Design of reactive power compensators for distribution systems with harmonic distortion

Abstract

The objective of this paper is to derive a systematic algorithm to decide the optimal location and size of shunt capacitors and filters for distribution systems with harmonic distortion. In this paper, the problem of reactive power compensation is first formulated as a nonlinear programming of minimization of real power loss and capacitor cost under voltage constraint to decide the optimal locations and sizes of shunt capacitors. The harmonic load flow is then applied to solve the total voltage harmonic distortion factor (HDF). Finally, the tuning frequency of the single‐tuned filter and the capacity and voltage ratings of the corresponding reactor and capacitor are determined so that both the harmonic distortion and the reactive power compensation can be solved simultaneously. To demonstrate the performance and effectiveness of the proposed methodology, a practical distribution feeder with nine large industrial customers is selected for computer simulation. It is concluded that proper design of harmonic filters should be undertaken to solve the harmonic resonance problem, as well as the reactive power compensation for distribution systems with nonlinear loads.     

Reactive power/voltage control in distribution systems under uncertain environment

A novel method for reactive power/voltage control in distribution systems under uncertain data environment is presented. This is achieved by minimising boundary real power loss or boundary total real power demand while satisfying constraints on boundary bus voltage magnitudes. Such an approach is more realistic and intuitively satisfying as compared with the crisp solution with deterministic data assumption. On-load tap changing facility of the transformer at the substation and the shunt capacitors at the substation and feeders are used as control variables. A truly nonlinear fuzzy distribution power flow is used, in which simultaneous non-statistical uncertainties in load forecast, load model coefficients and network parameters are incorporated. Genetic algorithm is used to solve the problem. In order to demonstrate the effectiveness of the proposed method, results for balanced 30-bus and unbalanced 25-bus and modified 123-bus systems have been obtained.     

A multi-objective GRASP procedure for reactive power compensation planning

A multi-objective approach based on the GRASP (Greedy Randomized Adaptive Search Procedure) meta-heuristic is proposed to provide decision support in the problem of locating and sizing capacitors for reactive power compensation in electrical radial distribution networks. The installation of capacitors (local sources of reactive power) in the network is aimed at correcting the power factor to improve the quality of service, particularly the network voltage profile, and reduce energy losses and power peak. The mathematical model explicitly considers two conflicting objective functions: the minimization of the network active losses and the minimization of the capacitor installation cost. An algorithmic approach based on GRASP is presented for the characterization of the non-dominated solution set.     

Selection of capacitors to regulate voltage of a short-shunt induction generator

A self-excited induction generator (SEIG) has poor voltage regulation and that restricts wide applicability of the generator. A simple method of selecting the values of fixed and switched capacitors in a short-shunt SEIG driven by a regulated prime mover to maintain the load voltage within the upper and lower acceptable limits is proposed. The values of the capacitors are selected very carefully to minimise the number of switched capacitors needed to satisfy the above voltage criterion, and that would minimise the cost and complexity of the voltage regulator. This requires evaluating the generator characteristics under constant voltage operation. The equations needed to obtain such characteristics are also derived and solved using a numerical based routine 'fsolve' given in MATLAB. The proposed method of selecting the capacitor values is then tested on a three-phase, 1.5 kW induction generator operating in a short-shunt configuration. The simulation results obtained by the proposed method are also compared with the corresponding actual values found through an experimental setup and are observed to be in very good agreement.     

Conic programming approach for static voltage stability analysis in radial networks

That the problem of computing the capacity limit of a radial distribution system can be formulated as a second-order cone program is shown. The implications of the conic programming formulation are 2-fold. First, the load capability of the radial system can be obtained using existing efficient implementations of polynomial time interior-point algorithms, thus avoiding the need for running a sequence of load flow solutions. Secondly, the conic objective function yields a voltage stability indicator (SI). This indicator quantifies the maximum percentage by which the current load profile can be uniformly increased before voltage collapse occurs. The proposed method is validated by computing the load capability and voltage SIs of 11 different distribution systems. Comparisons are carried out with five previously published voltage SIs     

Distribution system reliability enhancement using optimal capacitor placement

Failure statistics of most utilities indicate that distribution systems make the greatest individual contribution to the unavailability of supply to customers. Optimal capacitor placement in distribution systems has a number of advantages such as reducing losses, improving voltage profile, improving power factor and so on. The conventional objective function of the optimal capacitor placement consists of the total cost of losses and investments. Since capacitors supply reactive loads locally, they improve the load-carrying capability of the lines and therefore play the same role as redundant lines. Thus, optimal capacitor placement can also improve the reliability indices of a distribution system. Therefore two new objective functions are defined here. The first one is defined as the sum of reliability cost and investment cost. The second is defined by adding the reliability cost, cost of losses and investment cost. The latter is a comprehensive objective function which is the resultant of the conventional and reliability-based objective functions. This problem is solved using a particle swarm optimisation-based algorithm. The effectiveness and applicability of the proposed approach are examined using a distribution network.     

