A Novel Solution for Solving the Frequency Regulation Problem of Renewable Interlinked Power System Using Fusion of AI

Abstract

The requirement for clean energy has increased drastically over the years due to the emission of CO₂ and the degrading of the environment by introducing Renewable Energy Systems (RES) into the existing power grid. While these systems are a positive change, they come at a cost, with some issues relating to the stability of the grid and feasibility. Hence, this research paper closely investigates the modeling and interlinking of photovoltaic (PV)-based solar power and Double-Fed Induction Generator (DFIG)-based wind turbines with the conventional power systems. RES has been known to contribute to a highly non-linear system and complexity. To return the power systems to their original state after a load disturbance, a novel control technique based on the fractional-order Type-2 Fuzzy logic system, well developed via particle swarm optimization (PSO), has been utilized for solving the frequency control problem of a renewable interlinked power system. The efficacy of the proposed technique is validated for various possible operating conditions and the system results are compared with some of the recent methods with and without including non-linearity, and the performance of the controllers is superimposed on frequency/time graphs for ease of understanding to show the benefits of the proposed research work.

1. Introduction

In recent years, the implementation of clean energy into the power system has been the focus of the modern era. Multiple applications, such as hydro, wind, and solar power, are being interconnected with the existing power system to help curb some of the negative environmental effects. These methods are highly sought after but have negative effects when increasing the system frequency disturbances and financial costs [1]. Renewable energy has been known for its highly non-linear contribution to the grid. For instance, PV-based solar energy makes use of the unlimited light energy from the sun called irradiance. The energy output is dependent on the amount of irradiance that can be produced. This contributes to a highly variable system due to the fluctuations of sunlight that are available in a particular area. Further, wind energy has been shown to have a similar effect, with the wind becoming highly unpredictable with its constant wind speeds. Even though this is the case, the temperature of the world has been rising every year, which makes solar energy a good alternative for energy generation. Similarly, studies have shown that wind levels are bound to increase in the future.

DFIG wind-based energy schemes have been shown to assist with system stability after a fault has occurred but rely on the type of control method option. One of the phenomena experienced by series-compensated wind power systems is sub-synchronous resonance. Dynamic reactive power reference signals at the point of common coupling are required to ensure that the reactive power supply is upheld [2,3]. DFIG shares properties of inductive and synchronous generators, which further contribute to the power system stability. Without interfering with voltage control, the damping of power variations in the power system can be improved through effective control. One of the control methods that researchers use is diode rectifiers for wind power systems, which contributes to stability error reduction while the output active power increases. With active and reactive power playing an important role, information gathered from scholars states that wind turbines with varying wind speed over time decrease voltage fluctuations [4,5,6,7]. The governors of thermal power units do not have the necessary measures to reduce frequency deviations, with its stagnant response and lack of control.

The PV-based solar system incorporates an inverter within its system, which reduces system inertia and makes the system more susceptible to disturbances. While disturbances pose a problem to the power grid, the efficiency of wind and solar systems is very low and they are proposed, depending on the application, to be used as a coupled generation system. Maximum Power Point Tracking (MPPT) control for the renewable system is an effective way to maximize the low efficiency given while being connected to the power grid [8,9,10,11,12,13,14,15]. This system inertia was responsible, in conventional power systems, for suppressing the small frequency excursions in the wake of unexpected load alterations.

One of the frequency control methods used is fractional-order PID (FOPID). This type of controller has been shown to positively abolish steady-state error, transient disturbance reduction, system non-linearities, and uncertainties. With its multiple parameters that are required, which are difficult to determine, manual tuning or algorithms are used to decipher the appropriate gains. The system’s robustness and dynamic characteristics improve to a certain extent.

Performance criteria are used to prove this by calculating the area of the control. One such method is used is Integral Time Absolute Error (ITAE), which can be tabulated to evaluate the system with ease of understanding [16,17,18,19]. It is important that, if fluctuations occur, the system must return to its nominal value. In a two-area power system, these controllers are required in both areas to maintain the power interchange at scheduled values, as well as to minimize the frequency deviations for unexpected load alterations. PID controllers have the disadvantage of noise occurring in the derivative area of the equation. They also are linear and symmetric, which makes the performance of the controller vary. Therefore, the additional parameters for FOPID are input into the formula to help mitigate these [20].

