Comparing the Effectiveness of Feedback and Load Compensation Techniques in Controlling the Disturbed State of Nominal-T Configuration

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1 Comparing the Effectiveness of Feedback and Load Compensation Techniques in Controlling the Disturbed State of Nominal-T Configuration Thomas O. Ale Abstract Stability of Power system is the ability of a system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded so that practically the entire system remains intact. This research work stated clearly the effectiveness of the feedback and load compensation techniques in stabilizing a disturbed state of a medium transmission line using a Nominal-T configuration network. In order to achieve the set objectives, Osogbo - Akure transmission line data was obtained from Akure 132kV transmission substation. This configuration was modeled into transfer s, the compensator circuit which happens to be the phase lag circuit was also modeled. The transfer function model contained the line s extracted from this transmission substation logbook. A state space model was obtained from the transfer function model with a code written in MATLAB environment. The effectiveness of these compensation techniques were compared. The result revealed that load compensation technique offered a perfect compensation to unit step disturbance and unit impulse disturbance. While feedback compensation technique provides perfect compensation to unit impulse disturbance only. Index Terms Medium Transmission Line; Nominal-T Configuration; Compensation Technique; Transfer Function Model; State Space Model; System Response; MATLAB. I. INTRODUCTION Compensation is a very paramount tool for system control engineers, when debating on how to make an unstable system to become stable. This tool is imperative in the sense that an unstable and disturbed system can be compensated for, so that the optimal performance and operation of the system can be fully achieved. There are three techniques by which compensation of a system can be achieved, these are: series technique, feedback technique and load technique [1]. But as stated earlier on this research work focused mainly on two of these techniques; feedback and load technique. The technique here is being conceived as the way and manner in which the compensating network is positioned relative to the controlled system, intended to be compensated. Feedback technique is the process by which the compensating network is positioned in the feedback path relative to the controlled system that is in the forward path. Load technique is an embedded technique in the sense that, two techniques were employed here. In nutshell, load Published on July 31, T. O. Ale is with Electrical & Electronics Engineering Department, Federal University of Technology Akure, Ondo State, Nigeria. ( toale@futa.edu.ng, aleto04@yahoo.com) technique is a technique that combined series and feedback techniques to compensate for the controlled system. Compensation is needed in any controlled system to improve the performance of the system which is classified into transient performance and steady state performance [1]. But the compensation is considered in this research work to make the disturbed state of Nominal-T configuration to be stable. According to [1], compensator circuit is classified as phase lag circuit, phase lead circuit and phase lag-lead circuit. But phase lag circuit is considered in this research work, the reason being that the circuit provides the better steady state performance of a system, slower response to disturbance and reduction in bandwidth leading to large settling time. According to [3], phase lag circuit yields an appreciable improvement in steady state accuracy at the expense of increasing the transient response time. Fig. 1. Feedback Compensation Technique Fig. 2. Load Compensation Technique Fig. 3. Phase lag Network II. METHODOLOGY The methodology employed in this research work involved modeling the Nominal-T configuration into transfer function model and state space model [4]. As stated earlier on, the transfer function model of the Nominal-T configuration was obtained through the line s extracted from the data obtained. While the state space model was obtained through the conversion of the transfer DOI: 48

2 function model using MATLAB script file found in MATLAB environment. There is transfer function model for the compensated system and the uncompensated system; likewise, there is state space model for the compensated and the uncompensated system. For the analysis, a code was written in MATLAB object for the two system models using impulse and step input signals to obtained impulse and step response to be analyzed. It should be stressed here that the uncompensated system represents the disturbed state of the system and the compensated system represents the designed compensator using Fig. 1, 2 and 3 respectively. T fc (s) = 2s s s s The load compensation technique (Fig. 2) was calculated using block in cascade approach because the outcome of feedback technique is in series with the compensated system; this was obtained as shown in (4). T lc (s) = (2s )(s ) (0.495s s s )(s ) (4) As part of the analysis, the disturbed state in (1) was converted to state space model to check for the controllability and observability of the disturbed state, this was achieved in MATLAB environment. A. M-file written to take the transfer function model of the disturbed state to state space model to check for controllability and observability (3) clear all, clc Fig. 4. Nominal-T Configuration Fig. 4 was modeled into transfer function model using the extracted line s of the transmission line used as case study. The line s values are 2.43Ω, 69.98mH and µF respectively. These values were used to obtain the transfer function model equation shown in (1). I r (s) = 4V s (s) + 2D s (s) s s s s s+2 (1) Where; V s (s) represents the sending end voltage (measured in Volts.) D s (s) represents the disturbed (which is inform of voltage.) I r (s) represents the receiving end current (measured in Amps.) s represents the complex frequency variable Equation 1 revealed that the Nominal-T configuration modeled has two effects on its transfer function model; the normal state and the disturbed state. Since there is present of disturbed state in the transfer function model equation, there is needs for compensation of the disturbed part of the equation. To achieve this, a compensator circuit was designed with Fig. 3 using root locus technique to obtain the transfer function model of the compensator circuit shown in (2). Vr=126420; % receiving voltage [V] % an arbitrary value assumed Ds=n*Vr; % disturbed value [V] s=tf ('s'); % creation of transfer function from Laplace operator sys_tf=2*ds/ (0.165*s^ *s+2); model of the disturbed state % to create ss model from tf model of the disturbed state % state space model of the disturbed state % to obtain the observability and its rank Ob=obsv (sys_ss); % control of the system from output r_ob=rank(ob); % rank of the observability matrix % to obtain the controllability and its rank co=ctrb(sys_ss); % control of the system from input r_co=rank (co); % rank of the controllability matrix T c (s) = s s (2) The transfer function model of the compensator circuit represents the compensated system while the uncompensated system is for the disturbed state found in the transfer function model of the Nominal-T configuration. So the overall transfer function model is obtained for the feedback compensation technique and the load compensation technique. The overall transfer function model for feedback compensation technique was calculated using the closed loop transfer function formula and was obtained as shown in (3). DOI: 49