Solution of fixed cost trans-shipment problems by a branch and bound method

Varied problems in the fields of operation, scheduling, allocation and design in power systems analysis can be formulated as fixed cost trans-shipment problems. This paper indicates possible areas of application of such formulations, and by exploiting specific characteristics of certain power systems problems presents an efficient branch and bound method for solving them.     

A multi-objective simulated annealing approach to reactive power compensation

Reactive power compensation is an important problem in electrical distribution systems, involving the sizing and location of capacitors (sources of reactive power). The installation of capacitors also contributes to releasing system capacity and improving voltage level. A multi-objective simulated annealing approach to provide decision support in this problem is presented. This approach is able to compute a set of well-distributed and diversified solutions underlying distinct trade-offs, even for a challenging network. The characterization of the non-dominated front is relevant information for aiding planning engineers to select satisfactory compromise solutions (compensation schemes) to improve the network operation conditions.     

Three-phase balancing of distribution feeders using immune algorithm

The immune algorithm (IA) is proposed to derive the rephasing strategy arrangement of laterals and distribution transformers to enhance three-phase balancing of distribution systems. The multi-objective function is formulated by considering the unbalance of phasing currents, the customer service interruption cost (CIC) and labour cost to perform the optimal rephasing strategy. For each feasible rephasing strategy, the number of customers affected with total interruption load demand and outage duration time are used to calculate the impact of system reliability because of rephasing engineering works. To demonstrate the effectiveness of the proposed methodology, a practical distribution feeder in Taipower with 271 customers is selected for computer simulation. By minimising the objective function subjected to the operation constraints, the rephasing strategy has been derived by selecting the laterals and distribution transformers for phasing adjustment. It is found that the neutral current of test feeder has been reduced to be less than the neutral overcurrent limit by executing the rephasing of laterals and distribution transformers.     

A novel closed‐loop reconfiguration for radial distribution systems with dispersed generation

Abstract

Currently, Tai‐power Company is attempting to change its power distribution systems from radial distribution configurations to closed‐loop configurations in order to enhance the quality of the supply of electricity. Besides, the dispersed generation (DG) should be considered in making the reconfiguration suitable for present circumstances. To form a closed‐loop configuration, a new tie‐line is added in this paper to interconnect two different feeders of the original radial power distribution systems. The multi‐objective is, not only to reduce power transmission loss, but also reduce the cost representative of power distribution reconfiguration. Assuming that the cost representative is a linear function of the system's short‐circuit capacity, line current and bus voltage. The problem solution procedure in this paper is mainly divided into two steps. The first step is to form objective function by determining the weighting factor of each objective term based on the cost‐benefit analysis scheme. Then, the optimum solution is pursued for the objective function by means of refined genetic algorithm (RGA). An example is studied by using the proposed methodology. The results show that the cost‐benefit analysis scheme is verified capable of finding the weighting factors, that the RGA can render stable solutions and that the transmission loss reduction ratio is satisfactory.     

Reducing power loss in magnetic bearings by optimizing current allocation

Conventional magnetic bearings control current or flux by operating symmetrically about a bias current or bias flux. This approach is known to be much easier to control than operating without a bias but has the disadvantage of introducing additional power loss. Although one obvious way to minimize the power loss is to alternate activation of the two opposing electromagnetic actuators, this single actuator allocation strategy has not been successful in practical applications because it results in severe performance degradation. In this paper, we investigate the fundamental reasons behind the performance degradation under the single actuator allocation strategy. One major reason is voltage saturation in the circuit systems. On the basis of this result, we formulate the problem of minimizing the energy consumption by allocating the currents under the constraint of bounded voltages. We establish necessary conditions and properties for the optimal solution, which we use to determine the optimal allocation strategy for some common force signals. Since the optimal solution is very sensitive to the variation of the force signal, we propose a simple static allocation strategy to approximate the optimal solution.     

基于模型的区域物流配送系统规划研究

以经济区域的卷烟配送物流系统规划为背景,将整个区域划分为若干个配送单元,依据各配送单元的需求量、物流中心的建设投入和运行成本,并将物流中心的成本分为固定成本和变动成本,特别地将送货过程的车辆费用从变动成本中划分出来,建立了物流系统的运筹学模型,并通过模型求解获得该物流系统的优化布局方案.     

