Resiliency oriented control of a smart microgrid with photovoltaic modules

0 Introduction

Harvesting renewable energy resources(RESs)to meet the ever-increasing power demand,mitigate the energy crisis,and reduce carbon emissions are important issues with extensive global concerns[1].Decreasing dependency on depleting fossil fuels and environmental costs are major driving forces for this change.The availability of solar,wind,wave,and tides as natural resources,and sufficiently advanced technology have paved the way for extensive RES applications.Among the available RESs,wind and solar resources are the most prominent,with a very high share of electrical energy production[2].

The wide use of renewable energy generation and distributed generation could possibly enhance the power supply resilience.Because in this case,electrical energy can move in both directions,and an interrupted supply from the main power grid does not cause immediate black-out.MPPT controllers were used to capture the PV irradiance variation.A DC/DC converter is used for maximum power transfer from a PV system.The well-established perturb and observe(P&O)algorithm is used for MPPT in reference[3].However,the P&O algorithm has some negative aspects,such as slow response speed,oscillation in the-steady state,and even incorrect tracking under rapidly changing atmospheric conditions,as clarified in reference[4].A fuzzy logic converter provides improved outputs and quicker reactions to the model changes[5].A very detailed PV module simulation along with control schemes are presented in reference[6]for both the MPPT and inverter to attain a proficient representation.

A current control method is presented in reference[7]for the boost converter along with a momentum based perturb and observe MPPT.This method is used to improve the tracking speed by adding momentum to the hill climbing procedure.A frequency modulated hybrid MPPT algorithm for the LLC resonant converter is presented in reference[8],and is used to improve the MPPT by reducing the oscillation across the peak power.A combinatorial hybrid algorithm is presented in reference[8]based on a neural network along with the P&O algorithm to improve the efficiency of a PV storage system.An optimal frequency-modulated hybrid MPPT algorithm is presented in reference[8]for the LLC resonant converter in PV power applications.A fuzzy logic control based MPPT for a PV system with a silicon carbide boost converter is presented in reference[8].A modified zeta converter based on the ANFIS controller for MPPT control is investigated in reference[8].

Improved performance of PV panels is achieved by using an adaptive neuro fuzzy interface system in reference[9].A hybrid ANFIS based MPPT controller for a PV system with anti-islanding grid protection is demonstrated by experiment in reference[10].The application of ANFIS for electric vehicles was explored in reference[11].A Simlulink model for ANFIS based MPPT control is presented in reference[12].A bidirectional MPPT for a distributed energy system is presented in references[13,14,15].A review of ANFIS methods alongside a novel hill climbing algorithm was presented in reference[16].An efficient maximum power point tracker was experimentally verified and presented in reference[17].A field-programmable gate array(FPGA)circuit implementation of ANFIS is presented in reference[18].

This paper is organized into six sections.For the MPPT control,both the P&O algorithm and fuzzy logic-based control strategy are described in Section 2.In Section 3,a fuzzy inverter model with a fuzzy control scheme is presented.In Section 4,the PV array is presented,considering the mathematical PV cell model.The simulation results are presented in Section 5.Finally,Section 6 concludes the paper.

1 MPPT Control schemes

1.1 MPPT Control schemes

The maximum power point tracking operates the PV modules in such a way that they produce as much power as they are capable of generating[19].Based on the irradiation and temperature variation,the maximum PV power was obtained with the MPPT algorithms.The maximum power point(MPP)is the voltage at which the PV module is able to produce maximum power.Solar radiation,ambient temperature,and PV cell temperature affect the maximum power capability[20].

The algorithm works by perturbing the duty cycle of the power converter and voltage between the PV array and power converter.Perturbing the duty cycle means that the voltage between the PV array and converter is modified.The only problem with the algorithm is that when it reaches the MPP,it does not stop and continues changing the perturbation direction,thus causing power fluctuation[21].Fig.1 shows the P&O model used in this study.This model implements a basic 1-D gradient search with a fixed step size.

