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Determining contingency aware dispatch decisions by solving a security-constrained optimal power flow (SCOPF) is challenging for real-world power systems, as the high problem dimensionality often leads to impractical computational requirements. This problem becomes more severe when the SCOPF has to be solved not only for a single instance, but for multiple periods, e.g. in the context of electricity market analyses. This paper proposes an algorithm that identifies the minimal set of constraints that exactly define the space of feasible nodal injections for a given network and contingency scenarios. By internalizing the technical limits of the nodal injections and enforcing a minimal worst-case impact of contingencies to line flows, computational effort can be further improved. The case study applies and analyzes the methods on the IEEE 118 and A&M 2000 bus systems, as well as the German and European transmission systems. In all tested cases the proposed algorithm identifies at least 95% of the network and security constraints as redundant, leading to significant SCOPF solve time reductions. Scalability and practical implementation are explicitly discussed. The code and input data of the case study is published supplementary to the paper under an open-source license. [ABSTRACT FROM AUTHOR]

Chance-constrained economic dispatch (CCED) is widely used to cope with uncertainties brought by renewable energy sources. In CCED, security of power system is guaranteed by restricting risks under permitted level. As the penetration rate of renewable energy increases rapidly, the CCED model may be infeasible because of inadequate system reserve and/or transmission congestion under certain circumstances. Therefore, the curtailment of renewable energy is indispensable to guarantee security in some scenarios for power systems with high penetration of renewable energy. To address this crucial issue, this paper proposes a novel CCED model, where generation of conventional units and curtailment strategies of renewable energy are co-optimized to minimize total operational cost and restrict operational risks. An efficient solution method is developed to schedule generation and curtailment sequentially, in which tractable optimization models are formulated for each step. Numerical tests demonstrate that the proposed model can significantly reduce the probability of emergency control of curtailment compared with conventional CCED models. Furthermore, this solution method also outperforms scenario-based method with significantly improved computational efficiency and higher-quality solution. [ABSTRACT FROM AUTHOR]

The work reported in this paper aims at developing an algorithm for identifying the worst contingencies to be used in a security-constrained optimal power flow problem. A bilevel max-min optimization model is proposed to find the worst contingency scenario while solving an ac optimal power flow problem and considering corrective actions. The objective is to minimize the total cost including generation and load shedding cost while satisfying all relevant constraints. The upper-level problem allows representing contingencies using binary variables. We formulate a second-order cone problem in the lower-level to represent the ac power flow equations. Duality is used to merge the upper- and lower-level problems into a single-level one. The resulting mixed-integer second-order conic problem can be efficiently solved. Three case studies are presented as applications of this novel technique. [ABSTRACT FROM AUTHOR]

In this paper, we propose a scalable and configurable decomposition framework for solving large-scale transmission capacity expansion planning with security constraints under uncertainties. This framework is capable of using both progressive hedging and Benders decomposition algorithms to decompose and parallelize a large-scale problem both vertically and horizontally. A scenario bundling method is also developed to create bundles through three steps, i.e., classification, clustering, and grouping with the objective of maximizing similarity between bundles. This bundling method can improve both quality of results (decreasing optimality gap) and performance (reducing computational time) of the proposed framework. To verify capabilities of the proposed method, it is applied to a reduced ERCOT system with 3179 buses, 4458 branches, and 10 scenarios. The numerical result for this case study shows that the proposed framework can make solving large-scale problems tractable, and provides high quality results (with less than $1\%$ optimality gap) in a reasonable time (around 2.8 days). [ABSTRACT FROM PUBLISHER]

One of the most used methods for long-term hydrothermal operation planning is the stochastic dual dynamic programming (SDDP). Using this method, the immediate and future water opportunity cost can be balanced and an economic-dispatch policy can be defined for multiple reservoirs under inflow uncertainty. In this framework, equipment outages and reserve deliverability are generally disregarded, despite their strong impact on the operative plan. However, recent advances in robust optimization have shown how to endogenously account for security criteria in scheduling models with reduced computational burden. Within this framework, reserve deliverability is ensured across the network via the co-optimization of energy and reserves (ancillary services). In this paper, we propose a new multistage model for planning hydrothermal coordination that co-optimizes the nominal energy dispatch and individual up and down reserve allocations. The main goal of this paper is to address a general $n-K$ security criterion, such that, for each inflow scenario, the system is capable of withstanding the loss of up to $K$ components, i.e., generation or transmission assets. The proposed methodology uses the column-and-constraint generation algorithm to efficiently incorporate a compound umbrella set of contingencies in the SDDP algorithm. Results for the Brazilian power system data corroborate the effectiveness of the proposed model. [ABSTRACT FROM PUBLISHER]

