Transient Stability Constraints Research Articles

Transient stability-constrained optimal power flow for online dispatch and nodal price evaluation in power systems with flexible AC transmission system devices

This study develops a new method for economic dispatch together with nodal price calculations which includes transient stability constraints and, at the same time, optimises the reference inputs to the flexible AC transmission system (FACTS) devices for enhancing system stability and reducing nodal prices. The method draws on the sensitivity analysis of time-domain transient stability simulation results to derive a set of linearised stability constraints expressed in terms of generator active-powers and FACTS devices input references. The optimal power flow (OPF) formulation based on the Newton's algorithm augmented with the set of stability inequality constraints is applied for forming economic dispatch solution and nodal prices. The solutions obtained also include the Lagrange multipliers associated with all of the constraints. Based on the Lagrange multipliers, individual components, including those associated with stability constraints, of the nodal prices are directly identified for assisting the market participants to make investment decisions. The sensitivity technique for forming the set of transient stability constraints lends itself to parallel-computing implementation. Therefore the additional computing-time requirement is minimal, given that the transient stability simulations can be performed independently of one another and outside the OPF loop. Representative studies and results are presented here.

The Study of Fast Optimal Generator Shedding Based on Predictor-Corrector Method

This paper presents a fast optimal generator shedding algorithm which is on the basis of predictor-corrector method and time domain simulation for transient stability. It includes two parts that are the fast time domain simulation and optimal generator shedding. On the basis of the generator's classical model and load's constant impedance model, this paper use fourth-order Hamming predictor-correction formula to compute differential equations of the system with large step length, in order to improve computing speed. The second part shows how to calculate the sensitivity of transient stability constraint function to control variables, by the application of optimal control theory. Combined with the discrete characteristics of generator shedding, “Micro-step discrete method” is proposed, which is fast, accurate and so on. The advantages of this method are verified by analysis results of New England 39-bus test system.

Allocating the cost of transient stability constraint relief in bilateral electricity markets

In this study, the issue of allocating the cost of transient stability relief in a bilateral electricity market is investigated. The results of a constrained generation scheduling problem can be utilised in two ways to price the cost of a constraint. In the first method, which is the basis of nodal pricing, the Lagrange multipliers of the nodal power balance constraint are used as the price of electricity at various buses. In the second method, which is used in this study, the constraint relief scheme is based on a bid-based adjustment market of increments and decrements offered by generators to be involved in the constraint relief process. In the scheme used in this study, the cost of transient stability relief is first allocated to the individual constraints by different methods and the allocated costs are then allocated to the transactions in proportion to the degree of involvement in that constraint. Three methods are proposed and discussed for allocation of cost to the constraints and the results are compared and commented. The transient energy function (TEF) method is used to calculate the contribution of transactions in the constraints.

An Enhanced Numerical Discretization Method for Transient Stability Constrained Optimal Power Flow

Although many efforts have been made in past years, transient stability constrained optimal power flow (TSOPF) remains one of the most difficult problems in power system. A popular approach to deal with transient stability constraints is the numerical discretization method, in which TSOPF is converted to a generalized large-scale nonlinear programming problem, and interior point method is preferred to solve it. In the numerical discretization and interior point method based TSOPF, more than 80%-90% CPU seconds are used in solving the primal-dual linear system. In order to improve the computational efficiency of numerical discretization TSOPF, an enhanced numerical discretization method is proposed in this paper. The key enhancement of the proposed approach is: considering the truncation error of specific numerical integration algorithm, the transient differential equations are discretized to inequality constraints instead of equality constraints. This key enhancement reduces nearly 50% of the primal-dual linear system's dimension and greatly improves the computational efficiency of interior point based TSOPF algorithm. Case studies on several test cases up to 678-bus system indicate that the enhanced approach is much more computationally efficient than the conventional numerical discretization method and is promising to solve larger TSOPF problems.

