Robust Fuzzy-PID Technique for the Automatic Generation Control of Interconnected Power System with Integrated Renewable Energy Sources

This paper proposes a robust hybrid fuzzy PID controller, with the PID gain values tuned using the particle swarm optimization (PSO) technique for the automatic generation control (AGC) of the two-area hybrid power system. PSO Algorithm is applied to reduce the integral of time-weighted absolute error (ITAE) of the frequency and tie-line power variations of the two-area interconnected power system. The suggested method’s efficacy is examined on an interconnected two-area power system with Area 1 containing thermal reheat plants, hydropower plants, and diesel generating units, and Area 2 comprising thermal reheat plants and renewable energy sources (RES): wind energy conversion system, solar photovoltaic system, and electric vehicles. The thermal reheat power plants are modelled taking into consideration the governor dead band (GDB) and the generation rate constraints (GRC). The performance of the presented controller is compared with the genetic algorithm-optimized PID AGC and the PSO-optimised PID AGC. The simulation outcomes show superior results of the proposed controller against other controllers. Further, sensitivity analysis reflects that the proposed technique provides better dynamic response and robustness than the other techniques.

Introduction

In the electrical power grid, maintaining a consistent power supply and demand is vital to enhance the quality, reliability and stability of the power grid. Failure to control the power generated against power demand following a sudden load change or power system disturbance will lead to frequency deviation of the power system from its nominal values and in some cases to a total blackout of the power system [1]. Moreover, power grids are becoming more complex and the integration of RES, such as wind plants, solar and tidal turbines into multi-area hybrid power systems has increased significantly in recent years. In addition, the emersion of new concepts like micro-grids and smart grids has increased both the complexity and uncertainty of modern power grids [2]. The main goal of AGC is to automatically control any variation of frequency tie-line power to zero and keep their values consistent with their nominal predefined values [3]. Recently, several advanced methods have been introduced for AGC in multi-area conventional as well as hybrid power grids. Classical controllers such as PID controllers have been used to manage frequency and tie-line power changes [4]. Although classical controllers have a simple design and are well-investigated controllers for AGC, drawbacks such as their weak dynamic response, inaccurate results, long settling time and dependency on trial-and-error procedures limit their applications [2]. Fractional order PID controllers have also been proposed over conventional integral controllers for AGC [5]. The major drawbacks of fractional order controllers are their increased computational requirements and complexity [6]. The other advanced control techniques proposed in the literature include sliding mode controllers [7], H-infinity controllers [8] and model predictive control approaches [9]. The drawbacks of these controllers are their complexity, and uncertainty in their performance, and further, these are not commonly utilized in the industry [10]. Heuristic methodologies like genetic algorithm [11], particle swarm optimization techniques [12], differential evolution algorithm [13], firefly algorithm [14], and grey wolf optimization algorithm [15], have been used to optimize PID gain parameters. However, mostly these optimization approaches are applied in conventional power systems without considering the renewable energy sources and any of the nonlinear constraints of the system components [10]. Many researchers have introduced cascaded controllers, which consist of two controllers, one of which is positioned inside the feedback loop of the other, and the output of the first controller acts as the set-point for the second.

The major drawbacks of the cascaded controllers are the time consumption, the high level of tolerance required, and the complexity of its design [6]. The developments in artificial intelligence have increased significantly and artificial neural network (ANN) controllers have been utilized which update the training sets based on continuous learning. Moreover, the knowledge of the controller is updated continuously via a set of training rules resulting in estimation convergence to zero. ANN-based controllers have been used for AGC in interconnected hybrid power systems using several algorithms such as fractional order ANN Controller [16] and ANN-tuned PID controller [17]. Tilt integral derivative controllers (TID) give better performance compared to conventional controllers [2]. TID has been used for AGC of power systems using several algorithms like fractional order TID controller using pathfinder algorithm [18] and hybrid modified particle swarm optimization with genetic algorithm [19]. The major drawbacks of TID controllers are that these controllers take more time to achieve a stable state and more numbers of control parameters are needed to be tuned in the optimization process [20]. Research interest in the fuzzy logic approach to system dynamics control has increased because of its reasonably wide application range and its fast response. Fuzzy logic Controllers and ANFIS controllers have been introduced in [21], [22]. However, a fuzzy system alone requires a lot of experience for tuning the membership functions. Therefore, the best dynamic performance of fuzzy logic control has been achieved by utilizing optimization techniques [23]. Thus, several publications are there in the field of AGC of power systems. In this paper, a hybrid PSO-fuzzy PID controller is suggested to optimize PID gain values for the AGC of a two-area interconnected power grid comprising thermal reheat, hydro, diesel, wind and solar photovoltaic power plants together with electric vehicles. PSO method is utilized to obtain the best PID gain parameters enabling the fuzzy logic controller to provide optimal response.

