One of the problems of the selective harmonic elimination pulsewidth modulation (SHE-PWM) method is a limited range of feasible solutions. In many practical applications, the inverter is required to produce a variable output voltage within a wide range (e.g., 0.1 to 1). When the inverter operates in a low modulation index (low output voltage), the output harmonic distortion increases. This article introduces a method to use the SHE-PWM technique for a wide range of modulation indices, which allows achieving a high-quality output waveform in a cascaded H-bridge multilevel inverter. In a five-level case, a dc–dc converter regulates the dc-link voltage of only one bridge. In this way, the extra hardware requirement is reduced, and also a higher number of voltage levels is achieved, which improves the waveform quality. The particle swarm optimization algorithm is used to solve the SHE problem for different output voltage values. Two strategies are proposed to obtain the variable dc-link voltage; one of them is suitable for the lower output voltage values and the other one is more suitable for high values of the output voltage. The proposed strategies have been tested through simulation and experimental studies in different conditions. The results indicate a considerable improvement in the output waveform quality.

Uncertainty management is a challenging task in decision making of the operators of the power systems. Prediction of the system state is vital for operation of a system with stochastic behavior especially in a power system with significant amount of renewable energies such as wind power. Predictable power systems are in more interest of operators, of course. This paper proposes a multi objective framework for optimal placement and parameters setting of a unified power flow controller (UPFC) considering system predictability. The well-known multi objective non-dominated sorting genetic algorithm (NSGA-II) is implemented to handle various objective functions such as active power losses and predictability of system in the presence of operational constraints and uncertainties. Point estimate method (PEM) is used for modeling probabilistic nature of the wind power. Using the proposed method, statistical information of voltage magnitude and apparent power of converters of UPFCs can be obtained, which are very useful in making decision on sizing of UPFCs. Comprehensive discussions are provided using the simulations on IEEE 57-bus test system. Also, in order to validate the obtained results a multi objective particle swarm optimization (MOPSO) algorithm is implemented, too and the results of two algorithms are compared with each other.