Stability-constrained Optimal Power Flow Research Articles

Self‐adaptive differential approach for transient stability constrained optimal power flow

A new transient stability-constrained optimal power flow (TSCOPF) model for power system optimal operations is presented in this study. The proposed model is a non-linear, non-convex, discrete, and non-differentiable optimisation problem, and very difficult to be solved by classic programming algorithms. In this study, an effective optimisation framework is developed to address the TSCOPF problem. The self-adaptive differential evolution (SaDE) algorithm is employed in the framework, which can effectively eliminate the needs for the strategy selection process and at the same time improve the robustness of the DE search process. The benchmark New England 10-generator, 39-bus system is used to verify the efficacy of this algorithm. The simulation result obtained using SaDE is compared with both conventional mathematical method and the recently published heuristic methods for OPF problems. The simulation results reveal that the SaDE optimisation technique outperforms other algorithms in both terms of robustness and solution quality.

Dynamic Market-Clearing Model in a Hybrid Power Market Using Parallel Processing

AbstractElectricity sector restructuring has introduced competition to the electric power industry by establishing appropriate pricing signals that can maintain the security and economic performance of the power market and help minimize stability problems. In this paper, a market-clearing model for pricing system security in a hybrid power market utilizing pool and bilateral transactions is proposed. The market-clearing procedure uses small-perturbation stability-constrained optimal power flow (SSC-OPF) to help independent system operators (ISOs) adhere to required stability criteria. A contingency screening method in which only transmission line outages that threaten system stability are also considered to reduce the size of the SSC-OPF problem. Using a decomposition method, the determination of small-signal instabilities under an N-1 contingency criterion is specifically divided from the main SSC-OPF problem, and the results of the required stability criteria, along with those of decomposition formulae ...

Advanced application of transient stability constrained‐optimal power flow to a transmission system including an HVDC‐LCC link

In this study, a transient stability constrained-optimal power flow (TSC-OPF) model is proposed and applied to a real case in the currently interconnected Balearic Islands-Iberian Peninsula system. The TSC-OPF retains the dynamics of all generators in the islands with fourth degree transient synchronous generator models and includes a representation of a high-voltage direct current (HVDC) link on the inverter side. The proposed large-scale non-linear optimisation problem, programmed in GAMS and solved using the CONOPT tool, is used to assess the economic impact of the HVDC on the Balearic Islands generation cost under different circumstances, using TSC-OPF and traditional OPF on the dispatch. Different recovery patterns of the HVDC link after a severe fault in the transmission grid are evaluated from the viewpoint of the cost and stability of power generation.

Improving the transient stability-constrained optimal power flow with Thyristor Controlled Series Compensators

Due to the rapid increase of electricity demand and the deregulation of electricity markets, power systems tend to operate closer to stability boundaries. The scheme of preventive control should bring in a tradeoff between economics and security, which are often the two major inconsistent requirements for the daily operation of many power systems in the world. Optimal power flow (OPF) is a powerful tool to weaken the conflict between economy and security, but the main obstacle faced is that, the complexity involved for OPF with transient stability constraints is several orders of magnitude higher than that of conventional OPF with merely static constraints. Therefore, consideration of Transient Stability Constraints in Optimal Power Flow (OPF) problems is becoming more and more imperative. FACTS devices such as Thyristor Controlled Series Compensator (TCSC) can be very effective to power system security in case of a contingency. In this paper, we concentrate on the improving transient stability-constrained optimal power flow to against single contingencies via the use of TCSC. Study results on IEEE 30-bus system have proved the effectiveness of using TCSC to improve transient stability-constrained optimal power flow (TSCOPF).