Further enhancement and optimization, such as artificial intelligence (AI) techniques, i.e., fuzzy logic (FL), have been integrated and tested successfully for applications that require control. An extension and advancement to conventional FL is the Fuzzy Type-2 system, which includes an NT-type reduction process that converts type-2 to type-1 and then obtains the final defuzzification result. The Fuzzy Type-2 system is much more suitable for highly non-linear systems such as renewable interlinked power systems. Fuzzy Type-2 has been shown to have better performance than Fuzzy Type-1 and PI controller methods in multi-area power systems.

Optimization techniques applied, such as particle swarm optimization, are proven to positively affect results, further enhancing them. Artificial intelligence, used for optimization, has been shown to utilize multiple methods structured from the behavioral patterns of living organisms to successfully solve uncertainties in the power system. The tuning of adaptive parameters by performing an input delay has also been illustrated to produce positive results for the load frequency of a two-area power system.

By utilizing a PID controller with a Type-2 Fuzzy system, the output scaling factor has increased system performance and maintained stability, with an input delay and uncertainties. By adjusting or including an increased number of rules for the interference mechanism, the controller’s performance can be increased in fuzzy logic systems, according to some researchers. The control algorithm has been shown to be highly effective and contributes to a significant performance increase regarding settling times, overshoots, and other performance criteria [21,22,23,24,25,26].

Given the above discussion, this work sets out to achieve the following:

• To model a two-area interlinked power system with coal-based generation and with an equal capacity for each area. These systems’ areas are connected via an AC tie-line.
• To model the solar PV model in the transfer function domain and to interlink it in the coal-based power system. To model the wind system with DFIG and to use this model to assist in frequency excursion of the power system.
• To interlink the concept of Fuzzy Type-2 with fractional-order PID and result in a Fuzzy Type-2 FOPID for a renewable integrating power system. The proposed design is tested for various cases, including and without including non-linearity, and the application results are shown graphically to demonstrate the benefits of the proposed research work.

This research paper is divided into five sections. Section 1 is the introduction, with a literature review of the problem. Section 2 discusses the model of the conventional system with PV and DFIG. The concept and model of Fuzzy Type-2 with FOPID are formulated in Section 3. Section 4 shows the detailed explanation of results, with conclusions in Section 5.

2. Modeling of Renewable Interlinked Power System

2.1. Interlinked Power System with Wind and Solar Energy Systems

An interlinked thermal power system with a solar farm and wind farm connected to each area is shown in Figure 1, with an electrical representation in Figure 2. These areas are interconnected via an AC tie-line. Both areas have a thermal power system, which consists of a governor, turbine, and generator model that has the relevant parameters for gains and time constants. The non-linearities present, such as Governor Dead Band (GDB) and Generation Rate Constant (GRC), have been included to consider the ramp rate constraints and upper to lower bound constraints. The signal from both areas connects to the synchronizing coefficient via the tie-line and provides the relevant inputs and outputs for the rest of the interconnection power system. The interconnected system integrates with primary control action, which is well known as the speed governor mechanism, and the proposed Fuzzy Type-2 FOPID. This controller uses multiple parameters for fine-tuning to reduce the uncertainties and disturbances in the system. The change in power demand is present in both Area 1 and Area 2 for analysis of the controller performance to bring the system back to steady-state condition, i.e., frequency and tie-power deviations.

2.2. Solar PV System

A PV system consists of the PV panel, Maximum Power Point Tracking (MPPT), Sinusoidal Pulse Width Modulation Inverter (SPWM), and filter. A solar cell panel is made up of semiconductors that have been doped to contribute to the deficit of free electrons on the reverse side and surplus on the front side. This panel works with the photovoltaic process, where photons are absorbed in the solar cells. The solar cell can produce an output voltage of 0.3–0.6 V. This is dependent on the temperature and irradiance [8,9,10]. The solar equivalent circuit is shown in Figure 3. An equation for the solar panel can be derived from Equations (1) and (2) and is shown below:

$$I=I_1-I_0 \left(e^{\frac{\left(V-I{R}_S\right)}{AkT}}-1\right)-\frac{V-I{R}_S}{R_{SH}}$$