Rescheduling of power systems constrained with transient stability limits in restructured power systems

This paper investigates various approaches to relieve the transient stability constraint in restructured power systems. The approaches adopted fall into two broad categories: those based on eliminating the constraint in the least-cost way and those based on eliminating with the least possible rescheduling. The latter group can, on the other hand, emerge in the form of a pool-protected policy in which the bilateral contracts are rescheduled to maintain the stability or in the form of a contract-protected policy in which the realizable bilateral contracts are maximized while minimizing the rescheduling in pool market. Transient energy function (TEF) method is used as a tool to calculate the sensitivity of energy margin to the variations in the magnitude of generation and load. The effectiveness of the method is illustrated by case studies on Western System Coordinating Council (WSCC) 3-machine 9-bus power system and on the 10-machine 39-bus New England test system and the results are compared. The results are also verified by time domain simulations.

Power system blackout model with transient constraints and its criticality

Based on the self-organized criticality (SOC) theory and OTS (OPF with transient stability constraints), this paper proposes a new blackout model which contains three different time scale dynamics, that is, transient dynamics, power flow dynamics, and power system planning dynamics. Not only the cascading failure process but also the characteristics of SOC in power system evolution are investigated in this model. The stability of transient dynamics is evaluated by the transient stability margin index based on stability region boundary. By this index, transient stability constraints of differential-algebraic equations are converted to algebraic equations through sensitivities, thus proper preventive and emergency controls against random contingencies can be determined. On the basis of Value at Risk (VaR) and Conditional Value at Risk (CVaR), two blackout risk assessment indices are proposed in this paper. These two indices could quantitatively reflect the tail property of large-scale blackout distribution, reveal criticality characteristic, and compare the reliability of different systems or the same system under different operation conditions. Simulation results on New England system indicate that the proposed model can represent the dynamics in power system operation and construction, simulate cascading failure, and reveal SOC of power system evolution. Therefore, this model can be applied to assess the power system security level in multi-time scale, and formulate preventive and emergency control strategies. VaR and CVaR indices quantitatively describe the large-scale blackout distribution and reveal criticality characteristics. Copyright © 2010 John Wiley & Sons, Ltd.

Securing Transient Stability Using Time-Domain Simulations Within an Optimal Power Flow

This paper provides a methodology to restore transient stability. It relies on a well-behaved optimal power flow model with embedded transient stability constraints. The proposed methodology can be used for both dispatching and redispatching. In addition to power flow constraints and limits, the resulting optimal power flow model includes discrete time equations describing the time evolution of all machines in the system. Transient stability constraints are formulated by reducing the initial multi-machine model to a one-machine infinite-bus equivalent. This equivalent allows imposing angle bounds that ensure transient stability. The proposed optimal power flow model is tested and analyzed using an illustrative nine-bus system, the well-known New England 39-bus system, a ten-machine system, and a real-world 1228-bus system with 292 synchronous machines.

Total Transfer Capability Assessment Incorporating Corrective Controls for Transient Stability using TSCOPF

Advancements have been made towards inclusion of both static and dynamic security into transfer capability calculation. However, to the authors' knowledge, work on considering corrective controls into the calculation has not been reported yet. Therefore, we propose a Total Transfer Capability (TTC) assessment considering transient stability corrective controls. The method is based on the Newton interior point method for nonlinear programming and transfer capability is approached as a maximization of power transfer with both static and transient stability constraints are incorporated into our Transient Stability Constrained Optimal Power Flow (TSCOPF) formulation. An interconnected power system is simulated to be subjected to a severe unbalanced 3-phase 4-line to ground fault and following the fault, generator and load are shed in a pre-defined sequence to mimic actual corrective controls. In a deregulated electricity market, both generator companies and large load customers are encouraged to actively participate in maintaining power system stability as corrective controls upon agreement of compensation for being shed following a disturbance. Implementation of this proposal on the actual power system operation should be carried out through combining it with the existing transient stabilization controller system. Utilization of these corrective controls results in increasing TTC as suggested in our numerical simulation. As Lagrange multipliers can also describe sensitivity of both inequality and equality constraints to the objective function, then selection of which generator or load to be shed can be carried out on the basis of values of Lagrange multipliers of its respective generator's rotor angle stability and active power balance equation. Hence, the proposal in this paper can be utilized by system operator to assess the maximum TTC for specific loads and network conditions.

