VAr Planning Research Articles

Parameter Optimization for Var Planning of Systems With High Penetration of Wind Power: An Adaptive Equivalent Reduction Method

Voltage-related issues such as dramatic voltage fluctuation, lack of Var reserves, become more prominent in high wind power penetration (HWPP) system, leading to increasing of large-scale cascading trip risks within 100-200ms. During the cascading process, fast dynamic Var support, which is strongly related to internal parameters of Var devices, is quite crucial for HWPP system security. If device parameters optimization is also considered in the Var planning, it will be more promising to achieve less investment cost and guarantee transient security for HWPP system. However, the complex control elements and numerous internal parameters optimization cause a huge computational burden of planning issues. Therefore, this paper proposes an adaptively parameter order equivalent reduced optimization (APO-ERO) approach to efficiently and accurately solve the Var planning problem with parameter allocation. First, the original high-order Var device model is adaptively reduced to an optimal low-order model that minimizes the reduced order error. Next, an equivalent low-order optimization model in the upper layer and an inverse mapping parameter allocation model in the lower layer are established to relieve the computational burden. Finally, the two different test systems with HWPP verify that the proposed method can improve computational efficiency on the premise of guaranteeing accuracy.

Zoning‐based candidate bus selection for dynamic VAR planning in power system towards voltage resilience

Dynamic VAR planning for voltage stability enhancement is a challenging topic for power systems with a growing penetration level of wind power. As a critical step of VAR planning, candidate bus selection (CBS) can reduce the scale of the problem and improve the optimality of the planning decisions. This study proposes a new zoning-based CBS method towards multiple voltage resilience indices. First, a set of resilience-oriented metrics are proposed to comprehensively evaluate voltage performance in pre-contingency and post-contingency stages, considering the extent of the voltage deviation and voltage recovery time, as well as the post-contingency steady-state voltage profile. Then, a zoning-based approach is developed based on fuzzy C-means clustering and Morris screening to categorise buses into different zones with capacity sensitivity analysis. Finally, a comprehensive multi-objective CBS scheme is proposed for voltage resilience enhancement. Simulation results show that, compared with conventional approaches, the method can achieve more voltage stability improvement with the fewer or the same number of candidate buses.

Coordinated VAR Planning for Voltage Stability Enhancement of a Wind-Energy Power System Considering Multiple Resilience Indices

Modern power systems are facing greater challenges in dynamic voltage performance due to the increased wind power penetration and proliferation of induction loads. This paper proposes a multi-stage coordinated var source planning method for voltage resilience enhancement. A set of novel voltage resilience metrics are proposed to quantify the steady-state and short-term voltage stability, as well as the defensive capability and restorative performance of the system. The planning model coordinates the deployment of both fixed capacitor banks and STATCOM with coordinated defensive and restorative control actions including wind power curtailment, excitation system compensation, demand response, and load shedding. Three sub-objectives are optimized simultaneously: 1) planning cost and operation mitigations cost, 2) resilience indices of defensive capability, and 3) resilience indices of restorative performance. Finally, a robust parameter design technique called Taguchi's Orthogonal Array Testing is employed for uncertainty quantification and Pareto optimal solutions are provided for a flexible decision-making. The computation burden is mitigated by candidate buses selection with Morris Screening Method and critical contingency identification. The efficiency and effectiveness of the proposed approach are validated on the New England 39-bus system.

Multi‐objective robust dynamic VAR planning in power transmission girds for improving short‐term voltage stability under uncertainties

Modern power transmission grids are facing more and more critical short-term voltage stability problems. This study proposes a novel robust dynamic VAR planning approach for improving the short-term voltage stability level under uncertainties including the peak load level, the maximum proportion of dynamic load, fault clearing time and deviation of the actual capacity of dynamic VAR compensators from rated capacity when contingencies occur. The robust dynamic VAR planning problem is formulated as a multi-objective optimisation model with objectives including the investment cost, the expectation and robustness of the short-term voltage stability level. The complexity of the planning model is firstly reduced by selecting severe contingencies and potential buses, leading to a simplified multi-objective optimisation model. Latin hypercube sampling is then used for the uncertainty quantification. The simplified multi-objective optimisation model is then solved by the combination of a multi-objective evolutionary algorithm called ${\rm \epsilon }$e-NSGAII and extreme learning machine-based surrogate modelling with adaptive training data sampling. This combination significantly reduces the unaffordable computing burden. Simulations are carried on the IEEE 39-bus system, illustrating that the authors proposed methodology is reliable with high computational efficiency, and offering decision-makers planning solutions with high mean performance and strong robustness with respect to the short-term voltage stability level.

