Fuzzy Logic Controller-based Synchronverter in Grid-connected Solar Power System

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(Department of Electrical and Computer Systems Engineering (ECSE),School of Engineering,Monash University Malaysia,Subang Jaya 47500,Malaysia)

Abstract:In recent years,renewable energy sources,specifically solar power systems,have developed rapidly owing to their technological maturity and cost effectiveness.However,its grid integration deteriorates frequency stability because of insufficient rotating masses and inertial response.Hence,a synchronverter,which is an inverter that mimics the operation of a synchronous generator,is crucial to interface solar power in a power grid.It stabilizes the power grid by emulating a virtual inertia.However,a conventional proportional-integral (PI)-based synchronverter is not equipped with an adaptive damping factor (Dp) or a digitalized smart controller to manage fast-responding solar inputs.Hence,a novel fuzzy logic controller (FLC) framework is proposed such that the synchronverter can operate in a grid-connected solar power system.In this study,Dp is controlled in real time using an FLC to achieve balance between speed and stability for frequency error correction based on frequency difference.Results of four case studies performed in Matlab/Simulink show that the proposed FLC-based synchronverter can stabilize the grid frequency by reducing the frequency deviation by at least 0.2 Hz (0.4%),as compared with the conventional PI-based synchronverter.

Keywords:Fuzzy logic controller (FLC),synchronverter,renewable energy system (RES),grid stability,solar power system

1 Introduction

The demand for global electricity has increased significantly in the past decade[1].To fulfill electricity demand,many grid operators from different countries have transitioned toward renewable energy sources(RESs)[2]owing to their cost effectiveness and environmental friendliness[3].Among RESs,solar power systems are popular because of their cost effectiveness[4],sustainability,and technological maturity[5].As the power system evolves from centralized generation from oil and gas to distributed generation from RESs[6],the involvement of power-electronics-based converters is indispensable for ensuring power system stability[7-8].Unlike the conventional synchronous machine (SM),solar inverters[9-10]in grid-connected solar power systems present disadvantages of zero inertial response,fast-changing behavior,and insufficient rotating masses[8].The static structure of a converter deteriorates the frequency instability because of its inability to inject or absorb active power (P) from the rotating inertia based on the power demand[11].If a sudden load change that causes power imbalance occurs[12],then the grid alternating current (AC)frequency will deviate from its nominal operating value[13].This will affect the power supply quality and result in power supply discontinuity[14].The current solution for controlling the solar power system is to inject the maximum power into the power grid[15];however,this method is only suitable when solar power contributes insignificantly to the grid power capacity.Maximum power point tracking (MPPT)[16]can be performed to extract the maximum power from a solar array[17];however,it does not contribute to the system inertia[18].Such a problem can be mitigated using large-scale grid power.In addition to frequency regulation via active power (P),reactive power manipulation is performed to regulate the grid voltage[19]for the grid integration of RESs with low voltage ride through capability[20].

To alleviate the aforementioned problems,an inverter that mimics the inertial response of an SM must be used to integrate a solar power system with a power grid[21].This type of inverter is known as a synchronverter or virtual synchronous generator[22],which is based on virtual inertia (VI) emulation[23].A synchronverter can stabilize the operating frequency[24]when a sudden load change occurs by altering the electric torque (T) and active power (P).This emulatedTis the synthetic inertia in the synchronverter.Research pertaining to synchronverter controllers has been performed in several areas,such as power frequency (p-f) control,direct-current (DC)link voltage controllers[25],self-synchronous controllers,damping correction loops[26],neural networks[27],and model predictive control[28].

However,research pertaining to digitalized fuzzy logic for synchronverter smart controllers is limited.Moreover,the damping factor (Dp) is fixed and cannot be adjusted based on the frequency deviation.To overcome the limitations of existing studies,a digitalized fuzzy logic controller (FLC) framework is proposed herein to control a synchronverter using an adaptiveDp.The core idea of the proposed FLC-based controller is to utilize the frequency difference (e) and rate of change of the frequency difference (de/dt) as inputs to fuzzy logic.Subsequently,a set of fuzzy rules is determined to control theDpof the synchronverter.The adaptive value ofDpdepends on the values ofeand de/dtfor balancing between transient recovery speed (lowerDp) and dampening stability (higherDp).By controllingDp,the operating frequency can resume to its nominal value even when sudden changes or faults occur.Four case studies were simulated in Matlab/Simulink,and the results are presented herein.The main contributions of this study are as follows.