(1)

where

• $I$ = Output current of PV array;
• $I_1$ = Array current generated by the incident sunlight;
• $I_0$ = Reverse saturation current of the PV array;
• $V$ = Output voltage of the PV array;
• $R_S$ = Equivalent series resistance of the array;
• $R_{SH}$ = Equivalent parallel resistance of the array;
• $A$ = Diode quality factor (ranging 0–2);
• $k$ = Boltzmann constant (1.380649 × 10⁻²³ m² kg s⁻² K⁻¹);
• $T$ = Temperature (°C or K).

$$I_1=\left(\frac{\lambda }{1000}\right)\left[I_{SC}+k_1\left(T-25\right)\right]$$

(2)

where

• $\lambda$ = Irradiance (0–2500 W/m²);
• $I_{SC}$ = Short-circuit current.

Figure 3. Solar cell equivalent circuit.

Figure 3. Solar cell equivalent circuit.

To harness the maximum power from a solar panel, a method called Maximum Power Point Tracking (MPPT) is utilized to provide input voltage regulation and improve efficiency. The voltage can be regulated through a booster DC/DC converter to deliver maximum power to the load. This type of converter can provide a higher output voltage than input voltage, which is discovered with the duty cycle of the gate pulse to the MOSFET switch [10]. Boost converters have two modes, which are the ON and OFF states, as shown in Equations (3) and (4), respectively. The ON and OFF state operation is shown in Figure 4 and Figure 5.

$$ON STATE \{L\frac{d{i}_1}{dt}=V_{PV}, C\frac{d{V}_0}{dt}+\frac{V_0}{R}=0$$

(3)

where

• $L$ = Inductance (H);
• $C$ = Capacitance (F);
• $R$ = Resistance (Ω);
• $V_0$ = Output voltage (V);
• $V_{PV}$ = Photovoltaic voltage (V).

$$OFF STATE \{L\frac{d{i}_2}{dt}+V_0=V_{PV}, i_2-C\frac{d{V}_0}{dt}+\frac{V_0}{R}=0$$

(4)

where

• $i_2$ = Current in the inductor (A).

Figure 4. ON state operation.

Figure 4. ON state operation.

Figure 5. OFF state operation.

Figure 5. OFF state operation.

For the conversion of DC to AC power, an inverter is utilized in this application. The Sinusoidal Pulse Width Modulation inverter is used to maintain a constant voltage. Finally, a filter is used to remove disturbances within the output power signal. From these components, a transfer function equation is derived, which can be seen in [8], and finally, the structure of the equation can be seen in Figure 6.

2.3. Wind Turbine System

DFIG can contribute to frequency regulation, but the frequency changes of the wind turbine are ignored previously due to the separate inertia. The operations are controlled via electronic controllers for communication between the grids. Power reserve control through speed and pitch control can assist with frequency control in the power system. The DFIG releases kinetic energy to support system inertia due to the additional inertia control loop that is frequency-sensitive to the system. Governor setting and system inertial response are researched for the frequency control of DFIG. Extracting the kinetic energy of the turbine blades from DFIG-based wind turbines contributes to the reduction of the rotor speed, which responds to the deviation in frequency to improve the frequency of the power system [3,4,5]. As the only form of tracking of non-conventional machine equivalent controllers, the inertial control adds a signal to the power reference output in Equation (5) according to [5]. The frequency behind a high-pass filter is represented as $\Delta f$, the constant weighting the frequency deviation derivative is $K_{df}$ and the frequency deviation is $K_{pf}$. When the frequency transient is over, the equivalent non-conventional machine moves back to the optimal speeds. By forcing the speed to track the desired speed reference, a power reference in Equation (6) is devised. The PI controller is utilized with design constants of $K_P$ and $K_I$. This controller is used for fast recovery speeds and transient speed variations. For non-conventional generators, from Equations (5) and (6), the total active power reference for non-conventional generators is given in Equation (7). In a short period, frequency transients generally occur. A slow PI controller is provided by $p_{\omega }^{*}$. There are no dynamics in the power reference $p_f^{*}$ and non-conventional total power injection if the power $p_{NC}$ is regulated by high-speed power electronics. The equation can be seen in (8). The injected power before the frequency transient is shown as $p_{NC}^0$. The inertial control affects the power system. The system damping is provided by $K_{pf}$ and system inertia is regulated by $K_{df}$. The non-conventional generating machine contributes to system inertia, and in conventional inertial control, the system inertia converts to $H^{*}$, as shown in Equation (9). The modified inertial control for a DFIG is given in Equation (10). We use a washout filter for the change in frequency having a time constant $T_{\omega }$. The reference point is given in Equation (11). The frequency change measured where the wind turbine connects to the network is $\Delta X_2$, and $R$ is the speed regulation. Using the stored kinetic energy, the change in frequency during load disturbance is detected by the DFIG. The proposed controller provides fast active power injection control. During any disturbance, active power is injected by the wind turbine, which is $\Delta P_{NC}$. By maintaining the reference rotor speed where maximum output power is obtained, the power injected by a wind turbine is differentiated with $\Delta P_{NC,ref}$. The wind turbine’s mechanical power is shown in Equation (12). The model of the DFIG system is shown in Figure 7. The wind model is made up of frequency measurement, a washout filter, droop, a speed controller, mechanical inertia, and finally the wind turbine.

