Quasi-Z Source lnverter Control of PV Grid-Connected Based on Fuzzy PCl

Tao Hou | Chen-Yang Zhang | Hong-Xia Niu

Abstract—The photovoltaic grid-connected inverter is an important interface between the photovoltaic power generation system and power grid.Its high-quality operation is directly related to the output power quality of the power grid.In order to further optimize the control effect of the quasi-Z source grid-connected photovoltaic inverter,a fuzzy proportional complex integral control (PCI) method is proposed for the current internal loop control.This method can eliminate the steady-state error,and has the characteristic of zero steady-state error adjustment for the AC disturbance signal of a specific frequency.The inductance-capacitance-inductance (LCL) filter is adopted in the grid-connected circuit,and the feedback capacitive current is taken as the control variable of the inner loop to form the active damping control method,which can not only effectively suppress the resonance of the LCL circuit,but also significantly inhibit the high-order harmonics in the grid-connected current.Finally,a system simulation model is built in MATLAB/Simulink to verify the superiority and effectiveness of the proposed method.

1.lntroduction

With the rapid development of the world economy,the use of non-renewable energy and the pollution caused by energy consumption are becoming more and more serious.Countries all over the world have gradually realized the importance of developing new energy,and China is facing severe challenges.According to [1],China’s proven coal will only be available for exploration for 105 years,oil will be exhausted in 15 years,and natural gas will be exhausted in 30 years.Because of the above reasons,the development of new energy has made great progress in recent years.Photovoltaic (PV) power generation and wind power generation,as important forms of new energy generation,have attracted more and more attention from countries all over the world.PV power generation has become one of the important branches of renewable energy generation due to its advantages of clean and pollution-free,short construction period,and load allocation[2],[3].At present,the PV grid-connected mainly adopts a two-stage or single-stage structure.Among them,the two-stage structure of the converter at all levels has their own control objectives,does not affect each other,and can cope with the irregular change of the PV array input voltage.But its structure is relatively complex,high costs,and large losses.However,there is only one DC/AC link in the single-pole gridconnected PV inverter system to realize energy transformation,therefore,maximum power point tracking(MPPT),grid voltage synchronization,and output current sine control are all realized by the DC/AC link.The control is relatively complicated,which decreases the response speed and generation efficiency of the whole system[4].The above two kinds of structures adopt the traditional inverter,and the same bridge arm is not allowed to directly join in the dead band time,thus deteriorating the output power quality.The Z source inverter (ZSI)[5]and quasi-Z source inverter (QZSI)[6]applications of the photovoltaic generating system,not only have the traditional two-stage type with all the advantages of the single stage type structure,at the same time,they allow direct access,which increases the system reliability and further reduces the grid current harmonic distortion rate (THD)[7]-[9].

When the fixed topology is selected,the control strategy is particularly important,which largely determines the performance of the grid-connected inverter and thus improves the grid-connected power quality.Therefore,the research on the control strategy has become the focus of grid-connected control research[10].At present,the control methods of QZSI/ZSI mainly include proportional integral (PI) control,proportional resonant (PR) control,hysteresis control,sliding mode control,and repetitive control.Each of the above control methods has its own advantages,but the PI controller needs to be decoupled and is complex.And if the control object is an AC signal,the PI controller cannot achieve error-free adjustment[11].Theoretically,PR control can realize the non-error tracking of AC signals,but can only be quasi-PR control with complex operation and difficulty[12].Due to poor dynamic performance and the complex structure,only when the repetitive control is combined with other methods,the better control effect can be achieved[13].Hysteresis control acts on QZSI/ZSI requires constant frequency control and independent control of each phase.Its structure is very complex[14].When the sliding mode control is adopted,it is difficult to select the ideal sliding mode surface and adjust the sliding mode coefficient[15].In [16],fuzzy sliding mode control was applied to QZSI,which has strong robustness.In [17],fuzzy PI was applied to the grid-connected study of ZSI,which reduced THD and enhanced the robustness of the system,but could not eliminate the steady-state error.This paper,in view of the QZSI parallel alternating current steady-state error,puts forward the fuzzy proportional plural integrals proportional complex integral (PCI) control method.The gain of the control method is infinite at the fundamental frequency and the steady-state error can be completely eliminated theoretically[18],[19].And after combining the fuzzy control,this method can adjust the proportion of the adaptive online coefficientKpand integral coefficientKi,at the same time improve the control precision and dynamic performance of the controller,and effectively reduce the grid current harmonic.As a result,the quality of grid-connected power is further improved.The filter in the grid-connected system adopts the inductance-capacitance-inductance (LCL)type,which can reduce THD and the higher-order harmonic of the grid-connected current.Moreover,after the Clarke transformation of the LCL equation of state,there is no coupling term in the equation,thus avoiding complex decoupling[20].The experimental results agree with the theory.