3 B. M-file written to obtain the step response of the disturbed state for transfer function model and state space model clear all, clc, close all entry Vr=126420; % receiving end of the line % an assumed value for the disturbance Ds=n*Vr; % disturbed value % to create the system tf model s=tf ('s'); sys_tf=2*ds/ (0.165*s^ *s+2); % to create the system ss model % to obtain the step response of the tf model and ss model step (sys_tf,'g'); xlabel ('Time'); model', 'location, Southeast'); title('step response for disturbed state in TF MODEL'); step(sys_ss,'y'); model', 'location, Southeast'); title('step response for disturbed state in SS MODEL'); C. M-file written to obtain the impulse response of the disturbed state for transfer function model and state space model. clear all, clc, close all entry Vr=126420; % receiving end of the line % an assumed value for the disturbance Ds=n*Vr; % disturbed value % to create the system tf model % to create the system ss model % to obtain the impulse response of the tf model and ss model impulse(sys_tf,'g'); model', 'location','southeast'); title('impulse response for disturbed state in TF MODEL'); impulse(sys_ss,'y'); model', 'location','southeast'); title('impulse response for disturbed state in SS MODEL'); After writing an m-file to generate the nature of response for the disturbed state of Nominal-T configuration [2] in the two models used in this research work, the next step was to write an m-file to compare the response of the two compensation techniques, to see which one will provide effective compensation and also to determine the level of compensation provided by these two compensation technique. D. M-file written to obtain the step response for the compensation provided by feedback compensation technique for the disturbed state response obtained. sys_tf=(2*s )/(0.495*s^ *s^ *s ); % to obtain the step response for transfer step(sys_tf,'g'); title('step response for feedback compensation in TF model'); step(sys_ss,'y'); title('step response for feedback compensation in SS model'); E. M-file written to obtain the impulse response provided by the feedback compensation technique to the disturbed state of the configuration. sys_tf=(2*s )/(0.495*s^ *s^ *s ); % to obtain the impulse response for transfer impulse(sys_tf,'g'); title('impulse response for feedback compensation in TF model'); impulse(sys_ss,'y'); title('impulse response for feedback compensation in SS model'); DOI: 50

4 F. M-file written to obtain the step response provided by load compensation technique to the disturbed state of the configuration. sys_tf=(2*s )*(s )/(0.495*s^ *s^ *s )*(s ); % to obtain the step response for transfer step(sys_tf,'g'); title('step response for load compensation in TF model'); step(sys_ss,'y'); title('step response for load compensation in SS model'); G. M-file written to obtain the impulse response provided by load compensation technique for the disturbed state of the configuration. sys_tf=(2*s )*(s )/(0.495*s^ *s^ *s )*(s ); % to obtain the impulse response for transfer impulse(sys_tf,'g'); title('impulse response for load compensation in TF model'); impulse(sys_ss,'y'); title('impulse response for load compensation in SS model'); H. M-file written to show the level of compensation provided by feedback compensation to the disturbed state of the configuration using step input % creation of transfer model for I. M-file written to show the level of compensation provided by feedback compensation to the disturbed state of the configuration using impulse input. % creation of transfer model for % defining the tf model for feedback compensated state sys_tf_fb=(2*s )/(0.495*s^ *s^ *s ); % to obtain the step response for step(sys_ss,'r',sys_ss_fb,'g'); legend(' ',' compensated title('compensation level shown by feedback % defining the tf model for feedback compensated state sys_tf_fb=(2*s )/(0.495*s^ *s^ *s ); % to obtain the impulse response for impulse(sys_ss,'r',sys_ss_fb,'g'); legend(' ',' compensated title('compensation level shown by feedback DOI: 51

