Application of optimal artificial intelligence based tuned controllers to a class of embedded nonlinear power system

Received May 19, 2019 Revised Oct 20, 2019 Accepted Nov 15, 2019 This paper studies the implementation of the Bat Inspired Algorithm (BIA) as an optimization technique to find the optimal parameters of two classes of controllers. The first is the classical Proportional-Integral-Derivative (PID). The second is the hybrid fractional order and Brain Emotional Intelligent controller. The two controllers have been implemented, separately, for the load frequency control of a single area electric power system with three physical imbedded nonlinearities. The first nonlinearity represents the generation’s rate constraint (GRC). The second is owing to the governor dead band (GDB). The last is due to the time delay imposed by the governorturbine link, the thermodynamic process, and the communication channels. These nonlinearities have been embedded in the simulation model of the system under study. Matlab/Simulink software has been applied to obtain the results of applying the two classes of controllers which have been, optimally, tuned using the BIA. The Integral of Square Error (ISE) criterion has been selected as an element of the objective function along with the percentage overshoot and settling time for the optimum tuning technique of the two controllers. The simulation results show that when using the hybrid fractional order and Brain Emotional Intelligent controller, it gives better response and performance indices than the conventional ProportionalIntegral-Derivative (PID) controllers.


INTRODUCTION
Due to unremitting development of size and complexity of electrical power system, the problem of maintaining the power and frequency free from oscillations has become rapidly crucial because of irregular load variations and imbedded system nonlinearities [1]. These unexpected load variations result in the mismatch of generated power and load demand for consumption. This will finally distresses the quality and reliability of electric power supply. This can be achieved by the load frequency control (LFC) ideologies. Nowadays, a lot of work is going on to make the systems intelligent so the systems can successfully serve the benefits of mankind [2][3].
The main goal of operation of the LFC in the single area or multi area power systems is to maintain the frequency within the permissible limits. In the past few years, enormous improvement has been made in the area of load frequency control of a single area power system and multi area as well [4][5]. Designing the LFC with the help of PID controllers makes it prominent and trustworthy, but the main challenge is to decide the parameters of controllers [6][7].
To have better behavior from any controller, its parameters should be optimally tuned. The conventional methods face some difficulties to achieve this purpose, such as complex mathematical equations for large systems. Several approaches such as optimal, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO), etc., for the design and optimization of the LFC system, have been reported in the literature [8]. Modern optimal control concept for AGC designs of interconnected power system was firstly presented by [9]. Genetic algorithms (GAs) have been extensively considered for the design of Automatic Generation Control (AGC). Optimal PID and fractional-order PID control parameters have been applied by the GAs technique for interconnected, equal non-reheat and reheat type two generating areas [10]. In [11], the parameters of PID sliding-mode used in LFC of multi-area power systems with nonlinear elements are optimized by GA. In [12], GA is used to compute the decentralized control parameters to reach to an optimum operating point for a realistic system comprising generation rate constraint (GRC), dead band, and time delays. AGC using integral controller and PI controller based on PSO is reported in [13]. In [14], the parameters of PI controller are evaluated using PSO [13]. In [15], a robust PID controller based on ICA is used for LFC application. The authors of [16][17][18] have proposed bacterial foraging optimization algorithm (BFOA) for designing PI and PID-based load frequency controllers.
For a single area power system, the problem of LFC and AGC has been treated by several researchers. This includes a variety of techniques such as gravitational search algorithm [19], the modified particle swarm optimization [20], the application of artificial neural network [20], optimal control design [21], fuzzy logic [22][23], proportional-integral-observer techniques [24], and LQR and Legendre wavelet function [25]. Finally, the automatic generation control of single area power system with multisource power generation has been studied in [26]. All these researches deal only with the case where no nonlinearities exist in the control loops.

CLASSICAL PID CONTROLLER
The PID controller is considered to be an important component in industrial control systems. This is because of its capability of reducing the steady state error and enhancing the dynamic response and other static characteristics. The PID controller is expressed, mathematically, by the next equation [36]: Where e(t) is the system error, p is the proportional gain, i is the integral gain, d is the derivative gain and ( ) is the output of the controller.

