Recently evolutionary algorithms are used more often. **Differential** **evolution** (DE) is a method that repeats the attempt to find optimal points by differentiating a criterion. In classical optimization methods, such as gradient and Newton, a derivative operator is used, while in results of DE the quality criterion search method is used [15]. DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones according to its simple formulae, and then keeping the candidate solution which has the best score or fitness on the optimization problem at hand. In this way, an optimization problem is treated as a black box that merely provides a measure of quality given by a solution, therefore the gradient is not needed.

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In this study, a new grey wolf optimized LFC has been investigated for automatic **load** **frequency** **control** of a two **area** **interconnected** **power** systems. It is shown analytically and graphically that there is a substantial improvement in the time domain specification in terms of lesser rise time, peak time, settling time as well as a lower overshoot. The proposed controller **using** GWO **algorithm** with PID controller is proved to be better than the conventional PI controller. The simulation results are given to validate the disturbances for LFC. From the simulation results, the tabulated settling time of 2% and 3% disturbances are shown in graphical representation. Therefore, the proposed GWO-PID controller is recommended to generate good quality and reliable electric energy. In addition, the proposed controller is very simple and easy to implement since it does not require many information about **system** parameters. Comparison of the proposed GWO-PID controller with Genetic, Particle Swarm, Flower Pollination, Fire Fly, Ant Colony Optimization Algorithms along with PI-PID controllers in **multi**-**area** **interconnected** **power** **system** will be subject to the future work.

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2 are under unchanged condition. Fig 7 shows that the variation in **frequency** of **area** 3. The simulation proved that the presented FOPID controller improves the operation of **multi** **area** **interconnected** **power** **system** by reducing the steady state error and oscillations present in the responses. Table V displays the evaluation of settling time for the change in **frequency** of all **area**, for 0.1 p.u change in **load** demand of **area**-3 with different controllers. The settling time and peek overshoot is reduced for the **interconnected** three **area** **power** **system** with FOPID controller than the PID controller.

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The crucial objectives of **load**-**frequency** **control** (LFC) to a **multi**-**area** **interconnected** **power** **system** are to maintain the **system** **frequency** at a nominal value (50 Hz or 60 Hz) and the tie-line **power** flows at predetermined values. Based on tie-line bias **control** strategy, conventional regulators, such as I, PI and PID, were initially used for solving the LFC problem. Due to the complexity, nonlinearity and uncertainty of a **multi**-**area** **power** **system** in practice, the conventional regulators may not obtain the **control** performances good enough to bring the network back to the steady state as soon as possible. Meanwhile, intelligent controllers, such as fuzzy logic (FL)-based controllers, are able to completely replace these conventional counterparts. The superiority of the FL-based LFC controllers over the conventional ones for a typical case study of five-**area** **interconnected** **power** grids is validated in this paper through numerical simulations implemented in Matlab/Simulink package. It should be apparent from this comparative study that the LFC controller based on FL technique is a feasible selection in dealing with the LFC problem of a **multi**-**area** **power** network.

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are decreased so that the regional **control** error will pass zero after a while to ensure the stability of the entire **system**. This paper constructs the model for three areas with hydro, thermal, and wind **power**. The IEEE standard mathematical model for hydro and thermal **power** used in this paper is composed of the governor, water turbine, steam turbine, and generator individually. The schematic diagrams of **load** **frequency** **control** models for thermal- and hydro-powers are shown in Fig. 1 and Fig. 2 [14]–[19].

