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Scientific Reports volume 14, Article number: 22846 (2024 ) Cite this article 200kw built in bypass soft starter
Nowadays environmental concerns and fossil fuel limitations, as well as economic benefits and technical issues such as reliability lead conventional distribution networks to smart microgrids, where the renewable energy resources are merged with the grids. Nevertheless, the systems face new challenges due to the intermittent nature and uncertainties in the distributed generations, which cause frequency fluctuations in the microgrid. The photovoltaic cells are the main part of the contemporary microgrids. Although the photovoltaic (PV) systems depend on solar irradiance, and temperature and are affected by the partial shading phenomenon they could contribute to improving the microgrid frequency stability with a proper control scheme. In this paper, the frequency control strategy is designed for a hybrid stand-alone microgrid, which is robust against load disturbances, variations in weather conditions, and uncertainties in the microgrid parameters. The proposed intelligent control scheme relies on the Recurrent Adaptive Neuro Fuzzy Inference System (RANFIS). The Whale Optimization Algorithm (WOA) is employed to optimize the RANFIS controller structure and generate the parameters of membership functions. In this multi-objective optimization, the objectives are settling time (ST), overshoot (Osh), and Integral Square Error (ISE). The simulation results verify the high robustness and performance of the proposed RANFIS controller, compared to other controllers, during various operational circumstances, as well as the sporadic behavior of renewable energy resources (RES) such as fluctuations in solar radiation and certain uncertainties in the microgrid parameters.
Today, energy is considered not only as a necessity for human life but also as a measure of the economic and social growth of different societies. Therefore, researchers and engineers around the world are looking for solutions to reduce dependence on energy imports, global warming, and electricity generation objectives, as well as increase energy efficiency1,2,3,4. Given the limited non-renewable energy sources on Earth and the Irregular use of fossil fuels that have led to many environmental pollutions, the importance of replacing energy sources that are healthier and safer is well known It is clear. For this reason, the use of other energy sources for electricity generation, including solar power generation using photovoltaic systems, has increased5.
Energy storage systems, distributed generation units (DGs), and loads are often the main components of a microgrid. Microgrids can be connected or disconnected from the main network by a common coupling point (PCC)6. One of the most important features of a microgrid is its ability to island and operate independently. In the case of connected to the network, the voltage and frequency of the network are controlled by the main power network and the sources also generate active and reactive power to a predetermined amount7. It is necessary to maintain the voltage and frequency of the microgrid in the allowable range and supply the required load in this microgrid8. The imbalance between power generation and load variations may cause frequency fluctuations and instability of microgrids with low inertia9. Therefore, this coincidence of random power and uncertainty may cause frequency instability, and create unexpected problems for the safe operation of the microgrid10. Changes in the output power of distributed generation, such as wind turbines and PV systems, and variations in load consumption have led to fluctuations in the microgrid frequency, necessitating the design of controllers to enhance frequency stability11.
Among renewable sources, the PV source has become one of the important sources of distributed generation due to its numerous advantages12,13. However, the persistence of low panel efficiency and susceptibility to weather changes remains a drawback in solar PV panels. To mitigate this issue and enhance power conversion efficiency, PV systems employ maximum power point tracking (MPPT) methods14. Under different weather conditions, the behavior of PV systems is different. When uneven radiation and partial shading occur due to the passage of clouds, it causes uncertainty in the generation capacity of solar cells15. Also, uncertainty in some parameters of Microgrids such as microturbine time constants, governor time constants, speed regulation constants, the load damping coefficient, and load fluctuations can cause frequency deviation and instability of islanded microgrids16.
In recent years, various control techniques have been developed to address the challenges of frequency stabilization in microgrids, particularly those incorporating renewable energy sources like photovoltaic (PV) systems. The use of Fuzzy Logic Control (FLC) for virtual inertia control in isolated microgrids is explored in17. This approach supports frequency stability but may have limitations in handling environmental variations and uncertainties inherent in renewable resources. In18, a PID controller combined with Superconducting Magnetic Energy Storage (SMES) is proposed to maintain stable load frequency and enhance dynamic response. While effective, this method does not comprehensively address the impacts of environmental changes on renewable generation. The study in19 investigates fuzzy adaptive frequency control in microgrids that include Wind Turbine Generators (WTGs). This approach provides valuable insights into integrating wind power with fuzzy logic control but does not cover the full range of renewable resources like PV systems. A predictive controller integrated into a modern fuzzy adaptive model is implemented in20. Although this technique improves frequency control, it does not specifically address the uncertainties related to renewable resources or their environmental impact.
The work in21 employs a fuzzy logic controller optimized using Particle Swarm Optimization (PSO) for PV-integrated systems. This method shows good performance in controlling load frequency but does not consider partial shading effects, which can affect real-world performance. In22, an improved FCS-MPC strategy is proposed to stabilize low-frequency oscillations in PV-based microgrids by accounting for DC-link voltage dynamics. This approach effectively addresses certain operational challenges but may overlook environmental uncertainties. The comparative study in23 analyzes load frequency control using fuzzy logic and neural network-based methods. Despite a thorough comparison, the study does not address parameter uncertainties and weather variations impacting renewable resources. The introduction of a Fuzzy-based Proportional-Integral-Derivative Filter (FPIDF) controller optimized with the Salp Swarm Algorithm and coupled with a Redox Flow Battery (RFB) is discussed in24. This solution offers effective frequency stabilization but faces challenges such as high implementation costs and practical complexities.
