2. Table of Contents
Contents
introduction ____________________________________________________________________ 1
Objective functions ______________________________________________________________ 2
OPF Objective Function for Fuel Cost Minimization ___________________________________ 3
3. Pg. 01 introduction
introduction
definition
The Optimal Power Flow module is an intelligent load flow that employs techniques to
automatically adjust the power system control settings while simultaneously solving the load
flows and optimizing operating conditions within specific constraints.
Load (power)flow
power-flow study is to obtain complete voltage angle and magnitude information for each bus
in a power system for specified load and generator real power and voltage conditions. Once
this information is known, real and reactive power flow on 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 with in an acceptable
tolerance.
Bus type
There are three types of buses in Power System:
i. Load Bus (PQ Bus)
ii. Generator Bus (PV Bus)
iii. Slack Bus (Swing Bus)
In each bus there is four variable to be consider two variables is known and two is unknown.
Variable of power system
I. Real Power (P)
II. Reactive Power (Q)
III. Voltage Magnitude (V)
IV. Voltage Angle (δ)
4. Pg. 02 Objective functions
Objective functions
Because the optimal load flow is aloud flow with objective so it will be necessary to show the
optimal power load flow objective.
Active power objectives
1. Economic dispatch (minimum cost, losses, MW generation or transmission losses)
2. Environmental dispatch
3. Maximum power transfer
Reactive power objectives
MW and MVAr loss minimization
General goals
1. Minimum deviation from a target schedule
2. Minimum control shifts to alleviate Violations
3. Least absolute shift approximation of control shift
Among the above the following objectives are most commonly used:
(a) Fuel or active power cost optimization
(b) Active power loss minimization
(c) VAr planning to minimize the cost of reactive power support
5. Pg. 03
OPF Objective Function for Fuel Cost
Minimization
OPF Objective Function for Fuel Cost
Minimization
The OPF problem can be formulated as an optimization problem and is as follows:
Total Generation cost function is expressed as:
The objective function is expressed as:
Subject to satisfaction of Nonlinear Equality Constraints:
The vector x containsdependentvariables including
1. Bus voltage magnitudes and phase angles
2. MVAr output of generators designated for bus voltage control
3. Fixed parameters such as the reference bus angle
4. Non controlled generator MW and MVAr outputs
5. Non controlled MW and MVAr loads
6. Fixed bus voltages, line parameters
6. Pg. 04
OPF Objective Function for Fuel Cost
Minimization
The vector u consists of controlvariables including:
a. Real and reactive power generation
b. Phase – shifter angles
c. Net interchange
d. Load MW and MVAr (load shedding)
e. DC transmission line flows
f. Control voltage settings
g. LTC transformer tap settings
The equality and inequality constraints are:
a. Limits on all control variables
b. Power flow equations
c. Generation / load balance
d. Branch flow limits (MW, MVAr, MVA)
e. Bus voltage limits
f. Active / reactive reserve limits
g. Generator MVAr limits
h. Corridor (transmission interface) limits
Constraints for Objective Function of Fuel Cost Minimization
The network equality constraints are represented by the load flow equations
7. Pg. 05
OPF Objective Function for Fuel Cost
Minimization
The Inequality constraints representing the limits on all variables, line
flow constraints,
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