2.Three-Phase Quasi-Z Source PV Grid-Connected System

The grid-connected system of this paper adopts three-phase QZSI PV grid-connected system.The system is mainly composed of the PV array,QZSI with the function of lifting and lowering the voltage,and the LCL filter circuit.The structure is shown inFig.1.InFig.1,SVPWM is space vector pulse width modulation;PLL is phase locking loop;abc/αβis the Clarke transformation;dq/αβis the Park transformation.

Fig.1.Structure of three-phase quasi-Z source PV grid-connected system.

2.1.PV Array

Silicon solar cells are widely used in the current PV system.The PV array is composed of many small PV cells,and its equivalent circuit[21]is shown inFig.2.

Its output current is

Fig.2.PV cell equivalent model.

whereIis the output current of the PV cell;Iphis the photovoltaic generating current;IDis the equivalent model diode current;Rsis the series resistance;Rshis a shunt resistor;is the resistance current in parallel;Vis the output voltage of the PV cell;Qis the amount of charge contained in one electron;Kis the Boltzmann constant;Tis the surface temperature of the PV panel;nis the ideal factor of the PV panel andnis in the range of 1 to 5.Under the reference conditions,Iscis the short-circuit current;Vocis the open-circuit voltage;ImandVmare the current and voltage of the maximum power point,respectively;then when the PV array voltage isV,the corresponding current is

where

When considering the changes in solar radiation and the effects of temperature,

where

where ∆I,∆V,and ∆Trespectively represent the change values of current,voltage and temperature.RrefandTrefare the reference values of solar radiation and photovoltaic cell temperature,generally taken as 1 kW/m2and 25 °C;αis the temperature coefficient of current variation (Amps/°C) under reference sunshine;βis the temperature coefficient of voltage variation (V/°C) under the reference sunshine.

2.2.QZSl

In recent years,ZSI has been regarded as a research hotspot because it can actively realize the rise and fall of voltage and has no limitation on the inverter power supply.However,the capacitor voltage of ZSI is too high,resulting in strong voltage resistance and large capacitance volume,which increases the cost.At the same time,the start-up impulse current is large,which causes the current to exceed the steady-state value and damages the inverter.In view of the above disadvantages,some scholars proposed QZSI.Compared with ZSI,QZSI has the advantages of the low voltage stress,continuous input currents,DC side of inverter bridge,common grounding of DC source,etc.At the same time,it has the characteristics of ZSI and is more suitable for the PV grid-connected.

The inverter includes energy storage inductorsL1andL2,energy storage capacitorsC1andC2,and a diodeD1,which constitute a quasi-Z source network,andCis the DC filter capacitor.The structure of QZSI is shown inFig.3.

Fig.3.Topological structure of quasi-Z source PV gridconnected inverter.

Compared with traditional inverters,QZSI introduces the quasi-Z source network and adds the direct-through working state.Energy storage capacitors and inductors in the quasi-Z source network absorb or release energy through the change of the directthrough state,so that the system has the characteristics of voltage boosts.SupposeL1=L2andC1=C2,in one switching cycleTsand in the through timeT0of a certain bridge arm,the inductor stores energy and the capacitor releases energy;the inductor releases energy and the capacitor stores energy in the non-direct time.QZSI works in the same mode as the traditional inverter.D=T0/Tsis defined as a direct duty cycle,andBis the boost factor[22].Under one cycle,according to the voltage-second balance,the relationship of the DC chain voltageUDC,capacitor voltagesanddirect duty cycleD,and PV array output voltageUpvat the steady state can be obtained,as shown in (6):

The output voltage base amplitude of QZSI is

whereMis the modulation ratio.In order to improve the utilization ratio of the DC voltage and reduce the switching frequency as much as possible,the space vector pulse width modulation (SVPWM) is adopted in this paper.

