GATE EE 2021 Set 1 — Question 19
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Power Systems → Per-Unit System & Load Flow → Gauss-Seidel & Newton-Raphson
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Question
Consider a power system consisting of number of buses. Buses in this power system are categorized into slack bus, PV buses and PQ buses for load flow study. The number of PQ buses is . The balanced Newton-Raphson method is used to carry out load flow study in polar form. and are sub-matrices of the Jacobian matrix as shown below:The dimension of the sub-matrix is
Correct answer
(A) N_L × (N-1)
Solution
In the Newton-Raphson load flow method (polar form), the Jacobian matrix is:Where:
Its dimension is (number of equations) (number of variables) = .
- is the vector of active power mismatches for all buses except the slack bus. Dimension: .
- is the vector of reactive power mismatches for PQ buses only. Dimension: .
- is the vector of voltage angle corrections for all buses except the slack bus. Dimension: .
- is the vector of voltage magnitude corrections for PQ buses only. Dimension: .
Its dimension is (number of equations) (number of variables) = .
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