Article Performance Analysis of Generator Excitation System

Study Case Performance Analysis of Generator Excitation System Voltage Response to Parameter Changes University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States Abstract In power systems, voltage stability in the excitation system is an important factor that must be considered because it has a direct impact on the stability of the entire power system. Several previous studies have shown that the voltage performance of the generator excitation system is still not optimal under operational conditions. To overcome this, a dynamic study of the generator excitation system voltage response was conducted by applying pole placement methods using the Bass-Gura, Ackerman, and Robust Pole Placement algorithms. In addition, the results of this method are compared with the use of a stabilizer. The analysis is done with the help of MATLAB software. The results show that the pole placement method is able to improve the voltage performance of the generator excitation system compared to the system without this method and the system using a stabilizer. Keywords: Power system voltage stability, generator excitation system, pole placement method, Bass-Gura algorithm, Ackerman algorithm, Robust Pole Placement, stabilizer, MATLAB. INTRODUCTION The excitation system is an important device in maintaining the voltage stability and reactive power of the generator to keep it in line with the desired working value. An increase in reactive power on the load side can cause a decrease in terminal voltage magnitude. This decrease is then detected by the potential transformer, which further corrects the excitation voltage through comparison with the reference value. The regulator will control the amplifier error signal to adjust the excitation voltage, so that the voltage generated by the generator can increase again. In the power system, the stability of the excitation system voltage greatly affects the overall stability of the power system. Voltage instability can hinder the quality of power supply and the efficiency of power transfer from generators to consumers. Under MICHAEL KURNIAWAN 1 Study Case extreme conditions, these disturbances can trigger load shedding mechanisms. In large-scale interconnection systems, manual voltage regulation is no longer used, but replaced by Automatic Voltage Regulator (AVR) on each generator to ensure voltage stability automatically. Various factors affect voltage stability, including increased transmission loads, disturbances in reactive power regulation, On-Load Tap Changer (OLTC) dynamics on transformers, and load characteristics. Power system voltage stability is highly dependent on the voltage regulation system controlled by the generator excitation system and various other control circuits that work in an integrated manner. Previous research has evaluated various methods in controlling the excitation system voltage, including Proportional Integral Differential (PID), Fuzzy Logic, Genetic Algorithm, and H∞ Method. The results show that the voltage performance of the excitation system at its operating point is still not optimal. Therefore, this study analyzes the voltage behavior using the pole placement method to ensure system stability. With this method, the roots of the characteristic equation are placed in a stable position, so it is expected to improve the voltage stability of the excitation system. LITERATURE REVIEW This section describes the block diagram of the generator excitation system under three conditions, namely without stabilizer, with stabilizer, and with pole placement method. The elements in the excitation system, both without stabilizer and with stabilizer, are further explained in. Based on Figure 1, the open-loop transfer function and closed-loop transfer function for the generator excitation system, both without stabilizer and with stabilizer, are obtained. In this analysis, Vt(s) represents the output voltage, while Vref(s) serves as the reference voltage of the system. The model of the generator excitation system with the pole placement method is shown in Figure 3. The application of this method is based on the system state model, which is expressed in the following equations (1) and (2). The control input u(t) is a state function expressed in equation (3). Equation (2) is known as the control law. In the application of the pole placement method, the control law is expressed through equation (4), MICHAEL KURNIAWAN 2 Study Case Where K is a constant gain vector. This control law allows all poles of the closed-loop system to be placed in the desired position, as expressed in equation (5). Based on equation (5), it can be seen that the signal fed back into the control input is a finite sum of all the states of the system. By substituting equation (4) into equation (1), equation (6) is obtained. The constant gain vector K is determined using the Bass-Gura algorithm [6], Ackerman algorithm [6], and Robust Pole Placement algorithm. Figure 1: Generator Excitation System Model Without Stabilizer Figure 2: Generator Excitation System Model With Stabilizer Figure 3: Generator Excitation System Model With Pole Placement Method MICHAEL KURNIAWAN 3 Study Case RESEARCH METHOD This section includes research methodology, generator excitation system parameter data, generator excitation system transfer function without stabilizer, generator excitation system transfer function with stabilizer, and design criteria which are explained as follows. Research Steps Mathematical Modeling of Generator Excitation System, The mathematical modeling process is carried out for the generator excitation system, including amplifier components, exciter, generator, stabilizer, and sensor.This model is expressed in the form of linear differential equations and Laplace transformations. Each component has a first-order transfer function that is then combined to obtain open-loop and closed-loop transfer functions, which show the relationship between the output voltage and the