The increasing penetration of solar distributed generations (SDGs) and wind distributed generations (WDGs) together with plug-in electric vehicles (PEVs) will lead to a promising amount of reduction in greenhouse gas emissions. Nevertheless, they bring about adversities such as uncertainty in production-load sides, augmented power loss, and voltage instability in the power system, which should be carefully addressed to increase the reliability. In this concern, this paper proposes a multi-objective optimization methodology for sizing and siting of SDGs, WDGs, and capacitor banks (CBs) in the power system considering uncertainties stemmed from PEVs load demand, solar irradiance, wind speed, and the conventional load. The understudy objectives are the voltage stability index, green-house gas emissions, and the total cost. An unconventional point estimate method (PEM) is used to handle the related uncertainties, and chance-constrained programming method is deployed to deal with smooth constraints. The corresponding probability distribution functions of output variables are estimated by the maximum entropy method. Furthermore, robustness analysis is made by Monte Carlo simulation (MCS). The proposed methodology is applied to a typical radial distribution network. The results show that the presence of PEV’s significantly increases the load demand, which results in voltage collapse in the distribution system without the presence of distributed generations. However, the proposed probabilistic method ensures the safe operation of the distribution system with the optimal allocation of renewable distributed generations and CBs. Moreover, the results of deterministic and probabilistic cases are compared under different penetration levels of PEVs. The best tradeoff solution of the Pareto front is selected by the fuzzy satisfying method.

Introduction

The leading motivations in integrating distributed generations (DGs) in power systems are loss reduction, increasing reliability and voltage profile improvement [1]. However, the well-known defects of conventional DGs and the evident improvement in the competitiveness of renewable energy sources (RES) in terms of capital cost are encouraging investors to replace conventional DGs with solar distributed generations (SDGs) and wind distributed generations (WDGs) [2,3]. Optimal integration of these renewable DGs in power systems is crucial for their safe and economical operation [4]. Natural intermittencies of solar irradiation, wind speed, and plug-in electric vehicles (PEVs) load demand as a new aspect of power system should also be assimilated into sizing and siting problems, which is a mixed-integer nonlinear problem subjected to multiple objectives and constraints and many local optimums [5]. Additionally, the problem should handle these uncertainties with a reasonable tradeoff between computational burden and accuracy. Moreover, it might be in favor of the system operator to ignore the small probabilities of violation for soft constraints such as voltage and power limits [6]. According to the literature, DG planning can be generally categorized into single objective and multi-objective formulation [7]. They can also be categorized into subcategories such as deterministic, probabilistic, or in terms of the algorithm they apply, such as metaheuristic, analytical, etc. [5]. In the field of multi-objective DG allocation and sizing problems, some significant contributions have been made by [8–13].

This paper presents an optimization problem formulation for allocation and sizing of single tuned passive filters in power distribution systems with the objective of minimizing total harmonic distortion. Inequality constraints are considered to determine upper and lower bounds for power factor correction, tuned frequency, voltage unbalance factor, voltage magnitudes and harmonic distortion based on power quality standard limits. The optimization problem is solved using genetic algorithm in which the filters locations, their connection types and parameters for each phase of the system are determined. Simulations are carried out using three-phase unbalanced 33-bus and 69-bus distribution test feeders to demonstrate the viability and efficiency of the proposed formulation to obtain results with total harmonic distortion lower than 5%, voltage unbalance factor lower than 1%, power factor greater than 0.92 and voltage magnitudes between acceptable limits. The main contributions of this paper are the formulation considering multiple power quality indexes in three-phase unbalanced distribution systems, the possibility of the filters to be connected in Y or Δ to satisfy the objective function and the constraints of the optimization problem. Additionally, security constraints related to the operation of the capacitor banks of the filters are considered in this paper.

Introduction

The main consequence of using loads with non linear characteristics and power electronic based devices is the generation of harmonic components in electric power systems [1]. Their proliferation causes several problems such as malfunction of machines, electronic equipment, protection relays, telecommunication conflicts, increasing of power losses, temperature rise in cables and overhead lines [2]. It is extremely important to mitigate and reduce harmonic levels in power grids for power quality improvement. There are many different solutions for harmonic mitigation, including passive, active and hybrid filters. Passive filters are often used for bigger installations due to lower cost when compared to other alternatives [3] and simplicity of implementation and maintenance [2]. They are basically shunt devices, which consist of the connection of inductors, capacitors and resistors that in a specified tuned frequency act as a resonant element with low impedance, forcing the current at that specified frequency to be absorbed, flowing to the earth. Harmonic filters are generally installed in sensitive parts of the networks with large non linear loads and higher harmonic distortion levels for mitigation purpose. However, their allocation is not a trivial task when the objective is to provide a global benefit to a power system in which they are allocated, once they can improve not only harmonic distortion but also provide power factor correction in industrial plants [4] and voltage profile improvement of power systems [3]. Depending on the filters location, harmonic distortion can increase at other nodes of the system according to [5]. Consequently, it is necessary to analyze the filters allocation and sizing with adequate methodologies.

I- Introduction

II- Two-Terminal Active Capacitor Concept

III- Component Sizing of the Active Capacitor for Cost-Constraint Applications

IV- Impedance Characteristics of the Active Capacitor

V- Start-Up Solutions for the Active Capacitor

VI- A Case Study for A Capacitive Dc Link Application And Experimental Verifications

VII- Conclusions

References

Abstract

A two-terminal active capacitor concept is proposed recently based on an active power electronic circuit with a voltage control method and self-power scheme. It retains the convenience of use as a passive capacitor with two power terminals only without any additional required connections, and has the potential to either increased power density or reduced design cost depending on the applications. Based on the previously proof-of-concept study, this paper addresses the design constraints, impedance modeling, and start-up solutions of two-terminal active capacitors. A design method for functionality, efficiency, lifetime and cost constraints application is applied to size the active components and passive elements. A voltage feed-forward control scheme is implemented to improve its dynamic response. Two start-up solutions are proposed to overcome the issues brought by the self-power scheme. A case study of an active capacitor for the DC link of a singlephase full-bridge rectifier is presented to demonstrate the theoretical analyses.

INTRODUCTION

The applications of power electronics consume unprecedented quantities of capacitors for harmonic filtering, power balancing, and/or short-term energy storage. In a singlephase voltage-source rectifier or inverter system, the capacitive DC link needs to filter low-frequency current components while limiting the voltage variation within a specific range. In a three-phase system, possible unbalances appearing in line voltages and/or loads introduce low-frequency harmonics in the DC link [1]. Therefore, a bulky capacitor bank is required for the capacitive DC links in most single-phase and three-phase applications. Moreover, large capacitor banks are also necessary for the AC filters in MW-level highpower inverter applications [2]. Electrolytic capacitors, film capacitors, and ceramic capacitors have been applied for one or more of those applications by considering their respective electrical characteristics, cost, volumetric efficiency, and reliability performance. Capacitor technology advancements have introduced to the market high-performance products, such as high-density, long-lifetime, low Equivalent Series Resistance (ESR), or high-temperature series. However, capacitors are still one of the highest failure components in power electronic systems, and the design constraints in cost and/or power density compromised with electrical and reliability performance still impose a great challenge even with the state-of-the-art capacitor technologies [3].