$$P_f^{*}=-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f$$

(5)

$$P_{\omega }^{*}=K_P\left({\omega }_e^{*}-{\omega }_e\right)+K_I{{\displaystyle \int }}^{ }\left({\omega }_e^{*}-{\omega }_e\right)dt$$

(6)

$$P_{f\omega }^{*}=\left[-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f\right]-\left[K_P\left({\omega }_e^{*}-{\omega }_e\right)+K_I{{\displaystyle \int }}^{ }\left({\omega }_e^{*}-{\omega }_e\right)dt\right]$$

(7)

$$P_{NC}=\left[-K_{df}\frac{d\Delta f}{dt}-K_{pf}\Delta f\right]-P_{NC}^0$$

(8)

$$\left(2H+K_{df}\right)\frac{d\Delta f}{dt}=P_f-D\Delta f=P_G+P_{NC}+P_T-P_L-\left(K_{pf}+D\right)\Delta f$$

(9)

$$\frac{2H}{f}\frac{d\Delta f}{dt}=P_f-D\Delta f=P_G+P_{NC}+P_T-P_L-D\Delta f$$

(10)

$$P_f^{*}=\frac{1}{R}\left(\Delta X_2\right)$$

(11)

$$P_{mech}=\left(\frac{\frac{1}{2} \left(\rho Ar\right)}{S_n} C_{p.opt}\right){\omega }_s^3$$

(12)

3. Modeling of Fuzzy Type-2 FOPID Controller

The controller consists of a FOPID together with fuzzy action due to its positive advantages in solving disturbances and stability applications. The tuning of FOPID consists of five parameters, which are K_P, K_I, K_D, λ, and μ. These parameters are highly variable according to the output and are complex; they must be tuned via well-known Particle Swarm Optimization (PSO). The chosen variables are selected to provide the best possible outcome for the controller. Further, various optimization techniques can be utilized but are not guaranteed to provide the optimal outputs. Through fractional calculus, more adjustable parameters can be provided, which assist with tuning the controllers. The flexibility, stability, and control effect are improved with FOPID, which acts as a filter for an infinite dimension. The FOPID has a memory function that is related to the entire history in the fractional differentiation. The far and close errors have small and larger response factors, respectively. The future and present information is influenced through this. Therefore, this provides good applications for boiler–turbine systems. The arrangement of the controller can be seen below in Figure 8.

The Fuzzy Type-2 controller consists of five elements. These elements are the fuzzifier, fuzzy interference, fuzzy rules, type reducer, and defuzzifier. Each process plays an important role in the output of data. The input of data is fuzzified through the introduction of membership functions for ease of understanding and classification. The data are changed to a fuzzified input by the use of fuzzy applications into membership functions to establish a rule strength. The Mamdani fuzzy interference system is used due to its advantages of intuitiveness, widespread acceptance, and interpretable rule base. Combining the rule strength and the output membership function to find the consequence of the rule, Mamdani FIS is used. The structure of a Fuzzy Type-2 system is similar to that of a Fuzzy Type-1 system, with the only difference being the type reduction process function, which allows the controller to better handle system uncertainties because it can model them and minimize their effect. If all uncertainties disappear, the Type-2 Fuzzy sets convert to Type-1, which thereafter leads to the final defuzzification result (Figure 9).

