12-12-2012, 01:12 PM
Power Flow Analysis
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The Power Flow Problem
Power flow analysis is fundamental to the study of power systems.
In fact, power flow forms the core of power system analysis.
power flow study plays a key role in the planning of additions or expansions to transmission and generation facilities.
A power flow solution is often the starting point for many other types of power system analyses.
In addition, power flow analysis is at the heart of contingency analysis and the implementation of real-time monitoring systems.
Power Flow Study Steps
Determine element values for passive network components.
Determine locations and values of all complex power loads.
Determine generation specifications and constraints.
Develop a mathematical model describing power flow in the network.
Solve for the voltage profile of the network.
Solve for the power flows and losses in the network.
Check for constraint violations.
Formulation of the Bus Admittance Matrix
The first step in developing the mathematical model describing the power flow in the network is the formulation of the bus admittance matrix.
The bus admittance matrix is an n*n matrix (where n is the number of buses in the system) constructed from the admittances of the equivalent circuit elements of the segments making up the power system.
Most system segments are represented by a combination of shunt elements (connected between a bus and the reference node) and series elements (connected between two system buses).
Bus Admittance Matrix
Formulation of the bus admittance matrix follows two simple rules:
The admittance of elements connected between node k and reference is added to the (k, k) entry of the admittance matrix.
The admittance of elements connected between nodes j and k is added to the (j, j) and (k, k) entries of the admittance matrix.
The negative of the admittance is added to the (j, k) and (k, j) entries of the admittance matrix.
Difficulties
Unless the generation equals the load at every bus, the complex power outputs of the generators cannot be arbitrarily selected.
In fact, the complex power output of at least one of the generators must be calculated last, since it must take up the unknown “slack” due to the uncalculated network losses.
Further, losses cannot be calculated until the voltages are known.
Also, it is not possible to solve these equations for the absolute phase angles of the phasor voltages. This simply means that the problem can only be solved to some arbitrary phase angle reference.
Remedies
The slack bus is chosen as the phase reference for all phasor calculations, its magnitude is constrained, and the complex power generation at this bus is free to take up the slack necessary in order to account for the system real and reactive power losses.
Systems of nonlinear equations, cannot (except in rare cases) be solved by closed-form techniques.