The paper is arranged as follows: Description and component modeling of the hybrid power system is introduced in the following section followed by an overview of the GA-PID AGC and PSO-PID AGC in Section 3. Section 4 discusses the proposed PSO-optimized fuzzy-PID AGC design followed by the test system data and the simulation outcomes with discussion in Section 5 and the conclusion in Section 6.

System Description and Modelling

The system investigated is composed of two different areas connected with each other. Area 1 comprises thermal plants with reheat turbines, hydro plants and diesel generators while Area 2 integrates wind power plants, solar photovoltaic systems, and electric vehicles altogether with thermal power plants. Fig. 1 represents the AGC block diagram for the suggested power system model under study.

Fig. 1. Block diagram for AGC of two-area hybrid power system.

Area control error (ACE) corresponding to Areas 1 and 2 are: where

(1) $$\begin{array}{r}{\text{ACE}}_1=\mathrm{\Delta }{P}_{tie}+B_1\mathrm{\Delta }{f}_1\end{array}$$

(2) $$\begin{array}{r}{\text{ACE}}_2=\mathrm{\Delta }{P}_{tie}+B_2\mathrm{\Delta }{f}_2\end{array}$$

$B_1$ and $B_2$: bias parameters of areas 1 and 2, respectively.

$\mathrm{\Delta }{f}_1$ and $\mathrm{\Delta }{f}_2$: frequency variation in areas 1 and 2, respectively. where

(3) $$\begin{array}{r}{B}_i=\frac{1}{R_i}+D_{\text{i}}\end{array}$$

R_i: regulation parameter of the turbine-generator unit.

D_i: frequency dependency of load.

The modelling aspects of various system components are given in this section.

Thermal Power Plant

The representation of a thermal reheat model taking into consideration (GRC) and (GDB) is illustrated in Fig. 2 [24], [25].

Fig. 2. Thermal power plant with non-linearities representation.

Hydro Power Plant

The representation of a hydro plant model is illustrated in Fig. 3 [26].

Fig. 3. Hydropower system representation.

Diesel Generating Unit

The representation of a diesel generator is illustrated in Fig. 4 [27].

Fig. 4. Diesel generator representation.

Solar Photo-Voltaic Energy Conversion System

The transfer function of a solar PV plant with a maximum power point tracking facility (MPPT) is shown in Fig. 5 [10].

Fig. 5. PV system representation.

Wind Energy Conversion System

The output power generated from wind system is represented by: where

(4) $$\begin{array}{r}{P}_{WT}=\frac{1}{2}\rho A_{sr}{C}_p{V^3}_W\end{array}$$

$\rho$: air density.

A_sr: blade swept area.

C_p: power coefficient.

$V_W$: wind velocity.

The transfer function of the wind system is: where

(5) $$\begin{array}{r}{G}_{WTG}=\frac{K_{W1}(1+s{T}_{W1})K_{W2}}{(1+s{T}_{W2})(1+s)(1+s)}\end{array}$$

$K_{W1}$ and $K_{W2}$: gains of the wind system.

$T_{W1}$ and $T_{W2}$: time constants of the wind system [10].

The system block diagram is shown in Fig. 6.

Fig. 6. Wind generation system representation.

Battery Energy Storage System (BESS)

The intermittent nature of the power outputs from wind and solar PV systems can be managed to a certain extent by the provision of a BESS. The transfer function of BESS is illustrated in Fig. 7: [28].

Fig. 7. BESS representation.