In25, a fuzzy-based Proportional Fractional integral derivative with a Filter controller optimized using the COA algorithm is utilized for wind-integrated power systems. While it demonstrates strong performance, it does not fully address minor environmental effects. The study in26 proposes a Combined Fuzzy-based and Fractional-order Integral-Derivative (CFP\(\:{D}^{{\upmu\:}}\) F-PI) controller, which shows improvements in handling changes from renewable sources. However, the combination of controllers may introduce complexities that limit its practical application. An optimized Tilted-Integral-Derivative (TID) controller using the Salp Swarm Algorithm is presented in27. Although this approach positively impacts frequency stability, it does not address variations due to parameter uncertainties or environmental conditions comprehensively. The use of the Artificial Cooperative Search (ACS) algorithm for tuning the Adaptive Network-Based Fuzzy Inference System (ANFIS) in deregulated environments is examined in28. While it focuses on optimal load frequency control, it does not address the impacts of parameter uncertainties and weather conditions on PV systems. An adaptive fuzzy model predictive control strategy for frequency regulation with uncertain and time-varying parameters is proposed in29. This strategy shows effectiveness compared to traditional methods but does not fully consider practical conditions related to renewable energy sources. Finally30, presents the use of ANFIS controllers and deep neural networks to enhance frequency control in PV-integrated microgrids, optimized using the hybrid HB-GWO algorithm.
According to previous research, the authors in these articles have concentrated more on the design of controllers without delving into the intricacies of renewable energy dynamic models and the dynamic models used as energy sources in hybrid microgrids. They are so simple that the presumed models ignore the real dynamic behaviors of the microgrids during LFC studies. The authors also employ simple first-order transfer functions for Energy Storage Systems (ESS) such as batteries and flywheels, and dynamic models and behavior of photovoltaic systems under different weather conditions and shadow effects, as well as some uncertainties in the parameters of microgrids have been ignored.
The most important purpose of this research is to propose a complementary control strategy for the contribution of photovoltaic systems in LFC in the isolated microgrid. This research introduces an adaptive fuzzy droop control system with an intelligent learning process capability for the contribution of photovoltaic systems to reduce frequency fluctuations. In this research, a dynamic model of PV systems under different weather conditions including uniform radiation and partial shading is designed. Due to the low efficiency of the photovoltaic panel and the effect of partial shading due to some phenomena on photovoltaic arrays, an MPPT method based on a fuzzy controller has been used to increase the output power of photovoltaic systems.
Solar PV generation can also benefit the power system frequency regulation via fast active power control. Therefore, it can contribute to the microgrid frequency control scheme by considering a fraction of PV generation as headroom. If the power reserve is available, solar PV generation can also emulate the frequency droop characteristics (‘governor response’) or even the automatic generation control (AGC) function of conventional synchronous generators.
During this contribution, photovoltaic panels reduce the frequency deviation of the microgrid, in addition to the behavior of the photovoltaic system in different weather conditions, some uncertainties in important parameters of the microgrid including the speed droop regulation constant (R), the load damping coefficient (D), the time constant of the governor (\(\:{T}_{\text{g}}\) ), and the time constant of micro-turbine (\(\:{T}_{\text{t}}\) ) are also considered in the design of the microgrid model.
Furthermore, intricate models of energy storage systems have been employed, which incorporate specific system delay blocks possessing a distinct capability to utilize them during frequency deviations. It seems necessary to study the frequency of an isolated microgrid during changes in weather conditions, changes in load, as well as uncertainty in an important parameter of the microgrid. Therefore, intelligent and flexible self-tuning techniques, such as a RANFIS method, are necessary due to the unpredictable frequency response behaviors.
The proposed photovoltaic system, by dynamically adjusting the active power output in real time and providing reserve power within a range of 0 to 15%, not only enhances the response to frequency fluctuations but also contributes to the overall stability of the microgrid, maintaining frequency against load changes and environmental conditions. In this study, in addition to droop control in the primary loop and integral control in the secondary loop, an adaptive fuzzy droop method has been used for the photovoltaic system to reduce the microgrid frequency deviation. The RANFIS method has been employed to address these uncertainties, along with fluctuations in solar cell power under varying radiation conditions, leveraging its intelligent learning capabilities. The RANFIS method is logically trained to enhance the performance of the aforementioned droop control under these uncertainties. Intelligent determination of membership function parameters is achieved through the Whale Optimization Algorithm (WOA), which incorporates several objectives, including the square integral of the error, percentage of overshoot, and settling time.
Figure 1 illustrates the overall structure of an isolated hybrid microgrid that has been investigated in this study. In this microgrid, a dynamic model of a photovoltaic system along with other renewable sources such as wind turbines as well as microturbines battery storage systems, and flywheels have been used in designing the microgrid structure. In the following sections, the details of each of these energy sources will be discussed. To approach the microgrid frequency response to reality, some uncertainties in important microgrid parameters such as (\(\:{T}_{\text{t}}\) ), (\(\:{T}_{\text{g}}\) ), (R), and (D) in the microgrid structure are considered. Due to the uncertainty in renewable energy sources such as photovoltaic systems and uncertainties in microgrid parameters, it is very important to design intelligent controllers for this system. In this study, an R droop control at the primary control level has been used to tune the microturbine speed and improve the microgrid stability and the appropriate and efficient dynamic response to changes in power generation and load. An integral controller is also used as a complementary control to correct the frequency error and tune it within the allowable range. However, due to the photovoltaic system’s complex structure and dynamic model, a robust and intelligent controller of the photovoltaic system is needed. Therefore, PV is responsible for controlling the load frequency of the microgrid.
Microgrid structure with renewable energy sources and energy storage system (ESS).
Each photovoltaic array is comprised of a set of solar cells connected in series and in parallel to enhance both voltage and current levels, thereby achieving the desired output. The efficiency and effectiveness of the PV system are entirely contingent upon the configuration of these arrays, alongside variations in weather conditions. The primary challenge in utilizing a solar cell revolves around attaining its peak power generation potential, a value that varies in response to alterations in radiation and temperature levels. Instances of shading, as well as partial shading, impacting the photovoltaic array yield multiple local maxima on the power-voltage (P-V) curve. Employing maximum power point tracking (MPPT) methods ensures the convergence towards these peaks. Thus, this study focuses on achieving optimal maximum power point tracking under conditions of uniform radiation and partial shading using the fuzzy MPPT approach.