Fig.1 (a)Flowchart of MPPT with P&O algorithm(b)simulation model

The PV power measurement passes through a zeroorder sampling block.The integer delay block holds the sampled power for one stepping interval,such that the subtraction block subtracts the current power reading from the previous reading to obtain the algebraic power change sign.This sign is used to set a flag in the block-labeled subsystem.If the change in power is positive(output of the Compare to Zero block is 1),the flag is set to +1,and if negative or zero(output of the Compare to Zero block is 0),the flag is set to -1.The flag then multiplies a user set table MPPT increment,which,in turn,is added to the present PV+ capacitor current to increase or decrease it as appropriate.In this model,the current between the PV array and the converter is regulated.Using the inputs,the change in power is determined.If the change in power is positive and the power keeps rising,the current also increases.If the change in power is negative,the current is decremented,and the power is increased again to match the MPP.

1.2 MPPT with fuzzy logic

Fuzzy logic controllers(FLCs)are becoming increasingly popular for MPPTs[22].The FLCs can work with imprecise inputs without requiring an accurate mathematical model.

The FLC contains three stages:fuzzification,rule-based table lookup,and defuzzification.During fuzzification,numerical inputs are converted into linguistic variables based on the membership functions.The inputs for the MPPT FLC are usually error(E)and change in error(CE).The error(E)and change in error(CE)must be calculated before feeding them to the FLC.The FLC output usually changes with the duty ratio(in this model case,the output is the duty cycle(D),which also represents the change in duty ratio[21].Fig.2 presents a flowchart of the fuzzy logic algorithm for MPPT control.The following formulations are used for simulating the subsystem to the fuzzy logic controller:

Fig.2 Flowchart of the fuzzy logic algorithm[27]

where E(K),CE(K),ΔI,ΔV,I(K),and V(K)represent error generation,change of error,change in current,change in voltage,PV current,and PV voltage,respectively.

The subsystem outputs are error generation(E)and change of error(CE).These are fed to block the fuzzylogic controller with the rule viewer.The output of the fuzzy logic controller with the rule viewer block is the duty cycle.The rule settings used for the fuzzy logic MPPT,are as shown in Table 1.The tuning of forty-nine rules is quite a time-consuming,but it represents improved accuracy and dynamic response.The rule parameters used were negative big(NB),negative medium(NM),negative small(NS),zero(ZE),positive small(PS),positive medium(PM),and positive big(PB).Membership functions are used to determine the weights of the rules and provide an eligible output.Membership functions were built for the inputs and output.The membership function appropriately weights the linguistic characteristics that are attributed to it,and by combining the results,the output is given.The membership functions of the input error(E)are shown in Fig.3[23].The proper operation of the fuzzy controller was verified with the surface view of fuzzy inputs versus output functions,as shown in Fig.5[23].

Fig.3 Membership functions of error

Fig.5 Membership functions generated for the input change in error(de)by ANFIS

Table 1 Forty-nine fuzzy rules of the fuzzy system[27]

E CE NBNMNSZEPSPMPB NB ZEZEZENBNBNBNB NM ZEZEZENMNMNMNM NS NSZEZENSNSNSNS ZE NMNSZEZEZEPSPM PS PMPSPSPSZEZEZE PM PMPMPMZEZEZEZE PB PBPBPBZEZEZEZE

The PV can only generate power during the day and yields significantly higher power in the summer[24].For PV plants to make a significant contribution to the power supply,the further increase in solar power generated must be underpinned by an expansion in storage capacity.The only instant industrial volume storage currently available is a battery[25].Therefore,a battery was used in the model.The battery uses excess power from the PV arrayfor charging.After fully charging,it provides energy to the load and discharges.To control the battery charging and discharging,a control system was created.