Electric Vehicle Charging System

Converters in electric vehicles (EVs) have become a reliable backup for frequency support in power systems due to their bidirectional connection capabilities [29]. In this paper, the linearized model, as shown in Fig. 8 [30] is used to represent EV System.

Fig. 8. Block diagram of electric vehicle model.

GA and PSO Techniques—An Overview

To attain the optimum AGC performance, it is important to choose an objective function to be minimized to optimize the gain values of the PID controller accordingly. The major performance indices commonly utilized for optimizing PID parameters of the AGC are absolute error integral (IAE), integral of time multiplied by absolute error (ITAE), integral of squared error (ISE), and integral of time multiplied by squared error (ITSE) [31] These are given by:

(6) $$\begin{array}{rl}{J}_1& =IAE={\sum }_{i=1}^{NA}{\int }_0^{t_{sim}}({\alpha }_i\left|\mathrm{\Delta }{f}_i\left(t\right)\right|\\ & +{\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^{NA}{\alpha }_{ij}|\mathrm{\Delta }{P}_{ti{e}_{i-j}}(t)|)\times dt\end{array}$$

(7) $$\begin{array}{rl}{J}_2=ISE& ={\sum }_{i=1}^{NA}{\int }_0^{t_{sim}}({\alpha }_i\left|\mathrm{\Delta }{f}_i\left(t\right)\right|\\ & +{\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^{NA}{\alpha }_{ij}|\mathrm{\Delta }{P}_{ti{e}_{i-j}}(t)|{)}^2\times dt\end{array}$$

(8) $$\begin{array}{rl}{J}_3& =ITAE={\sum }_{i=1}^{NA}{\int }_0^{t_{sim}}({\alpha }_i\left|\mathrm{\Delta }{f}_i\left(t\right)\right|\\ & +{\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^{NA}{\alpha }_{ij}|\mathrm{\Delta }{P}_{ti{e}_{i-j}}(t)|)\times t\times dt\end{array}$$

(9) $$\begin{array}{rl}{J}_4& =ITSE={\sum }_{i=1}^{NA}({\alpha }_i|\mathrm{\Delta }{f}_i(t)|\\ & +{\sum }_{\begin{array}{c}j=1\\ j\ne i\end{array}}^{NA}{\alpha }_{ij}|\mathrm{\Delta }{P}_{ti{e}_{i-j}}(t)|{)}^2\times t\times dt\end{array}$$

where ${\alpha }_i$ and ${\alpha }_{ij}$ are weighting for frequency and tie-line power errors respectively in both areas which are used to provide importance index. these variables are given an appropriate weightage in the equations. In the current work, ITAE is considered as the fitness function to improve the PID gain parameters of the AGC. Thus, the ITAE is: [32]

(10) $$\begin{array}{r}\text{ITAE}={\int }_0^{t_{sim}}t|\mathrm{\Delta }{f}_i+\mathrm{\Delta }{f}_i+\mathrm{\Delta }{P}_{ti{e}_{i-j}}|dt\end{array}$$

Particle Swarm Optimization (PSO)

PSO is a stochastic optimization algorithm based on swarm of birds and schooling of fish. It is processed by the imitation of a bird flocking in multiple-dimensional area. Every particle is represented by a position (x) and velocity vectors (v). The particle is updated based on its position and its velocity information. In every iteration, the particle is evaluated via ITAE fitness function to obtain its best value (P_best) and its position. Further, every particle has the optimum value so far in the group (G_best) out of P_best of all particles. Position and velocity of the particle are updated as [32]

(11) $$\begin{array}{r}{x_i}^{k+\mathbf{\text{1}}}={x_i}^k+{v_i}^{k+\mathbf{\text{1}}}\end{array}$$

where k is the iteration number, i is the particle index, P_best is the global best solution, x₁ and x₂ are acceleration factors, ra₁ and ra₂ are uniformly random numbers, and w is inertia weight. The particle swarm optimization algorithm proceeds as follows:

(12) $$\begin{array}{rl}{V_i}^{k+1}& =w{v_i}^k+x_{1}ra1({P^k}_{best}-{x_i}^k)\\ & +x_2{ra}_2({G^k}_{best}-{x_i}^k)\end{array}$$

1. Initialize the positions and velocities of particles, also population size, iteration number, and upper and lower bounds of controller variables.
2. Calculate the ITAE fitness function of each particle.
3. Assign The minimum function value as P_best, and the best fitness function value among the all P_best as G_best.
4. Utilize (17) and (18) in each iteration and update x and v of the particles, respectively.
5. If the stopping criteria are reached, proceed to the last step 6. Otherwise, return to step ii and repeat the procedure.
6. In the last iteration, the optimum controller parameters are obtained by the minimum objective function which is the latest G_best [33].

