Voltage Stability Constraints Research Articles

A Stochastic Optimal Power Flow Problem With Stability Constraints—Part I: Approximating the Stability Boundary

Stochastic optimal power flow can provide the system operator with adequate strategies for controlling the power flow to maintain secure operation under stochastic parameter variations. One limitation of stochastic optimal power flow has been that only line flows have been used as security constraints. In many systems voltage stability and small-signal stability also play an important role in constraining the operation. In this paper we aim to extend the stochastic optimal power flow problem to include constraints for voltage stability as well as small-signal stability. This is done by approximating the voltage stability and small-signal stability constraint boundaries with second-order approximations in parameter space. Then we refine methods from mathematical finance to be able to estimate the probability of violating the constraints. In this first part of the paper, we derive second-order approximations of stability boundaries in parameter space. In the second part, the approximations will be used to solve a stochastic optimal power flow problem.

Quantitative method for evaluating generation margin for power system planning

AbstractAs the power system advances, the competition among the power companies becomes heated, and they seek more efficient system planning using existing facilities. Therefore, an efficient system planning method is desirable. This paper proposes a quantitative evaluation method for the (N–1) generation margin considering overload and voltage stability constraints. Concerning the generation margin related to overload, a fast solution method without recalculation of the (N–1) Y‐matrix is proposed. With reference to voltage stability, this paper proposes an efficient method of seeking the stability limit. The IEEE30 model system, composed of six generators and 14 load nodes, is employed to validate the proposed method. According to the results, the proposed method can reduce the computational cost for obtaining the generation margin related to the overload and the voltage stability limit under the (N–1) condition, and can specify the value quantitatively. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 181(4): 19–28, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). doi 10.1002/eej.21234

Research on Wind Farm and Energy Storage System Integration on Power System

Based on power system static voltage stability constraints, by theoretical analysis, calculation method of injection power for each node in power system is given. Compared with power flow simulation, results show that this method can be used to obtain nodes with relative large injection power, and calculation accuracy in a certain extent depends on the accuracy of power system Thevenin equivalent impedance. In addition, the application of energy storage systems to improve wind farm power injection is analyzed preliminarily. Simulation results show that locations of energy storage system in power system have impacts on the improvement of wind farm power injection.

Online voltage security assessment considering comfort-constrained demand response control of distributed heat pump systems

A resilient strategy for optimal demand response control based on the management of highly-distributed electric loads is presented to meet transmission-level control aimed at maintaining voltage stability. The proposed load control scheme balances device- and grid-level objectives simultaneously, and is demonstrated for a system comprising a distributed responsive population of 14,000 residential-sized buildings integrated in a transmission system network consisting of six buses. Air-source heat pumps are implemented as the primary heating source in the responsive building population, and are introduced as a dispatchable grid-side energy resource, where aggregated output can be objectively ramped up or down through the use of an optimal centralized control strategy. A two step multi-objective optimization procedure is implemented to simultaneously satisfy balancing of the power system and customer objectives across a multi-scalar system. At the power system-level, the optimal preventive control scheme is obtained based on steady-state voltage stability constraints. At the customer-level, an optimal demand response strategy is proposed, wherein the aggregate power demand from a population of heat pumps is controlled to follow load-shedding requirements. The customer comfort is continuously maintained by constrained regulation of the thermal set-point governing operation of the heat pump device.The proposed demand-side strategy achieves similar goals to conventional approaches to regulation and spinning reserve ancillary services, but with the significant benefit of higher efficiencies. Under the proposed scheme, ancillary services provided by the electric loads effectively become virtual generators that enhance the voltage stability in power systems operating under increased uncertainty, and replace severe or multiple contingency reserves typically supplied by conventional generators. The proposed demand response control scheme can be extended to other potentially responsive end-use appliances, and opens avenues for increased exploitation of intermittent renewable energy resources while reducing operating costs and emissions.

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.