(1) A novel digitalized FLC framework is designed for a synchronverter controller to stabilize the operating frequency of a grid-connected solar power system under sudden load changes.

(2) TheDpof the synchronverter is manipulated to be adaptive using an FLC to achieve balance between speed and stability based on the frequency deviation.

(3) The solar power system in a real-world environment with varying irradiance and temperature is considered for the design of the FLC framework.

The remainder of this paper is organized as follows.An overview of the synchronverter modeling is presented in Section 2.Section 3 describes the methodological setup of the FLC-based synchronverter in Matlab/Simulink.The simulation results from the four case studies are presented in Section 4.Finally,conclusions are provided in Section 5.

2 Modeling of synchronverter

In general,a synchronverter is defined as a power-electronics-based inverter that converts a DC to an AC while emulating the dynamic behaviors of a conventional synchronous generator (SG)[29].A synchronverter comprises a conventional DC-AC inverter[30]that includes an inductor-capacitor (LC)filter,electronic switching devices,and an electronic pulse width modulation controller[31].It is segregated into power (hardware) and electronic (controller)sections[32].The power section converts DCs to ACs,whereas the electronic section is a measuring and control unit[33],which will be focused on herein.

As shown in Fig.1,a synchronverter is used to interface the DC input from the solar panel with the power grid at the point of common coupling (PCC)[34],whereVdc,Vabc,Vm,andV*represent the direct current voltage,three-phase voltage,measured feedback voltage,and reference voltage,respectively;LandLgrepresent the inductor and grid inductance,respectively;PeandPtrepresent the electromagnetic power and mechanical power,respectively;C,i,Eo,f,andQare the capacitor,current,generated output voltage reference,frequency,and reactive power,respectively.

In their hurry they had, however, forgotten two things: a bundle of keys which lay on the table, and the girl whom the pin had pricked, and who now stood pale and helpless beside the wood stack

Fig.1 Power section of synchronverter

The synchronverter exhibits the advantages and disadvantages of an SM.For example,loss stability due to oscillation around the synchronous frequency may occur in an SM and synchronverter.However,the parameters of a synchronverter,such as the moment of inertia (J),mutual inductance (LM),field inductance (LF),andDpcan be manipulated and varied,unlike an SM.Fig.2 shows the electronic section (controller) of a synchronverter,whereJis the moment of inertia,1/sis the integrator,Pis the active power,Qis the reactive power,eisthe generated reference voltage output,andVmis the measured feedback voltage.

Fig.2 Electronic section of synchronverter

Eqs.(1),(2),and (3) are used to model the SM for the controller of a synchronverter[35].These equations mathematically describe the dynamics of an SM[36].The power section of the synchronverter interacts with the controller using feedback measurement signalseandi.

The controller of a synchronverter comprises an active power loop (APL) and a reactive power loop(RPL)[37].The function of frequency droop control or APL is to controlPwhen regulating the grid frequency (fg),and the function of voltage droop control or RPL is to controlQwhen regulating the grid voltage.The rotor speed of the SG is maintained by the prime mover,andDparises from mechanical friction.When the demand forPincreases,the electromagnetic torque increases as well,resulting in a decrease in speed.Consequently,the power regulation system will increase the mechanical power required to achieve a new power balance.This mechanism is known as frequency droop,which has been implemented in a synchronverter.Because the synchronverter does not have a prime mover (unlike an SM),this mechanism can only be achieved by comparing the virtual angular speedθ·and angular frequency referencerθ·[38].Based on the block,the effect of the frequency droop control loop is equivalent to a significant increase inDp,whichis the combination of an imaginary mechanical friction coefficient and the drooping frequency coefficient.The expression forDpis shown in Eq.(4).By adding this mechanism,the synchronverter shares the load variation with other inverters automatically.

Eqs.(5) and (6) express the rotor motion of the SG,whereNωandωare the nominal and actual values of the rotor angular speed,respectively;PtandPerepresent the mechanical and electromagnetic powers of the synchronverter,respectively;Jis the moment of inertia,andDis the damping ratio of the system.

When the system is grid connected,the frequency must be adjusted via governor control,as shown in Eq.(7).

whereNPis the rated power of the synchronverter;KfandKiare the proportional gain and integral gain of the proportional-integral (PI) controller,respectively.Hence,the parameters that affect the response of the synchronverter controller areJandDp.Instead of setting both parameters as fixed values,manipulating their values based on the frequency error tracking will significantly improve the performance of the synchronverter controller.

3 FLC for synchronverter

In this section,the proposed FLC framework for the synchronverter in a grid-connected solar power system is discussed and presented.

