Microsoft Word - 37-3318_s_ETASR_V10_N1_pp5301-5306 Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5301-5306 5301 www.etasr.com Shahami et al.: Steady State Stability Analysis and Improvement using Eigenvalues and PSS: A case … Steady State Stability Analysis and Improvement using Eigenvalues and PSS A Case Study of a Thermal Power Plant in Jamshoro, Pakistan Zulfiqar Ali Shahani Department of Electrical Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan zulfiqar.shahani57@gmail.com Ashfaque Ahmed Hashmani Department of Electrical Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan ashfaquehashmani1@gmail.com Muhammad Mujtaba Shaikh Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology Jamshoro, Pakistan mujtaba.shaikh@faculty.muet.edu.pk Abstract—The efficient handling and distribution of electrical power consist one of the most complex and appealing research problems. Due to the interconnection of different power plants and intensity of load, which gradually changes due to continuous change in load on generating units, careful treatment of the small disturbances in a power system which may lead to severe disturbance is necessary. Stability is an essential part in electrical power system operation and control. The stability problem is related with the behavior of synchronous machine after the power system is subjected to trouble. This work presents Steady State Stability (SSS) analysis of a Jamshoro Thermal Power Plant (JTPP) by using eigenvalue analysis of the different cases by varying load at three different positions. A mathematical model has been used for the JTPP with real data in order to examine the behavior of the system and to find the eigenvalues. A Simulink model of the JTTP for waveform analysis in MATLAB/Simulink has been used without and with Power System Stabilizer (PSS). Numerical quantification of the eigenvalues under the examined cases categorizes the stability of the system. The waveforms of the system are analyzed, and in cases of instability, the proposed procedure utilizing PSS helps in maintaining the system’s usual working conditions. The eigenvalue analysis and simulation results show the behavior of synchronous machines when loading changes gradually. The existing system becomes stable after more swings, whereas by using PSS in the existing system, stable regimes are attained in less time. The obtained results demonstrate the effectiveness of the proposed solution for SSS examination and securing of the disturbances of the JTPP. Keywords-steady state stability; power plant; eigenvalues; power system stabilizer; MATLAB I. INTRODUCTION In an electrical power system, it is essential to transmit reliable, secure and free from disturbances power, but load and external faults are independent which may affect voltage and frequency values, or even cause loss of synchronism [1]. The ability of a power system to remain stable after facing a small or large disturbance, which occurs in the existing system, is called power system stability. Stability problems are divided into two categories: Transient Stability (TS) and Steady State Stability (SSS) [2]. In TS, the power system remains in normal condition when a large disturbance occurs such as a loss of excitation, fault on the system, a sudden outage of line, removal of large load, etc. [3]. On the other hand, in SSS, the power system remains in normal condition when small disturbances occur, such as gradual variation in electrical load [4]. Nowadays, electrical power systems grow day by day, with increase of interconnection, installation of very large units, and extra high voltage (EHV) tie-lines [5]. TS is usually analyzed through Euler method, modified Euler method, and Runge- Kutta (RK) methods whereas SSS of the power system is usually examined using eigenvalues [6]. Eigenvalues and wave-forms of synchronous machines were analyzed in [7]. The examination was carried out by varying faults at three different locations: generating point, middle of transmission line, and an infinite position. The fault near the machine appeared to be most severe. In [8], by varying instantaneous power disturbance, eigenvalues and wave forms were analyzed in power system generating units, disturbance of waveforms dependence on the amplitude and location of disturbance. According to [9] the SSS of power systems by increasing loads is complementary to the usual TS investigations. To study the SSS of a complex power system, eigenvalue analysis was used. In [10], analysis of SSS on the near connection between