5 J. M-file written to show the level of compensation provided by load compensation to the disturbed state of the configuration using step input % creation of transfer model for for controllability and observability, because if the state of a system is not controllable, then there is no point in trying to compensate for the disturbed state. But from the script file, it was discovered that the disturbed state of the network is controllable and observable, because it is full of rank [1]. % defining the tf model for load compensated state sys_tf_fb=(2*s )*(s )/(0.495*s^ *s^ *s )*(s ); % to obtain the step response for step(sys_ss,'r',sys_ss_fb,'g'); legend(' ',' compensated title('compensation level shown by load K. M-file written to show the level of compensation provided by load compensation to the disturbed state using impulse input. Fig.5. Disturbed state response in TF and SS model. (a: Step Response, b: Impulse Response) % creation of transfer model for % defining the tf model for load compensated state sys_tf_fb=(2*s )*(s )/(0.495*s^ *s^ *s )*(s ); % to obtain the impulse response for impulse(sys_ss,'r',sys_ss_fb,'g'); legend(' ',' compensated title('compensation level shown by load III. RESULTS AND DISCUSSION After analyzing the two models in MATLAB environment, the following responses were obtained. Also, the disturbed state of Nominal-T configuration was taken from transfer function model to state space model to check DOI: 52

6 Fig. 6. Feedback compensation response in TF and SS model (a: Step Response, b: Impulse Response) Fig. 8. Level of compensation provided by feedback technique (a: Step Response, b: Impulse Response) Fig. 7. Load compensation response in TF and SS model (a: Step Response, b: Impulse Response) Fig. 9. Level of compensation provided by load technique (a: Step Response, b: Impulse Response) Fig. 5 shows the nature of response obtained for the disturbed state of Nominal-T configuration when modeled in transfer function model and state space model using step and impulse input. It is obvious that the response is oscillatory in nature with high steady state value of the order of 2.53x10 5 and settling time of 44.3seconds. These two specifications of the disturbed state indicate that the system is prone to failure and collapse, thereby reducing the system optimal performance. So there are needs for compensation to correct these two specification defects presenting itself in the disturbed state. Fig. 6 shows the nature of response obtained as the consequence of using feedback compensation technique to compensate for the disturbed state both in transfer function model and state space model using step input and impulse input. From the figure, with step input it is obvious that the compensation provided by this technique has succeeded in DOI: 53

7 reducing the steady state value from the stated value to 0.2. Also the bandwidth present in the disturbed state has been reduced but at the expense of the settling time, which is now 450seconds. This implies that feedback compensation will provide a rapid and fast stability to any disturbance be it unit step disturbance or unit impulse disturbance [1]. Fig. 7 shows the response obtained when load compensation technique was used to compensate for the disturbed state of the configuration. From the figure, the compensation technique here has succeeded in reducing the oscillatory nature of the disturbed state. The settling time provided by this compensation technique was smaller than that of the feedback compensation techniques, which was of the order of 3.91seconds. Also, the compensation technique provides a better steady state value to unit step disturbance and unit impulse disturbance. As measured from the response, the steady state is of the value of 7.23µ. Fig. 8 and 9 show the level of compensation provided by feedback compensation and load compensation technique. It is obvious that load compensation technique provides a perfect compensation to unit step disturbance and unit impulse disturbance. Also, feedback compensation technique provides a perfect compensation to unit impulse disturbance that leads to oscillatory transient disturbance. But for disturbance originating as a result of unit step input, feedback compensation takes a longer time to settle down as obvious from the settling time value. IV. CONCLUSION So far, the effectiveness of feedback and load compensation techniques in compensating for the disturbed state of Nominal-T configuration has been compared. And it can be concluded that load compensation technique provides a perfect compensation to any form of disturbance that emanates within the transmission station. This is also true from the fact that load compensation technique combines the effect of series compensation and feedback compensation to give a perfect compensation of any nature of disturbance emanating from the transmission station. REFERENCES [1] SAEED S. H. (2012): Automatic control systems (with MATLAB programs), S.K. Katara and sons, seventh revised edition. [2] SEYMOUR J. (2000): Seven types of power problems, APC white papers, Electric Power Research Institute, first revision, the Cost of Power Disturbances to industrial and Digital Economy Companies, [3] SRINDHI, R. (2006): Faculty of Mechanical Engineering, SJCE Mysore [4] SAMMY O. and MICHAEL B. (2007): MATLAB Control Systems Toolbox Compendium. ETH Zurich edition. Thomas Olabode Ale completed his tertiary education in Federal University of Technology Akure with Second Class Upper Division in Electrical and Electronics Engineering in He had his Master of Engineering in Electrical and Electronics Engineering (Power Option) in He is a PhD holder in Power Systems Engineering. Dr. Ale is a Corporate Member, Nigerian Society of Engineers, a registered member of the Council for the Regulation of Engineering in Nigeria (COREN). He is a lecturer at Federal University of Technology, Akure. He has published papers, conference proceedings and research findings at both Undergraduate and Postgraduate programmes. DOI: 54