Fig.4 Surface view of fuzzy input versus output functions

2 Inverter Control Scheme

Inverters are used in PV systems to convert DC current into AC current.The purpose of the inverter is to connect the PV system with the grid and feed the solar power to the grid with the highest possible efficiency[21].For inverter control,the ANFIS control strategy is implemented.Fig.s 6 and 7 show the controller topology and created controller models,respectively.Three-phase current is transformed to d-q current with the Park transformation block,as shown in Fig.6,and the d-axis current(Idref)is used to regulate the inverter current,and the q-axis current(Iqref)is regulated to zero to obtain a unity power factor(Iqref= 0).The d-qcurrent values obtained from the Park transformation were divided to obtain the error e(k).The error is then fed with the change in error to the FLC.Current is regulated by FLC.Two FLCs were used to regulate the d-axis and q-axis current,respectively.To sense the grid frequency changes,a phase-locked loop(PLL)block is added at the start.The inverter controller output is the control voltage,which is then fed to the inverter through a pulse width modulation(PWM)block to create signals[12].The FLC contains four parts:fuzzification,rule base,inference,and defuzzification.The inputs for the FLC are the change in error(e)and previous error(e(k1)),and the output is the change in the reference signal amplitude du(k)[25].The first step is input fuzzification,which transforms the numerical values into linguistic values.The membership function used for the error change is shown in Fig.5.In the deerror case,five different functions were generated.The FLC rule base is used to provide an appropriate output depending on inputs,membership functions,and rules.The inference is the decision from the previous parts,which is then de-fuzzified.For crisp quantity the output is defuzzified.In the FLC,the ANFIS was used to create membership functions and rules.The ANFIS joins the fuzzy logic and neural system points and provides an enhanced fuzzy derivation.Neural systems are the best learning machines in the field[27].Fuzzy systems lack the ability to learn and can’t adjust themselves[28].The ANFIS is used because it allows fuzzy systems to learn from the data they are modeling(membership function parameters are tuned)[29].To train and check the ANFIS model,the input and output parameters of the proposed FLC were used.After training,ANFIS creates membership parameters and rules.

Fig.6 Inverter controller topology

Fig.7 Fuzzy inverter model

Working principle of the ANFIS is illustrated in Fig.8.The ANFIS inputs are error and change in error.Incoming parameters are organized and then fuzzified,meaning that crisp input values are given linguistic values.The rule strengths were then normalized to prepare them for regulation.Next,the consequent parameters and firing strengths of the rules are estimated.The rule firing strengths estimate the output of each rule.The rule outputs are then added to each other.The sum is de-fuzzified,giving it a crisp value.The retrieved crisp value is the output.

Fig.8 Working principle of ANFIS

3 PV Array

Fig.9 Model of the Grid-connected PV array

A PV array is a set of PV modules,and the PV module is a set of PV cells.A grid-connected PV array mode,created during this study,is depicted in Fig.10.A number of solar cells electrically connected to each other and mounted in a support structure or frame is called a PV module[12].The PV array has two inputs:irradiance and temperature.The PV array model calculates the output current,power,and voltage using these inputs.In the PV array model,the current iseis fed to the controlled current source to obtain the DC circuit output.A PV park with a 135 kW capacity was modeled with individual 225 W PV modules.The PV array has six modules in series,which means that the PV array voltage output is 156 V.The PV array has 100 modules in parallel,meaning the array output current is 867 A.The PV array output is 156 V.400 V is required to connect it to the grid and supply consumers.For this reason,a converter is implemented,which boosts the voltage by lowering the current and regulating power For the PV array,the MPPT is also modeled and added to the converter to regulate the output.Two MPPTs were modeled.The experiments were performed using both models.Fuzzy and P&O MPPTs were created.The MPPTs are used to maintain the PV array output near maximum power.By using MPPTs with a converter,the output voltage is maintained near the desired value after being boosted.The fuzzy MPPT uses the PV array current and voltage as inputs.

Fig.10 Model of the PV cell

These values are used to calculate the error generation E(K)and the error change CE(K).These two outputs are fed to a fuzzy logic controller that uses the inputs,rules,and membership functions to provide the duty cycle(D)as the output.The duty cycle is then fed to the PWM generator,which generates outputs for the IGBT converter.

