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Techniques for distributed generations (DGs) have attracted increasing attention due to considerations of environmental sustainability. Wind farms are one of the DGs, and they have intermittent characteristics. This paper presents a method using wind generator voltages, static compensators, and transformer taps as controllers to regulate the voltage profile for operation planning in a distribution system. Wind power generations and bus loads are modeled with random variables. Through gray-based genetic algorithms (GAs), the MW loss in the system is minimized and the operational constraints are fulfilled. Moreover, this paper uses the cumulant method to calculate the bus voltage fluctuation by using the algebraic addition and multiplication to avoid convolution. The probability density function of the voltage fluctuation can be further expressed by the Gram-Charlier series expansion. Applicability of the proposed method is verified through simulation by using a 17-bus system and an autonomous 24-bus (Penghu) system.

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This article proposes an active balancer, which features bidirectional charge shuttling and adaptive equalization current control, to fast counterbalance the state of charge (SOC) of cells in a lithium-ion battery (LIB) string. The power circuit consists of certain bidirectional buck-boost converters to transfer energy among the different cells back and forth. Owing to the characterization of the open-circuit voltage (OCV) vs SOC in LIB being relatively smooth near the SOC middle range, the SOC-inspected balance strategy can achieve more precise and efficient equilibrium than the voltage-based control. Accordingly, a compensated OCV-based SOC estimation is put forward to take into account the discrepancy of SOC estimation. Besides, the varied-duty-cycle (VDC) and curve-fitting modulation (CFM) methods are devised herein to tackle the problems of slow equalization rate and low balance efficacy, which arise from the diminution in balancing current as the SOC difference between the cells decreases in the later duration of equalization especially. The proposed strategies have taken the battery nonlinear characteristic and circuit parameter nonideality into account and can adaptively modulate the duty cycle with the SOC difference to keep balancing current constant throughout the balancing cycle. Simulated and experimental results are given to demonstrate the feasibility and effectiveness of the same prototype constructed. Compared with the fixed duty cycle and the VDC methods, the proposed CFM has the best balancing efficiency of 81.4%, and the balance time is shortened by 27.1% and 18.6%, respectively. K E Y W O R D S bidirectional buck-boost converter, equalizer, lithium-ion battery (LIB), state of charge (SOC) 1 | INTRODUCTION Secondary batteries have been widely utilized recently owing to the increasing attention paid to the issues on eco-friendly consciousness, energy-saving, and carbon This paper is an extended and revised article presented at the

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