28-12-2012, 04:41 PM
ESTIMATION OF UPFC VALUE USING SENSITIVITY ANALYSIS
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ABSTRACT
This paper presents an estimation technique to obtain a value of the
unified power flow controller (UPFC) using sensitivity analysis.
Modelling of the UPFC inserted in a transmission line is presented
for use in an optimal power flow (OPF). An efficient technique
to obtain the first- and second-order sensitivities of the generation
cost with respect to UPFC control parameters, are described. A
case which shows the limitations of our sensitivity method is also
analyzed.
INTRODUCTION
The UPFC is one of the most promising devices in the Flexible AC
Transmission systems (FACTS) family since it can control three
basic parameters of power flow for AC transmission: voltage magnitude,
phase shifting angle, and VAR injection. The UPFC has
completed the transition from innovative concept to successful application
at the AEP Inez substation. Since the UPFC requires a
higher capital cost to install, it can not be installed in all possible
transmission lines. Thus, transmission utilities are confronting an
enormous challenge regarding where to locate an UPFC and how
to represent its models for planning studies [1].
Several techniques have been proposed for optimally locating
the FACTS devices. Optimal locations based on sensitivity analysis
have been presented in [2, 3]. In [2], the UPFCs are located to
minimize the transmission line loss. However it did not consider
the ability of the UPFC to allow for the use of more economic
generating units, which may increase the transmission line loss.
In [3], the optimal locations of thyristor-controlled series compensators
(TCSC) and phase shifter were suggested based on the sensitivity
of transmission line loss and real power flow. Again, the
sensitivity of transmission line losses has less importance in economic
dispatch for TCSCs and phase shifters than total generation
costs, and minimization of total costs does not necessarily result
in loss minimization. In addition, [2] and [3] only give the firstorder
sensitivities of a transmission line loss and real power flow,
respectively, after exhaustive calculations. It did not estimate how
much cost is saved by installing the devices on transmission lines,
which is more important in system planning.
SENSITIVITY ANALYSIS
In order to estimate the UPFC values, we use the first- and secondorder
sensitivities of the system generation cost with respect to
the UPFC control parameters. For the implementation of the sensitivity
analysis, we insert the UPFCs on all transmission lines.
Then, it is possible that the solution algorithm does not converge
to the solution if the UPFC control variables are not constrained.
This is because there are more variables than the number of equations,
which yields a degenerate problem. However, since we set TUXW BAon all UPFCs, degeneracy does not arise in the OPF solution.
Here, we consider the case where the UPFC is inserted only
in line rq for clear mathematical derivation.
First-Order Sensitivity
Suppose we are considering installing a new UPFC in line rq. The
marginal values (MVs) of the UPFC, to be installed in line ;q, are
simply the amounts by which the total cost of system operation
could be decreased by allowing a small change of the UPFC control
variables in line rq. We can obtain the MVs by assuming that
there is an UPFC in line rq, but that the UPFC control variables
are artificially constrained to be A, so that we add the constraint TUXW BAto the original OPF problem. The Lagrange multiplier for
this constraint will be denoted xK,PTY and we are most interested
in xK,PAY since they are the marginal values of the UPFC installed
in line rq.
CONCLUSION
We have presented a new technique to estimate the UPFC value
using the first- and second-order sensitivities. Thus, this technique
can reduce the computational burden of determining the optimal
location of the UPFC in a large power system. The sensitivity technique
has the potential for estimating the value of other resources
such as a generation plant, a transmission line, and various FACTS
devices. Currently, we are implementing this technique for IEEE
5-, 14- and 30-bus systems.