To explain the occurrence of partial shading, a series connection of 3 PV modules is exposed to shading. Partial shading entails the uneven exposure of irradiation across a PV string, stemming from factors such as building shadows, cloud cover, and bird droppings. The presence of partial shading results in distinct steps in the I-V curve and multiple peaks in the P-V curves. The schematic of a PV string incorporating 3 modules, under both partial shading and uniform irradiation, and the I-V and P-V curve for uniform irradiation and partial shading conditions is illustrated in Fig. 2. Consequently, the aforementioned discourse underscores the necessity of employing Maximum Power Point Tracking (MPPT) methods to trace the global maximum power point under partial shading conditions. Therefore, in this study, a fuzzy-based MPPT controller is utilized. The MPPT control strategy for the proposed system employing a DC-DC boost converter is illustrated in Fig. 3.
PV Patterns and I-V and P-V curve for (a) uniform irradiation and (b) partial shading conditions.
Control strategy for MPPT implementation.
The distinct advantage of employing fuzzy logic controllers resides in their capability to operate with imprecise and nonlinear inputs. These controllers facilitate rapid convergence and minimal oscillation at the maximum power point. Furthermore, the fuzzy logic-based method does not necessitate a precise mathematical model. Additional attributes of online fuzzy tracking systems encompass the determination of the utmost power output and robustness against variations in radiation and temperature for computing the optimal operating point. In essence, fuzzy methods demonstrate remarkable suitability in accommodating diverse weather fluctuations.
Given the intricate structure and dynamic model of the photovoltaic system, a robust and intelligent controller is integrated into the photovoltaic system to regulate microgrid frequency. This study proposes the RANFIS method as a controller and compares it against other controllers. Figure 4 illustrates the dynamic model of the photovoltaic system and the controller’s placement during the microgrid frequency load control process. The PV system assumes responsibility for microgrid frequency control. In this dynamic model, an initial frequency measurement is considered to account for various delays. Subsequently, to mitigate low-frequency fluctuations, a high-pass filter is implemented, encompassing the time constant of the internal device connection and the time constant of the DC-to-AC converter.
Ultimately, a control framework is introduced, comprising constant droop, optimal PID, optimal fuzzy, and recurrent adaptive neural fuzzy controllers. This framework is proposed as a means to optimally regulate photovoltaic panels during microgrid frequency fluctuations. The microgrid frequency deviation (∆f) and variations in the photovoltaic system’s output power (∆P) across distinct operational conditions serve as input signals for the dynamic photovoltaic system model. Finally, the changes in the overall power of the PV system \(\:{(\varDelta\:P}_{\text{p}\text{v}}\) ) following the microgrid frequency control process by the LFC block, are injected into the microgrid as the output signal of the dynamic photovoltaic system model31,32.
Dynamic model of small-signal of PV panels.
In modern power systems, photovoltaic (PV) systems play a key role in maintaining frequency stability. To effectively leverage this potential, it is essential to design a system that integrates PV power efficiently and employs advanced control strategies. This study focuses on utilizing PV systems for micro-grid frequency control through dynamic adjustment of active power output, utilizing the RANFIS controller.
Fundamentally, photovoltaic (PV) systems operate at their maximum power output point to effectively utilize their complete capacity in meeting system demands. The PV system operates at its maximum power point and reserves a portion of its power, denoted as \(\:{P}_{\text{r}\text{e}\text{s}}\) to assist in frequency regulation, as shown in Fig. 5. This system dynamically modulates the output power between \(\:{P}_{\text{M}\text{P}\text{P}\text{T}}\) (Maximum Power Point Tracking) and \(\:{P}_{del}\) (power delivery) to effectively respond to frequency variations. The output power of PV panels can vary from 0 to 15% depending on operational conditions, providing a flexible response to frequency fluctuations.
To optimize this process, a Recurrent Adaptive Neuro-Fuzzy Inference System (RANFIS) controller is employed. This controller adjusts the active power injection in real time based on changing system conditions. It helps maintain frequency stability under various operational scenarios and responds to fluctuations in power demand. Integrating the RANFIS controller with PV systems ensures that frequency control remains robust and efficient amidst the complexities of load variations and renewable energy integration.
Photovoltaic power-voltage (P-V) characteristic curve.
Figure 6 illustrates the transfer function of microturbines (MT) under the frequency control process. As evident, this model comprises a governor, generator, and wise delay block represented by first-order modeling. In this dynamic model, \(\:\varDelta\:f\) represents the frequency deviation, while \(\:{T}_{\text{g}}\) , \(\:{T}_{\text{t}}\) and \(\:{T}_{\text{D}\text{e}\text{l}\text{a}\text{y}}\) denote the time constants for the governor, generator, and wise delay, respectively. Furthermore, R illustrates the speed regulation coefficient of the microturbine33.
Model of micro-turbine for frequency analysis.
The flywheel energy storage system (FESS) stores electrical energy in the form of kinetic energy in a high inertia rotating mass (flywheel). Battery energy storage systems (BESS) can also play an important role in stabilizing power systems due to their very fast dynamic response. Batteries and flywheels store excess energy in the microgrid and supply the lack of electrical energy. In small signal analysis, the dynamic model of the battery and the flywheel are modeled with Measurement delay time constant, Command delay time constant, and DC/AC converter time constants, respectively. Also, in the battery storage system, a PI controller with constant coefficients is used. To control the injection of BESS power and make the best use of its capacity to increase stability, the dynamic model and transfer function of the battery storage system and the flywheel are illustrated in Fig. 7, and Fig. 8, respectively34.