Unified Analysis of Single Machine Equivalent and Trajectory Sensitivity to Formulate a Novel Transient Stability-constrained Optimal Power Flow Approach

—This article proposes a new transient stability constraint that permits quantifying the degree of instability of a power system from the active power dispatched by generators. Based on this constraint, which is derived from both single machine equivalent and trajectory sensitivity methods, a new transient stability-constrained optimal power flow is formulated in the Euclidian space to preventively control the transient stability in realistic power systems. The validity and the effectiveness of the proposed method are numerically demonstrated in the WSCC 3-machine, 9-bus and Mexican 46-machine, 190-bus systems.

A Hybrid Dynamic Optimization Approach for Stability Constrained Optimal Power Flow

Stability-constrained optimal power flow (SOPF) is an effective and economic tool to enhance stability performance by adjusting initial steady-state operating conditions, with the consideration of rotor angle and short-term voltage performance criteria. SOPF belongs to the category of dynamic optimization problems which are computationally expensive. In order to reduce its computational complexity, a hybrid dynamic optimization approach is proposed for efficient and robust solving SOPF problems. Based on the direct multiple shooting method, this approach combines the algorithmic advantages from existing direct sequential and simultaneous approaches. Coarse-grained parallelism among multiple shooting intervals is explored. A modular-based implementation architecture is designed to take advantage of the loose coupling between time-domain simulation and optimization. Case studies on various test systems indicate that the proposed approach is able to reduce computation time compared with other direct approaches for dynamic optimization. Also, the investigated parallelizations are effective to achieve acceleration on a symmetric multiprocessing platform.

Selective transient stability-constrained optimal power flow using a SIME and trajectory sensitivity unified analysis

A novel approach based on both single machine equivalent (SIME) and trajectory sensitivity methods is proposed to formulate a transient stability-constrained optimal power flow (TSC-OPF) in the Euclidian space, where only one single stability constraint is necessary in the optimization problem to represent all dynamic and transient stability constraints of the multi-machine system. This formulation remarkably reduces the dimension of the optimization problem to one similar to a conventional OPF, resulting in a tractable approach to the preventive control of transient stability in realistic power systems. A unified framework of time domain analysis is proposed, where the transient stability, trajectory sensitivity and SIME analyses are all combined to assess the system's stability and to compute the sensitivity coefficients of the proposed transient stability constraint. Based on these sensitivity coefficients, three non-heuristic selection criteria are proposed to perform the preventive control by rescheduling only a selected number of generators, which is the commonly accepted practice followed by the system's operators. The validity and the effectiveness of the proposed method are numerically demonstrated in the 10-machine 39-bus New England system and Mexican 46-machine 190-bus system.

Eigenvalue‐optimisation‐based optimal power flow with small‐signal stability constraints

The occasional oscillation in large interconnected power system can cause the small-signal stability problem. As a complement to the damping controllers, the small-signal stability constrained-optimal power flow (SSSC-OPF) model has been used to obtain the required stability margin. Applying the approximate technique to SSSC-OPF may not only increase the value of the objective function, but also suffer the oscillation of the iterations during the solving process. In this study, an eigenvalue-optimisation-based non-linear semi-definite programming (NLSDP) model and algorithm is proposed for the small-signal stability constraints. It is a significant challenge to model the SSSC-OPF directly because of the implicit and non-Lipschitz property for the spectral abscissa of the system state matrix. Based on the Lyapunov theorem, the positive definite constraints can express the small-signal stability accurately and equivalently, so that SSSC-OPF can be modelled as NLSDP. Afterward, the NLSDP model is transformed into a non-linear programming problem by formulating the positive definite constraints into non-linear ones, which can be solved by the interior point method finally. Numerical simulations for two systems confirm the validity of the model and the robustness of the algorithm.

Solution of transient stability-constrained optimal power flow using artificial bee colony algorithm

The transient stability constraint should be taken into consideration for the solution of the optimization problems in power systems. This paper presents a solution for the transient stability-constrained optimal power flow (TSCOPF) by a novel approach based on the artificial bee colony algorithm. The formulas of TSCOPF are derived through the addition of rotor angle inequality constraints into optimal power flow relationships. In this nonlinear optimization problem, the objective function is taken into consideration as the fuel cost of the system. The proposed approach is tested on both a WSCC 3-generator, 9-bus system and a IEEE 30-bus system, and the test results obtained are compared to prove the efficiency and effectiveness of the approach with other approaches in the literature.

