# Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy
## Abbreviations  
OPF Optimal Power Flow  
WFs Wind farms  
PVSs Solar photovoltaic systems  
JSA Jellyfish search algorithm  
MSA Moth swarm algorithm  
SSA Salp swarm algorithm  
WCA Water cycle algorithm  
PSO Particle swarm optimization  
GA Genetic algorithm  
**Nomenclature**  
\(Sys_{Profit}\) Profit of the considered system  
\(ToRe_{Elc}\) The total revenue of electricity sale  
\(Cost_{Fund}\) The total fuel cost of all thermal units in the transmission power networks  
\(ce_{1k}\), \(ce_{2k}\), \(ce_{3k}\) Given coefficients in fuel cost function of the \(k\)th thermal unit  
\(NT_{Uls}\) Thermal unit number  
\(N_{Loads}\) Load number  
\(EP_{1}\) Electricity price ($/MWh) at the \(l\)th load  
\(Pload_{j}\) Load demand at the \(l\)th load node  
\(N_{WP_{S}}\) Number of wind turbines installed in the system  
\(PW_{m}\), \(QW_{m}\) Active and reactive power generation of the \(m\)th wind turbine  
\(QT_{k}\) Reactive power generation of the \(k\)th thermal unit  
\(N_{Brs}\) Number of transmission lines  
\(P_{Loss,b}\), \(Q_{Loss,b}\) Active and reactive power loss on the \(b\)th transmission lines  
\(QC_{c}\) Reactive power generation of the \(c\)th capacitor  
\(N_{Caps}\) Number of capacitors  
\(QLoad_{j}\) Reactive power demand of load at the \(l\)th load node  
\(PT_{i}\), \(PW_{i}\), \(PLoad_{i}\) Active power generation of thermal unit and wind turbines at the \(i\)th node  
\(Vol_{i}\), \(Vol_{j}\) Voltages of the \(i\)th and \(j\)th buses  
\(BS_{ij}\), \(GC_{ij}\) Transfer susceptance and the conductance between the \(i\)th node and the  
\(j\)th node  
\(N_{nodes}\) Number of nodes  
\(\theta_{j}\) and \(\theta_{i}\) Angles of voltage at the \(j\)th node and the \(i\)th node, respectively  
\(QC_{i}^{Min}\), \(QC_{i}^{Max}\) The lowest and highest generation of the capacitors at the \(i\)th node  
\(PT_{k}^{Min}\), \(PT_{k}^{Max}\) The smallest and highest active power generations of the \(k\)th thermal unit  
\(QT_{k}^{Min}\), \(QT_{k}^{Max}\) The smallest and highest reactive power generations of the \(k\)th thermal unit  
\(PW_{m}^{Min}\), \(PW_{m}^{Max}\) The smallest and highest active power generations of the \(m\)th wind turbine  
\(QW_{m}^{Min}\), \(QW_{m}^{Max}\) The smallest and highest reactive power generations of the \(m\)th  
wind turbines  
\(Tp_{n}\) Tap value of the \(n\)th transformer  
\(Tp^{Min}\), \(Tp^{Max}\) The smallest and highest tap values of all transformers  
\(N_{\rm{T}}\) Number of used transformers  
\(dr_{1}\), \(dr_{2}\), \(dr_{3}\) Random numbers within 0 and 1  
\(SN_{n}\), \(SN_{mid}\) The best and mean solutions of the current population  
\(SN_{n}\) A random solution in the present population  
\(Fit_{rd}\), \(Fit_{j}\) Fitness values of two solutions, \(SN_{rd}\) and \(SN_{j}\)  
\(L_{WP_{m}}\), \({\rm PF_{WP_{m}}}\) Location and power factor of the \(m\)th wind farm  
\(SN_{j}^{Min}SN_{j}^{Max}\) Lower and upper boundaries of the solution \(SN_{j}\)  
\(DS_{j}^{i}\) The \(j\)th dependent variable set  
\(DS_{j}^{Min}\), \(DS_{j}^{Max}\) Lower and upper boundaries of the \(j\)th dependent variable set  
\(Fit_{j}^{new}\) Fitness value of the new solution \(j\)th