The battery and variable load are connected to the model’s DC side.The battery takes input from the array and stores it until needed by the load and inverter when the PV array is unable to maintain them.To control the inverter,an inverter control system was implemented.The inverter control system uses a three-phase current and voltage as input with currents Iqand Id.Currents Iqand Idare regulated by two fuzzy logic controllers,one converter for each.In the FLC controller,the ANFIS is used to obtain the correct outputs;whereas the ANFIS adapts itself to the situation and is perfect for this type of system.The control voltage is provided from the inverter controller as the PWM generator output,which then provides the output to the three-level bridge.After the inverter has changed the DC input to the three-phase AC output,it is connected to a three-phase mutual inductance,which determines the line impedance.The model relates to the workload for work and conduct.This completes the model without a grid.The grid side was modeled to connect the model to the grid.A boost converter is a DC-DC power converter.

Boost converters are usually a combination of semiconductor switches and energy storage elements[13],[14].In addition,a capacitor is added to the output to reduce the output voltage ripple.The boost converter topology,as shown in Fig.11,is implemented.The boost converter increases the input voltage to the desired level.The working principle of the PV module is shown in Fig.12.

Fig.11 Boost converter topology

Fig.12 PV Module Topology

A mathematical model of the PV module was created using the following equations and the corresponding simulation model implementation presented in Fig.10.

In Fig.13,the P-V characteristics of the PV module under constant temperature and differing irradiance are illustrated.The figure shows how different irradiance levels affect the output power.The I-V characteristics of the PV module under constant temperature and differing irradiance(left)and I-V characteristics from the PV module datasheet under differing irradiance and constant temperature(right)are shown in Fig.14.By comparing the I-V characteristics of the data sheet and model at different modeled PV module parameters,validity is concluded.

Fig.13 P-V characteristic of the PV module under constant temperature and differing irradiance

Fig.14 I-V characteristic of the PV module under constant temperature and differing irradiance(left)and datasheet I-V characteristic of the PV module under differing irradiance and constant temperature(right)

4 Results

In this study,a detailed mathematical PV module model is presented,considering practical reference values used in the industry.The mathematical model was then validated using the(current-voltage)I-V curve.The I-V curves were created under different cases of irradiance,demonstrating how irradiance affects the output voltage and current.At the MPP,the voltage and current achieved their optimal values.When moving left or right on the I-V line,either voltage or current begins decreasing,resulting in final values of opencircuit voltage(VOC),meaning that current is zero,or short circuit current(ISC),which means that the voltage is zero.In addition,a P-V curve was created to analyze the output power in a PV module under various irradiance conditions.Further,it was noted that in both cases of short-circuit current,and in the open-circuit case,power is zero.

A converter is used when the necessary output voltage is higher than that of the PV array.The PV array output is boosted to a higher level through the converter.The voltage is boosted by the converter but needs to be controlled as well.The MPPT was used for voltage control.An MPPT with a P&O algorithm and an MPPT with a fuzzy algorithm was created.The MPPT ensures that solar modules produce as much power as possible for them.In collaboration with the converter,the MPPT regulates the power to help the converter provide the necessary output voltage.Both the MPPT with the P&O algorithm and the MPPT with fuzzy logic algorithm were used in the final model and were tested.The MPPT with the P&O algorithm tracks the maximum power and regulates the current between the PV array output and converter input to control the voltage in the controller output.In the MPPT with a fuzzy logic algorithm,the FLC was used to calculate the duty cycle.The FLCs change mathematical inputs to linguistic inputs,and by using the membership functions and fuzzy rules of the fuzzy system,they provide the duty cycle change value to the converter for controlling the voltage.Next,a battery was used,and a battery control was created for the PV system.The battery was used to help the PV system provide a more stable output voltage.A battery control system was created to regulate battery charging and discharging.After the controlled voltage in the controller output was received,a device for changing the DC output to three-phase AC output was needed to connect the PV array with the load.An inverter was used for this purpose.The inverter changes the PV arrays in the DC output to the three-phase AC output.An inverter controller was created for proper inverter operation.The created inverter controller uses FLCs.In FLC,ANFIS is used because ANFIS is able to learn from the simulation and provide more regulated outputs to the system.The system was connected to a three-phase AC load.Simulations were performed using both created MPPT models.The outputs of the PV array power,converter output voltage,and inverter output voltage were plotted and investigated.The graphs were analyzed,and it was noted that the model needs more development because the AC side voltage was not maintained at the required level,and it dropped after 0.9 seconds.The reason behind this was the inverter controller,which obtains its information only from the AC side of the model,so it cannot know how much power the PV array can provide to the load.The converter and MPPTs managed to control the voltage as necessary.

