Enhancing Power Quality in Grid-Integrated Hybrid Renewable Energy System using ANFIS-FBSO

Power is produced by the PV system by converting solar energy into electricity. The maximum power point tracker and DC-DC converter are incorporated into the PV system. In typical irradiance circumstances, obtaining maximum power output requires a maximum power point tracker. To maximise PV voltage and achieve the minimum power point voltage, it calculates the duty cycle for the converter. The duty cycle of a power electronic converter determines how long a converter’s switch is turned on within one switching period. It is defined as the ratio of ON period of switch to the total switching period.

Consequently, data on the electricity produced by the PV are required by the HRES. The equation for power produced by PV is given as: (1) PPV=IR×PEff×REff×PArea {{\rm{P}}_{{\rm{PV}}}} = {{\rm{I}}_{\rm{R}}} \times {{\rm{P}}_{{\rm{Eff}}}} \times {{\rm{R}}_{{\rm{Eff}}}} \times {{\rm{P}}_{{\rm{Area}}}} where P_PV is the PV’s output power (W), I_R is the PV’s irradiance (W / m²), P_Eff is the PV’s efficiency, R_Eff is the efficiency decrease factor because of shadows and direction and P_Area is the PV’s total installed area (Rekioua et al., 2023).

The WTECS transforms kinetic energy into electrical energy. The WTECS includes the WT, shaft and permanent magnet synchronous generator (PMSG) that are utilised to produce energy. A generator and a shaft are rotated by the wind energy in a WT, which transforms mechanical energy into electrical energy. The MPPT and tip speed ratio (TSR) are the factors that regulate the WT system. The power generated by WTECS is given as: (2) PWind=12×Pcof×ρ×A×VWind {P_{Wind}} = {1 \over 2} \times {P_{cof}} \times \rho \times A \times {V_{Wind}} where P_Wind is the power generated by WTECS, P_cof is the coefficient of power, ρ is the air density, A is the windswept area and V_Wind is the wind velocity (Prasad et al., 2022).

In a smart grid, the storage system is essential because load demand may sometimes exceed PV and WTECS production. Overage electricity is chemically stored in a battery bank. Through electrochemical processes, the battery may be charged and discharged, turning chemical energy into electrical energy whilst charging and vice versa when discharging. The power needed to fulfill load demand in the event of no generating power and to store extra power above and beyond load demand is taken into account whilst designing the size of the battery storage. When generation exceeds load demand, stored power makes up for a power loss during low generation. The SOC, which may be calculated at any given time using the following equation, is used to evaluate battery performance. (3) SOCt=SOCt−1+PWindt+PPVt−PGirdtVB×CB SOC\left( t \right) = SOC\left( {t - 1} \right) + {{{P_{Wind}}\left( t \right) + {P_{PV}}\left( t \right) - {P_{Gird}}\left( t \right)} \over {{V_B} \times {C_B}}} where P_Wind (t) is the WTECS power generation, P_PV (t) is the PV power generation, P_Grid (t) is the load demand, V_B is the battery voltage and C_B is the battery capacity.

The battery discharge rate, which is commonly represented by the C-rate or current over time, is based on how rapidly energy is extracted from the battery. C-rate, which shows how quickly a battery is depleted in relation to its maximum capacity, is expressed as I = C × CAP. Here, I represents the discharge current in amperes (A), C for C-rate and CAP for battery capacity in amp-hours (Ah). To develop the smart grid-connected HRES system, battery banks, WTECS and PV are used. The energy management of the smart grid-connected HRES system structure is accomplished with the help of the proposed UPQC controller (Lei et al., 2022).