For this research, the Nie–Tan reduction method (NT) was utilized with no iterative process, which improves the type reduction efficiency. A Fuzzy Type-2 system has more design degrees of freedom than a Fuzzy Type-1 system, because Type-2 has more parameters than Type-1. As random uncertainties flow through a system and their effects can be evaluated using the mean and the variance, linguistic and random uncertainties flow through a Fuzzy Type-2 system, and their effects can be evaluated using the defuzzified output and the type-reduced output of the system. Often used in intervals, the variance provides a measure of dispersion about the mean. The defuzzified output, which provides a measure of dispersion, is the interpretation of the type-reduced output. The type-reduced set also increases as linguistic or random uncertainties increase, because the variance increases as the random uncertainty increases. A Fuzzy Type-1 system is comparable to a probabilistic system through the first moment, whereas a Fuzzy Type-2 system is comparable through the first and second moments. The rules are based on the individual’s application of the information data. The fuzzy yield is made up of 49 laws from seven triangular membership functions on information and yield data. The logic statements “if” and “then” are used to determine the yield at this point. These rules have been utilized for FT2-FOPID, which can be seen in

Table 1. Fuzzy Type-2 FOPID rule base.

ACE/dACE	NB	NM	NS	ZE	PS	PM	PB
NB	NB	NB	NB	NB	NM	NS	ZE
NM	NB	NB	NB	NM	NS	ZE	PS
NS	NB	NB	NM	NS	ZE	PS	PM
ZE	NL	NM	NS	ZE	PS	PM	PB
PS	NM	NS	ZE	PS	PM	PB	PB
PM	NS	ZE	PS	PM	PB	PB	PB
PB	ZE	PS	PM	PB	PB	PB	PB

and

Table 2. Rule base statements.

Rule	Statement
1	If ACE is A and dACE is A, then dACE is NB
2	If ACE is B and dACE is A, then dACE is NM
3	If ACE is C and dACE is A, then dACE is NS
4	If ACE is D and dACE is A, then dACE is ZE
5	If ACE is E and dACE is A, then dACE is PS
6	If ACE is F and dACE is A, then dACE is PM
7	If ACE is G and dACE is A, then dACE is PB

. The output distribution is defuzzified to produce crisp outputs. The membership functions are generally used from negative one to positive one and the design membership functions for error and error deviation are shown in Figure 10.

The rules are based on a Boolean system of true or false statements to provide valuable flexibility for reasoning, thereby considering the inaccuracies and uncertainties in the system. In a fuzzy logic system, there is no absolute true or false, but it is partially true or false. The rule base contains if and then conditions to govern the decision-making system, which is very important for the output results. The rules are input into the interference system, which matches the current fuzzy inputs with each rule statement, which then produces the required outputs to perform control actions. This helps to remove uncertainties and disturbance to an acceptable level. Some of the rule base statements are shown in Table 2, where the two inputs are checked against the interference system consisting of the set of rules and the output is given to the type reducer.

The input values of a Fuzzy Type-2 system have membership functions ranging from upper membership functions to lower membership functions. This provides two fuzzy values for each Type-2 membership function. With the rules discussed previously, the fuzzy operator is applied to the fuzzified values of the membership functions. The minimum and maximum output value for the fuzzy set of each rule is the result of the fuzzy operator to the fuzzy values of upper and lower membership functions.

4. Simulation and Analysis of Results

The research work displayed shows the analysis of the thermal power system integrated with PV and wind-based power generation in each area, which is connected via an AC tie-line that contributes to the role of balancing supply and demand loads. The frequency of the designed interconnected system is analyzed and studied for the behavior of the signal. The investigation is meant to demonstrate the integration of clean energy through renewable energy sources effectively within existing thermal power systems while assisting with variable load changes within the grid. Each control area action is limited by using the GDB and GRC non-linearities as it makes the action of secondary controllers more practical and realizable.