reference voltage as input. In addition, the open loop and closed loop transfer functions are also designed using a stabilizer as a representation of a conventional control system. Determination of Excitation System Parameters The parameters used in the formation of the generator excitation system switching function include: • Amplifier: amplifier constant (𝐾𝐴 ) and time constant (𝜏𝐴 ) • Exciter: amplifying constant (𝐾𝐸) and time constant (𝜏𝐸 ) • Generator: constant amplifier (𝐾𝐺) and time constant (𝜏𝐺) • Sensor: constant amplifier (𝐾𝑅) and time constant (𝜏𝑅 ) • Stabilizer: boost constant (𝐾𝐹) and time constant (𝜏𝐹) Conversion of Transfer Functions to Equations of State The open and closed loop transfer functions are converted into equations of state using MATLAB software to facilitate further analysis. Voltage Performance Analysis of Generator Excitation System Without Pole Placement Method • Open Loop: The voltage stability is analyzed based on the steady state error with respect to the unit step input. • Closed Loop: The analyzed parameters include steady state time, maximum lapse, as well as the peak value of the switching voltage response. • Voltage Stability: The stability of the system is evaluated through root-root analysis of the characteristic equation. • Voltage Performance Analysis by Pole Placement Method MICHAEL KURNIAWAN 4 Study Case Bass-Gura algorithm is used to determine the desired voltage design criteria. The pole location of the generator excitation system is determined based on the characteristic equation obtained from the denominator of the closed loop switching function. The determination of pole location is done through an iterative approach (trial and error). The gain constant is calculated using the Bass-Gura algorithm by referring to the equation of state of the generator excitation system and the pole location in vector form. Once the gain constant is obtained, the equation of state of the generator excitation system is updated, then voltage performance analysis is performed with the pole placement method. The same analysis process is applied to Ackerman algorithm and Robust Pole Placement algorithm. Voltage Performance Analysis with Stabilizer The analysis steps were performed similarly to the generator excitation system without the pole placement method to ensure the consistency of the comparison results. Comparison of Analysis Results The generator excitation system performance analysis results are compared based on the Bass-Gura, Ackerman, Robust Pole Placement, and stabilizer methods to determine the most optimal voltage control strategy. Generator Excitation System Parameter Data The parameters of the generator excitation system used in this study are shown in Table 1 below: Table 1. Generator Excitation System Parameter Values Generator Excitation System Transfer Function By substituting the parameter values from Table 1 into the block diagrams in Figure 1 and Figure 2, the transfer functions of the generator excitation system are obtained. The open-loop transfer function is represented by Equation (7), while the closed-loop switching function is given in Equation (8). When incorporating a stabilizer, the open-loop switching function is described in Equation (9), and the closed-loop switching function is outlined in Equation (10). Additionally, the state equations for the generator excitation system, both with and without a stabilizer, are derived from Equations (7) to (10) using MATLAB software. MICHAEL KURNIAWAN 5 Study Case Design Criteria In order for the pole placement method to produce optimal generator excitation system performance, the following voltage behavior design criteria are required: • Steady state error for unit step input is less than 0.0500. • Maximum skip is less than 5%. • Steady state time less than 2.5 seconds. • Peak value close to the given input value. RESULTS AND DISCUSSION The voltage performance analysis of the generator excitation system is carried out for several conditions, namely without the pole placement method, with the pole placement method, and using a conventional method in the form of a stabilizer. In the system without pole placement method, the voltage performance is analyzed in the time domain for the condition of the generator excitation system with open loop and closed loop. The performance of the openloop system is evaluated based on the magnitude of the steady state error, while the closed-loop system is evaluated based on the percentage of maximum skip, the time to reach steady state, and the peak value. Details of the voltage performance of the generator excitation system without pole placement method can be seen in Table 2. From Table 2, it can be seen that the performance of the generator excitation system with both open and closed loops has not met the expected criteria. This is indicated by the magnitude of the steady state error, the high percentage of maximum misses, the length of time to reach a steady state, and the peak values that are still too high. The voltage behavior of the generator excitation system under transient conditions without the pole placement method can be seen in Figure 4, while the roots of the characteristic equations of this system are shown in Table 3. To improve the performance of the generator excitation system, a pole placement method is analyzed using three algorithms, namely the Bass-Gura algorithm, Ackerman algorithm, and Robust Pole Placement algorithm. Before the analysis is carried out, the appropriate pole location is first determined in order to meet the expected criteria. The determination of the pole locations was done through a trial-and-error approach. Using the Bass-Gura algorithm, the selected pole location is shown in Equation (11), and its feedback gain value is obtained from Equation (12). MICHAEL KURNIAWAN 6 Study Case For the Ackerman algorithm, the polar locations used are shown in Equation (13), and the feedback gain value is obtained from Equation (14). Meanwhile, in the Robust Pole Placement algorithm, the