Reactive power planning using a new hybrid technique

Voltage deviation and stability constrained VAr planning or reactive power planning (RPP) is an important challenging issue in power systems. This paper presents a new hybrid technique for modeling and solving RPP problem taking into account the static voltage stability constraint. First, the uncertain fuzzy clustering theory is employed to select new candidate VAr source locations. Then, modified gray code is applied and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Based on the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability and new VAr capacity is derived and applied as static voltage stability constraint in RPP problem. Last, the RPP optimization problem is solved by a self adaptive fuzzy chaotic interactive honey bee mating optimization (FCIHBMO) technique taking advantage of the modified gray code. In the FCIHBMO algorithm, a modified definition of the updating factors on generation solution is proposed. In the case study, uncertain fuzzy clustering mechanism, the modified gray code, and the modified HBMO are applied to the IEEE 118-bus and IEEE 300-bus systems. Test results conclude that the proposed hybrid technique is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered.

Contingency Constrained VAr Planning Using Penalty Successive Conic Programming

This paper presents a new method for VAr planning under multiple operating scenarios, optimizing sizes and locations of new reactive compensation equipment to ensure that both the system voltage profile and voltage stability requirements are met. The approach is based on mbi L1-norm regularization for finding a solution with minimum VAr installation sites and on the mbi L2-norm penalty function for satisfying the multiple state constraints. The mbi L2-norm penalty function is exact in the sense that a finite penalty parameter is required to establish equivalence with the VAr planning problem, thus avoiding numerical ill-conditioning. The solution is obtained from a successive conic programming algorithm which makes use of adaptive trust-region control. The results of the new method are compared with those of an optimal power flow-based program for VAr planning.

Reactive Power Planning Based on Fuzzy Clustering, Gray Code, and Simulated Annealing

Voltage stability constrained reactive power planning (RPP) or VAr planning is a very challenging issue in power systems. This paper proposes a new approach for modeling and solving VAr planning problem taking into account the static voltage stability constraint. First, the fuzzy clustering method is employed to select new candidate VAr source locations. Then, modified Gray code is proposed and used to represent a series of non-uniform VAr capacity intervals at different candidate buses. Under the new ordering of the VAr capacity intervals, a simplified piecewise linear function between the total transfer capability (TTC) and new VAr capacity is derived and applied as static voltage stability constraint in RPP. Finally, the RPP optimization model is solved by an enhanced simulated annealing (SA) algorithm taking advantage of the modified Gray code. In the SA algorithm, a modified definition of the neighborhood selection and a novel approach to generate new random solutions are proposed. In the case study, fuzzy clustering method, the modified Gray code, and the improved SA are applied to the IEEE 30-bus system. Test results conclude that the proposed method is a simplified and effective approach for voltage stability constrained VAr planning with contingency considered.

Stability-index based method for optimal Var planning in distribution feeders

The problem of the reactive energy optimal planning can be solved in a fast and efficient way using heuristic techniques. The latter reduce the number of the control variables to be determined and lead to a near global optimal solution. The capacitor appropriate locations are firstly determined by decisive indices then, their optimal sizes are calculated. In this paper a stability-index based method is presented. The nodes stability-indices are calculated for identifying the most sensitive nodes to be candidate for receiving near optimal standard capacitors that, reduce the feeder power losses, improve the voltage profile and maximise the economic saving (objective function). In this multi-objective optimisation problem, the commonly used voltage constraint is substituted by a new constraint on the branch reactive currents. This new constraint, allows overcoming the over compensation phenomenon by setting positive branch reactive currents. The solution is further improved by regulating the source node voltage. The proposed approach has been tested on several feeder examples and its effectiveness has been demonstrated through comparative studies. The obtained results have shown that the proposed approach leads to a promising and feasible solution.