Voltage Stability Constrained Optimal Power Flow Using NSGA-II

Voltage stability has become an important issue in planning and operation of many power systems. This work includes multi-objective evolutionary algorithm techniques such as Genetic Algorithm (GA) and Non-dominated Sorting Genetic Algorithm II (NSGA II) approach for solving Voltage Stability Constrained-Optimal Power Flow (VSC-OPF). Base case generator power output, voltage magnitude of generator buses are taken as the control variables and maximum L-index of load buses is used to specify the voltage stability level of the system. Multi-Objective OPF, formulated as a multi-objective mixed integer nonlinear optimization problem, minimizes fuel cost and minimizes emission of gases, as well as improvement of voltage profile in the system. NSGA-II based OPF-case 1-Two objective-Min Fuel cost and Voltage stability index; case 2-Three objective-Min Fuel cost, Min Emission cost and Voltage stability index. The above method is tested on standard IEEE 30-bus test system and simulation results are done for base case and the two severe contingency cases and also on loaded conditions.

Two approaches to transient stability-constrained optimal power flow

Formulation of transient stability-constrained optimal power flow (TSC-OPF) and finding a practical solution for the problem have gained much attention recently. In this paper, two approaches to include transient stability constraints in the OPF problem considering detailed dynamic models for generators and their controls are introduced. The first method is based on the maximum relative rotor angle deviation (MRRAD) of generators which suits systems that have specific requirements on MRRAD. The second method represents the transient stability margin of the system based on generators output power (GOP) and hence does not rely on MRRADs. The transient stability boundary can be represented by a nonlinear function of GOP. The Artificial Neural Network (ANN) curve-fitting tool is used to derive a mathematical formulation for the transient stability boundary (TSB). The closed form representation of the TSB is then inserted in the OPF problem as a new constraint. The proposed method is examined using the WSCC 9-bus, the New England 39-bus and the IEEE 300-bus test systems. The results indicate that the proposed methods lead to lower computational time in solving TSC-OPF which has been a serious challenge for this problem.

A Hybrid Method for Transient Stability-Constrained Optimal Power Flow Computation

A hybrid method combining classical deterministic programming technique and evolutionary algorithm (EA)-enhanced stochastic optimization strategy is proposed for more effective and flexible computation of transient stability-constrained optimal power flow (TSC-OPF). The method consists of searching the maximum TSC-feasible solution region with EA and deterministically optimizing an operating point in the found region via a conventional OPF solution. Stability constraints are exactly treated by a rigorous transient stability assessment (TSA) procedure, where complex system model and multi-contingency can be readily considered and stability margin is applied as the transient stability index (TSI) to avoid over-stabilizing. Benefiting from both the EA and the deterministic programming, the proposed method can continuously approach the global optima in a robust, reliable and fast-convergent way. The method is verified on the New England test system and a dynamic equivalent system of a real-world large power grid. Comparing with existing methods, it has provided more economic solutions and better adaptability to multi-swing instability and multi-contingency stabilizing. It can also be a unified approach for solving other stability constrained-OPFs.

A New Practical Approach to Transient Stability-Constrained Optimal Power Flow

This paper presents a new, significantly improved, approach to formulate a global transient stability-constrained optimal power flow (TSC-OPF), where the sets of dynamic and transient stability constraints to be considered in the optimization process are reduced to one single stability constraint. This constraint is derived from dynamic information provided by the SIngle Machine Equivalent (SIME) method and is only expressed in terms of steady-state variables, which allows us to diminish the length of the time-domain simulation to be included into the global TSC-OPF to a single (initial) time step. In this way, the size of the resulting optimization problem is reduced to one very similar to that of a conventional OPF, overcoming the main drawback of global TSC-OPF techniques (its huge dimension) while maintaining its accuracy and improving its practical application to real power networks. Effectiveness of the proposal is demonstrated by numerical examples on the WSCC three-machine, nine-bus system and the Mexican 46-machine, 190-bus system.