Figure 9 illustrates a model of a wind turbine generator (WTG). A WTG extracts energy from the wind in the form of mechanical energy.
Model of wind turbine generator.
The mechanical power output of a WTG changes with the wind speed at that moment. The mechanical power output of the wind turbine is given by the following equation.
In this (1), ρ is the air density, A is the swept area of the blades and V is the wind speed \(\:{\text{C}}_{\text{P}}\) is the power coefficient that is a function of blade pitch angle and tip speed ratio. The \(\:{\text{C}}_{\text{P}}\) parameter is usually controlled at low to medium wind speeds. So that the wind turbine can work in its optimal conditions. The rate of change of wind output power can be approximated using the first-order transfer function as follows.
where\(\:\:{K}_{WT}\) and \(\:{T}_{WT}\) are interest and time constant, respectively35.
In contemporary microgrids, photovoltaic (PV) systems play a crucial role in maintaining frequency stability. These systems contribute to frequency control by providing active power during periods of load fluctuations and environmental changes. Various control strategies, such as PID and fuzzy controllers, have been employed; however, to effectively leverage the potential of PV systems, it is essential to utilize more advanced control strategies. Our proposed control strategy is based on the Recurrent Adaptive Neuro-Fuzzy Inference System (RANFIS). This controller can dynamically adjust the active power output, thereby assisting in frequency control within the microgrid. By modulating the output power across different ranges, including the Maximum Power Point Tracking (MPPT) and power delivery (\(\:{\text{P}}_{\text{d}\text{e}\text{l}}\) ), this control strategy responds to frequency fluctuations and appropriately balances power between these two states.
In the context of controlling the frequency of islanded microgrids, a common approach involves employing droop control based on active-frequency power droop characteristics. As depicted in Fig. 1, within the studied microgrid, the initial frequency control is executed through a microturbine droop loop, where ‘R’ represents the speed droop coefficient per unit. The fundamental concept behind this method centers on regulating frequency by adjusting active power in response to the dynamic behavior of microturbines. To enhance microgrid stability, this control level must exhibit a suitable and efficient dynamic response to changes in power sources and loads. While the primary control loop governs the drooped frequency, it cannot directly restore the frequency to its nominal value. Consequently, an additional interactive loop referred to as the secondary frequency control comes into play. In this research, a simple integral controller is employed as a supplementary component within the secondary loop33.
Proportional Integral Derivative Controllers, or PIDs for short, are another type of hybrid controller that combines all three types of proportional, derivative, and integral controllers.
The output of a PID controller is calculated as follows:
Furthermore, one of the main challenges is tuning the parameters kp, ki, kd, which must be adapted to cope with various constraints in the adjustment process. In this paper, the WOA is used to optimally tune the parameters of the PID controller36.
The Whale Algorithm is a nature-inspired metaheuristic optimization algorithm, drawing inspiration from the hunting behavior of whales. Specifically, it is modeled after the social behavior observed in humpback whales. In this method, humpback whales are seen hunting a group of small fish on the water’s surface. The mathematical model of the Whale Optimization Algorithm, which mirrors the bubble-net hunting strategy, encompasses three key components: the siege hunting method, an attack on the bubble-net, and a search for prey.
This algorithm commences with a set of random solutions. In each iteration, the search agents update their positions based on a randomized approach or concerning the best solution attained thus far. A visual representation of the Whale Optimization Algorithm’s workflow is provided in Fig. 1037.
Fuzzy systems are knowledge-based systems governed by rules. At the core of a fuzzy system lies a knowledge base comprising if-then fuzzy rules. The system that establishes a mapping from input to output through the principles of fuzzy logic is referred to as the Fuzzy Inference System (FIS). Essentially, fuzzy inference systems consist of five functional blocks: a rule base containing a set of if-then fuzzy rules, a database housing Membership Functions (MFs), a fuzzification interface, an inference engine that conducts operations based on rules, and a Defuzzification relationship that converts fuzzy outcomes into deterministic outputs. Typically, the rule base and database are collectively considered the knowledge foundation38.
In Fig. 11, the structure of the fuzzy controller employed in this study is depicted. Here, the fuzzy control inputs are introduced as the frequency deviation (∆f) from the reference value and the derivative of frequency deviation (∆f/∆t) from the reference value. These values are subsequently normalized using coefficients k1 and k2. The α and β coefficients are also linked to the output scale coefficients.
Structure of the fuzzy controller.
The limitations inherent in individual neural networks and fuzzy systems can be overcome by merging the training capability of neural networks with the flexible knowledge representation of fuzzy systems within a single framework. The Adaptive Neuro-Fuzzy Inference System (ANFIS) stands as a hybrid intelligence system capable of generating fuzzy rules from an input-output dataset, employing the principles of the Takagi-Sugeno fuzzy inference system. Leveraging the strengths of both artificial neural networks (ANN) and fuzzy systems, ANFIS proves to be an effective approach for addressing complex and nonlinear phenomena, even in the presence of uncertainty.
ANFIS is structured as a five-layer feedforward network, featuring supervised learning. These layers include fuzzy, rule, normalization, non-fuzzy, and a single aggregate node. This method can be trained using a hybrid learning algorithm, combining the backpropagation (BP) algorithm with the least squares method39.
The RANFIS employs a combination of the backpropagation learning method for teaching the parameters linked to MFs and the Least Squares Estimation (LSE) method to determine the final parameters. Each step within the learning process comprises two distinct phases. First, the input pattern is exposed, and the optimization parameters are estimated through the iterative LSE method. These assumed parameters are held constant during each training cycle. Following this, the template is re-exposed, and during this iteration, the backpropagation method is utilized to adjust the theorem parameters. The ANFIS fuzzy inference system follows the Sugeno type. For a visual representation of the ANFIS structure, please refer to Fig. 12, which illustrates the five distinct layers involved in the process.