Interpolation approximation of voltage stability constrained opf (vscopf) for reactive power planning

Reactive power planning (RPP), or Var planning, is to identify the optimal size and location of reactive power sources. In this paper, first, the previous work using least square method to simplify the voltage stability constrained OPF (VSCOPF) model for RPP is presented. Then, this paper presents a new model simplification solution using interpolation. The interpolation approach can be easily applied to a piecewise formulation while preserving the continuity at boundary points, which cannot be easily achieved by previous works like the least square method. The proposed interpolation approach is numerically tested and compared with the least square approach. It is concluded that interpolation is an improved model simplification approach for RPP.

Review of Reactive Power Planning: Objectives, Constraints, and Algorithms

The key of reactive power planning (RPP), or Var planning, is the optimal allocation of reactive power sources considering location and size. Traditionally, the locations for placing new Var sources were either simply estimated or directly assumed. Recent research works have presented some rigorous optimization-based methods in RPP. This paper will first review various objectives of RPP. The objectives may consider many cost functions such as variable Var cost, fixed Var cost, real power losses, and fuel cost. Also considered may be the deviation of a given voltage schedule, voltage stability margin, or even a combination of different objectives as a multi-objective model. Secondly, different constraints in RPP are discussed. These different constraints are the key of various optimization models, identified as optimal power flow (OPF) model, security-constrained OPF (SCOPF) model, and SCOPF with voltage-stability consideration. Thirdly, the optimization-based models will be categorized as conventional algorithms, intelligent searches, and fuzzy set applications. The conventional algorithms include linear programming, nonlinear programming, mixed-integer nonlinear programming, etc. The intelligent searches include simulated annealing, evolutionary algorithms, and tabu search. The fuzzy set applications in RPP address the uncertainties in objectives and constraints. Finally, this paper will conclude the discussion with a summary matrix for different objectives, models, and algorithms.

A Multiobjective Model for VAR Planning in Radial Distribution Networks Based on Tabu Search

In this paper, a tabu search (TS)-based approach to provide decision support in the problem of capacitor location in radial distribution networks is presented. The model explicitly considers two conflicting and incommensurate objective functions related to cost and operational aspects of evaluation. This offers the decision maker/planning engineer the possibility to expand the range of potential alternative solutions (since he or she is not limited to an optimal solution as in single objective models), also giving him or her an active role through the expression of his or her preferences to select a satisfactory compromise solution.

A new formulation for facts allocation for security enhancement against voltage collapse

This paper proposes a new formulation for reactive power (VAr) planning problem including the allocation of flexible ac transmission systems (FACTS) devices. A new feature of the formulation lies in the treatment of security issues. Different from existing formulations, we directly take into account the expected cost for voltage collapse and corrective controls, where the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal VAr planning. The inclusion of load shedding into the formulation guarantees the feasibility of the problem. The optimal allocation by the proposed method implies that the investment is optimized, taking into account its effects on security in terms of the cost for power system operation under possible events occurring probabilistically. The problem is formulated as a mixed integer nonlinear programming problem of a large dimension. The Benders decomposition technique is tested where the original problem is decomposed into multiple subproblems. The numerical examinations are carried out using AEP-14 bus system to demonstrate the effectiveness of the proposed method.

A New Formulation for FACTS Allocation for Security Enhancement against Voltage Collapse

This paper proposes a new formulation for var planning problems, including the allocation of FACTS devices. A new feature of the formulation lies in the treatment of security issues. Different from existing formulations, we directly take account of the expected cost for voltage collapse and corrective controls, in which the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal var planning. The inclusion of load shedding into the formulation guarantees the feasibility of the problem. The optimal allocation by the proposed method implies that the investment is optimized, taking into account its effects on security in terms of the cost for power system operation under possible events occurring probabilistically. The problem is formulated as a mixed integer nonlinear programming problem of a large dimension. The Benders decomposition technique is tested where the original problem is decomposed into multiple subproblems. The numerical examinations are carried out using AEP-14 bus system to demonstrate the effectiveness of the proposed method.

