Power Flow Analysis
To Study Load Flow and Transient AnalysisLoad Flow AnalysisLFA
is a Numerical Analysis of the Electric Power Flow in an
interconnected system.
LFA uses a One-Line Diagram and Per-Unit system.
It focuses on various aspects of AC power parameters, such as
Voltages, Voltage angles, Real power and Reactive power.
It analyzes the power systems in normal Steady-State
OperationLoad Flow AnalysisWhy Run Load Flows: To Check Loading
,Active and Reactive Losses and Voltage Profile in a Network.
Are there any Overloaded elements? Are the Voltage constraints
respected?
When to Perform Load Flows:Network Planning and Operation.
Generation Scheduling and Optimization. Steady State initial
Conditions for Short Circuit Analysis and Stability
Conditions.Power-Flow Problem Formulation
The goal of a Load-flow study is to determine the Magnitude and
Phase Angle of Voltages at each bus, and Active and Reactive Power
Flow in each Line..
Once this information is known, Real and Reactive power Losses
in each branch as well as Generator Reactive Power Output can be
analytically determined.
Due to the Nonlinear nature of this problem, Numerical methods
are employed to obtain a solution that is within an acceptable
tolerance.
Bus VariablesFour quantities are associated with each Bus.
Voltage Magnitude |V| Voltage Phase Angle Real Power (R )
Reactive Power ( Q )Classification of System BusesLoad Bus : Active
and Reactive Powers are specified at these buses. The magnitude and
Phase Angle of Voltages are Unknown. These buses are also called
P-Q Buses.
Generator Bus: A bus with at least one generator connected to it
is called a Generator Bus or PV Bus. For Generator Buses, it is
assumed that the Real Power GeneratedPGand the Voltage magnitude
|V| are known. The Phase angle of voltages and Reactive Power are
to be determined. The limits on the value of Reactive power are
also specified.
Slack Bus: is also known as Swing bus, is taken as reference
where the phase angle of voltage and Phase are specified.Solution
to the Power-Flow ProblemThe solution to the power-flow problem
begins with identifying the Known and Unknown variables in the
system.
The Known and Unknown variables are dependent on the type of
BUS. A bus without any Generators connected to it is called a Load
Bus or PQ Bus. It is assumed that the Real powerPDand Reactive
PowerQDat each Load Bus are known.
A bus with at least one generator connected to it is called a
Generator Bus or PV Bus. For Generator Buses, it is assumed that
the Real Power GeneratedPGand the Voltage magnitude |V| is
known.
The exception is one arbitrarily-selected bus that has a
generator. This bus is referred to as theSlack Bus.
Known and Unknown Variables
It is assumed that the Real powerPDand Reactive PowerQDat each
Load Bus are known. For each Load Bus, both the voltage magnitude
and Voltage angle are Unknown.
For Generator Buses, it is assumed that the Real Power
GeneratedPGand the Voltage magnitude |V| is known. for each
Generator Bus, the voltage angle and Reactive Power must be solved
for.
For the Slack Bus, it is assumed that the voltage magnitude |V|
and voltage phaseare known. There are no variables that must be
solved for the Slack Bus
Power Flow Analysis Assumption
Steady State Balanced Single Phase Network Network may contain
hundreds of Nodes and Branches with Impedance X specified in per
unit on MVA base.Power Flow EquationsBus Admittance Matrix of
node-voltage equation is formulated.
Currents can be expressed in terms of Voltages.
Resulting equation can be in terms of Power in MW.
Nodal Solution is based on the Kirchhoffs current law
Impedance is converted to Admittance
BUS ADMITTANCE MATRIX
Admittance is based on Bus-to-Bus If no Connection between
Bus-to-Bus, leave as zeroNode Voltage equation is in the formBUS
ADMITTANCE MATRIX
Node-Voltage Matrix
Node-Voltage MatrixSolution for Non-Linear Algebraic
EquationsDifferent Iterative techniques can be used for Solving
Non-linear Equations
Gauss-Siedal Newton-Raphson Quasi-NewtonSolution for Non-Linear
Algebraic EquationsGauss-Siedal Method :
It needs Many Iterations to achieve Desired Accuracy.
No guarantee for the Convergence ,depend on the location of
Initial Estimate.
Newton Raphson Method
Newton Raphson Method
Newton Raphson Method
Newton Raphson method for solving n variablesNewton Raphson
Method
Newton Raphson Method for n Dimensions
Newton Raphson Method for n Dimensions
Line Flows and Losses
Newton-Raphson Power Flow
Newton-Raphson Power Flow
Newton-Raphson Power Flow
Newton-Raphson Power Flow
Newton-Raphson Power Flow
Node-Voltage Matrix