5 Discussion

In this model,the fuzzy MPPT is used.Experiments were conducted with a grid-connected model and grid disconnected model to determine how the grid affects the model if the model is working as expected,and is stable.One second was used as a time interval because this was sufficient to determine the model behavior.The PV array output power changes as shown in Fig.15.

The PV output power is never constant and reaches its maximum power twice per second.Thus,the PV array power output is more realistic.As seen in Fig.15(left),the converter and fuzzy MPPT hold the PV array side output constant.The voltage changed slightly,but the change is not noticeable.It is concluded that the converter works well with the fuzzy MPPT and does its job at boosting and maintaining a constant voltage.In Fig.16,the AC voltage in each phase is shown.At the beginning of the model(0 to 0.015 s),the voltage is low because the modulation is just beginning,and the model is already providing the output it must provide later on.At 0.015 s,the voltage rises to a higher level of 160 V,where it should be.

Fig.15 PV array power(left)and converter DC voltage(right)

Fig.16 Alternating voltage after the inverter

The desired voltage level is 230 V,but it is not achieved because the inverter is not calibrated,and the model must be examined to remove this error.In addition,different module constants must be set or calculated to attain the expected voltage level.At 0.09 s,the voltage drops to 5 V.This occurs because the PV array is unable to produce sufficient power.At 5 V,sinusoidal graphs are observed.It is concluded that despite the desired voltage level not being achieved,the model is stable and works as intended because 400 V after the converter is achieved,and the voltage after the AC side is perfectly sinusoidal and continues to run at the same steady-state after the inverter,and the converter begins working as intended.

As seen in Fig.17(left and right),the PV array power and the voltage after the converter are the same as in the model without a grid.The fuzzy MPPT manages to maintain a steady-state in this case as well.

Fig.17 PV array power(left)and converter DC voltage(right)

In Fig.18,the inverter output voltages are observed after the model is connected to the grid.The grid-connected voltage differs from the output of the model without a grid.This difference originates from the supply.

After connecting the model to the grid,the supply from the grid side helps to feed the load.In Fig.18,at time 0 to 0.015 s,the voltage increased to 160 V.This occurs when the voltage from the DC side increases from 0 to 400 V.Subsequently,at time 0.015 s,the voltage drops because the converter is trying to maintain the voltage,and the inverter is calibrated with the grid,load,and supply.At a time of 0.9 s,the voltage rises to 160 V,and the desired level is 230 V,but the inverter needs to be further optimized to achieve the voltage level.Further studies are needed to address these problems.

Fig.18 AC voltage after inverter(with grid)

From Fig.17,it can be concluded that the converter is working,and the model works in a steady state because the voltage level remains constant.In Fig.18,sinusoidal waveforms are seen,which indicate that the model works in the steady-state even after it is connected to the power grid.In this experiment,the P&O MPPT was used,the model was working with constant inputs,and it was disconnected from the grid.As shown in Fig.19(left),the power output of the PV array is the same as that of the fuzzy MPPT.

