Simulink Block Diagram of Sixth-order Model for Power System Dynamic Study

DOI: http://dx.doi.org/10.24018/ejece.2021.5.4.338 Vol 5 | Issue 4 | July 2021 1 Abstract — The order model of synchronous generator plays very important roles of determine the accuracy of power system dynamic study. This paper presents the simulation and analysis of the sixth order model of synchronous generator for power system dynamic study by using Simulink. The mathematical model of stream turbine governor and exciter are also considered in this paper. The presented method is tested on the single machine infinite bus system.


I. INTRODUCTION
The dynamic behavior of power systems is important to both the system organizations, from an economic viewpoint, and reliability viewpoint. The power system dynamic study is one of the subject areas that has been increasing both in a graduate power engineering curricula and the power system industry. It is one of the subject areas that has been most affected by changing curricula patterns. It once formed the core of the power engineering syllabus. It is well known that the order model of the synchronous generator plays very important role to determine the accuracy of the simulation results [1].
There are two approaches of power system dynamic study. The first is referred to as the momentary mode. In this approach, all power system components including synchronous generator, exciter, and stream turbine are modeled in the detailed of three-phase sine functions. Most commercial software packages such as DigSilent, PSCAD, and EMTP are used this approach [2]- [3]. They are suitable for power engineering industry.
The second approach is called stability mode. In this approach, all power system components are model in the much simpler way by using one phase rms function [4]. This approach is very suitable for integrating in curricula. The numerical integration technique such as Euler's method is applied to visualize the dynamic behavior of the synchronous generator. Simulink is an interactive environment for modeling, analyzing, and simulating a wide variety of power system dynamic. It can be extended with bigger power system and the new components [5].
It is well known that the order model of the synchronous generator plays very important role to determine the accuracy of the simulation results. Reference [6], [7]  the second-order model of synchronous generator. Reference [8] used the third-order model. This paper will present Simulink block diagram of the sixth-order model of the synchronous generator. This paper has the following outline. Section II provides some a mathematical model of the synchronous generator, stream turbine governor, and exciter system. Section III presents the Simulink block diagram. In Section IV, the verification of the proposed control strategy and simulation method is tested on the sample system. Finally, conclusions are drawn in Section V.

A. Synchronous Generator
The second-order model of the synchronous generator is given by: The third-order model of the synchronous generator will include the d-axis voltage behind transient reactance of the i-th machine is written by: The fourth-order model of the synchronous generator will include the q-axis voltage behind transient reactance of the i-th machine is written by [9]: The fifth-order model of the synchronous generator will include the q-axis voltage behind sub-transient reactance of the i-th machine is written by [10]: The sixth-order model of the synchronous generator will include the q-axis voltage behind sub-transient reactance of the i-th machine is written by where qi E   is the q-axis voltage behind direct axis sub-transient reactance (

B. Stream Turbine
The stream turbine consists of mechanical-hydraulic governors for stream turbines. It is not only designed mainly to maintain a constant speed by controlling the stream energy input to the turbines but also enhanced power system dynamic performances.
The nonlinear differential equations of the stream turbine are given by [9]: where PS is the speed relay position; SR is the signal reference; b  is the speed base; KG is the constant gain; TSR is the time constant of the speed relay; TSM is the time constant of the servo motor; PV is the value position; PHP is the mechanical power output of the high pressure turbine; PIP is the mechanical power output of the medium pressure turbine; PLP is the mechanical power output of the low pressure turbine; TCH is the time constant of the stream chest; TRHi is the time constant of the reheater; TCO is the time constant of the crossover; FHPiis the fraction power of the stream chest; FLP is the fraction power of the reheater; FCO is the fraction power of the crossover; Pm is the total machanical power.

C. Exciter
The exciter system is designed to maintain the synchronous generator voltage terminal and controls the reactive power flow.
The nonlinear differential equations of the exciter system are given by [11]: where VO is the voltage sensor output; Vt is the terminal voltage; TR is the voltage sensor time constant; VA is the voltage regulator output; KA is the voltage regulator gain; TA is the voltage regulator time constant; Vref is the voltage reference; VF is the stabilizer voltage output; KE is the exciter gain; TE is the exciter time constant; SE is the saturation function of the exciter.

III. SIMULINK BLOCK DIAGRAM
The differential equations of above equations can be written in the general form of state variables as   u is the input. The Simulink block diagram is dawn from the above state variables is shown in Fig. 1 and given by: It is considered that a temporary three-phase fault occurs at bus 3. The clearing fault time (tcl) used in this study is firstly 20 msec and secondly 30 msec, respectively. Fig. 3 shows the swing curve of the system. It can be seen from the Fig. 3 and the (1)-(14) that the fault effect on the terminal voltage, terminal current, power flow, and synchronous generator speed thus results in dynamic response of the power system. The tcl is proportional to the magnitude of the swing curve. The magnitude of the swing curve of the tcl = 30 msec is greater than that of 20 msec. However, the stream turbine consists of mechanical-hydraulic governors for stream turbines and the exciter system can maintain the system returning to the steady state almost at the same time. The setting time of both tcl=20 msec and tcl=30 msec is around 20 msec. It can be mentioned here that governors and exciter system can improve the dynamic behaviors of power system.

V. CONCLUSION
This paper presented the method of analysis the sixthorder model of synchronous generator through Simulink. The presented method is based on the stability mode. Thus, the simulation time is much faster than the stability mode. In addition, it is also flexible for implement in the Simulink for power system dynamic study. It is very suitable for integrating in the classroom of graduate power engineering curricula. The dynamic behavior of the steam turbine and