Introducing LQR-fuzzy for a dynamic multi area LFC-DR model

ABSTRACT


INTRODUCTION
The primary objective of Load Frequency Control (LFC) is to match the demanded power and power that is being generated. Demand response (DR) proposes a variety of fiscal and outfitted benefits for customers of electricity, serving the load entities and operators of grid [1]. DR can be an effective tool in "providing balance between supplies and demand in real-time. Traditionally, such services, known as ancillary services, are provided by utility-owned operating (spinning and no spinning) reserves which are basically flexible capacity generators, available when needed, to maintain secure operation of power systems" [2]. Demand Response (DR) is the alternate in consumption by means of clients in response to charge alerts, incentives, or directions from grid operators in the grid. Although the idea of load following supply existed in advance, DR is rising as a vital feature in smart grid paradigm due to the fact effective DR can be executed best with the help of records conversation generation. DR extensively classified into fee primarily based and incentive based, has been notably studied and analyzed in various aspects. The focus become mainly on top clipping, load shifting and call for manage schemes. For residential load control, thermostatically controlled hundreds (TCL) like heating, ventilating and air conditioner (HVAC) masses are taken into consideration as they motive minimum inconvenience to the users when a generating unit trips or a block of load gets added to the system, the power mismatch is compensated by the primary response of the system, which is to extract kinetic energy from system inertial storage. This causes system frequency ISSN: 2088-8708  Introducing LQR-fuzzy for a dynamic multi area LFC-DR model (Palakaluri Srividya Devi) 863 Taking LQR feature into attention, a strong decentralized manage scheme is designed using Fuzzy approach [22], [23]- [25]. The proposed controller is simulated for a multi-area power system. Results of simulation show that the fuzzy controllers assure the study overall performance

SYSTEM MODEL
In general frequency-domain related power balance equation for small-order linearized system LFC representation for the use in frequency control synthesis and analysis is given by [7], [8]: The modified multi area block diagram considering demand response(DR) to thermal power system for load frequency control, with communication delay latency is shown [18]. Since spinning reserve in magnitude is performed using DR and with power flow direction, i.e., once deviation in frequency becomes negative (positive), it is required to turn OFF (ON) a part of the receptive loads for ancillary services (i.e., DR), Equation (1) can be modified as Equation (2): The power intake repute of controllable loads may be changed immediately by the command sign they acquire [26], [27]. In contrast to the same old spinning reserve-issuer power plants, there's no ramp up and down obstacles on the DR sources. The multi area power system with dynamic demand response load disturbance is shown in Figure 1. Area2: Therefore; the one primary problem for DR is communication delay, known as latency, affects the dynamic performance of the system.

State-space dynamical model for LFC-DR for two-area power system
Representing the LFC model in State space is one of the robust control theories. Now including the dynamic model DR with its latency to the traditional LFC model, modified matrix had obtained considering all non-linearities. The state-space realization of a two-area power system model with a non-reheat steam turbine and DR is given by Equations (5) and (6): Where: A -System matrix, B -control input matrix, ᴦ-Disturbance matrix, X -State vector, U (t) -input vector, Y-System output which are Δf 1 (s) and Δf 2 (s)

Padé approximation
There are various methods and techniques for the linearization of Time delays. From which one of the widely used approximation is "Padé approximation" with delivers strong and successive convergent results [22]. Padé approximations are the most frequently used methods which approximate using rational function. It basically approximates time delays by a quotient of polynomials. Classical control system theory provides the basic relation, but approximation with equal numerator and denominator degree are most broadly advised as shown in Equations (7) It is as follows: From above "P" and "Q" are the polynomials of order "m" and "n", respectively. The order usually varies between 1 and 10. The Padé approximation with 5th-order is recommended and used for the study, since the cut-off frequency usually less than 15 rad/sec. Simulation studies are carried over different values of communication delay latencies (T d ) and the proposed method shows the effective and robust dynamic performance.