This paper introduces a new method of removing thermal overloads and voltage limits in an electric power system by means of the Evolution of Corrective and Preventive control Actions (ECPA). The goal is to find the minimum number of control actions that solve the identified limit violations at minimum cost. A recombination operator based on form theory allows the codification of control actions in a natural and simple way. ECPA has been tested on the IEEE 30-bus and the IEEE 118-bus systems. The limit violations are solved at minimum cost and with fewer control actions on average than alternative methods. [ABSTRACT FROM AUTHOR]

Isolated microgrid power systems are prone to large frequency and voltage deviations, since they have limited generation and finite inertia and may include pulse power loads and large proportion of dynamic loads. Thus, they require effective power management methods to operate optimally, while satisfying operating and security constraints. In this paper, a novel integrated security-constrained model-based power management approach is proposed for isolated microgrids in all-electric ships during the normal/alert operating state. The new power management method was formulated as a multi-objective optimal control problem. A method based on the Nondominated Sorting Genetic Algorithm II was developed to solve the problem. The developed integrated security-constrained power management approach was applied to a notional all-electric ship computer model. The simulation results, conducted in PSCAD, showed the effectiveness of the new power management method. [ABSTRACT FROM PUBLISHER]

This paper presents a novel approach for the transmission network expansion planning under generalized joint generation and transmission n-K security criteria. The proposed methodology identifies the optimal expansion plan while modeling the power system operation under both normal and contingency states. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing the investment, operation, and system power imbalance costs. The middle-level problem identifies, for a given expansion plan, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency and investment plan by minimizing the system power imbalance. The resulting trilevel program is solved by a primal-dual algorithm based on Benders decomposition combined with a column-and-constraint generation procedure. The proposed approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models. [ABSTRACT FROM PUBLISHER]

This paper discusses how fast-response distributed battery energy storage could be used to implement post-contingency corrective control actions. Immediately after a contingency, the injections of distributed batteries could be adjusted to alleviate overloads and reduce flows below their short-term emergency rating. This ensures that the post-contingency system remains stable until the operator has redispatched the generation. Implementing this form of corrective control would allow operators to take advantage of the difference between the short- and long-term ratings of the lines and would therefore increase the available transmission capacity. This problem is formulated as a two-stage, enhanced security-constrained OPF problem, in which the first-stage optimizes the pre-contingency generation dispatch, while the second-stage minimizes the corrective actions for each contingency. Case studies based on a six-bus test system and on the RTS 96 demonstrate that the proposed method provides effective corrective actions and can guarantee operational reliability and economy. [ABSTRACT FROM PUBLISHER]

This paper studies key aspects of preventive and corrective security strategies to coordinate flexible transmission network infrastructure. To do so, we propose a two-stage stochastic optimization model that can efficiently coordinate available preventive and corrective control actions (pre- and post-contingency) from flexible network technologies, generation, and demand, while explicitly considering the likelihood of postcontingency events and wind/solar uncertainty. This stochastic/probabilistic model constitutes the counterfactual against which current deterministic, preventive operational practices are compared. Flexible network equipment such as HVDC and FACTS devices are efficiently modeled through a tight MILP representation and network losses are also included through a linear representation. Through several case studies, we demonstrate the advantages of probabilistic, corrective security to improve coordination of HVDC and FACTS setpoints and thus reduce network congestion and reserve holding levels, improving the overall efficiency of the system operation. We also quantify the value loss associated with current deterministic, preventive control operational practices when coordinating setpoints of flexible network equipment, demonstrating that adding flexible network technology could even increase system costs under a preventive security approach. [ABSTRACT FROM AUTHOR]