The DC bus in UPQC acts as an energy buffer between the input and output stages, keeps the voltage level steady for the inverter to operate properly, absorbs power imbalances from fluctuations in RESs and facilitates energy flow in both directions to and from energy storage (Gulzar et al., 2023). The intermittent nature of renewable sources, such as solar and wind, combined with storage, such as batteries in a hybrid renewable energy storage system, can result in changes in DC bus voltage. The shunt and series converters of UPQC exchange power primarily through the DC bus. Stability, PQ and energy management in a hybrid renewable energy storage system depend on accurate modelling and dynamic control of this DC bus (Axente et al., 2011). The dynamic behaviour of the DC bus can be expressed by the following equation (4) Cd Vdcdt=1VdcPSh−PSe+PRes−PL C{{d\;{V_{dc}}} \over {dt}} = {1 \over {{V_{dc}}}}\left( {{P_{Sh}} - {P_{Se}} + {P_{Res}} - {P_L}} \right) where V_dc is the DC link voltage, C is the capacitance of the DC bus, P_Sh is the power flow from the shunt converter, P_Se is the power delivered by the series converter, P_Res is the power generated by renewable sources (PV/wind) and P_L is the load power demand. The main control objectives of dynamic DC bus modelling include the maintenance of V_dc within specified limits, absorb or supply transient power through BESS and to coordinate power flow from PV/wind/battery to avoid over- or under-voltage (Fuyin et al., 2019).

In a smart grid-connected HRES, the recommended MRPID controller is utilised in conjunction with the ANFIS-FBSO algorithm to manage PQ problems related to voltage and current disturbances. Compared to more conventional controllers such as FOPID, PI and PID, the MRPID controller offers more flexibility in frequency management. With its three parameters, the MRPID controller gives the best results in the control process. The MRPID controller significantly reduces error voltage and error current levels by providing optimal pulses. These perfect pulses are chosen using the enhanced ANFIS-FBSO algorithm, which aims to minimise error voltage and error current. Through the use of series and SAPFs to enhance the control method of the UPQC device, this MRPID controller effectively mitigates PQ issues in the smart grid-connected HRES. An extensive overview of the MRPID controller is provided in this section.

The MRPID controller is critical to achieving optimal performance in reducing error voltage and error current in the super control of the smart grid-connected HRES. It does this by mitigating undershoot and overshoot issues in the signal, thereby reducing error signals and speeding up controller response. Along with increasing system performance and demonstrating reduced susceptibility to parameter changes, the MRPID controller may be utilised to rapidly provide isodamping characteristics (Deepa et al., 2023). The MRPID controller leverages the multi-resolution property of wavelets by using several mother wavelet dilations and translations to convert the error signal into a linear mixture of basic functions. Eq. (5) represents the result of a PID controller, which is the sum of three gain parameters, denoted as K_P, K_I and K_D. (5) UPID=KPE+KI∫Edt+KDdEdt {U_{PID}} = {K_P}E + {K_I}\smallint Edt + {K_D}{{dE} \over {dt}}

Here, U_PID is the PID controller output. The generated MRPID controller output signal is given by Eq. (6). (6) UMRPID=KHEH+KM1EM1+KM2EM2+…+KMx−1EMx−1+KLEL {U_{MRPID}} = {K_H}{E_H} + {K_{M1}}{E_{M1}} + {K_{M2}}{E_{M2}} + \ldots + {K_{M\left( {x - 1} \right)}}{E_{M\left( {x - 1} \right)}} + {K_L}{E_L} where U_MRPID is the MRPID controller output, and K_M, K_H and K_L are used as gain parameters for medium frequencies, higher frequencies and low frequencies, respectively, in the case of the MRPID controller. This procedure is shown in Figure 2.

Figure 2.

Diagram of the self-tuned, wavelet-based MRPID optimised controller. MRPID, multi-resolution proportional-integral-derivative.

The best values for accomplishing power management in the smart grid structure are found using the ANFIS algorithm. The FBSO method is used to get the optimum values of the parameters of the fuzzy interference system (FIS). Optimising parameters minimises the discrepancy between the reference and actual values. With the assistance of the improved algorithm, a blend of FBSO and ANFIS, the error value is reduced. Using the FBSO, the settings of the ANFIS are optimised. In this case, the membership functions influence the ANFIS parameters, which are premise parameters. Upon representation of the membership function, optimisation procedures are implemented in order to minimise the error value. The ANFIS algorithm’s parameter configuration enables FBSO to get data from the smart grid structure modelling. The rules listed below are part of the FIS system. (7) If M is M1 and N is N1, then Y1=i1M+j1N+k1 {\rm{If}}\;M\;{\rm{is}}\;{M_1}\;{\rm{and}}\;N\;{\rm{is}}\;{N_1},\;{\rm{then}}\;{Y_1} = {i_1}M + {j_1}N + {k_1} (8) If M is M2 and N is N2, then Y2=i2M+j2N+k2 {\rm{If}}\;M\;{\rm{is}}\;{M_2}\;{\rm{and}}\;N\;{\rm{is}}\;{N_2},\;{\rm{then}}\;{Y_2} = {i_2}M + {j_2}N + {k_2}

