVRT. The three-phase faultblock in Simulink is connected in utility grid to simulate athree-phase short circuit with arc resistances.

The feature of the PV system is tested first when the busvoltage decreases by 30% due to a grid fault. The referencevalue of the reactive current Iq is Iq re f = −0 6 pu on the basisof Figure 4. The limitation of Id is Id limit = 0 8, and the poweris EdId limit = 0 56 pu. The maximum power of the PV arrayat MPP is 0.48 pu when it is simulated at an irradiance of500W/m2 and a temperature of 25°C. The first controlstrategy is used because the maximum power of the PVarray at MPP is less than EdId limit. Iq re f = −0 6 is set;the other settings are equivalent to those used in the nor-mal operation simulation. Equations (22), (33), and (34)and MPPT are used. The RMS of the voltage va prim decreasesby 30% at t = 0 3 s, and the simulation results are shownin Figures 15–17.

Figure 15 depicts the reactive power injected into thegrid. The PV system provides the grid with a reactive powerof 42 kVar during the LVRT.

The active power injected into the grid is shown inFigure 16. The injected active power is 47.2 kW when thereactive power injected into the grid is 42 kVar at a 30%decrease of the grid voltage. The maximum power of the

PV array at MPP is delivered to the grid, and the solar energyis fully utilized.

The rated primary current is 3.3A. Figure 17 shows thatthe primary current is less than its rated value. Therefore,the PV system may stay connected to the grid and providethe grid with 47.2 kW and 42 kVar at a 30% decrease of thegrid voltage due to grid fault.

Then, simulations will test the performances of thesynergetic control when the grid voltage decreases to 0.2pu. The second control strategy is used because Iq re f = −1according to Figure 4 and Id limit = 0. The duty cycle D iscomputed according to (31) and (32). Equation (30) isrewritten using the symbols in [9]:

Vd conv =L3T1

Id re f − Id + R3Id re f − ωL3Iq re f + Vd mes

35

Equations (31), (32), (34), and (35) are used to computethe control variables for controlling the DC boost converterand the VSC converters during LVRT. The parameters areKPD = 0 01,KiD = 0 1,T1 = 0 01, and T2 = 0 01. The settingsare Vd re f = 500V,Iq re f = −1, and Id re f = 0 pu.

A three-phase short circuit occurs in the power distribu-tion system at t = 0 3 sec for the LVRT simulation. The busvoltage decreases to 0.2 pu during short circuit. va prim and

1 2 30

20

40

60

80

100

Time (s)

Reac

tive p

ower

(kV

ar)

Figure 15: Reactive power injected into the grid at a 30% decrease of the bus voltage.

1 2 30

20

40

60

80

100

Time (s)

Pow

er (k

W)

Figure 16: Active power injected into the grid at a 30% decrease ofgrid voltage.

0 1 2 3

‒4

‒2

0

2

4

Time (s)

Curr

ent i

a_pr

im (A

)

Figure 17: Primary current at a 30% decrease of grid voltage.


ia prim are shown in Figures 18 and 19, respectively. The25 kV bus voltage in Figure 18 decreases to 0.2 pu aftert = 0 3 sec.

Small fluctuations of primary current arise after thevoltage dip. The peak value of ia prim during LVRT is less thandouble of that in normal operation.

Currents Id and Iq are depicted in Figure 20. Id and Iqare regulated to 0 and −1 pu, respectively, after the dip.The PV system stays connected and supports the grid withreactive power.

The DC link voltage Vdc is shown in Figure 21. Itfluctuates slightly and then remains at 500V after the dip.

Another simulation is made for testing the performanceof the synergetic control at a bus voltage of 0.05 pu. The sec-ond control strategy is used. A three-phase short circuit isapplied in the bus at t = 0 3 sec, and the bus voltage decreasesto 0.05 pu to simulate the voltage of the fault arc. The currentsettings are Id re f = 0 and Iq re f = −0 9 pu, to avoid a largecurrent. The reference value of current Iq is Iq re f = −1 pu,to provide the grid with reactive power after t = 0 35 sec.Figure 22 shows three-phase currents flowing in the choke.The maximum value of the current is less than 2.0 pu.Synergetic control can limit the current peak during LVRT.