Genetic Algorithm (GA)

GA is an optimization technique used to optimize the PID controller gains due to its high optimization capability that guarantees the survival of the fittest. GA had been developed by the natural selection principle, a biological method where the stronger individual has a high probability of winning against weaker individuals. The technique begins with an initial random population of chromosomes, each chromosome consisting of genes represented by binary bits. These bits are appropriately decoded and mapped to give an appropriate string for the optimization problem. The initial population is then regenerated to obtain the new population and to converge to the fittest individuals by the utilization of the fitness function. The fitness function gives a value to each chromosome. After that, the outcomes are organized, and elected strings are selected to produce a new generation. GA applies selection, crossover and mutation to converge at the global optimum and to improve the selected individuals [11], [28]. To make a high correlation between parents and offspring, there is a need for a repair function which is necessary for defining the initial population of genetic algorithm individuals, mutation and crossover operators. AGC focuses on power flow balancing and frequency stability of interconnected systems during periods of generation-load mismatch. (ITAE) is utilized as the objective function to be reduced in the process of tuning the gain parameters of the PID controller. The genetic algorithm thus proceeds as follows:

1. Initiate a random population of chromosomes.
2. Calculate the fitness function of every chromosome in the population.
3. For the upcoming population, apply the following procedures: Selection: Based on the fitness function, defined as the process of choosing individuals from the current population to produce the new generation. Recombination: Crossover chromosomes and allows the exploration of new solution combinations by recombining genetic material from promising individuals. Mutation: The process of introducing random changes in individual solutions by mutating chromosomes. Acceptation: Refuse or accept a new candidate.
4. Replace the old generation with a new generation.
5. Test method criterion.
6. Repeat Step 2 to step 5 till the stopping criterion is met.

Proposed PSO-Optimized Fuzzy PID Controller

The structure of the proposed hybrid PSO-Fuzzy PID technique is demonstrated in Fig. 9. As shown in this diagram, the system consists of a fuzzy controller connected in parallel with the conventional PID controller. The gains of PID are tuned by employing the PSO technique. fuzzy logic controller has two inputs: area control error (ACE) and variation in area control error ΔACE. AGC output is the frequency deviation caused by the load variation in the power grid.

Fig. 9. The proposed hybrid PSO-Fuzzy-PID controller.

Figs. 10 to 12 show the membership functions defined for the input variables: ACE and ΔACE, and the output variable Δf. In this paper, the Mamdani method of fuzzy inference mechanism and the centroid method of defuzzification approach are utilized. As shown in these figures, the input variables, ACE and ΔACE are represented by seven fuzzy linguistic variables: Largely Negative Value (LNV), Average Negative Value (ANV), Slightly Negative Value (SNV), Zero (Z), Slightly Positive Value (SPV), Average Positive Value (APV), and Largely Positive Value (LPV) respectively. The FLC output variable Δf is fuzzified into seven subsets as that of the input variables. The rule base developed for the fuzzy Controller is given in Table I. The range of variation of ACE, ΔACE and Δf are assumed to be in the range (−0.2 to +0.2).

Fig. 10. Fuzzy subsets of ACE.

Fig. 11. Fuzzy subsets of ΔACE.

Fig. 12. Fuzzy subsets of Δf.

