Optimal Power Flow (OPF) Operation


The operation limitation (Constraints) arise from the fact that the generating units, transmission lines, transformers, phase shifts can not be loaded beyond the capacity. The constraints are equality and inequality constraints. In the electric utility the OPF is applied in the area of the system operations and planning. For operations, OPF is used for real time and study applications in the area of planning.

 OPF is used for capacitor placement studies and transmission capacity panning. The OPF should be able to optimize the power system in the normal state produce remedial action an any set of the selected post-contingency states and provide preventive scheduling for base-cases and post-contingency limit violations in a defined set of contingency cases. In the OPF, the controls are varied such that constraints are achieved and the objective function is either minimized or maximized. The OPF problem can be formulated as:
Minimize             F(u,x) with respect to u
Subjective to:                  g(u,x)=0 , h(u,x)<0
Where u is a vector of controllable variables and x is a vector of dependent or stable variables.


In this OPF formulation, power flow equations are the equality constraints and the limits on designated quantities are inequality constraints.


1-Objective Functions

The objective functions commonly used for operations and planning are as follows:

1.        Minimum const of operation.
2.        Minimum increase in cost.
3.        Minimum deviation or minimum control shift.
4.        Real power loss minimization.
5.        Reactive power loss minimization.
6.        Minimize the number of controls.
7.        Minimize the cost of installation of new capacitors and reactors.
8.        Minimize the cost of MVAR Supplied.
9.        Maximize MW transfers.
10.        Minimize the time to correct the violations.
11.        Minimize the total emission.


2-Constraints

The equality constraints are ones that must be exactly satisfied to have a feasible solution. In most of the optimization problems, the bulk of the effort and complexity are due to the inequality constraints. The inequality constraints must satisfy either an upper or lower bound on the value of the function to have a feasible solution.
At the optimum feasible point, all inequality constraints will be in the following two states. In state one, the inequality constraints will be fixed at the upper or lower limit and they are referred to as the active of binding inequality constraints. In second state, the constraints will be within the limits and they are referred to as inactive or not binding constraints is the most difficult part of solving the optimization problem. No direct method without any iterative process to find the active set is published.
Instead, various iterative methods are employed to gradually identify the correct active set over the course of optimization.
During the optimization, the following constraints are enforced:

1-Control limits.
2-Ampere flow limits on circuits.
3-Bus high and low voltage magnitude limits.
4-Generator MVAR outputs.
5-Active power import/export limits.
6-MW and MVAR reserve limits.
7-Reactive power import/export limits.
8-Sum of flows in any group of lines.
9-Control action response time.
10-Bus voltage angle differences.
11-Post contingency limits.
12-Environmental constraints.



3-Classification Of System Variables

1-Fixed:

         Such as parameter of the transmission lines ( R , XL , Xc )

2-State (X) :
Such as bus angles at all buses
bus voltage at load buses

  Where:
n  = Total no. of buses.
 ng = No. of generation buses.

3-Control (U) :

            Such as the voltage & power at generation buses:


4-Controls (Control Variables)

The elimination of constraints violations and achieving the objective can be accomplished through the use of controls. The operator may use the controls freely within their limits to achieve operational goals. A list of controls commonly used is shown below:

1-Generator MW output.
2-Voltage-ratio transformers taps.
3-Phase shifter taps.
4-MW interchange.
5-HVDC link power.
6-Load shedding.
7-Generator voltage set points.
8-Shunt reactor and capacitor.
9-Static VAR compensatory.
10-Synchronous condenser.


5-OPF Applications

The OPF can be used for many applications in electric utilities. Some of the major applications of OPF are listed below and followed by a brief description. For further detailed information, readers are encouraged to read the reference listed:

1-Security constrained economic dispatch.
2-MW or MVAR loss minimization.
3-Constraints priority optimization.
4-Hierarchical control.
5-Remedial actions or corrective rescheduling.
6-Preventive scheduling or contingency constrained dispactch.
7-Maximum transfers capacity.
8-Closed loop control.
9-Capacitor and reactor placement.
10-Switching action.
11-MVAR cost optimization.
12-Voltage control.
13-Sensitivity analysis.
14-Transaction evaluation.
15-Dispatcher training simulator scenario building.
16-Shadow price evaluation.
17-Wheeling loss computation.
18-Nodal price for power.
19-Environmental dispatch.
20-Constraint costing.
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Ahmad Mohammad

Hi. I’m Designer of Mawsoo3a Blog. I’m Electrical Engineer And Blogger Specializing In Electrical Engineering Topics. I’m Creative.I’m Working Now As Maintenance Head Section In An Industrial Company.

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