The values of D, R, \(\:{T}_{\text{t}},\) and \(\:{T}_{\text{g}}\) , which represent microgrid uncertainties, are utilized as inputs in this system. The output of this structure (F) represents the set of parameters a, b, c, and d corresponding to the MFs depicted in Fig. 12. These parameters dynamically adjust to optimize the objective function, which comprises various frequency response features40. The structure is outlined as follows for each layer:
The initial layer, referred to as the fuzzy layer, utilizes MFs to derive fuzzy clusters from input values. These MFs are shaped by hypothetical parameters, denoted as (a, b, c). The degree of membership for each function is determined using these parameters. As shown in Eqs. (4) and (5), the membership scores from this layer are represented as x and y.
The second layer, known as the role layer, corresponds to the “if” part of the rules. Firing strengths (\(\:{\omega\:}_{i}\) ) for rules are computed using the calculated membership values from the fuzzy layer. The value of \(\:{\omega\:}_{i}\:\) is determined by multiplying the membership values, as illustrated in Eq. (7).
In the third layer, named the normalization layer, the method calculates the normalized firing strengths for each rule. The normalized value represents the ratio of the firepower of Rule (i) to the total firepower, as defined in Eq. (8).
The fourth layer, known as the de-fuzzy layer, computes the weighted values of the rules in each node. This calculation is performed according to first-order polynomials. \(\:{\omega\:}_{i\:}\) represents the output from the normalization layer, while \(\:{p}_{i\:}\) , \(\:{q}_{i\:}\) and \(\:{r}_{i}\:\) are parameter sets are referred to as result parameters. The number of outcome parameters for each rule is one more than the number of inputs, as expressed in Eq. (9).
The fifth and final layer is the output layer. The actual output of the ANFIS is obtained by summing the outputs obtained for each rule in the de-fuzzy layer, as given in Eq. (10).
In this section, the frequency model of a microgrid with various distributed generation sources is first implemented to control the microgrid frequency. The proposed RANFIS controller is designed to reduce fluctuations in the microgrid frequency compared to other controllers. Photovoltaic (PV) systems play a crucial role in maintaining frequency stability by providing active power during periods of load fluctuations and environmental changes. Additionally, various controllers, such as PID and fuzzy controllers, are employed to enhance the performance of PV systems and respond effectively to frequency variations.
The RANFIS controller is utilized to adjust the active power output in real time based on changing system conditions. This controller demonstrates high performance, especially under variable load conditions and fluctuations in solar irradiance. For instance, PV systems can modulate their power output within a range of 0–15% to effectively respond to frequency fluctuations. The integration of the RANFIS controller with PV systems ensures that frequency control remains robust and efficient in the face of instabilities and load variations, as clearly observed in the simulation results.
Figure 13 illustrates the block diagram model of our simulated microgrid, encompassing dynamic models of photovoltaic systems, wind turbines, microturbines, battery storage systems, and flywheels. Additionally, we outline the placement and control of the microgrid frequency load by the proposed controller, which is focused on the photovoltaic system. Simulations are carried out within the Simulink MATLAB software environment. For reference, the parameters of the investigated microgrid, battery storage systems, and flywheels can be found in Tables 1 and 2, respectively. Moreover, Tables 3 and 4 present the parameters associated with the dynamic model of the photovoltaic system and the electrical characteristics of the solar panel, respectively.
The proposed microgrid frequency model.
In our investigation, we employ a constant droop control (R = 2 Hz/pu) as the primary control mechanism to regulate microturbine speed. This approach enhances microgrid stability and ensures a swift and efficient response to changes in power sources and loads. To further address frequency deviations and maintain them within acceptable limits, an integral controller (Ks) with a fixed value of 1.75 is introduced as a supplementary control.
Given the intricate structure and dynamic model of the PV system, a robust and intelligent controller is imperative. In this study, we employ an optimal Proportional-Integral-Derivative (PID) controller to manage microgrid load frequency within the photovoltaic system. The controller’s structure has been previously detailed in the preceding sections. We utilize the WOA to determine the coefficients of this controller and optimize the associated objective function. Table 5 provides the optimized PID controller parameters, encompassing proportional, integral, and derivative coefficients, along with the objective function value obtained after WOA optimization.
As previously introduced in the preceding sections, the fuzzy controller’s overarching structure entails two error inputs and an error derivative. These inputs, representing frequency deviation and its derivative, are fed into the controller. Within a predefined range, two input signals are manipulated using fuzzy logic, determined by the coefficients of interest denoted as k1 and k2 in the model.
The α and β coefficients, located downstream of the fuzzy controller in the applied model, are responsible for translating the computed output value of the fuzzy controller system into a tangible value for implementation within the system. The specific values of these gain coefficients can be found in Table 1. The fuzzy rule section comprises 49 meticulously detailed rules, as demonstrated in Table 6.
The MFs utilized for the inputs of the fuzzy controller are divided into seven sections for both frequency deviation inputs and frequency deviation derivatives, as outlined in Table 6. These functions employ a combination of triangular and trapezoidal shapes. The MFs associated with the output signal are likewise divided into seven parts, using triangular and trapezoidal shapes. The fuzzy control system follows the Mamdani fuzzy logic framework, and the non-fuzzy centroid of gravity method has been chosen for processing.
Figures 14 and 15, illustrate the MFs for the inputs and output of this fuzzy controller following optimization through the WOA. One of the inputs for this fuzzy controller is frequency deviation (Δf), while the other is the derivative of frequency deviation (Δf / Δt). It’s noteworthy that the performance of the controller depends on the parameters governing these MFs.
