**ABSTRACT**

The paper illustrates a procedure to develop a dynamic simulation program for a single machine infinite bus (SMIB) test system using MATLAB / Simulink software. The program is useful to demonstrate various operational and stability challenges in power system operations. The method can be extended to make a program to simulate network having multiple synchronous machines, asynchronous machines, FACTS devices, dynamic load etc.

**DYNAMIC MODELLING OF POWER SYSTEM**

A model of a power system is an integration of several dynamic models such as synchronous generators, asynchronous generators, load, FACTS devices, etc. Fig. 1 shows a top level view of the model, where various dynamic models are connected to a network model. The output of the network model is fed back to the dynamic models making it a closed loop system. The network model consists of all transmission network components except the components modeled separately.

**A. Synchronous Machine Model:**

A synchronous generator generally has two inputs, a torque input from a turbine coupled to its rotor and an excitation current to field winding in its rotor. The excitation current produces magnetic poles in the rotor. When the mechanical torque from turbine forces the rotor to rotate, a rotating magnet field will be created in the air gap which cuts the stationary coils in the stator, and induces a voltage in the stator winding. Hence the mechanical torque supplied by a turbine is converted to electrical torque through the flux linkage and transmitted to grid as voltage and current.

**DEVELOPMENT OF A SIMULINK MODEL**

This section explains steps involved in building a simulink model to simulate an SMIB test system. The model described in the previous section contains several differential equations. Hence to start with, section \ref{sec_sec1} describes how to program a simple first order differential equation using the Simulink. In section \ref{sec_sec2}, programming of the torque angle loop block is explained.

**SIMULATION RESULTS**

An SMIB system is used to demonstrate the programming. In the test system a synchronous machine is connected to a grid through a transformer and a double circuit transmission line. The grid is represented using impedance connected to an infinite bus. The infinite bus means that the bus has fixed voltage and frequency. The system can be used to study the interaction of the generator with the grid.

**A. Steady State Operating Condition of the SMIB Test System:**

Under steady state the active and reactive power output of the machine are assumed as Pt= 0.6, Qt= 0.0228. For an infinite bus voltage EB= 1.0, the terminal voltage of the generator is calculated as Vt= 1.05<21.83. Using the method described in the Section III-B following initial values are computed. δ0= 61.5 degree, E’q0= 0.9704, E’d0= -0.2314, id0= -0.3825, iq0= 0.4251, Efd0= 1.4802, Tm0= 0.6011.

**B. Response of the SMIB System to Step Change in Infinite Bus Voltage:**

A step change in the infinite voltage is applied at time t=1 which is plotted. The dynamic response of Vt, Pg, Qg, Te, δ are plotted. The variation in δ following the disturbance is with respect to the rotating reference frame.

**C. Suggestions for Further Work:**

The simulation set up described in this paper can be used to analyze the response of the machine under various system disturbances. Few examples are, three phase fault, transmission line trip, change in excitation reference voltage, change in input mechanical torque. A governor model can be added to the program to study the frequency response of the synchronous machine.

**CONCLUSION**

A programming approach for simulating a power system using MATLAB/ Simulink is discussed in this paper. The concept is explained using a SMIB test system simulation. The dynamic response of the test system to a disturbance in the grid is presented to further illustrate the method and several suggestions for further development are listed.

Source: IJAREEIE

Author: Linash P. Kunjumuhammed

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