In the **power** **system** operation and **control** the main constraints to be satisfied is to maintain the **system** **frequency** and terminal voltages within the specified limits. The **power** **system** should not only ensure a better quality but also reliable **power** supply by maintaining the above mentioned constraints. According to **power** **system** **control** theory, a nominal **system** **frequency** depends on the balance between generated and consumed real **power** [1]. If the amount of generated **power** is less than the demanded amount, speed and **frequency** of the generator units begin to decrease, and vice versa. Hence, the amount of **power** produced by each generators should take care in minimizing the **frequency** deviations occurred in the **power** **system** due to sudden change in **load**. For this purpose, **load** **frequency** **control** is being adopted and the main aim of this **control** is that the steady state error of the **system** **frequency** deviations following a step **load** demand should be made zero in a faster manner. The stabilization of **frequency** oscillations in an **interconnected** **power** **system** becomes challenging when implemented in the future environment due to unpredictable **load** demand. So advance economic, high efficiency and improved **control** schemes [2, 3] are required to ensure the **power** **system** reliability. Several indices have been proposed as methods to evaluates the success of **frequency** **control** between linked systems. For instance, the AR based standard

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A is **system** matrix, B is the input distribution matrix and Γ disturbance distribution matrix,𝑥 is the state vector,𝑢 is the **control** vector and 𝑑 is the disturbance vector of **load** changes of appropriate dimensions. The typical values of **system** parameters for nominal operation condition are given in appendix. This study focuses on optimal tuning of controllers for LFC and tie-**power** **control** **using** settling time based optimization to ensure a better **power** **system** restoration assessment. On the other hand in this study the goals are to **control** the **frequency** and inter **area** tie-**power** with good oscillation damping **using** the modern **control** theory concept and also to obtain a good performance under all operating conditions with various loading conditions and finally to design a low-order controller for easy implementation. To achieve the above said conditions a Feasible Restoration Index (FRI) and Complete Restoration Index (CRI) based on the settling time has been formulated in this proposed methodology in TATURIPS with the SMES unit and GT unit in **Area**-1and

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In literature, **control** strategies based on conventional and fuzzy logic controller are proposed [5]. Several authors suggest variable-structure systems, various adaptive **control** techniques and Riccati equation approach for **load** a **frequency** controller design [6, 7]. There are many studies about different **control** strategies having advantages and disadvantages [1, 2, 5, 8-10]. In Reference [9], a **load** **frequency** **control** **using** a conventional PID controller is applied and it is emphasized that the controller performance is better than others. However, if a **power** **system** structure has nonlinear dynamics and parts, the **system** operating point varies and conventional controllers needing **system** model must not be used. In Reference [5], a modified dynamic neural networks controller is proposed. It is determined that the proposed controller offers better performance than conventional neural network controller. In Reference [2], for a single **area** **system** and two areas **interconnected** **power** systems, artificial intelligence techniques are purposed for the automatic generation **control** and the comparison is performed between intelligent controllers and the conventional PI and PID controllers. In Reference [10], a robust decentralized **control** strategy is used for **Load** **frequency** **control** for four **area** **power** systems to obtain robust stability and better performances. In References [1, 8], **power** **system** **load** **frequency** **control** is realized by fuzzy logic controller.

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The **load** **frequency** **control** applies single **area** **system** and also **multi** **area** **system**. Past year **load** **frequency** **control** implemented without controller and optimization technique. Today we apply modern **control** technique of **load** **frequency** **control**. Modern technique maintains **frequency** when any change of **load**. To achieve this many controller such as PI, PID controller and many optimization technique as particle swarm optimization technique, genetic **algorithm**, fuzzy logic controller, artificial neural network, **differential** **evolution** etc. are used.