3.1 Proposed FLC-based synchronverter

Fuzzy logic can be categorized as Mamdani and Sugeno types[39].For the design of the FLC in this study,the Mamdani FLC with simple “if-then”relations were used[40].Defuzzification based on the center-of-gravity technique was used for the FLC.To design an FLC for the synchronverter,the value ofDpwas selected as the output of the FLC.It was used to balance the transient recovery speed and dampening stability offg.The frequency difference error (e=fn-fg),wherefnis the nominal frequency at 50 Hz andfgis the grid frequency,as well as de/dtserve as the inputs of the fuzzy logic,as depicted in Fig.3.These inputs are crucial for determiningDp,as the FLC must understand the frequency situation in real time.

Fig.3 Mamdani fuzzy inference engine

Fig.4 Membership function of FLC

Tab.1 shows the rule for the proposed FLC-based synchronverter.Input 1:eand input 2:de/dtdetermine the output values ofDp,where h,m,and l represent high (70 Nms/rad),intermediate (50 Nms/rad),and low (30 Nms/rad) values.

Tab.1 Fuzzy rules used for proposed controller

Ifeis negative,then the value offgis less than thefnat 50 Hz.By contrast,a positive value ofeimplies thatfgis higher thanfn.Iffgcontinues to decrease,then de/dtwill be negative.By contrast,a positive value of de/dtimplies thatfgincreases.When botheand de/dtshow either high positive or negative values,fgbecomes unstable because of sudden load changes or faults.Consequently,the FLC will output a higherDpsuch that the synchronverter can adjust the higher VI when dampeningfg.This is performed such thatfgcan resume to its nominal value at 50 Hz rapidly without stability issues.However,ifeand de/dthave lower values,thenDpwill be lower such that grid stability rather than recovery speed is emphasized.Fig.5 and Fig.6 illustrate the three-dimensional surface plot for the proposed FLC and the rule viewers of the implementation of the FLC,respectively.

Fig.5 Three-dimensional surface plot

Fig.6 The rules viewer of fuzzy logic controller

3.2 Modeling of FLC-based synchronverter controller in Matlab/Simulink

After designing the FLC framework in the built-in fuzzy logic toolbox,the model for the FLC-based synchronverter was developed in Matlab/Simulink.Using typical SM mathematical formulas,as stated in Section 2,the proposed FLC-based synchronverter model was built in a grid-connected solar power system.Fig.7 depicts the controller block diagram of a synchronverter,which includes ap-fcontroller for the APL,a voltage regulator for the RPL,and a synchronverter equation block.This study focuses on APL for frequency regulation.

Fig.7 FLC-based synchronverter controller

The APL controller uses theeof the system to simulate the mechanical power as a control input into the synchronverter block to emulate the VI,as illustrated in Fig.8.Fig.9 shows the rotor function block,which is a sub-block inside the synchronverter block.In this block,the inertia and damping factors are used to emulate the VI.The values ofDpare set as the nominal value before starting or initializing the system.After initializing the system,some of the error functions of the parameter can be determined,andDpcan be manipulated based on fuzzy rules.

Fig.8 The FLC-based framework in APL

Fig.9 Synchronverter internal block with rotor function

Tab.2 presents the simulation parameters for the proposed synchronverter.Dpranged from 30 to 70 Nms/rad (to be controlled by the FLC),and it was dependent oneand de/dt.The LC filter was used to filter the current and voltage ripples produced during the switching time.

Tab.2 Parameters of proposed synchronverter

3.3 Testing environment in grid-connected solar power system

After designing the FLC controller and modeling the synchronverter,the proposed FLC-based synchronverter was simulated in a testing environment comprising a solar panel with varying irradiance and temperature,incremental-conductance-based MPPT,and a power grid at the PCC.Fig.10 shows the overall simulation environment in Matlab/Simulink.The irradiance and temperature were varied to emulate a real-world environment with dynamic weather.The local resistive load was manipulated using a circuit breaker (CB) to emulate sudden load changes.Four test cases were considered to investigate the performance of the proposed FLC by varying the solar inputs and load changes,as shown in Tab.3.