2.3.LCL Filter Circuit

The filtering circuit plays a crucial role in the grid-connected system,mainly including the inductance-type(L-type),inductance-capacitance-type (LC-type),and LCL-type.The L-type adopts single-inductance filtering with limited filtering performance,and it is hard to achieve a good harmonic suppression effect[23].The LC-type is suitable for dual-mode systems with the independent operation or grid-connected operation.In gridconnected systems,THD and the filter capacitance value of the grid-connected current cannot be obtained simultaneously[24].The LCL filter is selected by this paper,the filtering effect is better than the L-type and LCtype,it can filter out higher harmonics and reduce the total inductance and volume,but LCL-type generates resonance,and has a high resonance peak at the resonance frequency,which has a great impact on the stability of the system.In order to restrain the resonant peak generated by the LCL-type,this paper adopts the active damping method with capacitor currents as the control variable of the inner loop,so that the system stability is not affected and the power factor required by the grid-connected is satisfied.According to the state space mathematical model of the three-phase grid-connected inverter of the LCL filter,the Clarke transformation is carried out on the state space equation in the three-phase static coordinate system.Assuming the three-phase equilibrium of A,B,and C,the state space equation in the static coordinate system ofαandβis obtained as

wheren=αandβ;andare the current passing through inductorsL1andL2,respectively;uCis the voltage at both ends of the filter capacitorC;iCis the current flowing through the filter capacitorC;unis the side voltage of the inverterC;is the grid voltage.After the Clarke transformation and simplification of the above formula into the matrix form,it can be found that there was no coupling term in the equation.After the Clarke transformation,the coupling problem is well solved to avoid a series of complex operations,simplifying the design of the controller.

3.PV Grid-Connected System Control Strategy

The structure of the three-phase QZSI PV grid-connected control system is shown inFig.1.The control system consists of three closed loops:The maximum power tracking direct voltage zero vector loop,DC chain voltage outer loop,and grid-connected current inner loop.

For the mutual influence between the control system of the whole closed loop,the main control process is as follows:Equipment sampling of the PV array output voltageUpvand output currentIpvas the input of the MPPT algorithm,after the calculation of the PV array maximum power point of the PV reference voltagewith the actual measured voltage,the PI controller can keep the difference between the input voltages stable.At the same time,using the duty ratio calculation formula,the duty ratioDcan be calculated.According to the given value of the DC chain voltageand the DC duty cycleD,the reference value of the voltage across the capacitorC1(denoted ascan be obtained.and the actual valuerealize the constant DC chain voltage through the PI controller.At the same time,the input current reference value is obtained,which is used as the input current reference valueof the whole system.Given the reactive current referencethe reference valuesandare obtained by transformation fromdqaxis toαβaxis.They are sent as the input of the fuzzy PCI controllers.The output stabilized by the controller is used as the modulation signal,and the modulation signal and the direct duty ratioDare sent to the straight-through segment SVPWM to realize the control of the quasi-Z source of the PV grid inverter.

3.1.Design of Controller

The traditional PI controller has the advantages of strong adaptability,wide application range,simple and easy operation,etc.,but it has a poor control effect on time-varying and nonlinear systems,resulting in poor dynamic performance,and is hard for parameter setting[25].The PCI controller is superior to the PI controller in the control effect,mainly aiming at the zero steady-state error of the AC signal.The transfer function of the PCI controller is

whereKpandKiare controller parameters,respectively;ω0is the angular frequency of the AC perturbation signal.Whenω=ω0,the gainis infinite.It can be seen that controller’s gain is infinite at the given AC frequencyω0,and there is no steady-state error for the stable operation ofωat this frequency.Whenω0is taken as 0,the PCI controller is equivalent to the PI controller,which can realize the zero steady-state error control of the DC signal.Therefore,the PCI controller can eliminate both the steady-state error of the AC signal at a specific frequency and the DC signal.It has all the advantages of the PI controller.However,KpandKiparameters of the controller are fixed at this time.When the instruction current signal jumps,the controller cannot make the corresponding adjustment.In order to achieve better control performance,parameters of the PCI controller need to be changed in real time,so the fuzzy controller is introduced,as shown inFig.4.

The instruction currentIrefis a given control current.Iois the inverter output current,and the difference is obtained.The deviation of them iseand the deviation rate is ec.The variation of the parameters of the PCI controller (KpandKi) are ∆Kpand ∆Ki.According to the fuzzy theory,by adjusting ∆Kpand ∆Ki,KpandKican be adaptively adjusted:Kp+∆KpandKi+∆Ki.The controller can achieve faster response speed and higher control precision.