Power systems are increasingly operated in a corrective rather than preventive security mode, which means that appropriate control actions must be taken immediately after a contingency has occurred. This paper proposes an online algorithm for automatically alleviating contingencies such as voltage limit violations and line overloads. Unlike previously proposed approaches, the network itself serves as a natural solver of the power flow equations. This makes it possible to start the implementation immediately and avoids problems caused by modeling errors. Every time the controller receives measurements from the grid, it evaluates the presence of contingencies and computes the optimal corrective actions that can be implemented before the next sampling period, subject to ramping constraints of the generators. These corrective actions are implemented through the standard automatic generation control. Finding the optimal incremental corrective actions is fast because this problem is linearized. The effectiveness of this algorithm at correcting both line overloads and voltage violations is demonstrated using the IEEE-118 Bus test system. [ABSTRACT FROM AUTHOR]

This paper presents a new approach for energy and reserve scheduling in electricity markets subject to transmission flow limits. Security is imposed by guaranteeing power balance under each contingency state including both generation and transmission assets. The model is general enough to embody a joint generation and transmission n-K security criterion and its variants. An adjustable robust optimization approach is presented to circumvent the tractability issues associated with conventional contingency-constrained methods relying on explicitly modeling the whole contingency set. The adjustable robust model is formulated as a trilevel programming problem. The upper-level problem aims at minimizing total costs of energy and reserves while ensuring that the system is able to withstand each contingency. The middle-level problem identifies, for a given pre-contingency schedule, the contingency state leading to maximum power imbalance if any. Finally, the lower-level problem models the operator's best reaction for a given contingency by minimizing the system power imbalance. The proposed trilevel problem is solved by a Benders decomposition approach. For computation purposes, a tighter formulation for the master problem is presented. Our approach is finitely convergent to the optimal solution and provides a measure of the distance to the optimum. Simulation results show the superiority of the proposed methodology over conventional contingency-constrained models. [ABSTRACT FROM PUBLISHER]

This paper proposes a two-stage robust optimization approach to solve the N-k contingency-constrained unit commitment (CCUC) problem. In our approach, both generator and transmission line contingencies are considered. Compared to the traditional approach using a given set of components as candidates for possible failures, our approach considers all possible component failure scenarios. We consider the objectives of minimizing the total generation cost under the worst-case contingency scenario and/or the total pre-contingency cost. We formulate CCUC as a two-stage robust optimization problem and develop a decomposition framework to enable tractable computation. In our framework, the master problem makes unit commitment decisions and the subproblem discovers the worst-case contingency scenarios. By using linearization techniques and duality theory, we transform the subproblem into a mixed-integer linear program (MILP). The most violated inequalities generated from the subproblem are fed back into the master problem during each iteration. Our approach guarantees a globally optimal solution in a finite number of iterations. In reported computational experiments, we test both primal and dual decomposition approaches. Our computational results verify the effectiveness of our proposed approach. [ABSTRACT FROM PUBLISHER]

For large power systems with huge proportions of industrial loads, dynamic var sources (DVSs) such as STATCOMs and generators provide significant protection against short-term voltage instability. Simultaneously optimizing the locations and capacities of STATCOMs and the settings for adjustment coefficients of generator excitation systems is a goal of this paper; thus, we formulate a multi-objective, mixed-integer dynamic optimization (MOMIDO) model subject to short-term voltage security and rotor-angle stability under multiple contingencies. We also present a reduced convex relaxation (RCR) method to handle STATCOM locations (which are integer variables) and to avoid their combinatorial explosion, and convert the MOMIDO model into a multi-objective nonlinear programming problem via Radau collocation. To obtain complete Pareto optimal solutions for the MOMIDO model, we propose a reduced wide normalized normal constraint (RWNNC) method by enlarging the Utopia plane so that the Pareto optimal solutions are covered completely by its vertical projection, while pruning redundant sections on the Utopia plane to reduce the amount of calculations. Moreover, the simulation results on an IEEE standard 39-bus system and a real provincial power system demonstrate that the proposed method can handle integer variables effectively and obtain complete Pareto optimal solutions. [ABSTRACT FROM PUBLISHER]