RESEARCH MENTOD 3.1. Linear quadratic regulator (LQR)
Numerous different classical and modern control theories have been utilized for the LFC problem. In this section, a general controller design(LQR) approach for the LFC problem with the DR control loop is presented. The theory of optimal control is concerned with operating a dynamic system at minimum cost, where the system dynamics are described by a set of linear differential equations and the cost is described by a quadratic function is called the LQ problem. The solution is provided by the Linear-Quadratic Regulator (LQR). Optimal control in state space is centered around the Riccati Equation (11) with state variable functions that must be solved to yield the control law or trajectory.
The simplified version of the LFC-DR with LQR problem is to design controller such that the performance index is minimized for the system given in Where ρ is the weighting factor chosen by the designer, Q is an n-by-n semidefinite symmetric state cost matrix is an m-by-m positive definite symmetric control cost matrix. With the modified state space Equation (12), ensuring the system matrix is controllable. The implementation of LQR method with required state and control matrices.

Fuzzy logic controllers
Fuzzy logic controllers are rule-based systems that are useful inside the context of complex unwelldescribed methods, especially those which may be controlled by means of a professional human operator without the understanding in their underlying dynamics [18], [28]- [30]. The critical part of the FLC device is a fixed of fuzzy control regulations (FCRs) associated by way of a fuzzy implication and the compositional rule of inference. Since power system dynamic traits are complicated and variable, traditional manipulate techniques can't offer preferred results. Wise controllers can be replaced with conventional controllers to get speedy and accurate dynamic reaction in load frequency control problems. If the device robustness and reliability are greater critical, fuzzy common-sense controllers may be greater useful in solving a huge range of manage issues since traditional controllers are slower and much less green in nonlinear system programs. Fuzzy logic controller is designed to limit fluctuation on device outputs. FLC is designed to cast off the want for non-stop operator attention and used routinely to alter a few variables the manner variable is stored at the reference price. The simple configuration of a fuzzy-common sense control is composed of four principle additives: a fuzzification, an information base, an inference engine, and defuzzification. The fuzzifier maps the enter crisp values into fuzzy variables the use of normalized membership functions and enter profits. The fuzzy logic inference engine then infers the right control motion primarily based at the available rule-base. The fuzzy manage action is translated to the proper crisp cost via the defuzzifier the usage of normalized membership functions and output gains. The block diagram of a fuzzy logic system is shown Figure 2.  Table II are applied and the robust performance for the proposed model can be achieved.

ANALYTICAL APPROACH FOR THE MODEL
The state equations of conventional load frequency control are well documented [1], [4]. However, the DR control loop is added to the LFC problem in this study. Investigations are done earlier on the impact of the DR control loop on the stability analysis and steady-state error of the given power system. Rewriting the Equation (2), the system frequency deviation can be expressed as follows: Based on the final value theorem, the steady state value of the frequency deviation can be obtained as follows [14]: (17) From the above Equation (17); the following conclusions can be made for the analysis of the model: a. As the frequency deviation will not be zero unless the supplementary and/or DR controls exist. b. With the availability of DR in the LFC, a higher reliability of frequency regulation can be achieved, since the DR control loop can complement the supplementary control loop. In cases when the supplementary control is not available, if enough DR resources are available, the performance of the frequency regulation can be guaranteed by the DR loop. c. To have zero frequency deviation at steady-state, the required control effort can be split between the supplementary and DR control loops. In other words, an ISO/RTO will have the opportunity to perform the regulation services in a cost-effective way and analyze the frequency response of the system quickly. This goal can be achieved only in the proposed formulation [20] with an added control loop for DR. Therefore, taking above conclusions into consideration: With DR availability in the LFC, the required control effort can be splitted in to two control loops based on their cost at real -time electricity market ΔP S (s)= α. control effort (18)

