Security-constrained Economic Dispatch Problem Research Articles

Interpretable data‐driven contingency classification for real‐time corrective security‐constrained economic dispatch

AbstractHigh penetrations of renewable energy are crucial for low‐carbon power systems. However, the higher volatility of renewable power generation pushes real‐time operations closer to equipment limits. It is thus important to utilize flexibilities in the system through corrective security‐constrained economic dispatch (SCED) that allows generators to take corrective adjustments after contingencies. The corrective SCED problem, containing a large number of contingencies, and corresponding post‐contingency decisions and constraints, is very large in scale and difficult to solve using purely model‐based methods within the strict time limits of real‐time markets. To accelerate the solution process, this paper develops a novel interpretable data‐driven contingency classification method. Historical data and their potentially useful patterns are utilized in interpretable data‐driven decision tree classifiers. To directly consider continuous features, such as net load values, and to consider imbalanced datasets without much additional complexity, Improved Strong Optimal Classification Trees (ISOCTs) are developed with new branching threshold constraints and category weights in the objective function. ISOCTs are then embedded into a hybrid model‐based and data‐driven framework to guarantee the accuracy of the real‐time active contingency set and the resulting security of dispatch decisions. Numerical testing results demonstrate the classification accuracy, computational efficiency, and interpretability of the proposed approach.

Robust optimisation framework for SCED problem in mixed AC‐HVDC power systems with wind uncertainty

Wind power uncertainties have made the large integration of wind power generating units in the power system highly challenging. One promising solution to overcome the challenges associated with the intermittency of the renewable energy resources (RESs) is to connect areas with diverse renewable energy portfolios via high voltage direct current (HVDC) transmission lines with controllable power transfer capability. The installation of HVDC transmission lines in the power system has resulted in the evolution of conventional alternating current (AC) networks to mixed AC-HVDC power systems. In this study, to address wind power uncertainties in mixed AC-HVDC multi-area power systems, a modified robust optimisation (RO) model for the security-constrained economic dispatch (SCED) problem is proposed. The proposed RO model is used to minimise the generation cost and wind power curtailment under the worst-case scenario of actual wind power. Unlike the existing RO models, the proposed RO model considers a modified uncertainty set based on the wind power admissibility and addresses the budget of uncertainty more accurately to adjust the solution's level of conservatism. Extensive numerical studies demonstrate the economic and operational advantages of the proposed RO model for solving the SCED problem in mixed AC-HVDC power systems with high penetration of RESs.

Fast Economic Dispatch in Smart Grids Using Deep Learning: An Active Constraint Screening Approach

In smart grids, the power supply and demand are balanced through the electricity market to promote the maximization of social welfare. An important procedure in electricity market clearing is to sequentially solve the security-constrained economic dispatch (SCED) problem. However, the scale of the SCED problem with all ${N}-1$ constraints is huge. Directly optimizing such a problem is inefficient and not robust. With the development of smart grids, the frequency of market clearing is increasing, which presents new requirements for fast calculation of SCED. To solve this problem, we propose an intelligent prescreening method to identify the active constraints of SCED based on deep learning. We utilize stacked denoising autoencoders (SDAEs) to extract the nonlinear relationship between the system operating condition and the active constraint set of SCED. Especially, the input/output feature vectors and learning strategy are designed to improve the training efficiency and guarantee the learning accuracy of the deep neural network (DNN). Besides, a fast tuning strategy of neural network parameters based on transfer learning is proposed to handle new scenarios such as topology change. The computational efficiency of the SCED problem is significantly improved while the accuracy is not influenced. The IEEE 30-bus, IEEE 118-bus, and practical utility 661-bus systems are used to demonstrate the effectiveness of the proposed method.

Security constrained economic dispatch of wind‐integrated power system considering optimal system state selection

The increasing penetration of wind power makes it a critical problem to maintain the security and economy in power system operations. This study proposes a security constrained economic dispatch (SCED) strategy that considers optimising system state selection and spinning reserve allocation. The system state selection is judged by the criterion of occurrence probability. Considering the impacts of wind power integration on the outage probability of system component, the over-current protection outage model and voltage protection outage model are employed to calculate the operational outage probabilities of transmission lines and generators, respectively. The fast sorting technique is adopted to select all system states with higher-occurrence probability than the system security threshold. Besides the traditional constraints on system demand and regulation range, the spinning reserve allocation additionally obeys the transmission constraints in the selected states to avoid transmission congestion in contingency situations. Benders decomposition is utilised to partition the SCED problem into the active power dispatch sub-problem and the optimal reserve allocation sub-problem for tractability. A numerical comparison with the traditional N−1 security assessment SCED is given to validate security and economic improvement of the proposed method.

