Energy saving dispatch with complex constraints: Prohibited zones, valve point effect and carbon tax

Economic Dispatch with High Penetration of Wind Power Using Extreme Learning Machine Assisted Group Search Optimizer with Multiple Producers Considering Upside Potential and Downside Risk

“…where a m , b m , and c m are cost coefficients of the m th unit; d m and e m are sinusoidal term coefficients that manifest the valve point effect [31]; P G m and Q G m are the active and reactive power outputs of the m th unit, respectively, m = 1 2...N G , and N G is the total number of thermal units; P G i and Q G i are the injected active and reactive power at the i th bus, respectively; P D i and Q D i are the corresponding active and reactive power demands, respectively; G ij and B ij are the conductance and susceptance between the i th and j th bus, respectively; V i , V j , Q C l , T k , and S n are the voltages at the i th and j th buses, the output of the C th l reactive compensation device, the tap ratio of the k th power transformer, and the apparent power flow in the n th branch, respectively; i = 12...N B , and N B is the total number of buses; j = 12...N i is the index of buses adjacent to the i th bus, N i is the number of buses adjacent to the i th bus; C l = 12...N C , and N C is the total number of reactive power compensation devices; k = 12...N T , and N T is the total number of power transformers; n = 12...N S , and N S is the total number of branches in a power grid; and…”

Optimal power flow calculation in AC/DC hybrid power system based on adaptive simplified human learning optimization algorithm

“…Taking minimum fuel costs of the conventional generators as the expected target as well as taking the valvepoint loading effects of generators, prohibited operating zones and carbon tax into account, the objective function of OPF model can be described in (1) [8,15],…”

“…Besides, the OPF model becomes more and more complex due to taking the practical operation condition into account, such as prohibited operating zones [7,8], valve-point loading effects of generators [9][10][11][12][13][14] and carbon tax [15][16][17]. Under the complex circumstance, the objective function in the constructed OPF model becomes as discontinuous, nonconvex and non-differentiable.…”

Wind-thermal power system dispatch using MLSAD model and GSOICLW algorithm

“…However, mathematical methods relies on the initial searching solution, and they are easily trapped in local optima. Therefore, evolutionary algorithms (EAs), the heuristic optimization algorithms inspired by natural mechanisms, have been used for solving PSDPs and the results are promising [6][7][8]. In recent years, an algorithm, i.e., group search optimizer (GSO), is proposed by simulating animal searching behavior [9], which is famous for its good global searching ability.…”