EEET 4074 - Operation and Control of Modern Power Systems SP5/2016 Practical/Simulation # 2 Power System Matrices and Steady State Equivalent Objective The objective of this practical/simulation is to establish bus admittance matrix and bus impedance matrix of a general power system. A reduced order steady state equivalent of the system is also obtained through system matrices. System Description The single line diagram of a 3-machine, 9-bus power system is shown in Fig. 1. The transmission line/transformer data of the system on a 100 MVA base are also shown on the diagram. Note that the transmission lines are represented by π-circuit model. The generator data and load data of the system are given in the following Tables. Generator data (on a 100 MVA base) Gen Internal voltage Eg, pu Angle, deg. Resistance, pu Reactance, pu 1 1.0566 2.2716 0.0 0.0608 2 1.0502 19.7316 0.0 0.1198 3 1.0170 13.1664 0.0 0.1813 Load data Load Load voltage, pu P, MW Q, MVAr A 0.996 125 50 B 1.013 90 30 C 1.016 100 35 Procedure: 1. Replace the loads by constant shunt impedances. The load impedance can be obtained as Zload = V2/(P - jQ) 2. Convert the generator voltage sources into current sources (phasor or complex) using the relation Ig = Eg/Zg.3. Write the impedance of various components of the system in a matrix form (z). The shunt capacitors of transmission lines (π-circuit model) should also be included in the z matrix. Note that ground is considered as bus '0'. Typical format of the z-matrix (for a different system) is shown in the following. 4. Obtain the bus admittance matrix Ybus of the system. You may write a simple program in MATLAB to construct the matrix. Alternatively, you may use "ybus1" routine to construct the admittance matrix. The Matlab instruction for that is Y = ybus1(z); 5. Obtain the bus impedance matrix Zbus (Note Zbus = Y-1bus]. Determine the Thevenin impedance seen by each bus of the system. 6. Define the bus current vector I and obtain the voltage of all buses of the system (Note V = ZbusI). 7. Eliminate buses 4 to 9 to obtain a 3-bus reduced order steady state equivalent of the system. Use the relationship Yred = K – LM-1LT. Write the bus admittance matrix and the bus impedance matrix of the 3-bus reduced order system. 8. Obtain the Thevenin impedance seen by buses 1 to 3 (in the reduced order system) and compare the results with that found in step 5. Find the error in percentage. 9. Determine the voltage of buses 1 to 3 in the reduced order equivalent system (Note V = ZbusI) and compare the results with that found in step 6. Find the error in percentage. Report:  Results of steps 4 to 9 with critical analysis and discussions.  Draw the single line diagram of the 3-bus reduced order system and show the parameter values on the diagram.Fig. 1 Single line diagram (including data) of the 3-machine 9-bus system EEET 4074/M.H. Haque/2016