JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III Year POWER SYSTEMS ANALYSIS Previous Question Paper (August - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Construct the bus incidence matrix for the given power system (figure 1).
Answer
The bus incidence matrix A is a rectangular matrix of size b x n, where b is the number of branches and n is the number of buses (excluding the reference bus). The elements aij are defined as:
- aij = 1, if branch i is incident to and oriented away from bus j.
- aij = -1, if branch i is incident to and oriented towards bus j.
- aij = 0, if branch i is not incident to bus j.
To construct it, identify all branches and buses in the network, assign an arbitrary direction to each branch, and fill the matrix based on the incidence of branches at each bus node.
Explain step by step procedure for building Z bus of power system.
Answer
The Zbus matrix is constructed using the building algorithm, which adds one element at a time to an existing system. The procedure follows four basic modification cases:
- Case 1: Adding a branch from a new bus to the reference bus. The new bus is added as a new row and column in the Zbus matrix, with the new diagonal element equal to the impedance of the added branch.
- Case 2: Adding a branch from a new bus to an existing bus. The Zbus size increases by one. The new row and column are copied from the existing bus to which the new bus is connected, and the new diagonal element is the sum of the existing bus impedance and the new branch impedance.
- Case 3: Adding a branch from an existing bus to the reference bus. This is handled by adding a temporary bus connected to the reference bus (Case 2) and then performing a Kron reduction to eliminate the temporary bus.
- Case 4: Adding a branch between two existing buses. This is handled by adding a temporary bus connected to one of the existing buses (Case 2) and then performing a Kron reduction to eliminate the temporary bus.
Kron reduction is defined by the formula: Zij,new = Zij,old - (Zik * Zkj) / Zkk, where k is the bus to be eliminated.
Figure 2 shows a single-line diagram of a power system. The ratings of generators and transformers are:
Generator G1: 25 MVA, 6.6 kV, j0.2 pu
Generator G2: 15 MVA, 6.6 kV, j0.15 pu
Generator G3: 30 MVA, 13.2 kV, j0.15 pu
Transformer T1: 30 MVA, 6.6 Δ - 115 Υ kV, j0.1 pu
Transformer T2: 15 MVA, 6.6 Δ - 115 Υ kV, j0.1 pu
Transformer T3: Single phase units each rated 10MVA, 69/6.9 kV, j0.1 pu.
Draw impedance diagram with all values in pu on a base of 25 MVA, 6.6 kV in the circuit of generator G1.
Answer
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Figure 3 shows the one-line diagram of a simple three-bus power system with generation at bus 1. The line impedances are marked in per unit on a 100 MVA base. Find out the bus voltages after two iterations using Gauss-Seidel method.
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Figure 4 shows the one-line diagram of a simple three-bus power system with generation at bus 1. The line impedances are marked in per unit on a 100 MVA base. Find out the bus voltages after two iterations using Newton raphson’s method.
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Explain the fast decoupled load flow method.
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State the conditions where the solution for a power flow analysis problem cease to exit.
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What is the advantage of Newton Raphsons method when compared to Gauss Seidal Method?
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Illustrate the formulation of DC mismatch equations for solving a generalized DC power flow problem.
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What is meant by fault level at a bus and give the expression for the same in p.u?
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Determine the fault current in each phase following a double line to ground short circuit at the terminals of a star connected synchronous generator operating initially on an open circuit voltage of 1.0 p u. The positive, negative and zero sequence reactances are j0.35, j0.25 and j0.20, and its star point is isolated from the ground.
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State the limitations of equal area criterion.
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Figure 5 shows transmission network. The p.u reactances of the equipments are as shown. The voltage behind transient reactance of generator is 1.1 p.u. The infinite bus voltage is 1+j0 p.u. The system is transmitting 1 p.u power when fault occurs at the middle of the line. Determine (i) transfer reactance for prefault, during fault and post fault condition (ii) critical clearing angle.
Answer
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