For this work, the controller FT2-FOPID is showcased. While the Fuzzy Type-2 system can be coupled with either PI, PD or PID, the FOPID has been proven to provide favorable results in control problems due to the two additional freedom adjustable parameters. FOPID and FT1-FOPID have been shown to have difficulty in dealing with the uncertainty of systems; therefore, FOPID with Type-2 Fuzzy was applied. The controllers aim to restore the frequency and power deviations over tie-lines to their original state within the least amount of time while producing less settling time, low overshoot, and no oscillations. The different types of controller configurations are used for comparison of the outputs. The ACE and dACE are inputs of the fuzzy system.

The output of the fuzzy system is composed of seven areas: NB, NM, NS, ZE, PS, PM, and PB. These are used within the triangular uncertainty member function class for ease of understanding. The reduced rule base with non-linear membership functions for Fuzzy Type-2 is shown in Table 1 and Figure 10. The output of the fuzzy logic is defuzzified as Type-1 reduced sets, which produce real values from crisp values. The input of the FOPID is derived from the output signal of the fuzzy logic system. The parameter gains for the FOPID, i.e., K_P, K_I, K_D, λ, and μ, are calculated through PSO with 50 iterations to produce the best results.

The simulated results are quantitatively given using the performance index Integral of Time Absolute Error (ITAE) and Integral Absolute Error (IAE). These indices can calculate the area of the error, which assists with higher accuracy for the analysis of the controller performance, especially in graphical representations. The comparison of performance was carried out using the output values given in

Table 3. ITAE results obtained for various controllers for demand change of 1% in Area 1.

Controllers	ITAE
PID with no RES	0.9433
PID with RES	2.269
FOPID with RES	0.02066
FT1-FOPID with RES	0.01362
FT2-FOPID with RES	0.009286

,

Table 4. IAE results obtained for various controllers for demand change of 1% in Area 1.

Controllers	IAE
PID with no RES	0.05726
PID with RES	0.08157
FOPID with RES	0.007249
FT1-FOPID with RES	0.001953
FT2-FOPID with RES	0.001161

,

Table 5. ITAE results obtained for various controllers for demand change of 1% in Area 1 and 2% in Area 2.

Controllers	ITAE
PID with no RES	2.093
PID with RES	4.057
FOPID with RES	0.06176
FT1-FOPID with RES	0.0401
FT2-FOPID with RES	0.02749

and

Table 6. IAE results obtained for various controllers for demand change of 1% in Area 1 and 2% in Area 2.

Controllers	IAE
PID with no RES	0.1139
PID with RES	0.1638
FOPID with RES	0.02205
FT1-FOPID with RES	0.005757
FT2-FOPID with RES	0.00347

.

The integrated power system is simulated using a 1% load demand change in Area 1 for analysis purposes. The results of all the areas can be seen and are arranged in a way that is easy to analyze in Figure 11, Figure 12 and Figure 13, especially with the ITAE and IAE values. It can be easily seen that the penetration of RES affects the system negatively by providing high oscillations and making the system extremely non-linear in all three graphs. When comparing the results in Area 1, it can be seen that the FOPID has better results than traditional PID controllers, even though there are slight oscillations present. PID with RES has displayed higher overshoots than the rest of the controller configurations, with an ITAE performance of 2.269. PID has been shown to produce multiple larger oscillations in all three depictions and cannot overcome the fluctuations from the high penetration of renewable energy systems. Therefore, this type of controller is not suitable for these applications. In Area 1 and Area 2, and for tie-line deviations, the fuzzy integrated systems have shown good results, with the lowest settling time ranging from 0 to 5 s and returning to steady state, with little to no oscillations and minimum overshoot of these controllers. The controllers, including fuzzy, do not exceed 0.015, as displayed in the stand-alone FOPID and PID controllers for the area of error using ITAE. The stand-alone FOPID controller does return to the initial state but takes a long time, which is around 8–10 s, with an error of 0.02066 using ITAE. The FT2-FOPID has been shown to have the best results using IAE, with the smallest error of 0.001161. Therefore, the response time and performance of the FT2-FOPID are far superior to the traditional frequency controllers and Fuzzy Type-1 logic systems.