The example in [9] has the current regulator with PIcontrol and simulates only the normal operation of the PVsystem. The regulator from (31) and (32) is added to theexample to simulate the LVRT of the PV system. Id re f = 0and Iq re f = −1 pu are fixed. Two parameters of the currentregulator with PI control are changed from 0.3 and 20 (fornormal operation) to 0.03 and 0.002, respectively, for LVRT.Therefore, parameter tuning of the current regulator with PIcontrol is difficult. Chatter has been the main obstacle forsliding-mode control systems [10]. Probabilistic waveletfuzzy neural networks (PWFNNs) include a membershiplayer, probabilistic layer, wavelet layer, and rule layer [11].PWFNNs are very complicated, such that it is difficult to

0 1 2 3

‒20

‒10

0

10

20

Time (s)

Vol

tage

ua_

prim

(kV

)

Figure 18: 25 kV bus voltage during LVRT.

0 1 2 3‒8

‒4

0

4

8

Time (s)

Curr

ent ia_

prim

(A)

Figure 19: Primary current during LVRT.

0 1 2 3

0

1

2

3

Time (s)

Curr

ents

I d an

d I q

(pu)

Id

Iq‒1

‒2

‒3

Figure 20: Currents Id and Iq during LVRT.

0 1 2 3

200

400

600

800

Time (s)

DC

volta

ge (V

)

Figure 21: DC link voltage Vdc.

0 1 2 3‒800

‒400

0

400

800

Time (s)

Curr

ent i

n ch

oke (

A)

Figure 22: Three-phase currents flowing in the choke.


determine the PWFNN parameters. The gains of the PIcontroller in [13] must be changed online using the CMPNalgorithm for improving the LVRT capability of grid-connected PV systems.

The parameters of the synergetic controller described inthis paper are invariant during normal operations and duringLVRT, and parameter T1 equals T2. There is no need tochange the parameters of the synergetic controller with acomplicated algorithm. Therefore, parameter tuning of thesynergetic controller is easy, and the controller is sufficientlyrobust for use in the PV system. The design of the synergeticcontroller is simple and does not require linearization of thePV system. In addition, the proposed control schemes areeasy to realize. The synergetic control is chatter-free anddisplays good static and dynamic performance.

Asymmetric short circuit faults may occur in power sys-tems. Unbalanced grid voltages are comprised of positive,negative, and zero sequence voltage components. The zerosequence is not considered here because of three-wire systems.Unbalanced grid voltage sags will cause performance deterio-ration of the converter. Negative sequences result in DC-linkvoltage ripples and harmonic power. The positive and nega-tive sequence currents should be controlled simultaneouslyto improve control performance. Reference [20] used sepa-rate current controllers for positive and negative sequences.Synergetic control may be used in two current controllersto control positive and negative sequence currents separately.It is possible to use synergetic control for improving theperformance of PV systems during unbalanced voltage sags.

7. Conclusions

Solar PV is an important renewable energy technology anddoes not generate pollution. PV systems are developing rap-idly, and most PV systems are grid-connected. Research onthe control of grid-connected PV systems contributes to theimprovement of the operation of the distribution networkand the PV system.

Synergetic control can be used for the control of a grid-connected PV system. The design of a synergetic controllerdoes not require the linearization of the PV system. Themathematical expressions for computing control variablescan be derived according to the synergetic control algorithmand the mathematical model of a grid-connected PV system.Two control strategies are used in normal operation andduring LVRT. The parameters T1 and T2 of the two syn-ergetic controllers are the same. The parameters of thesynergetic controllers are easy to determine, and resultsindicate that the synergetic controllers are robust. The grid-connected PV system can obtain a maximum power pointand inject the power into the grid when the radiation andtemperature change rapidly. The DC link voltage and ACcurrents are limited, and the DC-AC VSC converters arenot damaged during LVRT. The PV system can run withIq = −1 pu continuously and supply reactive power to thegrid when the grid voltage decreases to 0.05 pu.

Synergetic control has good dynamic characteristics innormal operation and during LVRT and is the alternativesolution for grid-connected PV systems.

Conflicts of Interest

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work was financially supported by the National NaturalScience Foundation of China (51177074, 51407095) and theJiangsu Province Natural Science Foundation (BK20151548).

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