Security Constraint Unit Commitment on Combined Solar Thermal Generating Units Using ABC Algorithm

In this paper, Security Constrained Unit Commitment (SCUC) problem with combined Thermal- Solar generating units is solved using Artificial Bee Colony (ABC) algorithm. SCUC problem aims to obtain minimum generation cost while satisfying the system, network and security constraints. The SCUC problem is divided into Unit Commitment Problem (UCP) which is considered as the master problem and Security Constrained Economic Dispatch (SCED) is considered as the sub problem. Here, both thermal and solar generations are considered in UCP and SCED solutions. Binary Coded ABC Algorithm is used to solve the UCP and Real Coded ABC Algorithm is used for solving the SCED problem. The constraints such as spinning reserves, hourly load demands, ramp up/ramp down limits of generators, minimum up/down limits, line flow and voltage limits are considered in the problem formulation. Beta distribution function is employed to forecast the solar power generation in different seasons. The comparison is carried out with and without incorporating solar generation. The proposed method is validated on a 6 bus system and a South Indian 86 bus utility.

A new nonparametric density estimation for probabilistic security-constrained economic dispatch

Security-constrained economic dispatch (SCED) which is used to minimize the operation cost of the committed units with the constraints of power balance, ramp rate, and unit capacity is one of the routine challenges in power system operation. In this paper, a nonparametric estimation method based on kernel density and linear diffusion is proposed to obtain continuous probability density functions for probabilistic SCED outcomes. It is assumed that the probabilistic SCED problem is the second stage of a two-stage problem, while stochastic security-constrained unit commitment is the first stage. To evaluate the efficacy of the proposed method, a 6-bus test system and IEEE 118-bus system are used as case studies. Implementing the proposed method on these case studies demonstrates the accuracy of the proposed method for large scale power systems.

Measurement-Based Real-Time Security-Constrained Economic Dispatch

In this paper, we propose a measurement-based approach to the real-time security-constrained economic dispatch (SCED). The real-time SCED is a widely used market scheduling tool that seeks to economically balance electricity supply and demand and provide locational marginal prices (LMPs), while ensuring system reliability standards are met. To capture network flows and security considerations, the conventional SCED formulation relies on sensitivities that are typically computed from a linearized power flow model, which is vulnerable to phenomena such as undetected topology changes, changes in the system operating point, and the existence of incorrect model data. Our approach to the formulation of the SCED problem utilizes power system sensitivities estimated from phasor measurement unit (PMU) measurements. The resulting measurement-based real-time SCED is robust against the aforementioned phenomena. Moreover, the dispatch instructions and LMPs calculated with the proposed measurement-based SCED accurately reflect real-time system conditions and security needs. We illustrate the strengths of the proposed approach via several case studies.

Analytical Approach in Computing Nash Equilibrium for Oligopolistic Competition of Transmission-Constrained GENCOs

This paper proposes an analytical solution for bidding strategy problem of transmission-constrained generating companies (GENCOs) in an hour-ahead electricity market. Here, for modeling a bidding strategy problem under a supply function equilibrium model, a bilevel programming (BLP) method is used. In the upper level, the profit of an intended GENCO is maximized, and in the lower level, the independent system operator clears the market via solving a bid-based security-constrained economic dispatch (SCED), in which SCED can be parameterized by GENCOs' bidding strategies. We apply an active-set method to solve a parametric SCED problem. The idea of implementing the active-set method is based on the fact that the optimal solution of a parametric quadratic programming (QP) problem with linear equality constraints can be determined directly. We also decompose generation scheduling, locational marginal prices, and consequently GENCOs' profits, in terms of GENCOs' bidding strategies. In this situation, the BLP transforms to a single-level inequality-constrained optimization, which maximizes GENCO's profit subject to inactive constraints of the lower level. In addition, GENCOs' strategic interactions in oligopolistic marketplace are investigated by using a game theoretic framework, and optimal bidding strategies are determined then by finding the Nash equilibrium of GENCOs' noncooperative competition. Two case studies are provided to illustrate the proposed method; in addition, a numerical method has been conducted to validate the results. The results clarify the impact of each GENCO's bidding strategy on the power flows of transmission lines.