Optimization of Reactive Power Expansion Planning

This article presents a penalty successive linear programming approach for optimum investment of reactive power in networks. Unlike many successive linear programming algorithms, the proposed approach is based on a successive linear programming framework that admits a convergence proof for non-linearly constrained problems of general form. The penalty successive linear programming approach produces a pattern of new reactive sources that satisfy voltage profile requirements in normal and contingent states of operation, and it also accounts for voltage stability constraints that guard against voltage collapse. Numerical test results are presented and compared with an optimal power flow based planning method that processes the system states sequentially.

OBDD-Based Sectionalizing Strategies for Parallel Power System Restoration

After a power system is subjected to a blackout, parallel restoration is an efficient means to speed up the restoration process. The system sectionalizing strategy consists of determining the proper splitting points to sectionalize the entire blackout area into several subsystems, so that parallel restoration can be carried out within the subsystems. For a large-scale power system, this system sectionalizing problem is quite complicated when considering black-start constraints, generation/load balance constraints, and voltage stability constraints. This paper presents an ordered binary decision diagram (OBDD) -based system sectionalizing method, by which the splitting points can be found quickly. Simulation results on the IEEE 118-bus test systems show that the method can successfully sectionalize the system into subsystems satisfying black-start constraints, generation/load balance constraints, and voltage stability constraints.

State-of-the-art, challenges, and future trends in security constrained optimal power flow

Abstract This paper addresses the main challenges to the security constrained optimal power flow (SCOPF) computations. We first discuss the issues related to the SCOPF problem formulation such as the use of a limited number of corrective actions in the post-contingency states and the modeling of voltage and transient stability constraints. Then we deal with the challenges to the techniques for solving the SCOPF, focusing mainly on: approaches to reduce the size of the problem by either efficiently identifying the binding contingencies and including only these contingencies in the SCOPF or by using approximate models for the post-contingency states, and the handling of discrete variables. We finally address the current trend of extending the SCOPF formulation to take into account the increasing levels of uncertainty in the operation planning. For each such topic we provide a review of the state of the art, we identify the advances that are needed, and we indicate ways to bridge the gap between the current state of the art and these needs.

Generation rescheduling using ANN-based computation of parameter sensitivities of the voltage stability margin

This paper proposes a sensitivity-based methodology for voltage stability enhancement of a power system by rescheduling real power outputs of the participating generators. An enhanced radial basis function network (RBFN) is used to compute the sensitivities of the voltage stability margin with respect to the generator outputs. The sensitivities are used in formulating the linearized voltage stability constraints in the optimization procedure. Optimum generator outputs are determined to enhance voltage stability margin for multiple contingencies. Case studies are presented to illustrate the effectiveness of the proposed method.

열적용량과 전압안정도를 고려한 ATC 계산 방법에 관한 연구

본 논문은 가용송전용량(ATC)를 계산하기 위한 두 가지 빠른 계산 기법을 제안한다. 이 방법들은 선로의 열적 용량한계(Thermal ATC)와 전압 안정도한계(Voltage ATC)를 제약조건으로 ATC를 계산한다.<BR> 먼저 선로의 열적용량을 고려한 방법에서는 모선의 전력 변화에 대한 선로의 조류 감도인 PlDF와 n-1 상정사고를 고려한 LODF를 이용하였으며, 전압안정도를 고려한 방법에서는 2모선 등가 시스템을 이용하여 최대 전력을 구하는 방법을 이용하였다. 제안된 방법은 IEEE 30모선 계통에 적용하였으며 그 결과를 다른 방법과 비교하여 제안된 방법의 타당성을 입증하였다.

Dynamic voltage stability constrained ATC calculation by a QSS approach

The evaluation of Available Transfer Capability (ATC) in deregulated power system should take into account thermal limits, transient, steady-state and dynamic angle stability as well as the voltage stability limit. The consideration of voltage stability in the determination of ATC, however, was not well researched before. On the other hand, under the power market environment, voltage instability becomes a more important consideration in many countries in recent years, especially when following a large disturbance in a heavily stressed power system over long distances. A new ATC determination scheme using Quasi-steady-state (QSS) approximation is proposed in this paper and implemented on a test system. The performance of the QSS approximation is also compared with the Full-Time-Scale (FTS) simulation. From the results, it is shown that the proposed scheme can evaluate ATC with dynamic voltage stability constraints accurately and the calculation speed is accelerated considerably to meet the real-time requirement.