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.

Market-clearing for pricing system security based on voltage stability criteria

This paper presents a novel technique for representing system security in the operation of decentralized electricity markets, with special emphasis on voltage stability. The market-clearing algorithm is modeled as voltage stability constrained-optimal power flow (VSC-OPF) problem for providing market solutions by means of a function of complying with the required voltage stability criteria. Benders’ decomposition is applied for solving the VSC-OPF incorporating post-contingency control actions, which is motivated by the improvement of computational efficiency using parallel processing. The proposed VSC-OPF framework also takes into consideration the bilateral contract information, which is integrated into the market-clearing process and, at the same time, the optimal pricing expressions through computing local marginal prices (LMPs) with respect to ensuring voltage stability are derived. VSC-OPF is tested on the IEEE 14-bus benchmark system and the results obtained, when compared to those obtained by means of a conventional OPF, show that the proposed technique is able to improve system security while yielding better market solutions and total transaction levels.

Applications of Stability-Constrained Optimal Power Flow in the East China System

Stability-constrained optimal power flow (SOPF) models for reactive power reinforcement and HVDC control tuning are formulated, several derivative-free solution algorithms are presented and implemented in a prototype, and the behavior of the objective function value as injection space parameters vary is studied using a qualitative approach. Results of the East China 3296-bus system are provided.

Global Transient Stability-Constrained Optimal Power Flow Using an OMIB Reference Trajectory

This paper presents a new approach to transient stability control using global transient stability-constrained optimal power flow (TSC-OPF) methods. Its novelty consists in using the single machine equivalent (SIME) method to perform (and improve) two main important functions of global TSC-OPF approaches: first, SIME is used to efficiently perform the power system transient stability analysis; second, SIME determines a stable one machine infinite bus equivalent rotor angular trajectory that is used as the reference stability constraint, at one specific integration step. In this way, the stability constraint is adjusted by SIME, at each iteration of the TSC-OPF method, in order to accurately reflect power system dynamic behavior. The prowess and main characteristics of the proposed approach are shown by numerical examples.

Application of a Stability-Constrained Optimal Power Flow to Tuning of Oscillation Controls in Competitive Electricity Markets

A novel technique based on a stability-constrained Optimum Power Flow (OPF) algorithm that properly captures important rotor angle and voltage stability conditions is proposed and described. The application of this technique to the optimal tuning of both Power System Stabilizers (PSS) and thyristor controlled series compensators (TCSC) to damp power system oscillations within the context of competitive electricity markets is proposed and discussed as well. The proposed technique is tested on the IEEE 14-bus benchmark system and compared with a "standard" OPF algorithm. The results obtained demonstrate the advantages of the proposed technique over existent dispatching techniques from the point of view of power dispatch and system stability conditions, and especially locational marginal prices.

Enhancements to Stability Constrained OPF to Overcome Sub-optimality

This article revisits the stability constrained optimal power flow (SOPF) model originally developed by the authors. One of the limitations of the SOPF model is that the representation of angular stability rests on assumptions that can lead to a sub-optimal dispatch outcome. The present research enhances the SOPF model to improve upon the quality of the solution. This article demonstrates that the feasible set of a stability-constrained optimal power flow problem can be open and hence the optimal solution may not exist. The article then reviews a step-by-step integration (SBSI) based approach which has the limitation of yielding sub-optimal solutions. A primary objective of the present research is to introduce two algorithms that can be used to find an improved solution, starting with a sub-optimal solution. Finally, the article also discusses several implementation issues including the concepts for dealing with multiple contingencies. Numerical examples are presented to illustrate the methodological aspects.

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