Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III POWER SYSTEMS ANALYSIS Previous Question Paper (March/April - 2021 - R16)
Answer any five questions. All questions carry equal marks.
Main
Derive the bus admittance matrix by singular transformation.
Answer
The bus admittance matrix Ybus can be derived using the singular transformation method by relating the bus voltages to the branch currents. Let A be the bus incidence matrix of size b x (n-1), where b is the number of branches and n is the number of buses (excluding the reference bus). The branch current vector Ib is related to the branch voltage vector Vb by the primitive admittance matrix yb:
Using the relationship Vb = A Vbus and applying Kirchhoff's Current Law Ibus = AT Ib, we substitute to get:
Comparing this with the standard nodal equation Ibus = Ybus Vbus, the bus admittance matrix is defined as:
The four bus system having the line impedances as given in the table. The shunt admittance at all buses is assumed negligible. Draw one-line diagram and find YBUS assuming that the line between buses 1 and 2 is not connected.
Answer
To find the Ybus matrix for a 4-bus system where the line between bus 1 and 2 is removed, we first identify the remaining branches. The Ybus is a 4 x 4 matrix where the diagonal elements Yii are the sum of all admittances connected to bus i, and the off-diagonal elements Yij are the negative of the admittance of the line connecting bus i and j.
- Convert all given line impedances Zij to admittances yij = 1/Zij.
- Set y12 = 0 as the line is disconnected.
- Construct the matrix: Yii = Σ yij for all j ≠ i.
- Populate Yij = -yij for all connected buses i and j, and Yij = 0 if no direct connection exists.
The resulting matrix will have zeros at positions (1,2) and (2,1), reflecting the open circuit condition.
Assume the bus impedance matrix for a partial network is known. Now explain the ZBUS building algorithm for the following modifications: (a) Addition of a branch and (b) Addition of a link.
Answer
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Give detailed steps to implement Gauss-Seidal load flow algorithm taking voltage controlled buses into account.
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Explain the convergence criterion used in Newton-Raphson load flow studies.
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The load flow data for a three-bus system is given. The voltage magnitude at bus 2 is to be maintained at 1.04 p.u. The maximum and minimum reactive power limits for bus 2 are 0.3 and 0.0 p.u. respectively. Taking bus 1 as the slack bus, determine the voltages of the various buses at the end of first iteration starting with a flat voltage profile for all buses except slack bus using Gauss-Seidel method with acceleration factors 1.6.
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Obtain the Decoupled load flow model starting from Newton-Raphson method.
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What are the assumptions made in fast decoupled method to speed up the rate of convergence?
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For the system shown, find the voltage at the receiving end bus at the end of first iteration. Load is (2 + j0.8) p.u. Voltage at the sending end (slack) is 1 + j0 p.u. Line admittance is (1.0 – j4.0) p.u. Transformer reactance is j0.4 p.u. Use the Decoupled load flow method. Assume VR = 1.0 ∠0.
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Derive an expression for the fault current for a double-line to ground fault at the terminals of an unloaded generator.
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Discuss the application of equal area criterion for the system stability study when (a) a sudden increase in load takes place, and (b) a short circuit on one of the parallel feeders takes place which is cleared after certain time.
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