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POWER SYSTEM ENGINEERING CE Module Lecturer Vijayendra Kumar APIIT SD INDIA

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Tutorial 1 CE POWER SYSTEM ENGINEERING

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Signal Processing, CE First step in solving the power flow is to create what is known as the bus admittance matrix, often called the Y bus. The Y bus gives the relationships between all the bus current injections, I, and all the bus voltages, V, I = Y bus V The Y bus is developed by applying KCL at each bus in the system to relate the bus current injections, the bus voltages, and the branch impedances and admittances. Bus Admittance Matrix or Y bus Slide 3 of 11

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Signal Processing, CE Slide 4 of 11 Y bus Example Determine the bus admittance matrix for the network shown below, assuming the current injection at each bus i is I i = I Gi - I Di where I Gi is the current injection into the bus from the generator and I Di is the current flowing into the load.

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Signal Processing, CE Y bus Example… contd Slide 5 of 11

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Signal Processing, CE Y bus Example… contd for a system with n buses, y bus is an n by n symmetric matrix (i.e., one where y buskl = y buslk ).from now on, we will mostly write y for y bus, but be careful to distinguish y kl from line admittances. Slide 6 of 11

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Signal Processing, CE The diagonal terms, Y kk, are the self admittance terms, equal to the sum of the admittances of all devices incident to bus k. The off-diagonal terms, Y kl, are equal to the negative of the admittance joining the two buses. With large systems Y bus is a sparse matrix (that is, most entries are zero): sparsity is key to efficient numerical calculation. Shunt terms, such as in the equivalent line model, only affect the diagonal terms. Y bus General Form Slide 7 of 11

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Signal Processing, CE TWO BUS SYSTEM EXAMPLE Slide 8 of 11

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Signal Processing, CE Using the Y bus Slide 9 of 11

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Signal Processing, CE Solving for Bus Currents Slide 10 of 11

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Signal Processing, CE Solving for Bus Currents Slide 11 of 11

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