To ensure robust performance in maintaining microgrid frequency stability, the control function membership centroids of this controller are optimized using the WOA. Consequently, for each state of the examined system, the parameters of the MFs are updated. The optimal parameters of this controller and the optimized value of the objective function after WOA optimization, are summarized in Table 7. A three-dimensional surface representation of the fuzzy controller can also be seen in Fig. 16.
Membership function curves for inputs.
Membership function curves for output.
3D surface of the fuzzy controller.
The proposed RANFIS performance has a supervisory role during parameter uncertainties and changes in weather conditions. The structure of the proposed controller is illustrated in Fig. 17. The proposed droop control scheme takes two input signals: frequency deviation (\(\:\varDelta\:f\) ) and its derivative (\(\:\varDelta\:f/\varDelta\:t\) ). The adaptive fuzzy-neural inference system in this proposed controller is of Takagi-Sugeno type and the MFs of the inputs of this proposed droop are of Gaussian type and its output MFs are of Linear type.
Structure of the proposed controller.
Important microgrid parameters such as (\(\:{T}_{\text{t}}\) ), (\(\:{T}_{\text{g}}\) ), (R), (D), have been utilized as microgrid uncertainty parameters at the input of the RANFIS layer. The effectiveness of this controller depends on the parameters of the MFs. By changing the microgrid uncertainty parameters, the membership centroids of this controller are updated in each iteration.
In the proposed RANFIS controller design, a significant enhancement in the optimization of the controller parameters is achieved using the Whale Optimization Algorithm (WOA). This integration allows for a systematic adjustment of the membership function parameters, ensuring that the controller can adapt to dynamic changes in microgrid conditions. By optimizing the parameters of the RANFIS controller through WOA, the controller not only improves its response to uncertainties but also enhances its overall efficiency and stability during operational scenarios.
In the output layer of this system, parameters a, b, and c are obtained as the centroids of the membership function for inputs, While the d parameter represents the centroid of the output membership function of this controller. The 3D surface of the proposed controller is illustrated in Fig. 18. The parameters of the MFs and the objective function of the proposed RANFIS controller are presented in Table 8.
The 3D surface of the proposed controller.
To achieve optimal system performance, selecting the appropriate objective function is the most important aspect of any optimization algorithm in tuning controller gains. The purpose of the objective function is to minimize ∆f frequency deviation in the system under study. The objective function formulated to analyze the optimal performance of the LFC model of the power system under study is defined by the following equation:
In our objective function, we incorporate several crucial characteristics of the frequency response, including the error squared integral (ISE), settling time (ST), and its overshoot (OSh). To enable a numerical comparison of controller performance for microgrid load frequency control, we introduce the ISE evaluation index.
The ISE integral measures the square of the error, thereby swiftly attenuating large errors (as the square of a large error yields a significantly larger value), while accommodating stable small errors over extended durations. This characteristic yields a rapid response but exhibits a limited dynamic range and fluctuation. These unique features motivated our choice of implementing the ISE evaluation index in our current system41. The index is calculated based on frequency deviation and its changes, as per Eq. (12).
Settling Time (ST) is defined as the time taken for the system response to first remain within a specified percentage (commonly 2%) of the final value after a disturbance. This measure fundamentally indicates the speed of the system’s stability following changes and is typically estimated from the system’s step response. Settling Time can be calculated using the following equation:
Overshoot (OSh) refers to the additional amount that the response exceeds the desired steady-state value, usually expressed as a percentage of the desired value. Overshoot can be computed using the following equation:
where \(\:{\varDelta\:f}_{max}\) is the maximum value of frequency deviation during the transient response, and \(\:{\varDelta\:f}_{final}\) is the stable value after the system has stabilized. These indices allow us to accurately assess the performance of different controllers and ultimately lead to better designs for load frequency control in microgrids. In this research, we specifically examine these criteria in designing intelligent controllers to improve frequency stability in microgrids.
To demonstrate the robust design and superior performance of the proposed controller in comparison to other controllers examined in this study, we conducted a series of scenarios. These scenarios encompass various test cases, such as step load changes, uncertainties in critical microgrid parameters (micro-turbine time constant \(\:{T}_{\text{t}}\) , governor time constant \(\:{T}_{\text{g}}\) , speed droop regulation constant R, and load damping coefficient D, and fluctuations in photovoltaic system output power due to different weather conditions.
The simulation results, which evaluate the controller performance under different perturbations and uncertainties, are presented in four distinct scenarios.
In general, four case studies have been conducted in this article, and they are described as follows:
Scenario One: Analyzing the Impact of Contribution Photovoltaic Systems on Microgrid Load Frequency Control (LFC).
Scenario Two: Analyzing Controller Performance and Solar Panel Contribution under Parameter Uncertainty.
Scenario Three: The Microgrid Frequency Response to Rapid Solar Radiation Fluctuations during Parameter Uncertainty.
Scenario Four: The Microgrid Frequency Response under Uniform Radiation, Partial Shading, and Uncertainty Conditions on the PV Array.
In this scenario, to illustrate the influence of solar panel contribution on the frequency stability of the microgrid, a step overload of 0.1 per unit is imposed on the microgrid at t = 2 s. The performance of the microgrid is evaluated under two modes: with the contribution of solar panels utilizing a constant droop control, and without PV panels, relying solely on microturbines and BESS.