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Online fuzzy PI controller tuning **using** the bat **algorithm** method is presented in [ 24 ]. In addition, an artificial neural network is used to **control** **power** generation in a **multi**-**area** thermal **power** plant **system** in [ 25 ] and a third-order observer-based sliding mode **control** in [ 26 ]. An adaptive neural fuzzy **control** **system** was applied to improve LFC in both hydro and thermal **power** systems in [ 27 ]. In [ 28 ], a novel PID-like neural network controller is proposed. The resilient back-propagation **algorithm** with sign instead of the gradient is used to derive the rule of updating network weights. The simulation experiment was carried out on an inverted-pendulum **system**. Reference [ 29 ] presents an adaptive PID-like controller **using** a modified neural network for learning of **system** dynamics. This controller applied to speed **control** of DC machine. Moreover, a simplified adaptive neuro-fuzzy inference **system** (ANFIS) structure acting as a PID-like feedback controller to **control** nonlinear systems is presented in [ 30 ]. In fact, all of the above-mentioned studies focused on **system** dynamics. However, in our proposed method in this paper, the controller is not dependent on the **system** dynamic parameters, and **system** parameters are assumed to be uncertain, and the controller is designed online. The proposed controller is adaptive and adapts itself to **system** new conditions. It can be applied in practical and real-world applications including the standard 39-bus New England **system** that has satisfied our expectations despite nonlinearity of the **power** **system**. Furthermore, the proposed controller is based on type-2 neural fuzzy, which performs better than type-1 fuzzy and models more uncertainties. The **control** parameters were trained by the descending gradient method and the error back-propagation posture so that the **area** **control** error signal could be zero. Jacobian of the **system** model is extracted and is applied to the controller. Then, the **control** error signal is applied as a PID to the controller input in order to increase the speed and compensate for the slower speed due to parameter training. Then, the suggested method is compared with the PI, IMC-PID and PID controllers for evaluation and comparison. Finally, to show effectiveness of proposed **control**, we applied this method on New England test **system** 39-bus, which is widely used as a standard **system** for testing of the **power** **system** analysis and **control**. Compared to our previous work in [ 31 ], the distinct features of this paper are as follows:

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This paper presents the FLC **using** PI-fuzzy controllers. The proposed controller is tuned **using** PSO to obtain the controller gains in order to get an efficient fuzzy **control** on four of an **interconnected** electrical **power** **system**. This is a new approach to optimize the fuzzy controller that differentiates to other's methods. The simulation results are carried out in term **frequency** response for its damping under different **load** conditions and compared it to the effectiveness of proposed controllers with other controllers. Simulation results show that the undershot and settling times with the proposed controller are better and guarantees robust performance under a wide range of operating conditions.

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In Electrical **power** **system** network the efficient and stable operation round the clock is extremely important. With the growing **power** demand the need for more **power** generating station arises due to which the complexity of **power** **system** increased. Large number of interconnection has been made which makes the **control** of multipart **power** **system** even more tedious job to accomplish. Now a days most of the world **power** networks has more than two **interconnected** generating unit of different genera for which the reactive and active **power** **control** is needed. **Load** **frequency** **control** is one of the key variable to have a stable and reliable operation of the **interconnected** **system**. By definition, the **load** **frequency** **control** is a methodology that equates the **power** generation and demand while maintaining the **frequency** fluctuation with in the stipulated level. So a very sophisticated **control** is needed to maintain the **system** **frequency** and tie line **power** under **control**. In past time many controller has been developed which are widely based on PID **control** technique. But in modern time, modern controller is needed so, many research is going on in this direction.

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The LFC **system** investigated for present study is composed of an interconnection of two unequal **system** of **area**-1: 1600MW and **area**-2: 1800MW capacity. **Area**-1 is considered with single-stage reheats type thermal **system** and **Area**- 2 is a hydro **system** with Electrical type governor. Both thermal and hydro governors are studied with Dead Band type non-linearity. Overall block diagram of test **system** is shown in Fig. 1. 1% step **load** perturbation (SLP) in **area**-1 is considered for study. Nominal values of all parameters are given in Appendix-1. MATLAB version 2009 is used to study the dynamics of an **interconnected** **power** **system**. Integral (I), Proportional plus Integral (PI), Proportional plus Integral plus Derivative (PID) type of controllers are used for this study. Optimum values of controller parameters are determined by Integral Square Error (ISE) criterion through BBO **algorithm**.