Fig.4.Fuzzy PCI controller.

3.2.Design of PCl Controller Parameters

The parameters to be designed in this paper areKpandKi,and the mathematical model of the equivalent grid-connected system inFig.5is established,whereKis the equivalent gain of the inverter,KSVPWMis the equivalent gain of SVPWM,andugis the grid voltage.

The transfer function of the PCI controller isGc(s).According toFig.5,the closed loop transfer function of the grid-connected system is

Fig.5.Mathematical model of the grid-connected system.

where

Substituting in the parameters,according to the Rous criterion,when the system is stable,the value ranges ofKpandKican be calculated.Considering the stability margin and bandwidth of the system,the effective value ranges ofKpandKican be obtained:0＜Kp＜1.99 and 0＜Ki＜1200.

The selection ofKpandKiparameters has important influence on the stability of the system.Choosing the open loop transfer functions of the amplitude margin and phase margin as the analyzing objects,takeKi=500 fixed,whenKpis 0.3,1.0,and 1.7,respectively,the Bode diagrams of the amplitude margin and phase margin can be drawn,as shown inFig.6.WhenKptakes 0.3,the amplitude margin can satisfy the common requirements,but the phase margin is small;whenKpis 1.7,the situation is reversed;Kp=1.0 is ideal,so it is good for choosingKparound 1.0.WhenKpis fixed at 1.0,the Bode diagrams are shown inFig.7.Compared withKp,Kihas less influence on the stable operation of the system,for the shown situations inFig.7,both the amplitude margin and phase angle margin can meet the requirements.To obtain a smaller steady-state error,compromise and fuzzification are taken as the next step.The initial values areKp=1.0 andKi=500.

Fig.6.System Bode diagrams when Ki is kept as 500.

Fig.7.System Bode diagrams when Kp is kept as 1.0.

3.3.Fuzzification of Parameters

Fuzzy control is a computer control method based on the fuzzy set theory,fuzzy language variables,and fuzzy logic reasoning.As an important branch of intelligent control,fuzzy control has been widely used.The core of fuzzy control is the fuzzy controller,and the key of the fuzzy controller is the determination of fuzzy control rules,that is,the fuzzy control rule table,which is the core of fuzzy reasoning and the basis for modifying controller parameters[26].

The ∆Kpand ∆Kifuzzy rule tables are shown inTable 1andTable 2.According to the calculated ranges ofKpandKi,set the deviationeand the deviation rate ec as the inputs of the fuzzy controller,whose fuzzy comprehensive ranges are [1,1] and [0.5,0.5],respectively.The fuzzy subset is {negative big,negative medium,negative small,zero,positive small,positive medium,positive big},denoted as {NB,NM,NS,ZE,PS,PM,PB},and the quantification factorskeandkectake 1 and 0.5,respectively.

Table 1:Fuzzy rules for ∆Kp

Table 2:Fuzzy rules for ∆Ki

3.4.Solution of Fuzzy

The fuzzy quantity is obtained through fuzzy reasoning,which can also be regarded as a fuzzy set.The solution of fuzziness is to find a single value process that can best represent the fuzzy set in the fuzzy reasoning.There are many methods to solve the ambiguity,such as the maximum membership degree method,center of gravity method,membership degree limiter element average method,coefficient weighted average method,and median method.In this paper,the weighted average method is used,and the weighted factor is used to obtain the membership of the elements that make up the fuzzy control vector.Equation (12)gives the calculation method to understand the ambiguity:

In (12),mis the maximum effective rule number,wkis the weighting factor,andukis the corresponding value ofuin the membership function.

4.Simulation and Analysis

This paper builds a new grid-connected control system model based on fuzzy PCI control in MATLAB/Simulink and a system simulation model based on PCI control.System parameters and PV modules are shown inTable 3andTable 4.

Table 3:System parameters

Table 4:PV module parameters

Fig.8(a) andFig.8(b) are the output voltage and output current curves,respectively,for the PV array with 10 in series and 2 in parallel under the light intensity of 1000 W/m2and 25 °C temperature.Fig.8(c) is thePpv-Upvcharacteristic curve under different solar radiation intensities.When the temperature is constant,the output voltage of the PV array is 300 V,the output current is 8 A,and the maximum power point voltage under different light intensities is stable at about 300 V.