FRACTIONAL ORDER CONTROLLER
The fractional calculus is implemented to obtain the solution for many scientific and engineering applications. In last ten years it is being acknowledged by its ability to yield a better modeling and control in many dynamical systems [28]. The fractional order controller explores good robustness and gives better behavior due to tuning five or four parameters ( , . . . ) instead of three or two parameters ( , . ) in classical PID controllers [29]. The fractional controller form is expressed, mathematically, as follows [30]: Where E(s) denotes the error signal, U(s) is control signal, , and are proportional, integral and derivative coefficients respectively, λ and δ are power of 's' in integral action and derivative action respectively.
One of the methods to realize the fractional order controllers is known as the Oustaloup method [31]. This method relies on the approximation of a function as given by (3) and (4).
Some continuous filters have been summarized in [31]. Among the filters, the well-established Oustaloup recursive filter has an acceptable fitting to the fractional-order differentiators. Assume that the expected fitting range is (ωb, ωh). The filter can be expressed as Where the poles, zeros, and gain of the filter of order N can be evaluated as (4) and = ℎ Thus, any signal y(t) can be filtered by this filter and the output of the filter can be treated as an approximation for the derivative part of the FOPID with = or the integral counterpart with =-. The resulted transfer function of the FOPID is the sum of the proportional term plus the filter approximation of the integral term ( − ) plus the derivative term(  ).

BAT INSPIRED ALGORITHM (BIA)
The bat inspired algorithm (BIA) is a new artificial intelligence (AI) technique. It is based on the echolocation behavior of bats in searching their victims [35][36]. These bats locate its prey by emitting a series of ultrasound pulses and listen for the echoes. The reflected ultrasound waves have different levels of sound and time delays. This will enable each bat to get a specific prey. The BIA is summarized in the following steps, Step 1 : All bats use echolocation to evaluate the distance and identify between prey and barrier.
Step 2 : Each bat flies with a velocity (vi) at position (xi), having fixed frequency (fmin) varying wavelength (λ), and loudness (Lo) to seek a prey. The bat tunes the frequency of its emitted pulse in the range (fmin, fmax) and adjusts the rate of pulse emission (r) in the range of [0,1] according to target closeness.
Step 3 : Frequency, loudness, and pulse emission rate of each bat is varied.
Where  is a random value derived from a uniform distribution function. The current global best location * x is obtained after comparing all locations among all bats. Since the velocity is given Thus by using random walk, a new solution for each bat is developed locally.
Where  is a random number and L t is the mean loudness of all bats at this time step. Loudness decreases and the rate pulse emission increases after a bat get its prey then any convenience value can be selected for loudness. When the bat has just found a prey, this means that loudness is zero and the bat temporarily stops emitting any sound. This is governed by the following equations:

BRAIN EMOTIONAL LEARNING BASED INTELLIGENT CONTROLLERS (BELBIC)
BELBIC is an intelligent controller which is proposed by Caro Lucas [36]. It shown in Figure 1. It adopts the network model developed by Moren and Balkenius to mimic those parts of the brain which are known to produce emotion (namely, the amygdala, orbitofrontal cortex, thalamus and sensory input cortex). The main parts that are responsible for performing the learning algorithms are orbitofrontal cortex and amygdala. These are shown in Figures 2 and 3. The BELBIC has some sensory inputs. One of the designer's tasks is to specify the sensory inputs. The BELBIC has two states for each sensory input. One of these two is amygdala's output and another is the output of orbitofrontal cortex. From mathematical view point, this converts into supplementing the final result either through additions or subtraction respectively. It is apparent that orbitofrontal part takes care of the latter and amygdala produces the signal which aids to find the final result. Likewise, a plastic connection identifies connections without any adjustable weights and a connection which can learn indicates.
The Amygdala output is A and it can be represented as Where: is the weight factor of amygdala for input number I and is the sensory input number i. α denotes the learning rate parameter which is used to adjust the learning speed. Its value is set between 0 (no learning) and 1 (instant adaptation). The Orbitofrontal cortex output is O and can be given as Where: W is the weight of the orbitofrontal cortex for the related sensory input and denotes the Orbitofrontal learning rate. The output of BILBIC is given as U and can be denoted as U= Amygdala output -Orbitofrontal cortex = ∑ − ∑ (12)