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As mentioned in previous Chapters, the study of the AGC and POD is very important in both **power** **system** dynamic analysis [5.1]-[5.2] and changing conventional **power** **system** through deregulation [5.3], existing many proposals in these important research areas [5.4]-[5.5]. In parallel to liberalization in the **power** industry, high penetration of renewable resources and required technology for their integration provide new research challenges [5.6]. In this sense, recent trends of research lie with the adoption of previous concepts and conventional models considering new AC/DC complex scenarios with more application of DC interconnections and renewable energy systems (RES) penetration [5.7]-[5.8]. Since last decade, many researchers tried to propose new models for **load** **frequency** **control** considering the competitive environment, usually extending previous conventional approaches [5.4]-[5.5], by introducing more detailed models of generation based on renewable resources [5.5]-[5.8]. Nowadays, integration of RES is the main challenge of the industry. During the steady state operation, the generation and consumption of energy must be balanced and any imbalance could bring severe deviations on the **frequency** and on the transmitted **power**. As it is well-known, the rate of change of **frequency** depends on the initial **power** disparity and **system** inertia, which is a serious issue when dealing with a **power** **system** with high penetration of renewables with low inertia. Actually the lack of inertia, due to the high penetration of RES and systems based on **power** electronics, results in a big challenge for **power** systems **control** in future **power** systems. For example, in PV generation, there is not any mechanical parts with inertia. Likewise, in wind and wave **power** generation cannot contribute directly to the total inertial of the **system** because of decoupling the prime mover from electrical generator [5.8]. Therefore, technical solutions for providing additional inertia are very useful.

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suitable objective function is very important. Conventional objective functions used in the literature are Integral of Time multiplied by Squared Error (ITSE), Integral of Squared Error (ISE), Integral of Time multiplied by Absolute Error (ITAE) and Integral of Absolute Error (IAE). Three different objective functions are used for the design purpose in the present paper. The results obtained from the simulations show that the pro- posed **control** strategy optimized with a new objective function achieves better dynamic performances than the standard objec- tive functions. The superiority of the proposed approach has been shown by comparing the results with a recently published Craziness based Particle Swarm Optimization (CPSO) tech- nique for the same **interconnected** **power** **system**. It is observed that the proposed DE optimized PI controller outperforms the CPSO optimized PI controller and the best performance is obtained with DE optimized PID controller. Finally, the study is extended to a more realistic network of two-**area** six unit sys- tem with different **power** generating units considering physical constraints such as boiler dynamics for thermal plants, Gener- ation Rate Constraint (GRC) and Governor Dead Band (GDB) nonlinearity. It is observed that the proposed approach can be applied to **interconnected** **power** systems with diverse sources of generation with different PID controllers for each generating unit.

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Imbalances between **load** and generation must be corrected within seconds to avoid **frequency** deviations that might threaten the stability and security of the **power** **system**. The problem of controlling the **frequency** in large **power** systems by adjusting the production of generating units in response to changes in the **load** is called **load** **frequency** **control** (LFC). The Objectives of LFC are to provide zero steady-state errors of **frequency** and tie-line exchange variations, high damping of **frequency** oscillations and decreasing overshoot of the disturbance so that the **system** is not too far from the stability. The **load** **frequency** **control** of a **multi** **area** **power** **system** generally incorporates proper **control** **system**, by which the **area** frequencies could brought back to its predefined value or very nearer to its predefined value so as the tie line **power**, when the is sudden change in **load** occurs.

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The objective of this study is to investigate the **load** **frequency** **control** and inter **area** tie-**power** **control** problem for a **multi**-**area** **power** **system** taking into consideration the uncertainties in the parameters of **system**. An optimal **control** scheme based particle swarm optimization (PSO) **Algorithm** method is used for tuning the parameters of this PID controller. The proposed controller is simulated for a three-**area** **power** **system**. To show effectiveness of proposed method and also compare the performance of these three controllers, several changes in demand of first **area**, demand of second **area** and demand of three areas simultaneously are applied. Simulation results indicate that PSO controllers guarantee the good performance under various **load** conditions.

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