Table I. Rule Base of the Fuzzy Logic Control

$\mathrm{\Delta }\mathit{A}\mathit{C}\mathit{E}$	LNV	ANV	SNV	Z	SPV	APV	LPV
ACE
LNV	LNV	LNV	LNV	LNV	ANV	SNV	Z
ANV	LNV	LNV	LNV	ANV	SNV	Z	SPV
SNV	LNV	LNV	ANV	SNV	Z	SPV	APV
Z	LNV	ANV	SNV	Z	SPV	APV	LPV
SPV	ANV	SNV	Z	SPV	APV	LPV	LPV
APV	SNV	Z	SPV	APV	LPV	LPV	LPV
LPV	Z	SPV	APV	LPV	LPV	LPV	LPV

System Data and Simulation Findings

The efficacy of the proposed hybrid PSO-fuzzy PID method is analyzed on a two-area hybrid system discussed in Section 2, the data of which is given in the Appendix, by comparing its dynamic performance with those obtained using GA and PSO-optimized PID AGC. The GA and PSO parameters used for optimizing PID parameters of AGC are given in Tables II and III, respectively. The PSO method is utilized to improve the gain parameters of the fuzzy-PID controller of AGC. The data related to the genetic algorithm and the PSO techniques are shown in Tables II and III, respectively.

Table II. Data Related to Genetic Algorithm

Population size	60
Maximum number of generations	100
Elite count	3
Mutation method	Adaptfeasible
Crossover method	Arithmatic
Crossover probability	0.8
Creation method	Uniform
Selection method	Tournament

Table III. Data Related to Particle Swarm Optimization

Imax	50
Number of particles	15
c1 & c2 acceleration factors	2

In both genetic and particle swarm optimization processes, the variation of K_p, K_i, K_d parameter values are assumed to be within the limits from −2 to 40 as it is observed to be in this range from the conventional simulation studies. Table IV shows the gain parameters of the proposed PSO-optimized fuzzy PID controller of the two area AGCs together with those corresponding to GA-PID and PSO-PID controllers. The Table also shows the final values of the respective fitness functions. These results correspond to a step load change of 0.1 per unit step load change in Area 1 at zero time instant. As can be seen from this Table, the proposed controller has a lower ITAE value than the other two controllers. Moreover, it can be noticed that the results of PSO and PSO-Fuzzy PID controller obtained parameters and ITAE value are near together when compared with GA which has slightly further results. The ITAE value obtained by GA is much higher than PSO and PSO-Fuzzy PID controller which means that the PSO and PSO-Fuzzy PID controller are much better than the GA. The variation of the fitness function of the proposed controller with the increasing number of iterations is shown in Fig. 13. As noticed from this figure, it converges within 50 iterations to the minimum ITAE value of 0.91672.

Table IV. Gain Parameters of the GA, PSO and PSO-Fuzzy PID Controllers of the Two-Area AGC

Algorithm	Area 1			Area 2
	Kp1	Ki1	Kd1	Kp2	Ki2	Kd2	ITAE
GA PID	23.2193	2.9001	39.1807	7.9598	25.8566	22.0767	1.8510
PSO PID	23.3879	0.5323	40	32.7343	8.4668	23.4933	1.1546
PSO-Fuzzy PID	24.3840	0.6094	40	26.7018	5.6451	25.1473	0.91672

Fig. 13. Variation of fitness function with iteration number in PSO-Fuzzy PID controller.

For a 0.1 per unit step load variation implemented in area 1 at the time instant, t = 0 second, the variation of frequency in both areas $\mathrm{\Delta }{f}_1$, $\mathrm{\Delta }{f}_2$ as well as tie-line power exchange (∆P_tie) are demonstrated in Figs.14–16, respectively. These figures prove that the proposed PSO-Fuzzy PID method is more efficient in damping the oscillations compared to other controllers. From these figures and from Table V, it is obvious that the presented methodology is more efficient than others in handling dynamic issues related to settling time, peak overshoot and peak undershoot.

Fig. 14. Oscillations at area 1 $\mathrm{\Delta }{f}_1$.

Fig. 15. Oscillations at area 2 $\mathrm{\Delta }{f}_2$.

Fig. 16. Oscillations in tie line power.