The membership functions M and N in this case are represented by M₁, N₁ and M₂, N₂ as non-linear parameters, and the i₁, i₂, j₁, j₂, k₁, k₂ are the linear parameters. The structure of the ANFIS model is shown in Figure 3. The inputs to the ANFIS controller are the voltage and current errors, whereas the output of the ANFIS controller are error-minimised voltage and current values (Naphon et al., 2020).

Figure 3.

Structure of ANFIS model. ANFIS, adaptive neuro-fuzzy inference system.

The following steps provide a detailed explanation of the sequential procedure in each of the ANFIS layers.

The ANFIS algorithm’s learning function is accomplished via the FBSO algorithm. The way that bugs are sought is what drives the algorithm. Pyrrhocoris apterus, often known as firebugs, exhibit two primary behavioural types: firebugs may either walk and investigate in solitude or exhibit gregarious activity and form aggregations. The firebugs use these gatherings to lessen predator pressure and locate suitable partners for procreation. These are the gatherings that firebugs establish throughout the summer. It makes sense to think of firebug movement as an optimisation process as they search for the ideal spouse (Subarnan et al., 2023). The FBSO algorithm’s process is as follows:

Step 1: Initialisation

The initialisation step involves entering the population, voltage, higher and lower bounds, female and male bug input and algorithmic current values. The method generates the gain levels K_H, K_M and K_L for MRPID controller settings at random. (17) P=Fb1mf,Fb2mf,…,Fbnmf P = \left( {Fb_1^{mf},Fb_2^{mf},\; \ldots ,Fb_n^{mf}} \right) where Fb1mf,Fb2mf,…,Fbnmf Fb_1^{mf},Fb_2^{mf}, \ldots ,Fb_n^{mf} are the male and female bug inputs.

Step 2: Fitness function calculation

To provide the best pulses for the MRPID controller’s settings, the ANFIS-FBSO algorithm is used. ANFIS-FBSO algorithm’s initial population consists of MRPID controller settings and error values. Through an optimisation process powered by a fitness function, optimal pulses are produced. The following is the formulation of the optimisation problem for figuring out the MRPID controller parameters: (18) FF=MinSerror FF = {\rm{\;}}Min{\rm{\;}}\left( {{S_{error}}} \right) where S_error is the error signal’s value and FF is the fitness function, respectively.

Step 3: Formation of female colonies

The FBSO method begins with male bugs B_male and of female bugs B_female in a randomly dispersed colony in the search space. Every bug has a real scalar cost function value and a location (represented as a column vector). That is, within the search space, each female insect’s beginning location is regarded as a uniform vector random variable.

Step 4: Mate selection

The location of every male insect in a colony is initialised to that of the best female bug, as males only mate with the most physically fit females. Because of this, the location of every male insect in a colony is continuously adjusted to correspond with the best female.

Step 5: Chemotactic movement of female bugs

Each female insect inside a certain male’s colony has her position stored in a single, synchronously updated matrix. Using effective Hadamard multiplication operations, the following matrix update equations are used for the simultaneous updating of all female bugs in a given colony: (19) Mi←repmatmm′⋅i,1,Bfemale {M_i} \leftarrow repmat\left( {m\left( {m'} \right) \cdot i,1,{B_{female}}} \right) (20) Mj←repmatmr′⋅i,1,Bfemale {M_j} \leftarrow repmat\left( {m\left( {r'} \right) \cdot i,1,{B_{female}}} \right) where r′ is the random integer within the range [1 − B_female]. In response, a matrix containing m′ and n′ copies of the matrix R in row and column dimensions, repmat (R, m′, n′) is obtained, which replicates a matrix R to obtain a higher order matrix. Thus, if R is a u by v matrix, returns a matrix of m′u by n′v. (21) mm′⋅F←mm′⋅F+T1⊙Mi−mm′⋅F+T2⊙Mj−mm′⋅F m\left( {m'} \right) \cdot F \leftarrow m\left( {m'} \right) \cdot F + {T_1} \odot \left( {{{\rm{M}}_{\rm{i}}} - m\left( {m'} \right) \cdot F} \right) + {T_2} \odot \left( {{{\rm{M}}_{\rm{j}}} - m\left( {m'} \right) \cdot F} \right)

