Optimal power flow using multi-objective glowworm swarm optimization algorithm in a wind energy integrated power system

ABSTRACT

This paper solves a multi-objective optimal power flow (MO-OPF) problem in a wind-thermal power system. Here, the power output from the wind energy generator (WEG) is considered as the schedulable, therefore, the wind power penetration limits can be determined by the system operator. The stochastic behavior of wind power and wind speed is modeled using the Weibull probability density function (PDF). In this paper, three objective functions, i.e., total generation cost, transmission losses, and voltage stability enhancement index are selected. The total generation cost minimization function includes the cost of power produced by the thermal and WEGs, costs due to over-estimation and the under-estimation of available wind power. Here, the single objective optimization problems are solved using the Glowworm Swarm Optimization (GSO) algorithm, whereas the MO-OPF problems are solved using the multi-objective GSO (MO-GSO) algorithm. The proposed optimization problem is solved on a modified IEEE 30 and 300 bus test systems with wind farms located at different buses in the system. The simulation results obtained show the suitability and effectiveness of proposed MO-OPF approach.

KEYWORDS:

• Optimal power flow
• renewable energy sources
• multi-objective optimization
• generation cost
• system losses
• uncertainty
• voltage stability

Nomenclature

ai, bi, ci	=	Cost coefficients of ith thermal generator.
CGi	=	Quadratic cost function of ith thermal generator.
Cp,wj	=	Penalty cost function for jth WEG.
Cr,wj	=	Reserve cost function for jth WEG.
CWj	=	Direct cost function of jth WEG.
fp(p)	=	Weibull probability distribution function (PDF).
J1, J2, J3	=	Objective functions to be optimized.
N	=	Total number of buses.
NG	=	Number of generating units.
Nobj	=	Number of objectives to be simultaneously optimized.
NL	=	Number of load/demand buses.
$N_{line}$	=	Number of transmission lines in the system.
NW	=	Number of WEGs.
$n_t$	=	Neighborhood threshold.
$r_s$	=	Radial range of Luciferin sensor.
$r_d$	=	Local decision domain range.
$G_{ij}$	=	Conductance of a transmission line connected between the buses i and j (for i≠j).
kr,j	=	Reserve cost coefficient for jth WEG.
kp,j	=	Penalty cost coefficient for jth WEG.
$V_i$	=	Voltage magnitude at ith bus.
PGi	=	Active power output from ith thermal generator.
pr	=	Rated wind power output.
PWj	=	Scheduled power from jth WEG.
PWj,avg	=	Available wind power (random variable).
QGi	=	Reactive power output from ith thermal generator.
PDi, QDi	=	Active and reactive demands.
$P_{Gi}^{min}$, $P_{Gi}^{max}$	=	Lower and upper active power values of ith bus.
$Q_{Gi}^{min}$, $Q_{Gi}^{max}$	=	Lower and upper reactive power values of ith bus.
$Q_{Ci}^{min}$, $Q_{Ci}^{max}$	=	Lower and upper shunt capacitor values at ith bus.
$T_i^{min}$, $T_i^{max}$	=	Lower and upper values of transformer tap settings.
ρ	=	Luciferin decay constant between 0 and 1.
γ	=	Luciferin enhancement constant.
β	=	Constant parameter.
${\delta }_i$	=	Voltage phase angle at ith bus.
nt	=	Threshold parameter to control the number of neighbors.
v	=	Wind velocity (random variable).
$V_i^{min}$, $V_i^{max}$	=	Lower and upper voltages at ith bus.
x	=	Vector of decision variables.
Jj(t)	=	Objective function value at jth agent location at time t.
t	=	Time (or step) index
dij(t)	=	Euclidian distance between the agents i and j at time t.
ℓj(t)	=	Luciferin level associated jth agent at time t.
rid (t)	=	Variable local-decision range associated with ith agent at time t.
rs	=	Radial range of the luciferin sensor.

Additional information

Funding

This research work has been carried out based on the support of “Woosong University’s Academic Research Funding (2017-2019)”.