Single- and Multiobjective Optimal Power Flow with Stochastic Wind and Solar Power Plants Using Moth Flame Optimization Algorithm

ABSTRACT

The proposed article recommends a method for the solution of single and multiobjective optimal power flow without and with integrating renewable energy resources along with traditional coal-based generating stations. In the first part, the different objectives of optimal power flow problem with a single- as well as conflicting multiobjective manners are optimized. The efficiency of the recommended technique has been verified on three diverse standard test systems like IEEE-30 bus system, IEEE-57 bus system and large system like IEEE-118 bus network with the statistical analysis. The simulated results are equated to other reported meta heuristic methods. The second part consists of optimal power flow problem with the incorporation of solar and wind output energy. For forecasting solar and wind production, the proposed approach uses log-normal and Weibull probability density functions, combined. Penalties costs for undervaluation and a backup fee for oversimplification of unusual nonconventional power sources are included in the objective feature. The optimization problem is formulated using a nondominated multiobjective moth flame optimization method. To find the best compromise solution, the fuzzy decision-making technique is used. The results are confirmed using an updated IEEE-30 bus test system that includes wind and solar power plants.

GRAPHICAL ABSTRACT

KEYWORDS:

• Wind units
• meta-heuristics
• multi-objective optimal power flow
• solar PV energy
• stochastic
• probability density function

List of Nomenclature

OPF Optimal Power Flow

TG Thermal Generator

WG Wind Generator

PVPhoto Voltaic

ISO Independent System Operator

PDF Probability Density Function

BCS Best Compromise Solution

MOMFO Multiobjective Moth Flame Optimization

MOOPF Multiobjective Optimal Power Flow

FC Fuel Cost

VPE Valve Point Effect

MF Multiple Fuel

POZ Prohibited Operating Zone

$P_{TGi}$ Power output of $i^{th}$ thermal unit

$P_{ws,j}$ Scheduled power from $j^{th}$ wind power unit

$P_{ss,k}$ Scheduled power from $k^{th}$ solar PV unit

$P_{wav,j}$ Actual available power from $j^{th}$wind power unit

$P_{sav,k}$ Actual available power from $k^{th}$solar PV unit

$g_j$ Direct cost coefficient for $j^{th}$wind power unit

$h_k$ Direct cost coefficient for $k^{th}$solar PV unit

$K_{Rw,j}$ Reserve cost coefficient for overestimation of wind power from $j^{th}$unit

$K_{Pw,j}$Penalty cost coefficient for underestimation of wind power from $j^{th}$unit

$K_{Rs,k}$ Reserve cost coefficient for overestimation of solar power from $k^{th}$unit

$K_{Ps,k}$Penalty cost coefficient for underestimation of solar power from $k^{th}$unit

$C_{tax}$ Carbon tax in $/Tonne

$G$ Solar irradiance in $\mathrm{W}/{\mathrm{m}}^2$

$f_v\left(v\right)$ Probability of wind speed $v$ m/s

$f_G\left(G\right)$Probability of solar irradiance $G\mathrm{W}/{\mathrm{m}}^2$

$p_{wr}$ Rated power output of a wind turbine

$P_{sr}$ Rated power output of the solar PV plant

$c,k$ Weibull PDF scale and shape parameters respectively

$\mu ,\sigma$ Lognormal PDF mean and standard deviation respectively

$P_{loss}$ Real power loss in the grid

$VD$ Cumulative voltage deviation in a grid

Disclosure statement

No potential conflict of interest was reported by the author(s).