The term T₁ ⊙ (M_i − m(m′) · F) represents the pull in the direction of the target, M_i.The difference between the desired position and the current position of the firefly m is first calculated, and the difference is then scaled using the parameters in T₁. In the same manner, the term T₂ ⊙ (M_j − m(m′) · F) represents the pull in the direction of the target, M_j.The difference between the desired position and the current position of the firefly m is first calculated, and the difference is then scaled using the parameters in T₂. Eventually, the attraction parameters T₁ ⊙ (M_i − m(m′) · F) and T₂ ⊙ (M_j − m(m′) · F) are added to the present location m(m′) · F of the firefly to obtain the revised position. The FBSO algorithm simulates the movement and attraction behaviour of fireflies towards brighter spots by repeatedly applying this equation to every firefly in the swarm. Its goal is to converge towards optimal or nearly optimal solutions. Here T₁ and T₂ stand for the colonies of male and female insects, respectively. F is the matrix that shows the position of female bugs. Also ⊙ is the Hadamard product symbol.

Step 6: Attracting male insects to update female insects

Not in its colony, but to fit females, each male beetle is also drawn to them. The males migrate in the direction of the most fit female, which keeps the whole colony contained inside a certain area and prevents the swarm from spreading. To drive male bugs in the direction of the most fit female bug, the following updated rule is used: (22) mm′⋅i←mm′⋅i+T3⊙x−mm′⋅i m\left( {m'} \right) \cdot i \leftarrow m\left( {m'} \right) \cdot i + {T_3} \odot \left( {{\rm{x}} - m\left( {m'} \right) \cdot i} \right)

The term m(m′) · i shows the male bug’s modified position following the application of the movement equation, T₃ is a coefficient that regulates the bug’s motion in the direction of the global optimal position. x symbolises the top position in the search space on a worldwide scale. Amongst all the fireflies, it is frequently the position linked to the highest fitness or objective function value.

Step 7: Swarm cohesion

The individual bugs do not scatter; instead, the whole swarm travels as a cohesive entity. The swarm travels randomly as a single entity; therefore, each insect needs to mimic the path taken by its peers. A herd cohesion model is suggested using Eq. (23), which causes every male bug to migrate in the same direction as a randomly selected male bug in the direction of the most fit female bug. (23) mm′⋅i←mm′⋅i+T4⊙x−mb⋅i m\left( {m'} \right) \cdot i \leftarrow m\left( {m'} \right) \cdot i + {T_4} \odot \left( {{\rm{x}} - m\left( b \right) \cdot i} \right)

Here b is the number of defects, and the investigation of new solutions x is reduced. T₄ is a coefficient that affects how bugs go in the direction of the locations of the fourth colonies.

Step 8: Weak solution

Similarly, Eq. (24) explains why female insects move so weakly in the direction of a different male insect: (24) mm′⋅F←mm′⋅F+T1⊙Mi−mm′⋅F+T2⊙Mj−mm′⋅F m\left( {m'} \right) \cdot F \leftarrow m\left( {m'} \right) \cdot F + {T_1} \odot \left( {{{\rm{M}}_{\rm{i}}} - m\left( {m'} \right) \cdot F} \right) + {T_2} \odot \left( {{{\rm{M}}_{\rm{j}}} - m\left( {m'} \right) \cdot F} \right)

The two terms, T₁ ⊙ (M_i − m(m′) · F) and T₂ ⊙ (M_j − m(m′) · F), describe the movement of the random male insect and the dominant male bug, respectively.