The potential transformer bridge with current comparator formeasuring the voltage dependence of compressed-gas capacitors

In this paper, an alternative method for measuring the voltage dependent capacitance variation (VDCV) of compressed-gas capacitors is described. In the proposed method, the VDCV of the capacitor under test is measured by comparing it with a capacitor standard supplied with the secondary (low) voltage of a potential transformer. This transformer has its primary parallel connected with the capacitor under test. The paper presents and criticizes the test results obtained in which an uncertainty of at least 0.5 ppm is achieved     

基于LOF和SVM的配电网线变关系数据校验方法

针对配电网线变关系数据人工校验成本高、准确性差的问题,提出一种基于LOF和SVM的配电网线变关系数据校验方法.对于待校验配电线路,从用电信息采集系统提取其配电变压器最近一段时间的电压序列数据,当变压器A、B、C相电压不平衡时将其电压值归算为等效电压;基于不同变压器电压序列之间的相关距离,计算每台变压器的LOF值;统计变...     

Voltage stability analysis considering the uncertainties of dynamic load parameters

Many uncertainties exist in power systems and they will affect the stability analysis results. Voltage stability considering uncertainty in load parameters will be discussed. With the assumption that parameter variation is normal distribution, the probabilistic characteristics of eigenvalues under the uncertainties of dynamic load parameters can be obtained. Distribution of the critical eigenvalue will determine the stability probability of a power system. The stability margin can be inferred from the probabilistic critical load level, which is the maximal load level where system is `probabilistically` stable. Case studies on three test systems illustrate that the stability margin will be reduced with load uncertainty. The proposed probabilistic results are validated using deterministic method of Monte Carlo on multi 10`000 sample studies.     

Solving Fixed Charge Location-Allocation Problems with Capacity and Configuration Constraints

Location-allocation problems involve the selection of locations that will be used as sources to satisfy a demand at various destinations. Associated with each potential source is a capacity limitation on output and a cost function which is broken down into a fixed charge plus an output dependent variable cost. Linear distribution costs comprise the remaining part of the total system cost. Configuration constraints which rule that specific source combinations are infeasible may be included for consideration. A solution procedure is presented that finds the minimal cost solution. The procedure utilizes a new enumerative search scheme in conjunction with adaptive bounds on the fixed costs, and constraints based on the dual variables to reduce the feasible solution set to a manageable size. For each of the small number of enumerated source configurations that pass all fixed cost and duality tests, a transportation problem is optimized to determine the minimum cost allocation. An experimental computer code was developed and numerical results are presented.     

Thyristor converters using saturable reactors

The dc to ac and ac to ac series converters have been discussed in earlier publications.[1]-[3] These systems are used with minimum component ratings at a fixed load resistance and a fixed output frequency.[1] The ranges of operation of the load and the frequency can be increased by using saturable reactors and variable capacitors. These systems are analyzed and the preferred operating conditions are discussed. Theoretical results are supplemented with the experimental results.     

Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.     

Distribution planning for multi-echelon networks considering multiple sourcing and lateral transshipments

Nowadays, due to the increasing complexity of business environment, especially demand uncertainty, supply chain managers need to establish more-effective sourcing and distribution strategies to ensure high customer service and low stock costs. To overcome this challenge multi-echelon network structures and alternative distribution strategies such as lateral transshipments and multiple sourcing should be considered in inventory optimisation models. In this article, we propose a scenario-based modelling approach to solve a two-stage multi-echelon inventory optimisation problem with a non-stationary demand. The model is based on a distribution requirements planning (DRP) approach and minimises the expected total cost that is composed of the fixed allocation, inventory holding, procurement, transportation, and back-ordering costs. Alternative inventory optimisation models, including the lateral transshipment strategy and multiple sourcing, are thus built, and the corresponding stochastic programmes are solved using the sample average approximation method. Through a numerical investigation conducted with several generated instances and an empirical investigation based on the case of a major French retailer’s distribution network, we show the substantial benefit of lateral transshipments and multiple sourcing in reducing the expected total costs of the distribution network.     

Concurrent optimal allocation of design and process tolerances for mechanical assemblies with interrelated dimension chains

Concurrent tolerance allocation has been the focus of extensive research, yet very few researchers have considered how to concurrently allocate design and process tolerances for mechanical assemblies with interrelated dimension chains. To address this question, this paper presents a new tolerance allocation method that applies the concept of concurrent engineering. The proposed method allocates the required functional assembly tolerances to the design and process tolerances by formulating the tolerance allocation problem into a comprehensive model and solving the model using a non-linear programming software package. A multivariate quality loss function of interrelated critical dimensions is first derived, each component design tolerance is formulated as the function of its related process tolerances according to the given process planning, both manufacturing cost and quality loss are further expressed as functions of process tolerances. And then, the objective function of the model, which is to minimize the sum of manufacturing cost and expected quality loss, is established and the constraints are formulated based on the assembly requirements and process constraints. The purpose of the model is to balance manufacturing cost and quality loss so that concurrent optimal allocation of design and process tolerances is realized and quality improvement and product cost reduction is achieved. The proposed method is tested on a practical example.