In this scenario, the contribution of solar panels is determined based on a constant droop control. To showcase the performance of solar panels with a constant droop control, frequency deviation is depicted in Fig. 19. It is evident that the PV contribution enhances the system’s frequency response. The Integral of Squared Error (ISE) values for the microgrid with the contribution of PV panels using constant droop control and the microgrid without PV panels are 0.6027 and 1.7713, respectively. Furthermore, in Fig. 20, the frequency response of the microgrid using different controllers has been compared. Simulation results demonstrate that integrating photovoltaic (PV) systems into frequency control significantly reduces the Integral Square Error (ISE). Specifically, the ISE is reduced by 66% compared to the case without PV systems. In contrast, this reduction reaches 83% with optimized PID controllers and an impressive 96% with the proposed RANFIS controller. The integration of the RANFIS controller with PV systems ensures robust and efficient frequency control, even in the face of instabilities and load variations, as clearly observed in the simulation results.
Comparison of microgrid frequency response with and without PV contribution under constant droop control.
Comparison of microgrid frequency response to load disturbances with different controllers.
In this scenario, a step overload of 0.1 per unit is imposed on the microgrid at t = 2s. Also, to approach the real microgrid frequency response, some uncertainties including a micro-turbine time constant \(\:\left({T}_{\text{t}}\right)\) , governor time constant \(\:{(T}_{\text{g}})\) , speed droop regulation constant (R), and load damping coefficient (D) have been taken into account. The performance of the constant droop Optimal PID Optimal fuzzy controller and the proposed RANFIS controller to deal with microgrid frequency deviation are compared.
For this purpose, uncertainties in four different patterns during the Contribution of photovoltaic panels are presented in Table 9. As the RANFIS is responsible for fuzzy droop training during uncertainties, and with each change in the microgrid parameters, the proposed RANFIS membership function centroids are tuned and the microgrid frequency deviation is well controlled. This performance is further specified to reduce the sitting time, its extravagance percentage, and total error squares according to Table 10.
Finally, the frequency deviation results under the most adverse conditions (fourth pattern) during the incidence of load perturbation are illustrated in Fig. 21. Furthermore, Fig. 22, presents a comparison of the microgrid frequency response under four uncertainty patterns using both the optimal PID controller and the proposed RANFIS controller. According to the frequency behavior, it can be seen that the proposed RANFIS shows a more satisfactory performance during uncertainty. According to the data presented in Table 9, the performance of various controllers under four different uncertainty patterns is analyzed. This comparison indicates that the RANFIS controller, due to its ability to automatically adjust membership function centroids and adapt to changes in microgrid parameters, achieves the lowest settling time (ST) and overshoot (OSh) compared to the optimized PID controller and the optimized fuzzy controller.
For instance, in the fourth uncertainty pattern, which represents the most severe conditions, the proposed RANFIS controller experiences a 74% reduction in the Integral Square Error (ISE), a 92% reduction in overshoot (OSh), and a less than 1% reduction in settling time (ST) compared to the optimized PID controller. These results demonstrate that the proposed RANFIS controller exhibits significantly better performance in handling microgrid uncertainties, especially under conditions where parameter variations are substantial.
Microgrid frequency response under the uncertainty conditions (fourth pattern).
Comparison of microgrid frequency response under parameter uncertainty conditions.
To assess the robustness of the adaptive fuzzy droop controller under varying weather conditions, we introduce a solar radiation perturbation to the PV array, as depicted in Fig. 22. In this scenario, rapid fluctuations in radiation are simulated over 45 s. The microgrid’s frequency response to these changes is compared between the optimal PID controller and the proposed RANFIS controller, as illustrated in Fig. 23.
The results presented in Fig. 24 affirm that although the proposed RANFIS controller for PV effectively stabilizes the microgrid frequency during solar radiation variations, it also performs better than the PID controller. The ISE values for the optimal PID controller and the proposed controller are 0.0014 and 223 × 1\(\:{0}^{-4}\) respectively, indicating the superior performance of the proposed controller under changing weather conditions compared to the optimal PID controller.
A comparison of microgrid frequency response characteristics under rapid radiation fluctuations in different weather conditions and parameter uncertainties is provided in Table 11. This performance is further specified to reduce the sitting time, its extravagance percentage, and total error squares. In summary, the proposed adaptive fuzzy droop controller effectively mitigates the effects of irradiance fluctuations and surpasses the performance of the PID droop controller.
To evaluate the performance of the controllers in Scenario 3, which involves rapid solar radiation fluctuations under parameter uncertainty, the numerical results are presented in Table X. In the fourth pattern, which represents the most severe conditions, the results indicate that the RANFIS controller outperforms the optimized PID controller. Specifically, in this scenario, the Integral Square Error (ISE) for the RANFIS controller shows a 74% reduction compared to the optimized PID controller. Additionally, the settling time (ST) and overshoot (OSh) exhibit reductions of a less than 1% and 49%, respectively, compared to the optimized PID controller. These results demonstrate the superior performance of the RANFIS controller in managing solar radiation fluctuations and maintaining microgrid frequency stability under severe uncertainty conditions.
Rapid solar radiation fluctuations during variable weather conditions.
Microgrid frequency response to rapid solar radiation fluctuations during variable weather conditions.
In this scenario, to comprehensively assess the system’s stability with the proposed controller, we subject the PV array to perturbations in the form of uniform radiation and partial shading. To model partial shading, we connect the three panels in series and expose them to both uniform and partially shaded radiation.
To investigate this scenario, we conducted a simulation involving a gradual change in radiation levels to evaluate the adaptive fuzzy droop controller’s robustness during uniform radiation on three PV arrays, as depicted in Fig. 25. As shown in Fig. 26, the microgrid’s frequency response under these conditions proves highly favorable, offering a substantial advantage over the optimal PID controller.