An economical generation direction for power system static voltage stability

This paper proposes an economical generation direction for static voltage stability. The proposed generation direction minimizes the total operating cost at any loading level, up to the point of collapse. The proposed approach, named as EGD approach, is based on the economic load dispatch with load flow. Two alternative methods to identify the economic generation direction are proposed. Economical generation direction is used in the continuation power flow process to obtain the static voltage stability margin. Static voltage stability margin with economical generation direction is compared with the margins resulting from other existing generation directions in the modified IEEE 14-bus test system under various system operating conditions. Cost of providing loading margin as well as PV curves and losses under different generation directions resulting from various generation direction approaches are also studied and compared. The proposed approach provides an alternative way for utilities to obtain the lowest total operating cost with voltage stability constraint by using any existing commercial software.

AN APPROACH TO OPTIMAL DISPATCH OF BILATERAL ELECTRICITY CONTRACTS REGARDING VOLTAGE STABILITY

This paper proposes a methodology for optimal dispatch of bilateral electricity contracts, which may endanger the system voltage stability in light of short-term operational planning of a deregulated power system. In this framework the value that each owner of a transaction is willing to pay will reflect how much the electricity contract is important to be implemented physically. The proposed model dispatches optimally the bilateral transactions regarding the prices offered by owners of bilateral contracts for reactive power and transmission capacity utilization in one hand and, the total operational costs of reactive power resources in the other hand. The model also includes the limits imposed by the physical constraints on the power system such as nodal power flow equations, limits on capacity of resources, voltage stability constraint and etc. The proposed framework is formulated as an AC-OPF problem and is implemented over the IEEE 14 bus test system using CONOPT solver (GAMS) to illustrate the feasibility of the approach.

Voltage stability constrained OPF market models considering [formula omitted] contingency criteria

This paper proposes two novel techniques for including contingencies in OPF-based electricity market computations and for the estimation of a “system-wide” available transfer capability (SATC). The OPF problem formulation includes voltage stability constraints and a loading parameter in order to ensure a proper stability margin for the market solution. Two methods are proposed. The first technique is an iterative approach and computes an SATC value based on an N − 1 contingency criterion for an initial optimal operating condition, to then solve an OPF problem for the worst contingency case; this process is repeated until the changes in the SATC values are below a minimum threshold. The second approach solves a reduced number of OPF problems associated with contingency cases according to a ranking based on a power transfer sensitivity analysis of the transmission lines. Both methods are tested on a 6-bus system and on a realistic 129-bus Italian network model considering supply and demand side bidding. Local marginal prices and nodal congestion prices resulting from the proposed solutions as well as comparisons with results obtained by means of a standard OPF technique are also presented and discussed.

Transmission Congestion Management and Pricing in Simple Auction Electricity Markets

This paper presents a novel technique to analyze, manage and price transmission congestion in electricity markets based on a simple auction mechanism. The proposed technique is basically an iterative rescheduling algorithm, relying on an ``on-line'' evaluation of the transmission system congestion, as defined by a System Security Index (SSI), and associated sensitivities, which are all computed based on formulas that account for voltage stability constraints as well as thermal and bus voltage limits. The methodology is tested using a 3-area test system, a 6-bus test system with both demand-side bidding and inelastic demand, as well as a 129-bus model of the Italian High Voltage transmission system with demand-side bidding. The results obtained for these test systems with the proposed technique are compared with similar results obtained from an optimization-based method.