A fuzzy evolutionary programming-based solution methodology for security-constrained generation maintenance scheduling

A traditional mathematical model for maintenance scheduling of power generation systems may give an optimal schedule for a power system with known conditions. A change of the system condition due to uncertainties or sudden changes may render the resulting optimal schedule unsuitable or inapplicable for the power system under study. This paper presents a fuzzy model and an evolutionary programming-based solution technique for the security-constrained maintenance scheduling (MS) problem of generation systems with uncertainties in the load and fuel and maintenance costs. The proposed technique results are fuzzy optimal cost range that reflects the problem uncertainties. The technique solves a decomposed maintenance model of two interrelated subproblems, namely the maintenance and the security-constrained economic dispatch problem. Test results on the IEEE 30-bus system with six generating units reported in this paper are quite encouraging.

Security-constrained economic dispatch using dual quadratic programming

This paper presents a procedure for efficiently handling real power transmission constraints on branch flows and inter-area exchanges to supplement the classic economic dispatch (ED) formulation. A sequential quadratic programming (SQP) method is employed to solve the resulting non-linear programming problem. Each quadratic subproblem is approached by a dual programming technique — a dual feasible starting point is obtained by relaxing transmission limits; constraint violations are then enforced using the dual quadratic algorithm by Goldfarb and Idnani. The Hessian matrix of the Lagrangian function is approximated by a diagonal matrix thus keeping the objective function of each quadratic subproblem separable. Two versions of the proposed procedure exploit different assumptions in the evaluation of the sensitivities of the slack bus balance equation and of transmission constraints. For comparison purposes, the exact model of the security-constrained economic dispatch (SCED) is solved using a standard SQP algorithm taken from the NAG library. Tests on a CIGRE sample network and on actual medium and large-scale systems show that feasible and nearly optimal solutions of the SCED problem can be obtained. The proposed method presents limited computation times and a sufficiently good accuracy; it can be profitably employed whenever computation speed and algorithmic robustness are important issues as in real time operation to update the trajectories of thermal generations, as well as in system planning and hydro-thermal co-ordination studies.

A homogeneous linear programming algorithm for the security constrained economic dispatch problem

This paper presents a study of the simplified homogeneous and self-dual (SHSD) linear programming (LP) interior point algorithm applied to the security constrained economic dispatch (SCED) problem. Unlike other interior point SCED applications that consider only the N security problem, this paper considers both (N-1) and (N-2) network security conditions. An important feature of the optimizing interior point LP algorithm is that it can detect infeasibility of the SCED problem reliably. This feature is particularly important in SCED applications since line overloading following a contingency often results in an infeasible schedule. The proposed method is demonstrated on the IEEE 24 bus test system and a practical 175 bus network. A comparison is carried out with the predictor-corrector interior point algorithm for the SCED problem presented previously (see ibid., vol. 12, no.2, p.803-10, 1997).

An efficient predictor-corrector interior point algorithm for security-constrained economic dispatch

This paper deals with the application of an advanced interior point method to the security-constrained economic dispatch (SCED) problems through successive linear programming. The nonlinear SCED problem is linearized, and then solved by a predictor-corrector interior point method. Besides describing the basic algorithm, the paper focuses on several important issues that are critical to its efficient implementation, including the adjustment of barrier parameter, the determination of initial point, and so on. Computational experiments are conducted to evaluate their impact on the performance of the algorithm. Some suggestions, such as using the feasibility condition to adjust the way of computing barrier parameter /spl mu/ and customizing initial point by adopting a relative small threshold, are proposed to reduce the overall iterations required by the algorithm. The computational results on power systems of 236 to 2124 buses have shown that these suggestions are very effective, improving the performance of the algorithm by a factor of 2. Comparison with a pure primal-dual interior point method is also provided to demonstrate the superiority of the proposed predictor-corrector method.