Additionally, we conducted another simulation simulating partial shading, where the radiation level differs for the three panels. To model this partial shading, we considered three types of radiation for the solar cell array according to Fig. 27, with values of 1000 W/m² for the first array, 700 W/m² for the second array, and 500 W/m² for the third array. Considering that there are several peaks of the maximum power point (MPP) in partial shade conditions conventional MPPT controllers are unable to track MPP during radiation in partial shade conditions. Therefore, in this study, a fuzzy-based MPPT controller is used. Moreover, A comparison of microgrid frequency response characteristics under rapid radiation fluctuations in different weather conditions and parameter uncertainties is provided in Table 12.
Figure 28 illustrates the frequency response of the microgrid during solar radiation conditions under partial shade. Also in Fig. 29, the comparison of microgrid frequency response during four uncertainty patterns by the optimal PID controller and the proposed RANFIS controller is shown. The results show that the proposed controller improves the frequency fluctuations well in the condition of partial shading and uncertainty of microgrid parameters.
The simulation results demonstrate that the proposed controller exhibits significantly less overshoot and undershoot percentages compared to the optimal PID controller. Moreover, when evaluating the controller’s performance in controlling the microgrid frequency load, we calculated the Integral of Squared Error (ISE) index. For the optimal PID controller, the ISE values are 0.0020 in uniform radiation mode and 0.0011 in partial shading mode. In contrast, for the proposed controller, the ISE values are 5.5367 × 1\(\:{0}^{-4}\:\) in uniform radiation mode and 3.0475×\(\:{10}^{-4}\:\) in partial shading mode.
These results indicate that the proposed controller not only outperforms the PID controller in various weather conditions, including uniform radiation and partial shading but also offers significant advantages in terms of stability and control precision.
In the fourth pattern, which represents the most severe partial shading conditions, the results indicate that the RANFIS controller outperforms the optimal PID controller. Specifically, in this scenario, the Integral of Squared Error (ISE) for the RANFIS controller shows a 73% reduction compared to the optimal PID controller. Additionally, the settling time (ST) and overshoot (OSh) exhibit reductions of 0.04% and 50%, respectively, compared to the optimal PID controller. These results emphasize that the RANFIS controller has effectively managed the fluctuations caused by partial shading and uncertainties related to microgrid parameters, improving frequency stability under these challenging conditions.
The gradual variation in solar cell radiation levels during uniform irradiation.
Frequency response of microgrids during uniform irradiation of PV arrays.
Tested PV patterns under both uniform radiation and partial shading conditions.
Microgrid frequency response under partial shading conditions on PV array.
Microgrid frequency response under uncertainty and partial shading conditions.
The simulation results across all scenarios demonstrate the remarkable performance of the proposed RANFIS controller in enhancing the frequency stability of the microgrid under various operating conditions. The RANFIS controller consistently outperforms traditional control strategies, such as optimized PID and fixed-gain controllers, particularly in scenarios involving parameter uncertainties and rapid fluctuations in solar radiation. The Integral Square Error (ISE) metrics indicate a significant reduction in frequency deviations, highlighting the controller’s ability to effectively mitigate the adverse effects of load disturbances and variability in renewable energy generation. According to the simulations performed in this paper, the results of these simulations are presented by different controllers to improve the ISE performance index in Table 13. Furthermore, the results show that the RANFIS controller not only improves settling times and reduces overshoot percentages but also adapts seamlessly to the complexities introduced by partial shading conditions and other uncertainties. Overall, these findings confirm the robustness and adaptability of the proposed controller, making it a compelling solution for modern microgrid applications that require reliable frequency control in the face of fluctuating renewable energy inputs.
In conclusion, an important topic that arises in microgrids is frequency control in the presence of perturbations, uncertainties, and variations in load and power generation capacity from renewable energy sources. In this paper, we proposed a RANFIS controller to manage the frequency of a hybrid microgrid. To approximate the obtained results with real-world scenarios, various uncertainties were introduced into critical microgrid parameters. The structure of the proposed controller is designed to optimize the membership function parameters each time the microgrid parameters change, allowing the RANFIS to play a monitoring role during parameter uncertainties. The conducted scenarios confirm the robustness and sensitivity of the proposed controller to load disturbances and fluctuations in solar radiation under different weather conditions, including rapid changes in solar radiation, uniform radiation, and partial shading. Furthermore, given that multiple peaks of the maximum power point (MPP) occur under partial shading conditions, conventional MPPT controllers often struggle to track the MPP. Therefore, a fuzzy-based MPPT controller was utilized in this study. We analyzed and tested four types of controllers: constant droop, optimal PID with WOA, optimal fuzzy with WOA, and the proposed RANFIS controller. To effectively demonstrate the advantages of the proposed control system, the results of frequency deviation reduction were compared using the Integral Square Error (ISE) index. The results indicate that the frequency deviation in the proposed RANFIS controller is reduced by 7% compared to the optimal fuzzy controller, 74% compared to the optimal PID controller, and 88% compared to the constant droop controller. Additionally, the proposed controller outperforms the others in terms of settling time (ST), percentage of overshoot (Osh), square integral error (ISE), and steady-state error.
All data generated and analyzed during the current study are available from the corresponding author on reasonable request.
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Department of Electrical Engineering, University of Mohaghegh Ardabili, Ardabil, Iran
Ebrahim Alipour, Abdolmajid Dejamkhooy & Majid Hosseinpour
School of Engineering, RMIT University, Melbourne, Australia
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Ebrahim Alipour and Abdolmajid Dejamkhooy designed and performed data analysis, and documentation. Majid Hosseinpour and Arash Vahidnia performed data analysis and supervision. All authors reviewed the manuscript.
The authors declare no competing interests.
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Alipour, E., Dejamkhooy, A., Hosseinpour, M. et al. Enhanced frequency control of a hybrid microgrid using RANFIS for partially shaded photovoltaic systems under uncertainties. Sci Rep 14, 22846 (2024). https://doi.org/10.1038/s41598-024-73233-x
DOI: https://doi.org/10.1038/s41598-024-73233-x
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