Step 9: Termination

The calculation process halts upon meeting the stopping criteria, or the process repeats, returning to Step 2. To fulfil the fitness function and ultimately address PQ concerns, the optimal solution is selected during the updated process. The gain parameters of the MRPID controller are determined using these fitness functions. A final condition check becomes essential before implementing the optimal solutions, considering factors such as reaching the maximum number of iterations and verifying constraints. The perfect power flow in the HRES linked to the smart grid is then achieved by using the optimal solutions. The system’s PQ problems are successfully mitigated by using the improved ANFIS-FBSO algorithm. Additionally, the ANFIS-FBSO framework offers frequency stability and power balancing. In HRES s, this enables the dynamic control of energy flow and system stability. In addition to storage charging and discharging, power balancing ensures that total generation always meets the total demand. ANFIS predicts the ideal output levels from each source and learns non-linear mappings from system states (such as PV/wind power, load and SOC of battery) to necessary management actions. The FBSO optimises ANFIS parameters, battery charging and discharging levels, demand response, load-side management and generator dispatch. The subsequent section provides a comprehensive overview of the findings and discussions.

When loads are introduced into systems connected to the smart grid’s intended HRES, sag faults may occur. To mitigate and balance the load demand, the proposed system is designed using an MRPID controller based on the ANFIS-FBSO algorithm. In these systems, the WT speed and PV irradiation are maintained at constant levels. Specifically, the PV irradiance is set at 1,000 W/m², whilst the WT speed is held at 12 m/s. Additionally, the battery is in the charging state. This hybrid system is carefully configured to meet load requirements and address PQ issues.

Figure 5(a) illustrates that the power generated by the PV system is 7 × 10⁴ W at irradiance 1,000 W/m², whilst Figure 5(b) shows the power generated by the WT is 5,120 W at a constant wind speed of around 12 m/s. The battery power and SOC are depicted in Figure 5(c), with battery power ranging from 2,000 W to 1,400 W.

Figure 5.

Simulation output of (a) PV irradiance and power, (b) wind speed and power and (c) battery SOC and power. PV, photovoltaic; SOC, state of charge.

The smart grid-connected load system encounters a non-linear load, leading to sags in system voltage and current. The occurrence known as voltage sag arises when incorporating a non-linear load into the HRES. Addressing this phenomenon is crucial to ensure the system operates linearly and stably. The UPQC is used to supply the necessary electricity for meeting load demand and resolving PQ issues. The impact of voltage sag, corrected voltage and injected voltage from the UPQC is depicted in Figure 6(a). Similarly, Figure 6(b) illustrates the existing sag, corrected current and injected current from the UPQC. The implementation of the proposed controller alongside the UPQC effectively tackles PQ issues associated with voltage and current sags. The shunt and series active power filters serve as the primary controls for regulating voltage and current in the HRES system.

Figure 6.

Simulation output in a sag condition (a) source voltage, load voltage and injected voltage and (b) source current, load current and injected current.

The proposed technique’s performance is evaluated under swell conditions, induced by connecting a non-linear load to the system. This assessment of the swell state encompasses various scenarios and analyses their performances. PQ issues related to voltage and current swell scenarios are examined by altering PV irradiation conditions and WT speed. Figure 7 illustrates the variations in PV irradiance, WT speed, WT power and PV power. PV irradiance can be adjusted within the range of 0.7–1 s, with a default setting of 300 W/m² and 0.5–0.7 s. Additionally, it can be set within 0–0.5 s with a range of 1,000 W/m² to 300 W/m².

Figure 7.

Simulation output of (a) PV irradiance and power and (b) wind speed and power. PV, photovoltaic.

Figure 8 depicts the voltage and current swell scenarios. The introduction of a non-linear load induces a voltage surge within the system. As depicted in Figure 8(a), a voltage swell occurs between 0.2 -0.3 s, which is subsequently corrected using a UPQC. The required power is stored in the dc-link capacitor and utilised to alleviate PQ issues and meet load demand. The injected voltage and the corrected output voltage during the swell are also presented. Similarly, Figure 8(b) demonstrates the swell conditions for the current scenario. The proposed controller contributes to achieving load demand objectives and addressing PQ concerns. The selection of optimal system parameters is crucial for the series and SAPFs, which utilise the FBSO and the ANFIS controller-based MRPID controller, in detecting and rectifying incorrect values.

Figure 8.

Simulation output in a swell condition (a) source voltage, load voltage and injected voltage and (b) source current, load current and injected current.

