Backtracking Search Algorithm with Single and Multi-Objective Function for the Solution of Optimal Power Flow Problem

This manuscript investigates the performance of the backtracking search algorithm (BSA) to minimize various objectives for an economical and secure power system. A variety of single and multi - objectives are delineated and solved. This manuscript also includes the valve-point loading effect alongside the objectives considered. The simulation has been computed in the IEEE 30-bus, IEEE 57-bus and IEEE 118-bus test network. The simulation outcomes as obtained by the proposed BSA and various algorithms are compared. Convergence curves are plotted to testify the characteristics of the proposed BSA for proceeding towards the global minima.

Solution of the Optimal Reactive Power Flow Problem Using a Discrete-Continuous CBGA Implemented in the DigSILENT Programming Language

The problem of the optimal reactive power flow in transmission systems is addressed in this research from the point of view of combinatorial optimization. A discrete-continuous version of the Chu & Beasley genetic algorithm (CBGA) is proposed to model continuous variables such as voltage outputs in generators and reactive power injection in capacitor banks, as well as binary variables such as tap positions in transformers. The minimization of the total power losses is considered as the objective performance indicator. The main contribution in this research corresponds to the implementation of the CBGA in the DigSILENT Programming Language (DPL), which exploits the advantages of the power flow tool at a low computational effort. The solution of the optimal reactive power flow problem in power systems is a key task since the efficiency and secure operation of the whole electrical system depend on the adequate distribution of the reactive power in generators, transformers, shunt compensators, and transmission lines. To provide an efficient optimization tool for academics and power system operators, this paper selects the DigSILENT software, since this is widely used for power systems for industries and researchers. Numerical results in three IEEE test feeders composed of 6, 14, and 39 buses demonstrate the efficiency of the proposed CBGA in the DPL environment from DigSILENT to reduce the total grid power losses (between 21.17% to 37.62% of the benchmark case) considering four simulation scenarios regarding voltage regulation bounds and slack voltage outputs. In addition, the total processing times for the IEEE 6-, 14-, and 39-bus systems were 32.33 s, 49.45 s, and 138.88 s, which confirms the low computational effort of the optimization methods directly implemented in the DPL environment.

Novel models of power system components for implicit solution of the adjusted power flow problem

The solution of the adjusted power flow problem involves handling power system components whose control characteristics possess operational limits. Examples include generator reactive power limits, tap-changing and phase-shifting transformers, and FACTS devices. While the conventional method involves checking for limit violations in an outer loop drawn around the unadjusted power flow problem being solved by the Newton-Raphson (NR) method, for iterative processes, it is desirable to have smooth, continuously differentiable models implicitly handled within a single loop. A novel formulation for a subset of devices is presented for implicit handling within power flow. The steady state characteristics of tap-changing and phase-shifting transformers, and FACTS devices SVC and STATCOM, can be described using the “cut function”, a piecewise linear function traditionally employed in neural networks. A new approximation of the cut function is used for formulating novel equations describing the steady state characteristics. An augmented set of equations is formed and solved by the NR method, eliminating the need of an outer loop. The efficacy of the proposed method is demonstrated by employing it for plotting bus voltage profiles and determining maximum loadability of test systems. Comparisons with the conventional method show that significant savings in computation can be achieved.