Adaptive Evolutionary Programming Incorporating Neural Network for Transient Stability Constrained Optimal Power Flow

This paper presents an adaptive evolutionary programming incorporating neural network for solving transient stability constrained optimal power flow (TSCOPF). The proposed AEP method is an evolutionary programming (EP)-based algorithm, which adjusts its population size automatically during an optimization process. The artificial neural network, which classifies the AEP individual based on its stability degrees, is embedded into the search template to reduce the computational load caused by transient stability constraints. The fuel cost minimization is selected as the objective function of TSCOPF. The proposed method is tested on the IEEE 30-bus system with two types of the fuel cost functions, i.e. the conventional quadratic function and the quadratic function superimposed by sine component to model the cost curves without and with valve-point loading effect respectively. The numerical examples show that AEP is more effective than conventional EP in terms of computational speed, and when the neural network is incorporated into AEP, it can significantly reduce the computational time of TSCOPF. A study of the architecture of the neural network is also conducted and discussed. In addition, the effectiveness of the proposed method for solving TSCOPF with the consideration of multiple contingencies is manifested.

Optimal generation rescheduling with sensitivity-based transient stability constraints

A new generation rescheduling model is proposed for transient stability enhancement of power systems, which can optimally reallocate power generations for eliminating potential transient stability threat. The idea of angle norm has been introduced to develop a sensitivity-based transient stability constraints of the rescheduling model. Trajectory sensitivity mapping technique is studied to evaluate the sensitivity factor of the angle norm at maximum swing angle to the power input of generators. The augmented Lagrangian method is employed to solve the rescheduling problem in an iteration manner. Case studies on the IEEE 50-generator test power system are reported to verify the effectiveness of the proposed generation rescheduling method.

A Study on the Effect of Generation Shedding to Total Transfer Capability by Means of Transient Stability Constrained Optimal Power Flow

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In nowadays deregulated market, total transfer capability (TTC) calculation, which is the basis for evaluating available transfer capability (ATC), has been becoming more significant. During the last decade, transient stability constraints have been included in the optimal power flow approach to maximize TTC. However, no previous work on investigating the effect of generation shedding action to TTC has been reported. Therefore, in this paper, we propose a TTC maximization by means of transient stability constrained optimal power flow considering the generation shedding action. Proper selection of the generator to shed is based on its Lagrange multiplier value of transient stability constraint. Our simulation results show how TTC can be increased to anticipate possible generation shedding. </para>

A Novel PSO Algorithm for Optimal Production Cost of the Power Producers with Transient Stability Constraints

The application of a novel Particle Swarm Optimization (PSO) method called Fitness Distance Ratio PSO (FDR PSO) algorithm is described in this paper to determine the optimal power dispatch of the Independent Power Producers (IPP) with linear ramp model and transient stability constraints of the power producers. Generally the power producers must respond quickly to the changes in load and wheeling transactions. Moreover, it becomes necessary for the power producers to reschedule their power generation beyond their power limits to meet vulnerable situations like credible contingency and increase in load conditions. During this process, the ramping cost is incurred if they violate their permissible elastic limits. In this paper, optimal production costs of the power producers are computed with stepwise and piecewise linear ramp rate limits. Transient stability limits of the power producers are also considered as addi-tional rotor angle inequality constraints while solving the Optimal Power Flow (OPF) problem. The proposed algo-rithm is demonstrated on practical 10 bus and 26 bus systems and the results are compared with other optimization methods.

Optimal production cost of the power producers with linear ramp model using FDR PSO algorithm

AbstractIn practice, the power producers have to be rescheduled for power generation beyond their power limits to meet vulnerable situations like credible contingency and increase in load conditions. During this process, the ramping cost is incurred if they violate their permissible elastic limits. In this paper, optimal production costs of the power producers are computed with ramping cost considering stepwise and piecewise linear ramp rate limits using fitness distance ratio particle swarm optimization (FDR PSO) algorithm. Transient stability constraints are also considered while formulating the optimal power flow (OPF) problem as additional rotor angle inequality constraints. The proposed algorithm is demonstrated on a practical 39 bus New England and 62 bus Indian Utility system with different case studies. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Evaluating the impact of uncertain parameters in power system dynamic simulations

There are typically uncertain parameters in power system models. This paper presents a computational method for evaluating the effect of parameter uncertainty on the dynamic behaviors of power systems. The effect of parameter uncertainty is represented by system trajectory or performance bounds around nominal values. Based on the notion of optimal power flow with transient stability constraints, a set of nonlinear optimization problems is formulated to determine the upper and lower bounds of system trajectories. A successive linear programming approach is suggested to solve these nonlinear optimization problems. The proposed method is evaluated by several test systems. The results show that the proposed method is valid and potentially useful in quantifying the effect of parameter uncertainty in power system dynamic simulations.