Tab.3 Variation for case studies

Fig.10 Simulated solar panel with varying irradiance and temperature

To validate the effectiveness of the proposed FLC-based synchronverter,the solar inputs and load were varied for the case studies.The DC input side comprised either a constant DC input (ideal condition) or a solar panel input under dynamic weather.For the sudden load change,the resistive load was rated at 10 kW,which was then increased to 12 kW att=0.5 s and then decreased to 8 kW att=1 s.This was performed to investigate the frequency output performance of the proposed FLC-based synchronverter under sudden load changes.The simulation was conducted for 5 s.The performance indices of the FLC-based synchronverter were determined by two factors.First,the controller can execute frequency error correction,in which the frequency error will be controlled within ±1%(0.5 Hz) of the nominal value at 50 Hz.Second,the controller should be able to execute frequency error correction within a specific time range.Figs.11a and 11b show thecurrent-voltage(I-V)and power-voltage (P-V)characteristic curves of the solar panel (Model:SunPower SPR-305E-WHT-D),respectively.

Fig.11 I-V and P-V characteristics curves of solar array under varying input parameters

4 Simulation results and discussion

4.1 Constant DC input with sudden load change

In the first test case,the ideal constant DC input(battery) was used as the DC power source to investigate the performance of the synchronverter under a stable input.Fig.12 shows the load change over time.

Fig.12 Active power for varying resistive loads (RL)

The resistive load (RL) was rated at a nominal value of 10 kW.Using the CB block in Simulink,a sudden load increase was applied to the system att=0.5 s and the load side became 12 kW.Subsequently,a sudden load decrease was applied att=1 s and then decreased to 8 kW.TheRLremained at the same level for the remaining 4 s.Figs.13a and 13b present plots offgandDp.

Fig.13 Outputs of synchronverter for first case study

Att=0 s,fgdecreased significantly owing to the initialization of the system.At this time,fgdeviated significantly from thefnat 50 Hz.Hence,the FLC emulated a largeDpto dampen the decrease in frequency such that the transient of the decreasing frequency is reduced and thefnvalue will be resumed after the completion of error correction by the FLC.Att=0.5 s,a sudden load increase occurred when the CB with an additionalRLwas closed;it was observed thatfgdecreased slightly below its rated value because power demand was greater than power generation.An imbalance in power delivery and consumption caused frequency disturbance. Therefore,the FLC immediately manipulated the adaptive damping constant to recoverfgto its nominal value.Similarly,att=1 s,a sudden load decrease occurred when the CB with an additionalRLwas opened;the frequency of synchronverter was operated slightly above its rated value because power delivery exceeded power demand.In this opposing situation,the FLC instantly manipulated the damping constant to a higher value to recoverfg.The overall results validated the effectiveness of the synchronverter with FLC.The adaptive manipulatableDpof the FLC framework performed better in terms of frequency recovery speed and stability compared with the conventional PI-based synchronverter controller under a constant DC source input and a sudden load change.The proposed FLC can complete the frequency error correction to its rated value at 50 Hz within 5 s.By contrast,the conventional synchronverter can only stabilizefgat 50.07 Hz instead of at 50 Hz.

4.2 Solar panel input (constant irradiance and temperature) with sudden load change

In the second case study,we investigated the performance of the proposed FLC controller based on a real solar panel instead of a battery.As shown in Figs.14a and 14b,two inputs were used,i.e.,the solar irradiance and operating temperature,which were configured as a constant maximum at 1 000 W/m2and 50 ℃,respectively.Fig.14c shows thePof the resistive load.

Fig.14 Testing environment for second case study

In this case study,a sudden load increase and decrease were applied att=0.5 s andt=1 s,respectively.Figs.15a and 15b show the simulation results under this test condition.It was observed that thefgoscillated owing to the load changes;fgindicated a significant overshooting within the first 3 s owing to system initialization.

Fig.15 Outputs of synchronverter for second case study

However,the proposed controller was able to stabilizefgwithin a ±0.5% range after 3 s.The system simulated the different values ofDpbased on the different conditions and fuzzy rules.The sudden load change only affectedfgby ± 0.1.In summary,the proposed FLC maintainedfgat approximately 50 Hz ±0.1 Hz within 5 s.The conventional controller has a larger range offgoscillations of approximately ± 0.15.Although the proposed FLC controller exhibited a higher overshooting during the initialization,it demonstrated a better and more stable operating frequency after settling.

4.3 Solar panel input (varying irradiance and temperature) with constant load

In the third case study,the two inputs of the solar panel,i.e.,irradiance and temperature,were configured as ramp inputs with varying values.This was performed to investigate the performance of the proposed FLC-based synchronverter controller in a real-world environment with dynamic weather.The DC output of the solar panel depended significantly on the weather,particularly the irradiance and temperature.As depicted in Figs.16a and 16b,both the irradiance and temperature were varied at different time frames to emulate the real weather.Meanwhile,RLwas set to 10 kΩ.