Figure 14, Figure 15 and Figure 16 are graphically presented to show the load disturbance of both areas in the power system using 1% and 2%, respectively. The results displayed are similar to the previous depictions showing load disturbance in a single area. It is still evident that the inclusion of the RES in both areas contributes to a highly non-linear system, which negatively impacts the power system, as shown in Table 2 and Table 4 for PID with RES. However, comparing the tie-line representations in Figure 13 and Figure 16, Figure 16 showcases fewer oscillations for the inclusion of RES compared to no RES. The system balances itself with the load demands and supply for the areas that contribute to this. However, it still has oscillations present and does not return to a steady state. The FOPID has displayed better performance than the PID controller with the inclusion of the additional fractional-order parameters. Proof of this is shown in Table 4; for comparison, the error is simulated as 0.06176 for FOPID with RES and 4.057 for PID with RES. This can be confirmed with the second performance criterion in Table 6, with 0.02205 for FOPID with RES and 0.1638 for PID with RES. The controller brings the system to normal conditions with a lower wavelength and quicker response time. There are still minimal oscillations present but much less than the PID controller. The overshoot in Area 2 is shown to be very high due to the 2% load disturbance present, which contributes to the negative results displayed. In the graphs presented, the settling time has an average value of 5–10 s for FOPID. The integration of fuzzy logic in the system has drastically improved the performance of the controllers with the additional iterations of the logical system processes. With the fastest response time, least overshoot, best settling time, and no oscillations, the fuzzy logic controllers have the best performance with the lowest error for the two areas and the tie-line region.

The Fuzzy Type-2 system has superior performance to Type-1, which is evident in the depictions and the ITAE/IAE error values. With the NT-type reduction in Type-2, the results are further fine-tuned to provide optimal performance. The wind and solar power have made the system highly non-linear due to the changing of the wind rotor speeds and the irradiance from the solar panels, shading of panels, and also inverters. The individual RES does have components and mechanisms in place to help curb these disturbances, but does not fully reduce them to zero. Therefore, a secondary controller is required for additional assistance to mitigate these disturbances. Even though RES provides clean and renewable energy to the system, the higher the RES capacity, the greater the control required for interconnected systems to work together. From all the results displayed, the FT2-FOPID has the greatest performance compared to the rest of the controllers, with a slightly better edge than the fuzzy Type-1, which does not exceed ±0.005 Hz. The error between the Type-1 and Type-2 Fuzzy systems has a difference of approximately 0.02 for a change in demand for Area 1 and Area 2. The results illustrated on the above graph and the ITAE/IAE values clearly show that RES creates disturbances when coupled with the power system. With the introduction of PID, the results had some control but did not come to steady-state conditions. FOPID with RES has been shown to provide better results than PID with or without RES; therefore, FOPID was used as the coupling controller for the fuzzy logic systems. The FT2-FOPID has proven itself to have lower overshoot and almost non-existent oscillations present. Even with the penetration of RES, the Fuzzy Type-2 controller can handle the non-linearity that could harm the power system. The applications of artificial intelligence can assist with control methods and solve unprecedented problems. With more processes being introduced, the controller can obtain better outputs and help the power system to overcome the disturbances as soon as possible.

5. Conclusions

This paper presents an attempt to model and integrate renewable energy sources such as wind and solar power within a thermal power system. The thermal power system is interconnected via an AC tie-line to other areas having thermal power generation and resulting in an interconnected system. This system is controlled with the assistance of a Type-2 Fuzzy logic controller together with FOPID. Multiple configurations of controllers have been simulated, compared, and analyzed to produce the most efficient output. The controller’s main objective is to highlight the best performance in the overshoot, oscillations, and settling time of the frequency and power interchange over tie-lines while experiencing a sudden change in load demand. The addition of DFIG-based wind turbines assists with the stability of the power system, while the PV-based solar system introduces fluctuations in the system due to its inverter, contributing to the slight disturbances even after the signal has been filtered. The system when interconnected with clean energy systems can still become stable through the introduction of auxiliary control methods utilizing Type-2 Fuzzy logic with FOPID, well developed via PSO. The results guarantee that the proposed design is well suited for a renewable interlinked power system in comparison to results obtained via other control techniques. Further, the non-linearities’ inclusion has shown a negative impact on all controllers’ output; nonetheless, Type-2 Fuzzy logic with FOPID is effective in providing acceptable results for the power system. As an increase in renewable energy generation is becoming highly desirable, this research paper can assist as the foundation for the gradually increasing penetration of clean energy within various countries’ fossil-fuel-driven power systems.