Jawaharlal Nehru Technological University Hyderabad
Jawaharlal Nehru Technological University Hyderabad B.Tech III POWER SYSTEM OPERATION AND CONTROL Previous Question Paper (February/March - 2022 - R18)
Answer any five questions. All questions carry equal marks.
Main
Explain the necessity of a load flow solution. Derive the necessary equations for the load flow problem.
Answer
A load flow solution is essential for power system planning, operation, and control. It determines the steady-state operating condition of a power system by calculating the voltage magnitude and phase angle at each bus, and the real and reactive power flows through transmission lines. This information is critical for identifying line overloads, voltage violations, and assessing the impact of system expansions or contingencies.
For a bus i, the injected power is given by the complex power equation:
Substituting the current equation Ii = Σ Yij Vj, the power balance equations are:
where V is the voltage magnitude, δ is the phase angle, and Yij is the admittance matrix element.
Explain the Newton Raphson Load flow method in polar form, and derive the equations to compute the Jacobian matrix elements.
Answer
The Newton-Raphson method solves the non-linear power flow equations using an iterative Taylor series expansion. In polar form, the mismatch vector is related to the state vector (voltage angles and magnitudes) via the Jacobian matrix:
The Jacobian elements are partial derivatives of the power equations with respect to the state variables:
- J1 (∂P/∂δ): Off-diagonal elements are -|Vi||Vj||Yij| sin(θij - δi + δj); diagonal elements are Σj≠i |Vi||Vj||Yij| sin(θij - δi + δj).
- J2 (∂P/∂|V|): Off-diagonal elements are |Vi||Yij| cos(θij - δi + δj); diagonal elements are 2|Vi|Gii + Σj≠i |Vj||Yij| cos(θij - δi + δj).
- J3 (∂Q/∂δ): Off-diagonal elements are |Vi||Vj||Yij| cos(θij - δi + δj); diagonal elements are -Σj≠i |Vi||Vj||Yij| cos(θij - δi + δj).
- J4 (∂Q/∂|V|): Off-diagonal elements are -|Vi||Yij| sin(θij - δi + δj); diagonal elements are -2|Vi|Bii - Σj≠i |Vj||Yij| sin(θij - δi + δj).
The solution proceeds by calculating mismatches, evaluating the Jacobian, solving for corrections, and updating variables until convergence.
What is meant by optimal generation allocation? Derive the conditions for optimal allocation of generation among the generators in a thermal plant including transmission losses.
Answer
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A power system consists of two 200MW units whose input cost data are represented by the equations:
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For a single area system, show that the static error in frequency can be reduced to zero for single area load frequency control with integral control.
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Why transient state stability limit is less than the steady-state stability limit? Explain.
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Derive an expression for critical clearing angle for a power system consisting of a single machine supplying an infinite bus for sudden load decrement.
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What are the functions of SCADA? With a detailed diagram, describe the hardware components of SCADA as well as their functionalities.
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What is EMS? What are its major functions in power system operation and control?
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Explain the fast decoupled load flow algorithm. List out all the assumptions made in arriving at it from decoupled load flow.
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Explain the significance of equality and inequality constraints in the economic allocation of generation among different plants in a system.
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How is the speed governor mechanism modeled? And explain its operations with the speed load characteristics.
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