Page 110 - Mathematical Models and Algorithms for Power System Optimization

100 Chapter 4

After the optimization calculation, it is usually necessary to conduct the power flow calculation
to verify the nonlinear solution. This power flow calculation uses the integer solution of
reactive power output and tap ratio, as well as bus voltages and angles of optimized solution to
calculate the new bus voltages and angles, and generator reactive outputs. In this case, the
recalculated power flow can theoretically result in a solution identical to the optimized solution.
Therefore, it is unnecessary to calculate the power flow again after nonlinear optimization,
because the optimized solution has already provided the integer solution of reactive power and
tap ratio, bus voltages and angles, and generator reactive outputs.

In fact, the feasible solution obtained from the optimization algorithm is not necessarily feasible
in the power flow calculation. For example, the Q and U values of a generator bus may have
reached their limit values in an optimized solution, but due to reasons such as computer word
length, Q violations may be caused if the bus is treated as a PV bus or a U violation may be
caused if the bus is treated as a PQ bus. Therefore, the optimized power flow calculation may
cause the optimized solution to deviate from the optimal value to a certain extent or even lead to
an infeasible solution.

Hence, if the reactive power of the generator at a bus has reached its upper limit in an optimized
result, the reactive power is very likely to go beyond the upper limit at this bus in the power flow
calculation. There are two ways to address this problem: the first is to change the bus to a PQ
bus before the power flow calculation, and the second is to lower the upper and lower limits of
the reactive power. Generally, to obtain a satisfactory power flow solution, it is necessary to
make certain adjustments in the power flow calculation using the optimized configuration.

Besides, under the same conditions of power flow calculations, such as the integer fixed,
voltage of PV bus is known, and other constraints are removed; the same result as the power
flow calculation can also be obtained using the optimization program. This means that the
optimized solution process is even more widely applicable. Therefore, under the same
conditions, the optimization algorithm can produce a feasible solution, whereas the power flow
solution process may not.
In conclusion, the results of the power flow calculation after the optimization of initial value of
power flow show that the system operation condition is considerably improved. Any process
reliant on the power flow calculation alone will require much more effort and will not
necessarily produce a feasible solution. The greatest advantage of the optimization calculation
is that it helps the system planner quickly find a feasible solution and reduces the time spent on
adjustment of the input parameters, such as transformer tap T and capacitor bank number C.

4.6.2 Description of the Problem

The OPF problem becomes important as electric power system operations become increasingly
complex. Its objective is usually taken as the minimization of the sum of fuel cost of generators
under the conditions of operating constraints.