A spot pricing mechanism for voltage stability

Payment for reactive power services is a part of generator revenue in most established electricity markets today. However, such payments do not have a sound technical basis taking into account the critical role dynamic sources of reactive power play in maintaining voltage stability of the power system. It is also expected that the reactive power will eventually be traded under a spot market arrangement as the markets mature. This paper proposes a spot pricing mechanism for reactive power that takes into account the contributions made by generators both by providing reactive power to meet the current demand and also holding reactive power ‘reserve’ to maintain the system voltage stability in the face of a potential contingency. An OPF based dispatch/pricing model is proposed that optimally allocates real and dynamic reactive reserve among the generators to meet a pre-specified voltage stability margin. Nodal MW and MV Ar spot prices are affected by the desired stability margin because an increase in MV Ar and/or MW demand has the cascading effect of increasing the dynamic MV Ar/MW reserve requirement. Simplistic illustrative examples are presented to develop insights on the theoretical premise. Experiments conducted for a reduced New Zealand North Island power system reveal some interesting impacts of the voltage stability constraint on real and reactive power prices.

A method for voltage stability‐constrained optimal power flow (VSCOPF)

AbstractThis paper presents a novel formulation for solving optimal power flow (OPF) problems with voltage stability constraints. The proposed Voltage Stability Constrained OPF (VSCOPF) formulation is based on voltage sensitivity with respect to total load demand representing the gradient of the P‐V curve at the operating point. In the formulation, voltage constraints are given by a set of equality constraints which must be satisfied by the voltage sensitivity. Since the voltage stability constraints retain a sparse matrix structure, the method based on the proposed OPF formulation may effectively solve large‐scale problems. The feasibility and effectiveness of the proposed method are demonstrated on test problems with 2‐, 49‐, and 2312‐bus systems. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 29–39, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10125

Market dispatch incorporating stability constraints

Stability aspects have often been incorporated in the electricity market dispatch/pricing procedure using trial-and-error methods, or approximated in the dispatch optimisation directly as a set of linear constraints on generation/transmission. This paper presents the preliminary experiences with the development of a market optimal power flow (OPF) model that incorporates both transient and voltage stability constraints. The resultant dispatch and prices are expected to exhibit the impact of accurately modelled stability limits that are hitherto largely unknown. This model allows integrated representation of both voltage and transient stability. It, however, entails very significant computational complexities. A complete resolution of all these issues is beyond the scope of this paper, although some initial thoughts to simplify computation are discussed. The importance of stability constraints on market dispatch and prices is discussed around a simple 9-bus system example.

Reactive power planning incorporating voltage stability

This paper addresses some of the modeling and economic issues pertaining to reactive power planning. We present a new VAR planning model, propose an efficient solution algorithm, and discuss the economic issues. A contingency constrained OPF-based model incorporating (static) voltage stability constraints is developed to analyze VAR support decisions. DICOPT++, a state-of-the-art non-linear mixed integer programming (MINLP) algorithm, is proposed to solve the model efficiently. The sensitivity information elicited from the optimization model may also provide useful aid to network planning that are discussed. The VAR support cost allocation issue is addressed next. The Shapley value criterion of cooperative gaming is proposed to allocate VAR support costs among the loads contributing to voltage instability. The VAR planning model is implemented for the AEP 14-bus test system. The implications of the sensitivity information are discussed using the test system results. The result of the optimization approach is compared with two existing methods viz., Eigen Value (Modal) and Singular Value Decomposition (SVD) methods. Further, we discuss how the outcome of the Modal analysis could be integrated in the optimization model to form a hybrid approach. A numerical example of calculation of Shapley value is provided and, we also compare it with the conventional method of proportional allocation to gain better insight about this criterion.

Market dispatch incorporating stability constraints

Stability aspects have often been incorporated in the electricity market dispatch/pricing procedure using trial-and-error methods, or approximated in the dispatch optimisation directly as a set of linear constraints on generation/transmission. This paper presents the preliminary experiences with the development of a market optimal power flow (OPF) model that incorporates both transient and voltage stability constraints. The resultant dispatch and prices are expected to exhibit the impact of accurately modelled stability limits that are hitherto largely unknown. This model allows integrated representation of both voltage and transient stability. It, however, entails very significant computational complexities. A complete resolution of all these issues is beyond the scope of this paper, although some initial thoughts to simplify computation are discussed. The importance of stability constraints on market dispatch and prices is discussed around a simple 9-bus system example.