Using the disturbance condition, the proposed technique’s performance is examined. By connecting the non-linear load, the disturbance conditions are introduced into the system. This examination of the swell state looks at a variety of sources and analyses performances. Problems with PQ are analysed with different WT speeds and PV irradiation levels. The changes in WT power, PV power, WT speed and PV irradiance are shown in Figure 9.

Figure 9.

Analysis of (a) PV irradiance and power and (b) wind speed and power. PV, photovoltaic.

Analysing voltage and current disturbance circumstances caused by the application of non-linear loads in grid-connected load systems is necessary for the evaluation of the proposed technique. The corrected, injected and perturbations in voltage are shown in Figure 10.

Figure 10.

Simulation output of voltage disturbance circumstances in the source, load and injected voltage.

Signal disturbances are usually caused by the interaction of uneven load circumstances, critical loads and non-linear loads. Voltage disturbances in the system occur naturally when a non-linear load is introduced on the load side. In order to guarantee the steady functioning of the HRES, the proposed controller is implemented to rectify PQ concerns and adjust for load demand. When the proposed controller is used, the HRES system may operate steadily and lessen PQ issues in non-linear, critical and imbalanced load scenarios. The optimal gain parameters for the MRPID controller are determined through the ANFIS-FBSO technique, aiming to minimise error values in voltage and current signals. The demonstrated flexibility of the proposed controller in responding to load demand and mitigating PQ issues in the HRES is illustrated. To assess the efficacy of the proposed approach, a comparative analysis is conducted against existing design methodologies, and the outcomes of this comparison are presented in the following section. The HRES generating system with a storage system is shown in Figure 11, compensating grid power under various environmental circumstances, such as GWO-FUZZY, CFA-ANFIS, PSO-ANFIS and EHO-FUZZY. The proposed controller is essential for maintaining stable operation on the grid side since it uses the ANFIS-FBSO technique, which ensures the stability and reliability of system performance by achieving better results than the existing methods. The proposed controller is used in the HRES to compensate for load demand and handle PQ problems such as sag, swell, disturbances and harmonics. It also effectively mitigates current and voltage oscillations within the grid-connected HRES by generating optimal control pulses for the series and SAPFs.

Using comparative analysis, the assessment of the proposed methodology is investigated in various harmonic situations. THD is a general term used to measure the harmonic distortion present in a signal. THD is the fundamental measure of PQ, which includes both voltage and current THD. There is more distortion when the THD value is higher. THD of the proposed system is compared with already existing techniques, such as CFA-ANFIS, PSO-ANFIS, EHO-FUZZY and GWO-FUZZY. The signals’ harmonics before and after applying compensation were also examined and confirmed via the proposed method in Figure 12(a). Figure 12(b) provides the comparative analysis of the projected technique in terms of harmonics.

Figure 11.

Comparative analysis of output (a) real power and (b) reactive power.

Figure 12.

(a) Comparative analysis of THD of the proposed method and (b) comparative analysis of THD of existing methods. THD, total harmonic distortion.

Table 2 presents the comparison of THD achieved in the proposed technique with already existing techniques, and results are compared with the ASO algorithm (Goud and Rao, 2021). The calculation times of several methodologies are shown in Table 3, along with the operating times of different controlling schemes. The proposed controlling technique is the MRPID controller, which operates more quickly than other controlling strategies. The proposed technique for optimisation-based controllers achieves an execution time of 480 ms, which is less than the other techniques. Consequently, it works well for the PQ problem in real time.

There are numerous drawbacks and costs associated with ANFIS-FBSO, including a lengthy development period; the potential need for hardware such as graphics processing unit, digital signal processors and field programmable gate arrays if real-time optimisation is desired; complexity in the software that makes integration and maintenance challenging; low explain-ability due to the difficulty in interpreting fuzzy rules after tuning of FBSO; and a high operational delay during training or re-optimisation. Despite numerous drawbacks and costs, the benefits of ANFIS-FBSO outweigh its high cost. These include improved handling of complex inputs and disturbances, fine-tuned control logic for non-linear systems, the potential for adaptive and self-learning control and the ability to minimise operational delay through offline optimisation.