Because the MPPT works with the converter,the direct output from the power grid is not regulated.The converter output in Fig.19(right)varies slightly more than that of the fuzzy MPPT.The P&O MPPT cannot maintain its output at 400 V.This is due to the eccentricity of the P&O algorithm.The P&O algorithm cannot track quick changes in the model as well as the fuzzy MPPT can;therefore,it takes more time to achieve the model steady-state.In Fig.20,the voltage after the inverter is similar to the fuzzy MPPT model.However,at the beginning of the model,the sinusoidal voltage outputs are not symmetrical and converge at a time of 0.4 s.

Fig.19 PV array power(left)and converter DC voltage(right)without grid when P&O and MPPT is used

Fig.20 AC voltage after inverter(without grid)with P&O and MPPT is used

This occurs because P&O cannot track the model changes fast enough,and it takes time for the module to reach steady-state operation.In this case,the model with the P&O MPPT was connected to the grid to determine how the model behaved.In Fig.21(left),the PV array power remains the same.In Fig.21(right),the voltage at the converter output is better and more stable than that in the model without a grid,as seen in Fig.21(right).

Fig.21 PV array power(left)and converter DC voltage(right)when P&O and MPPT is used

6 Conclusion

It is concluded that despite the inverter not providing the required voltage level,the model was stable and outputs of devices other than the inverter were as expected,the converter maintained a voltage near 400 V,and the inverter gave a sinusoidal three-phase output,which means that the system manages to control the voltage as intended.By comparing the output graphics of the MPPT with the P&O algorithm and the MPPT with the fuzzy algorithm,the MPPT with the fuzzy algorithm provides a better converter voltage output,inverter voltage output had fewer fluctuations,and the system managed to provide a faster and regulated output voltage.In the case of the MPPT with the P&O algorithm,the voltage output of the converter and inverter fluctuated at the start of modulation because P&O was searching for the MPP.After settling down,the MPPT with the P&O algorithm gave better results but was not as good as the MPPT with the fuzzy algorithm results.To determine how the PV system works when included in a larger system,a grid system is modeled.The grid system contained transformers,a power station,feeders,and a grounding transformer.The grid was connected to a PV system through a three-phase switch.In this new system,both the PV array and power grid provide power for the load.By using both MPPTs in the grid connection,graphs of the PV array,controller,and inverter output power are created.In an actual power grid,a PV array is a small portion that does not significantly affect the voltage,and the output voltages are regulated fairly well by electronic devices.However,increasing PV installations may affect instantaneous voltage and frequency levels.From the graphs,it is also concluded that the MPPT with the fuzzy logic algorithm regulates the voltage output better than the P&O algorithm.

Nomenclature

IL—Light current A

Io—Saturation current A

I0,ref—Saturation reference current A

I—load current A

V—Output voltage V

Rs—Series resistance Ω

α—Thermal voltage timing completion factor V

ψ—Irradiance W/m2

Ψref—Reference irradiance(1000 W/m2 was used in this study)

IL,ref—Light current at reference condition A(1000 W/m2 and 25 °C)

Tc—PV cell temperature °C

Tc,ref—Reference temperature(25 °C is used in this study)

µI,SC—Temperature coefficient of short-circuit current AC

egap—Band gap of the material(1.17 eVfor Simaterials)

Ns—Number of PV module cells in series

q—Charge of an electron(1.6021773310-19C)

αref—Value of thermal reference voltage timing completion factor V at reference conditions

Voc,ref—Reference-condition open-circuit voltage(V)of the PV module

Vmp,ref—Maximum power point voltage at reference conditions V

Imp,ref—Maximum power point current at reference conditions A

Isc,ref—Short-circuit current at reference conditions A

Acknowledgement

This work was financially supported by a project under the scheme entitled “Developing Policies &Adaptation Strategies to Climate Change in the Baltic Sea Region”(ASTRA),Project No.ASTRA6-4(2014-2020.4.01.16-0032).

Declaration of Competing Interest

The authors have no conflicts of interest to declare.