ΔP DR (s)= (1-α). control effort (19)
And finally based on the control effort the supplementary and DR control loop of the system is modified and governed by the below equation: (1-α) G(s)+α.H(s) (20) where 0<α<1 is the share of traditional regulation services in the required control effort. It shows that if α=1, the total regulation is provided by traditional regulation services and if α=0 i.e. for this time the total control would be provided by DR. The decision of α should be made by ISO/RTO, based on the price of DR and Traditional regulatory services in the real-time market explored by authors [22]. Simulation studies are carried on the system frequency deviation considering two different values of α. a. If α = 0.1, 10% of the regulation id provided by the supplementary control and 90% from DR b. If α = 0.8, 80% of the regulation id provided by the supplementary control and 20% from DR In the next section, simulation results for the LFC-DR model of a single-area power system are presented to verify the effectiveness of the proposed model compared to that classic controller.

SIMULATION RESULTS
The result of several different simulation studies in this section provides an important feature of the proposed LFC-DR model. The parameters used in the simulation studies are given in Appendix Table for two different operating points. Using, the load disturbance, as the system input. It can be noticed from this table that a higher share of control effort for the DR control loop, i.e., smaller α, will provide a higher gain and phase margin, indicating a more stable system.

Case 1
In the first simulation study, a 0.1 pu load disturbance (with 10% Load perturbation) was applied to the two-area LFC-DR power system model with the parameters in Appendix Table Using proposed method, the frequency deviations is quickly driven back to zero and the controller designed using PID controller has the best performance in control and damping of frequency. Frequency deviation for LFC-DR models with different control effort for a Two area power system are shown in Figure 3.

Case 2
In the second simulation study, a 0.1 p.u. load disturbance was applied to the two-area LFC -DR model with the parameters shown in Appendix table. Using proposed method, the frequency deviations are driven back to zero and the controller designed using Fuzzy-PID controller has the good performance in control and damping of frequency with different control efforts. This proposed LFC-DR model has a superior performance over the conventional LFC during the transient period considering the both cases of control effort i.e. alpha values (DR participation). Frequency deviation for LFC-DR models (with Fuzzy-PID controller) with α values are shown in Figure 4.

Case 3
In this simulation study, a 0.1 pu load disturbance was applied to the two-area LFC -DR model with the parameters shown in Appendix. Using proposed method, the frequency deviations is quickly driven back to zero and the controller designed using LQR-Fuzzy controller has the robust and superior performance in control and damping of frequency when compared with conventional PID Controllers, Considering the both cases of control effort i.e alpha values (DR participation). Frequency deviation for LFC-DR models (with LQR-Fuzzy controller) with α value are shown in Figure 5.
For hree cases based on the settling time and Undershoot for all the models i.e. LFC-DR with PID controllers and the two-proposed approach (Fuzzy-PID and LQR-Fuzzy) the analysis is carried. From the analysis best system dynamic performance is achieved by the proposed LQR-Fuzzy approach. The proposed method shows the dynamic and robust response for this dynamic demand response LFC model. Comparisons are made with different controllers and with different control efforts for the model. The Figure 6 and Figure 7 show different comparative analysis.  From the simulation studies, it is seen that the proposed method also best for the different communication latencies when compared to the conventional controllers for LFC-DR model.

CONCLUSION
In this paper a new method for load frequency control with DR loop using LQR-Fuzzy and Fuzzy-PID controller for a two-area power system has been proposed. The proposed method was applied to twoarea non-reheat thermal power system for two different control effort (α) operating conditions. Simulation results obtained from the designed controller guarantees the robust stability and robust performance of the system. To demonstrate the robustness in the performance of the proposed method, settling time, and undershoot of the response of the system are being considered. Also, the simulation results show that the proposed method is robust to change in the parameter of the system and has good performance as compared to that of LFC-DR classical with controller in all the operation condition. In general, there exist large power systems of multi-area where different Gencos and Lagcos are available in each area. In future work, the application can be extended to LFC-DR in Hydro-Thermal power systems and by considering the effect of different latencies.