Voltage stability constrained VAR planning: model simplification using statistical approximation

This paper presents a statistical approximation procedure to simplify the voltage stability constrained VAR planning optimization model. One major source of complexity of the voltage stability constrained model is the requirement of having two sets of network variables and power flow constraints corresponding to the “normal operation” and “point of collapse (PoC)”. This effectively doubles the number of variables and constraints in the voltage stability constrained model as compared to the VAR planning model dealing solely with “normal operation” and limits on bus voltages alone. The present analysis explores the possibility to simplify the model using statistical approximation of the locus of the PoC. This approximation exploits the fact that the MINLP model utilizes only the PoC information of the nose curve. The locus can be reasonably approximated using a standard linear/quadratic ordinary least square multivariate regression model. Although the simplified model has lower computational complexity, the impact on the model results needs to be carefully examined. We have demonstrated using a high reactive power deficit contingency case for the AEP 14-bus system that the results of the simplified model are only marginally inferior to those of the globally optimal solution.

VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

Dynamic security constrained optimal power flow/VAr planning

Traditionally security constrained optimal power flow and VAr planning methods consider static security observing voltage profile and flow constraints under normal and post contingency conditions. Ideally, these formulations should be extended to consider dynamic security. This paper reports on a BC Hydro/CEPEL joint effort establishing a dynamic security constrained OPF/VAr planning tool which considers simultaneously static constraints as well as voltage stability constraints. This paper covers the details of formulation and implementation of the tool together with the test results on a large scale North American utility system and a reduced Brazilian system.

00/01363 Applying network window schema and a simulated annealing technique to optimal VAR planning in large-scale power systems

00/01363 Applying network window schema and a simulated annealing technique to optimal VAR planning in large-scale power systems

Large scale voltage stability constrained optimal VAr planning and voltage stability applications using existing OPF/optimal VAr planning tools

Traditionally in optimal VAr planning, the feasible operation has been translated as observing voltage profile criteria ensuring that the system voltage profile is acceptable for system normal and post contingency conditions. This feasibility definition is not sufficient when considering the VAr planning practice of the utilities concerned with voltage stability problems. Presently, these utilities use two reinforcement criteria for VAr additions. While for VAr design in the regions the voltage profile criteria is considered, for bulk transmission system VAr resources are designed to guard against voltage instability. This paper reports on the findings of a recently completed EPRI project evaluating the existing optimal VAr planning/OPF tools for voltage stability constrained VAr planning and voltage stability applications. Two of the selected tools were adapted to address these applications on four large scale utility systems (up to 6000 buses). The results were also verified using EPRI's voltage stability program (VSTAB). The results obtained indicate that OPF/VAr planning tools can be used to address voltage stability constrained VAr planning and voltage stability applications in an accurate way. Additional advantages offered by these tools are easier procedures, less computation and avoidance of engineering judgment in identifying the amount of VAr requirement at the candidate sites.

Improved interior point method for OPF problems

Since conventional optimal power flow (OPF) algorithms are limited and too slow for operational planning, power system operation and planning engineers have been seeking efficient OPF algorithms for three decades. The interior point method is one of the most efficient algorithms. In this paper, an improved quadratic interior point (IQIP) method is used to solve comprehensive OPF problems with a variety of objective functions, including economic dispatch, VAr planning and loss minimization. The IQIP method features a general starting point (rather than selected good point as in the general interior point method) and fast convergence. Consequently, the OPF package described in this paper offers huge improvements in speed, accuracy and convergence in solving multi-objective and multi-constraint optimization problems. It will be a very useful tool for the power industry.

Multiple indices for optimal reactive power pricing and control

An integrated approach for reactive power price and control is developed. Reactive power price is divided into fixed and variable parts. The fixed part is the operational cost of reactive power service. The variable part of reactive power price is determined based on capability and contributions to the improvement of system performance such as security, reliability and economics. These contributions can be evaluated by computing sensitivity of objective function with respect to reactive power support. The optimal power flow (OPF) approach is used to carry out this purpose. For VAr planning (or control) purposes, three parallel indices are first presented to determine the sites of new VAr sources. They are benefit-to-cost ratio index, voltage reactive sensitivity index, and the bus voltage security index. The analytic hierarchical process is then used to comprehensively consider the effect of the three indices and the network topology for each candidate VAr source site. The proposed approach was tested on an IEEE 30-bus system with satisfactory results.