the already-connected Luzon-Visayas grid with the isolated Mindanao power grid was investigated in free and open-source software. There are not publicly available studies regarding this inter-connection. In [11], small signal stability analysis for a hybrid renewable energy system was conducted and an integrated hybrid system was analyzed with the help of Lyapurav’s stability criteria and small signal stability disturbance with power system stabilizer (PSS) through MATLAB/Simulink. Power flow and SSS of interconnected three isolated Philippine power grids was studied in [12]. Eigenvalues analysis was employed to find the SSS of the main power grid and a model was developed in MATLAB/Simulink. According to [13], if the quantity of perturbation is very small, in the initial stage when there is small perturbation in the load, the system remains in stable condition (SSS). Under small perturbation if the eigenvalues of the mathematical model have Corresponding author: Muhammad Mujtaba Shaikh Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5301-5306 5302 www.etasr.com Shahami et al.: Steady State Stability Analysis and Improvement using Eigenvalues and PSS: A case … negative real parts, the system is under stable condition. In case the system becomes unstable, this means that the eigenvalues have positive real parts, while complex eigenvalues, produce oscillations in the system. In [14], the TS of a power system was verified by using time domain (TD) analysis, and eigenvalues analysis when the system was brought under small disturbances. The use of FACTS devices for TS was investigated in [15]. Other approaches like the use of fuzzy logic controllers [16] and harmonic function [17] have also been used to improve PSS under different conditions [18]. In this paper, stable and efficient operation of a JTPP have been considered. Stable operation, voltage stability, frequency stability, and rotor angle stability were studied. Voltage stability considered voltage control through an Automatic Voltage Regulator (AVR) for frequency stability. Focus was given on Primary Frequency Control (PFC) through governor, and rotor angle stability focus is on the deviation of rotor speed. This work analyzes small signal stability which can be modified by using PSS. In that way, the system becomes stable and will remain in stable condition for a long period of time. The proposed procedure assures the secure and reliable operation of the JTPP even in conditions when disturbance, either small or large, occurs in the system, by changing different loads. The objective of the current work is to analyze the stability of a power system under varying load at alternator side. By varying load at alternator side, it has been shown that the system has more swings when large load is connected on a power system. So, in order to remove more swings a PSS was used. By using PSS, the system became stable in less time. The main contribution of this work lies on the use of eigenvalues as indicators of the small signal stability in usual operation so that the unstable regimen may be analyzed and taken care of in order to retain stability. The use of PSS on usual operation has also been tested and found to improve the stability regimen. II. MATERIALS AND METHODS The JTPP has four units, one with 16.5KV rated voltage and three with 15.75KV rated voltage. Two transformers are used which step up from the rated voltage to 220KV transmission line voltage. A generating unit was developed in the mathematical model, at alternator side, at excitation side and at prime mover governing system side. The eigenvalues were found and the analyzed system’s stability was improved by PSS. A. Plant Overview The plant was visited and all the necessary data, parameters, and specifications mentioned in Tables I-II were collected. B. Small Signal Stability Analysis The ability of the running power system to maintain synchronism after the occurrence of small interruption is known as Steady State Stability [1]. As variations occur in the system, they cause small unbalances. A dynamic equation model of the system will be developed and will be linearized to understand SSS. TABLE I. SYSTEM PARAMETERS AND SPECIFICATIONS Type Units 1 Synchronous machine FTHRI 562/68-2 2-4 Synchronous machines QFSN-210-2 Connections 3-Phase star 3-Phase star Power in MW 250 210 Rated current 10.294KA 9.056KA Rated voltage 16.5KV 15.75KV Visual power 294200KVA 247000KVA Power factor 0.85 0.85 Speed 3000RPM 3000RPM Critical speed second order 3590RPM 3494RPM Critical