APPLICATION
The methodologies described herein can be applied on a single area power system where the objective is to maintain the working frequency change at a permissible range when the loads are changed suddenly over or under the planned values. The system consists of three main components. These are the governer, the turbine and the generator and load. The block diagrams implementing the PID and Hybrid FOPID-BELBIC controllers are delineated in Figures 4 and 5. The parameters for these diagrams are listed in Table 1. The systems are subjected to a sudden load change of 0.05 p.u. The characteristics of the turbine saturation (GRC), the GDB and the time delay as non-linear elements are displayed in Table 2. Noticeably, the proposed Simulink-based model can clearly accommodate the governor dead bands (GDBs), the generation rate constraints (GRC) and the transport delays are shown in Figures 4 and 5. Dead bands are imposed in the model using backlash nonlinearities where 0.05% is considered. The GRC of the thermal area is set to 0.01 p.u. MW/s.    The optimization fitness function i f at iteration i is given as So that Where ISEi is the integral-square-error index at iteration i, ei is the area control error index (ACE) at iteration i, P.O is the percentage overshoot of the frequency-time response curve. The definitions of P.O and settling time are depicted in [7].

RESULTS AND DISCUSSION
The frequency control single area power system with GRC, GDB, and time delay nonlinearities incorporating the PID and Hybrid FOPID-BELBIC controllers has been investigated in this research. The Bat Inspired Algorithm has been utilized to tune the proposed controllers. The tuning process of the two controllers has been achieved using the Matlab/Simulink software. The outcomes of the tuning procedure using the Integral Square Error criterion are summarized in Table 4.  12.1929 As stated in the literature, a proportional controller ( ) will have the effect of reducing the rise time and will reduce, but never eliminate, the steady-state error. An integral control ( ) will have the effect of eliminating the steady-state error, but it may make the transient response worse. A derivative control ( ) will have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response [7]. This is clear when we look at the frequency response of the system without controller (by setting the values of to 1, to o and to 0 in Figure 3. This response, as shown in Figure 6, is oscillatory with a little damping effect. This will explain why we should seek for a special controller which will damp this oscillation and achieve a system with steady-state error. As stated earlier, the first alternative is to implement the PID controller. The difference between PID and PID(s) in Figure 3 is that the parameters of the first controller ( , , and ) are tuned using the BIA but those of the second controller, PID(s), are obtained a special optimization technique associated with this block in Matlab.
The frequency response of the PID controller as shown in Figure 7 is somewhat acceptable but there are two main features. The first is the ripple effect when trying to reach the steady state. Second is the high value of ISE index. The tuned parameters of this controller are shown in Table 4. The tuning procedure using the BIA yields zero value for the integral gain . This is expected since we are trying to reduce the overshoot in the objective function. Trials have been made to limit the to values greater than zero in the tuning procedure but this leads to an unstable system.
On the contrary, the hybrid FOPID-BELBIC controller is shown in Figure 8. The tuning step has been achieved using the BIA. The results of the tuning procedure yield 5 parameters; , , , and ; for the FOPID controller and 2 parameters; α and β; for the BELBIC. The estimated values for these 7 parameters are delineated in Table 4. This has been achieved using the BIA parameter setting delineated in Table 3. It is clear that this hybrid FOPID-BELBIC will yield a smaller value for the ISE index compared with the conventional PID controller. This, of course, cab be arrived to with little high computation time.
The frequency response obtained by applying the classical PID controller and the hybrid FOPID-BELBIC is displayed in Figures 6 and 7. The two curves illustrate the fact that we can not arrived, exactly, to a zero state error. This is due to the GRC, GBD, and time delay nonlinearities. One more thing, the increase of the time delay will result in unstable system. The analysis of these effects will be studied in another endeavor.

CONCLUSION
In this paper, the application of two classes of controllers to a single area load frequency control has been investigated. The presented system has three sources of nonlinearities. These are the GRC, GBD, and time delay. The first controller is the classical PID controller while the second is the hybrid FOPID-BELBIC. The parameters of these two controllers have been optimally tuned using the BIA. Results show that the second controller will behave better than the first one. This is because of the nonlinearity nature of the second controller. Furthermore, the effect of dealing with the three embedded nonlinearities, the GRC, GBD, and time delay, have been studied but more detailed research is recommended.