pole location is shown in Equation (15), with the feedback gain value expressed in Equation (16). After the gain value is obtained, it is then substituted into the equation of state of the generator excitation system to form a new system. The performance of the system with the pole placement method is then analyzed in both open and closed loop conditions. In the open-loop system, the performance is analyzed based on the steady state error to the unit step input. While in the closed loop system, the performance is evaluated based on the percentage of maximum misses, the time to reach steady state, and the peak value. The results of the generator excitation system performance analysis with the pole placement method using the Bass-Gura algorithm can be seen in Table 4, while the results of the analysis with the Ackerman algorithm are shown in Table 5. For the analysis results using the Robust Pole Placement algorithm, the performance is shown in Table 6. From the evaluation results in Tables 4, 5, and 6, it can be seen that the generator excitation system with the pole placement method has met the expected performance criteria. The steady state error to the unit step input is less than 0.0500, the maximum skip percentage does not exceed 5%, the steady state attainment time is less than 2.5 seconds, and the peak voltage value is close to the unit input value. The voltage behavior of the generator excitation system under transient conditions with the pole placement method using the Bass-Gura algorithm can be seen in Figure 5, while for the Ackerman algorithm it is shown in Figure 6, and for the Robust Pole Placement algorithm it is shown in Figure 7. The roots of the characteristic equation for the generator excitation system with the pole placement method using the Bass-Gura algorithm are presented in Table 7, while the roots of the characteristics for the Ackerman algorithm and the Robust Pole Placement algorithm are shown in Table 8 and Table 9, respectively. From the three tables, it can be seen that all characteristic roots are real and have a damping of one, which indicates good system stability. MICHAEL KURNIAWAN 7 Study Case In addition to the pole placement method, the performance of the generator excitation system is also analyzed using a conventional method in the form of a stabilizer. The results of the performance analysis of the generator excitation system with a stabilizer, both in open and closed loop conditions, can be seen in Table 10. From Table 10, it can be seen that the system with the stabilizer has not fully met the expected criteria. One aspect that is not yet optimal is the steady state error to the unit step input which still exceeds 0.0500. The voltage behavior of the generator excitation system under transient conditions with a stabilizer can be seen in Figure 8. From the figure, it can be seen that the system does not experience oscillations, but the output voltage value has not reached the expected value. The roots of the characteristic equation of the generator excitation system with stabilizer are shown in Table 11. Table 2: Voltage Behavior Performance of Open-loop and Closed-loop Generator Excitation Systems without Pole Placement Method. Figure 4: Voltage Behavior of Generator Excitation System in Transitional State without Pole Placement Method against Unit Wave Input. Table 3: Characteristic Equation Roots of Voltage Behavior of Generator Excitation System without Pole Placement Method. MICHAEL KURNIAWAN 8 Study Case Table 4: Voltage Behavior Performance of Open-loop and Closed-loop Generator Excitation Systems with Pole Placement Method Using Bass-Gura Algorithm. Table 5: Performance of Voltage Behavior of Open-loop and Closed-loop Generator Excitation System with Pole Placement Method Using Ackerman's Algorithm. Table 6: Performance of Voltage Behavior of Open Ring and Closed Ring Generator Excitation System with Pole Placement Method Using Robust Pole Placement Algorithm. Figure 5: Voltage Behavior of Generator Excitation System in Transitional State with Pole Placement Method Using Bass-Gura Algorithm against Unit Wave Input. MICHAEL KURNIAWAN 9 Study Case Figure 6: Voltage Behavior of Generator Excitation System in Transitional State with Pole Placement Method Using Ackerman's Algorithm against Unit Wave Input. Figure 7: Voltage Behavior of Generator Excitation System in Transitional State with Pole Placement Method Using Robust Pole Placement Algorithm against Unit Wave Input. Table 7: Equation Roots of Generator Excitation System Voltage Behavior Characteristics with Pole Placement Method Using Bass-Gura Algorithm. Table 8: Equation Roots of Voltage Behavior Characteristics of Generator Excitation System with Pole Placement Method Using Ackerman's Algorithm. MICHAEL KURNIAWAN 10 Study Case Table 9: Root-Root Equation of Voltage Behavior Characteristics of Generator Excitation System with Pole Placement Method Using Robust Pole Placement Algorithm. Table 10: Voltage Behavior Performance of Open-loop and Closed-loop Generator Excitation Systems with Stabilizer. Figure 8: Voltage Behavior of Generator Excitation System in Transitional State with Stabilizer against Unit Wave Input. Table 11: Characteristic Equation Roots of Voltage Behavior of Generator Excitation System with Stabilizer. MICHAEL KURNIAWAN 11 Study Case CONCLUSION Based on the research results, the following conclusions are obtained: 1. The performance of generator excitation system with pole placement method using Bass-Gura algorithm, Ackerman algorithm, and Robust Pole Placement algorithm has met the expected criteria. 2. The stability of the generator excitation system with the pole placement method is proven to be good, which is indicated by the value of the real part of the roots of the characteristic equation which is negative. 3. Compared to a system using a stabilizer, the pole placement method shows superior performance, both in open-loop and closed-loop conditions. MICHAEL KURNIAWAN 12 Study Case REFERENCE MICHAEL KURNIAWAN 13