Table V. Performance Comparison of Controllers

Controller	Settling time (S)			Overshoot			Undershoot
	$\mathrm{\Delta }{\text{f}}_1$	$\mathrm{\Delta }{\text{f}}_2$	$\mathrm{\Delta }{\text{P}}_{tie}$	$\mathrm{\Delta }{\text{f}}_1$ (Hz)	$\mathrm{\Delta }{\text{f}}_2$ (Hz)	$\mathrm{\Delta }{\text{P}}_{tie}$ (pu)	$\mathrm{\Delta }{\text{f}}_1$ (Hz)	$\mathrm{\Delta }{\text{f}}_2$ (Hz)	$\mathrm{\Delta }{\text{P}}_{tie}$ (pu)
GA-PID	13.3094	18.7857	19.0264	0.6386	0.3361	0.0077	−0.8064	−0.5398	−0.0125
PSO-PID	12.4063	15.9994	15.8336	0.2607	0.0601	0.0014	−0.8062	−0.5327	−0.0126
Proposed PSO-Fuzzy-PID	11.2823	13.8157	13.3891	0.1558	0.0194	0.0004	−0.6941	−0.4481	−0.0106

To evaluate the system robustness, the sensitivity analysis is performed corresponding to ±50% variations from the nominal values in the following AGC system parameters:

1. Area 2 governor time constant (T_g2) and Area 2 turbine time constant (T_T2)
2. Wind turbine time constants (T_W2)
3. Regulation parameter (R for all the power plants included in the model)

Table VI shows the performance of the PSO-Fuzzy PID AGC corresponding to these variations in terms of settling time, the maximum under and overshoots in $\mathrm{\Delta }{f}_1$, $\mathrm{\Delta }{f}_2$, and ∆P_tie, respectively. The comparison of the deviation of these variables from their standard values verifies the efficacy of the presented controller against system parameter deviations.

Table VI. Sensitivity Analysis

Parameter variation		Settling time			Overshoot			Undershoot
		$\mathrm{\Delta }\text{f}1$	$\mathrm{\Delta }\text{f}2$	$\mathrm{\Delta }{\text{P}}_{\text{tie}}$	$\mathrm{\Delta }\text{f}1$ (Hz)	$\mathrm{\Delta }\text{f}2$ (Hz)	$\mathrm{\Delta }{\text{P}}_{\text{tie}}$ (pu)	$\mathrm{\Delta }\text{f}1$ (Hz)	$\mathrm{\Delta }\text{f}2$ (Hz)	$\mathrm{\Delta }{\text{P}}_{\text{tie}}$ (pu)
Nominal condition		11.2823	13.8157	13.3891	0.1558	0.0194	0.0004	−0.6941	−0.4481	−0.0106
Tg2 & TT2	−50%	11.3261	14.5019	13.7198	0.1858	0.0259	0.0006	−0.7220	−0.4698	−0.0111
	+50%	11.3357	14.9501	14.7373	0.2950	0.0683	0.0016	−0.7781	−0.5121	−0.0121
TW2	−50%	11.2072	13.5837	13.3975	0.1645	0.0201	0.0005	−0.6923	−0.4452	−0.0105
	+50%	11.0313	12.8017	12.5398	0.1377	0.0128	0.0003	−0.6779	−0.4356	−0.0103
Ri	−50%	11.2126	13.5012	13.2796	0.1441	0.0163	0.0004	−0.6833	−0.4381	−0.0104
	+50%	11.1638	15.8841	12.8985	0.1450	0.0163	0.0003	−0.6865	−0.4428	−0.0104

Conclusion

In this paper, a robust hybrid PSO-Fuzzy PID controller has been proposed for AGC of a two-area interconnected power system composed of thermal, hydro and diesel power plants together with the renewable energy resources: wind, solar PV energy conversion systems and in addition the electric vehicle loads. The proposed controller consists of the PSO-optimized PID controller in parallel with a fuzzy controller with ACE and changes in ACE as the inputs. The output is the area frequency deviations. The PSO optimization proceeds by minimizing the ITAE index value. Each of the input and output variables of the fuzzy controller are fuzzified into seven fuzzy subsets and the defuzzification is done by the centroid approach. A comparison of the dynamic performance of the proposed method for the two area AGC with those obtained using GA and PSO-optimized PID controllers indicates that the proposed method is significantly better than the other methods in damping the oscillations following the load disturbances. Further, the AGC controller remains practically robust in terms of the settling time, maximum and minimum overshoots of the frequency and the tie line power deviations of the interconnected power system irrespective of the variations in the system parameters.