speed first order 1200RPM 1263RPM Rated excitation voltage 370V 489V Rated excitation current 2020A 1867A Efficiency 99.02% 98.66% Pressure of h2 3Kg/cm 2 0.3MPa Water flow for stator winding ---- 35m 3 /h Insulation class F F TABLE II. POWER TRANSFORMER PROPERTIES AND SPECIFICATIONS Model Units 1 AD69030T1 2-4 SFP7- 250000/220TA Rated power 294.2MVA 250000KVA Rated current 772/10294A 656.1/9164.3A Rated voltage 220/16.5KV 220±4X2.5%/15.75KV Cooling type Oil immersed, (ODAF) cooled Oil immersed, (ODAF) cooled Frequency 50Hz 50Hz Poles 3 3 Temperature class A A Connection of symbol YN. d1 YN. d1 Noise level 90dB (A) 75dB Load loss <500KW 609.9KW No load loss <520KW 613.6KW No load current 0.2% 0.12% Impedance voltage 15% 13.5% Under balanced condition, we may define the system as: ∆ẋ = A∆x (1) It is defined as the rate of change of each state variable with the linear composition of all thee states available in the system. To inscribe the small signal analysis problem, the modified state vector z is described in equation (2): ∆x = ϕ� (2) The variable matrix Φ is the right modal matrix of vector A. A is consisting of n right eigenvectors φᵢ;i∈n . Equation (3) is developed by combining (1) and (2): ϕż = Aϕ� (3) By rearranging (3), we get: ż = Φ¯�AΦz = ⋀z (4) Λ represents a matrix having diagonal elements of eigenvalues where λ=I belongs to n, so (5) represents n Engineering, Technology & Applied Science Research Vol. 10, No. 1, 2020, 5301-5306 5303 www.etasr.com Shahami et al.: Steady State Stability Analysis and Improvement using Eigenvalues and PSS: A case … decoupled first order: żᵢ = λᵢz i (5) The resolved form of (5) is: zᵢ�t� = zᵢ�0���ᵢ� (6) To obtain zi(0), (7), can be written as: z�t� = Φ¯�∆x�t� = Ѱ∆x�t� (7) where Ψ is the left matrix of vector A, which consist of n left eigenvectors ψi, hence every variable of state and its starting condition are given as: zᵢ�t� = Ѱᵢ∆x�t� ;zᵢ�0� = Ѱᵢ∆x�0� (8) In accordance with (6), the actual state vector ∆x(t) is written as: ∆x�t� = ∑ Ѱᵢcᵢ��ᵢ��� � (9) with cᵢ as zᵢ(0). The actual state variable ∆xᵢ(0) can be extracted from (2) and (9): ∆xᵢ�t� = Ѱᵢ₁c₁��"� + Ѱᵢ₂c₂��%� +⋯+Ѱ'(c(�� ) � (10) Free motion quickness of the power system is determined by the linear composition of eigenvalues, dynamic modes and left/right eigenvectors. The frequency behavior of the system can be successfully examined and evaluated by using the SSA in terms of the time-domain simulation (TDS). Linear analysis can be obtained by using DIgSILENT software and the non- linear TDS of the dynamic system, which makes it easy by software. The major benefits of the linear model are that it gives the opportunity for using the eigenvalues to adjust the frequency handling controllers and the use of eigenvectors to trace the contents of the frequency regulation mode. Generators’ frequency shows the condition of the systems which may be scripted in the forms of entire eigenvalues and conditions of the system by using (10)[19]: ωᵢ�t� = Ѱᵢ�c�+, "- + Ѱᵢ.c.+, %- +⋯+Ѱᵢ(c(��)� (11) C. General Mathematical Model The electrical system exists on synchronous machines connected to an infinite bus bar. There are four conditions to sink the alternator with the infinite bus. It must have the same value of voltage, frequency, phase sequence, and phase angle difference. Every alternator has two main controllers, one for speed, called governor and another for voltage, the AVR. By varying load gradually at the alternator side through MATLAB/Simulink, we analyzed the small disturbances without PSS and with PSS. In the two axis model, the synchronous alternator consists of the transient and sub transient effect. The transient effects are taken into consideration and sub transient effects are considered as negligible, so the effects of transients are overcome with the rotor circuit which is the field circuit in the d-axis and q-axis formed by solid rotor [1]. 1) Swing Equation ω/ = �01 �P3 −D6ω− P7� (12) 2) Rotor Angle Equation ∂/ = �ω−ω9� (13) 3) Excitation System Every alternator has an AVR. Through the AVR we can control the terminal voltage of an alternator by varying field current and maintain the terminal voltage as per our needs. Usually loop gain KA must be as per command of AVR, if the loop gain is very high the system will be unstable, if it is very low the system performance of AVR step response will be unsatisfactory. Therefore, to enhance the related stability and steady state behavior, the transformer is used for stabilizing. Ė;< = � => ?−E;< +�AB7C − A� −AD�KFG (14) V/D = � =I ?−VD +E;