Optimal production cost of the power producers with linear ramp model using FDR PSO algorithm

Abstract

SUMMARYIn practice, the power producers have to be rescheduled for power generation beyond their power limits to meet vulnerable situations like credible contingency and increase in load conditions. During this process, the ramping cost is incurred if they violate their permissible elastic limits. In this paper, optimal production costs of the power producers are computed with ramping cost considering stepwise and piecewise linear ramp rate limits using fitness distance ratio particle swarm optimization (FDR PSO) algorithm. Transient stability constraints are also considered while formulating the optimal power flow (OPF) problem as additional rotor angle inequality constraints. The proposed algorithm is demonstrated on a practical 39 bus New England and 62 bus Indian Utility system with different case studies.

Dynamic ramping model including intraperiod ramp-rate changes in unit commitment

“…g , coinciding with (13). Notice how these constraints avoid big-M parameters, thus not damaging the tightness of the formulation.…”

“…For representing dynamic ramp rates in the UC, two equivalent mixed-integer linear programming (MILP) models have been proposed in [12]: one employs piecewise linear functions, and the other is based on stepwise linear representations. These approximations have been adopted by some system operators such as CAISO [8], MISO [13], ERCOT [14] and XM 1 [9], and the idea is to define a set of segments to limit the maximum energy change of a unit between two consecutive periods as a function of the output level.…”

Optimal placement method of multi UPFCs to damp power system oscillations

“…For this purpose, an IEEE 39‐bus system is selected. The single‐line diagram of this system is shown in the Figure .…”

Security Cost Analysis with Linear Ramp Model using Contingency Constrained Optimal Power Flow

“…In this picture, the ramping process with a piecewise linear ramping function can be modeled as shown in Fig 1. where α m is the linear ramp rate which differs from segment to segment. The power output of unit i for the first period, (0, T 1 ), is given by following equation [9].…”

“…System voltage limits: 2,N and t=1,2,…,nt (9) where r id and r iu are, respectively, the lower and upper ramp rate limits on the generation level of unit i during period t.…”