Security constrained distributed optimal power flow of interconnected power systems

The security constrained distributed optimal power flow (DOPF) of interconnected power systems is presented. The centralized OPF problem of the multi-area power systems is decomposed into independent DOPF subproblems, one for each area. The dynamic security region (DSR) to guarantee the transient stability constraints and static voltage stability region (SVSR) constraints, and line current limits are included as constraints. The solutions to the DOPF subproblems of the different areas are coordinated through a pricing mechanism until they converge to the centralized OPF solution. The nonlinear DOPF subproblem is solved by predictor-corrector interior point method (PCIPM). The IEEE three-area RTS-96 system is worked out in order to demonstrate the effectiveness of the proposed method.

Dynamic security risk assessment and optimization of power transmission system

The paper presents a practical dynamic security region (PDSR) based dynamic security risk assessment and optimization model for power transmission system. The cost of comprehensive security control and the influence of uncertainties of power injections are considered in the model of dynamic security risk assessment. The transient stability constraints and uncertainties of power injections can be considered easily by PDSR in form of hyper-box. A method to define and classify contingency set is presented, and a risk control optimization model is given which takes total dynamic insecurity risk as the objective function for a dominant contingency set. An optimal solution of dynamic insecurity risk is obtained by optimizing preventive and emergency control cost and contingency set decomposition. The effectiveness of this model has been proved by test results on the New England 10-generator 39-bus system.

Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.

New approach for the nonlinear programming with transient stability constraints arising from power systems

This paper presents a new approach for solving a class of complicated nonlinear programming problems arises from optimal power flow with transient stability constraints (denoted by OTS) in power systems. By using a functional transformation technology proposed in Chen et al. (IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48:327---339, [2001]), the OTS problem is transformed to a semi-infinite programming (SIP). Then based on the KKT (Karush-Kuhn-Tucker) system of the reformulated SIP problem and the finite approximation technology, an iterative method is presented, which develops Wu-Li-Qi-Zhou' (Optim. Methods Softw. 20:629---643, [2005]) method. In order to save the computing cost, some typical computing technologies, such as active set strategy, quasi-Newton method for the subproblems coming from the finite approximation model, are addressed. The global convergence of the proposed algorithm is established. Numerical examples from power systems are tested. The computing results show the efficiency of the new approach.

에너지함수법을 이용한 가용송전용량(ATC) 계산에 관한 연구

가용송전용량(ATC)은 계통내의 한 지역에서 다른 지역까지 실제 전력을 증가시키는 것이다. 지금까지 ATC 계산은 대부분 정상상태에서 실행가능성을 주로 고려하여 계산되어 왔다. 하지만 ATC 평가시 과도안정도로 제약된 ATC 계산은 매우 중요한 부분이다.BR ATC 평가시에는 제약조건으로 열적용량, 전압 및 과도안정도로 제약된 상정사고(n-1)시 안전도 명가가 요구된다.BR 본 논문은 자코비안 행렬의 고유치를 이용하여 상정사고 우선순위를 선정하였고, 에너지 함수법을 이용하여 선로의 열적용량, 전압안정도 및 과도안정도를 고려한 ATC를 계산하였다.

Power Supply Reliability Assessment in UPFC-installed Transmission System for ATC Enhancement Considering Transient Stability

With recent development of power electronics technology, power system stability enhancement and optimal power flow control by using Flexible AC Transmission System (FACTS) devices have so far been studied. The FACTS devices to relieve multiple constraints can also make it possible to enhance Available Transfer Capability (ATC) without construction of new transmission lines. The previous research revealed that ATC is expanded by avoiding multiple constraints in OPF using Unified Power Flow Controller (UPFC). For long-term operation of such ATC-expanded power system, it is necessary to evaluate power system reliability. In this paper, the evaluation method of supply reliability for UPFC-installed power system is proposed. Both thermal capacity and transient stability constraints are considered. The effectiveness of the proposed method is shown by numerical examples for IEEJ East10-machine test system.