The PCI controller parameters are designed,and the fuzzy algorithm is combined to control the gridconnected current into the network,to achieve the purpose of grid-connected with the same frequency,phase,and unit power factor,and the grid-connected current and instruction current are basically equal.The steady-state error is close to zero,and the harmonic contents are low.

In the simulation,the input instruction current of the controller is set as 32 A,and the direct current instruction is converted into the corresponding AC signal by the Clarke transformation as the input of the controller.The simulation time is 0.3 s,Fig.9shows the A phase power grid voltage waveform and A phase net current waveform.It can be seen that the controller can well control the net current,power grid voltage,frequency,and the phase,achieving the purpose of power factor interconnection.And throughFig.10,the grid current has little high harmonic contents.The THD value is low,which is only 1.36% and will not impact the power grid.Fig.11shows the waveform of the grid-connected current reference value,actual value,and tracking error under fuzzy PCI control,when the voltage frequency offset of the power grid is 0.5 Hz.As can be seen fromFig.11,when the grid frequency is offset by 0.5 Hz,the quasi-Z source PV grid-connected inverter controlled by fuzzy PCI can still achieve the no-static difference tracking control for a given current.The pink line is the actual current,and the blue line is the reference current.

Fig.12analyzes the steady-state errors of the fuzzy PCI controller,PI controller,and PCI controller,respectively.By setting up multiple sets of instruction currents and calculating the corresponding output currents,the relative error,that is,the steady-state error of the system can be calculated.The steadystate errors corresponding to the three different control methods are calculated by taking 10 sets of instruction current values.

The steady-state error corresponding to each control method is drawn inFig.12.The steady-state error under PI control decreases with the increase ofthe given current,which is consistent with the theory.However,PI control cannot eliminate the steady-state error of the AC signal.The steady-state error of the system under PCI control is much smaller than that of the previous method,basically stable between 1% and 2%,which is basically consistent with the theory.However,due to the existence of the practical model,signal delay,etc.,the steady-state error is small,but it cannot be eliminated.The control method combining the fuzzy algorithm and PCI control is adopted.Compared with the first two control methods,the results obtained by the fuzzy PCI method are obviously better,and the steady-state error of actual simulation is stable below 1%,that is,the fuzzy PCI controller is significantly better than the PI controller and PCI controller in steady-state error control.

Fig.8.Outputs:(a) output voltage curve,(b) output current curve,and (c) relation between output power and output voltage.

Fig.9.Grid voltage waveform and grid-connected current waveform.

Fig.10.Current harmonic analysis.

Fig.11.Simulation results under the voltage frequency of 50.5 Hz

Fig.12.Steady-state errors corresponding to the three different control methods.

Besides the advantages of the fuzzy PCI controller in the steady-state error,it is also superior to the PI controller and PCI controller in harmonic suppression.Under the same parameters and simulation conditions,the harmonic contents of three different controllers under several harmonics are recorded and compared,as shown inFig.13.The results show that the fuzzy PCI controller has the minimum harmonics,the least THD value,and the least impact on the large power network when connected to the network.This verifies that the fuzzy PCI controller is superior to the PI controller and PCI controller.

5.Conclusions

Fig.13.Corresponding harmonic contents of the three control methods.

In this paper,a fuzzy proportional integral controller is introduced to propose a type of the PV grid-connected control strategy for QZSI based on fuzzy PCI.The following conclusions are drawn.

1) The three-phase quasi-Z source PV gridconnected inverter controlled by fuzzy PCI can track the given current signal without the static difference in the static coordinate system,realize the gridconnected unit power factor,overcome the shortcomings of complex coordinate transformation and decoupling control,and reduce the control complexity of the whole system.

2) The quasi-Z source PV grid-connected system controlled by fuzzy PCI has strong robustness.With the grid frequency offset,it can still track the given value well.And it has strong resistance to the grid frequency offset,THD of the whole system is 1.36%.

3) The fuzzy PCI controller is adopted,which has the advantage of eliminating the steady-state error of an AC signal.Compared with the PI controller and PCI controller,it has a small steady-state error in the given signal,which is basically stable at less than 1%,and has a good inhibitory effect on high-order harmonics.

The grid-connected control strategy of fuzzy PCI can greatly reduce the steady-state error of the system,enhance the robustness of the system,and reduce the complexity of the control structure,which has a certain reference value in engineering applications.

Disclosures

The authors declare no conflicts of interest.