Fig.16 Testing environment for third case study

The irradiance value began at 1 000 W/m2and then slowly decreased at 0.6 s.It reached the value of 250 W/m2at 1.1 s and remained therein for approximately 0.1 s then increased again.It reached the value of 1 000 W/m2again at 1.7 s and remained therein until the end.Initially,the temperature was set to 25for 2 s.After 2 s,the temperature was increased to 50 ℃until the end.Because no changes occurred at the load side,the focus of this case study was to investigate the effects of irradiance and temperature on grid stability.The proposed synchronverter controller can perform frequency error correction under dynamic weather conditions.Figs.17a and 17b depict the frequency output and adaptiveDp,respectively.The frequency resulted in oscillation,which was caused by the instability of the solar panel as a power source under dynamic weather.The sudden decrease in solar irradiance att=1 s resulted in a decrease infgowing to an imbalance between power delivery and consumption.

It was observed that a sudden increase in the operating temperature causedfgto increase.This implies that the higher the input power,the higher isfgbecause power generation exceeds power consumption.Based on the fuzzy rules configured in the FLC,the synchronverter selects and emulates the most optimalDpvalue to control the VI-based synchronverter such that the frequency deviation can be corrected while balancing speed and stability,as shown in Fig.17b.Althoughfgexhibited a significant overshooting at the initialization time,the proposed FLC controller was able to dampen the overshooting frequency to its rated value at 50 Hz.The controller selected a higher value ofDpto dampen the overshooting at a faster rate than the conventional controller.The proposed controller performed error correction with high accuracy.The conventional controller can only limitfgwithin a certain range and does not enablefgto be resumed to the rated value.This can be easily verified by observing the simulation graph.The proposed controller was able to maintain afgof approximately 50 Hz with ± 0.1%error within 5 s.The conventional controller oscillated at approximately 50.1 Hz.Hence,the proposed FLC-based synchronverter controller enabled a better qualityfgto be obtained.

Fig.17 Outputs of synchronverter for third case study

4.4 Solar panel input (varying irradiance and temperature) with sudden load change

In the fourth case study,a sudden load change was applied at the PCC,in addition to the varying solar irradiance and temperature.Hence,it is important to prove that the proposed controller performs well.In this scenario,a controller that can provide a good function is the basic requirement.Fig.18 show the testing conditions for the fourth case study.

Fig.18 Testing environment for fourth case study

In this particular case study,the values of varying irradiance and temperature were similar to those in the third case study.The only difference was the sudden load change that occurred att=0.5 s (load increase) andt=1 s (load decrease) to investigate the performance of the proposed FLC controller when instabilities occurred at both the DC source andRLsides.The sudden load change was manipulated using the three-phase CB model in Simulink for automatic load switching.Att=0.5 s,a CB is switched on to increase theRLto 12 kW.Att=1 s,another CB was switched off to decrease the load to 8 kW.Fig.19 show the simulation results.The actions above are analogous to electricity consumers turning on and off their equipment or machines at different time frames.By emulating sudden load changes and dynamic weather for solar panels,the synchronverter controller can perform optimally in the most demanding situations that may occur in real life.

Fig.19 Outputs of synchronverter for fourth case study

The result indicates thatfgexhibited a significant overshooting att=1 s owing to a decrease in solar irradiance and a sudden load increase.Under this condition,the proposed FLC-based synchronverter can perform frequency error correction within 5 s.Thefgwas controlled in the range of ± 0.1.In the first 2 s,fgwas highly unstable and exhibited significant overshooting.The system began to stabilize slowly aftert=2.5 s,and the overshooting subsided.This case study proved that the performance of the proposed FLC controller was satisfactory under sudden load changes and dynamic weather conditions.The proposed FLC controller can perform a fast frequency error correction.By contrast,the conventional controller can only maintainfgat a certain value after a disturbance and cannot perform fast frequency error corrections.

5 Conclusions

Herein,a novel FLC-based framework was proposed to control a synchronverter in a gridconnected solar power system under dynamic weather conditions.Four case studies were simulated in Matlab/Simulink,and the results validated the ability of the proposed controller in stabilizingfgby reducing the frequency deviation by at least 0.2 Hz(0.4%),as compared with the conventional PI-based synchronverter.The performance of the FLC-based synchronverter was optimal even under sudden load changes or varying irradiances and temperatures.Pwas injected or absorbed whenever the frequency decreased or increased,respectively.TheDpcontrolled by the FLC was able to balance between transient speed and stability,whereby a largerDpafforded a more prominent dampening effect,and vice versa.