This paper presents a novel algorithm for the early detection and optimal corrective measures of power system insecurity in an enhanced look-ahead dispatch framework. By introducing short-term dispatchable capacity (STDC) into the proposed look-ahead security management (LSM) scheme, the algorithm is capable of predicting and identifying future infeasibilities that pose security risks to the system under both normal conditions and assumed contingency conditions. An optimal recovery plan can be computed to prevent system insecurity at a minimal cost. Early awareness of such information is of vital importance to system operators for taking timely actions with more flexible and cost-effective measures. This, in addition to the economic benefits studied in the literature, demonstrates the advantage of security improvement of the look-ahead dispatch framework. The performance of the proposed algorithms is illustrated in a revised 24-bus IEEE Reliability Test System as well as in a practical 5889-bus system. [ABSTRACT FROM PUBLISHER]

In response to the challenges brought by uncertain bus load and volatile wind power to power system security, this paper presents a novel unit commitment formulation based on interval number optimization to improve the security as well as economy of power system operation. By using full-scenario analysis, the worst-case impact of volatile node injection on unit commitment is acquired, so that the proposed model can always provide a secure and economical unit commitment result to the operators. Scenarios generation and reduction method based on interval linear programming theory are used to accelerate the solution procedure without loss of optimality. Benders decomposition is also implemented to reduce the complexity of this large-scale interval mixed integer linear programming, and prove the rationality and rigor of our proposed method. The numerical results indicate better secure and economical features of the proposed method comparing with the traditional one. [ABSTRACT FROM PUBLISHER]

This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an n - K security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to K generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions. [ABSTRACT FROM PUBLISHER]

The increased penetration of wind power introduces more operational changes of critical corridors and the traditional time-consuming transient stability constrained total transfer capability (TTC) operational planning is unable to meet the real-time monitoring need. This paper develops a more computationally efficient approach to address that challenge via the analytical deep learning-based surrogate model. The key idea is to resort to deep learning for developing a computationally cheap surrogate model to replace the original time-consuming differential-algebraic constraints related to TTC. However, the deep learning-based surrogate model introduces implicit rules that are difficult to handle in the optimization process. To this end, we derive the Jacobian and Hessian matrices of the implicit surrogate models and finally transfer them into an analytical formulation that can be easily solved by the interior point method. Surrogate modeling and problem reformulation allow us to achieve significantly improved computational efficiency and the yielded solutions can be used for operational planning. Numerical results carried out on the modified IEEE 39-bus and 68-bus systems demonstrate the effectiveness of the proposed method in dealing with complicated TTC constraints while balancing the computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In power system operation, transmission congestion can drastically limit more economical generation units from being dispatched. In this paper, optimal transmission switching as a congestion management tool is utilized to change network topology which, in turn, would lead to higher electricity market efficiency. Transmission switching (TS) is formulated as an optimization problem to determine the most influential lines as candidates for disconnection. In order to relieve congestion without violating voltage security, TS is embedded in an optimal power flow (OPF) problem with AC constraints and binary variables, i.e., a mixed-integer nonlinear programming (MINLP) problem, solved using Benders decomposition. Also, a methodology is presented which provides a guideline to the system operator showing the order of switching manoeuvres that have to be followed in order to relieve congestion. It is also shown that TS based on DC optimal power flow (DCOPF) formulation as used in the literature may jeopardize system security and in some cases result in voltage collapse due to the shortcomings in its simplified models. In order to evaluate the applicability and effectiveness of the proposed method, the IEEE 57-bus and IEEE 300-bus test systems are used. [ABSTRACT FROM PUBLISHER]

A response from the authors of the article "Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem" in the February 2013 issue is presented.

Security constraint is a key component in unit commitment to guarantee reliable generator commitment. Large set of security constraints are notorious for making the problem difficult to solve. Constraint screening, i.e., filtering out non-dominating constraints, is regarded as a powerful tool to address this challenge. This work presents a security-constraint screening that can effectively integrate virtual transaction and capture changes online in real-time or look-ahead markets. The proposed approach takes advantage of both deterministic and statistical methods, which leverages mathematical modeling and historical data. Effectiveness are verified using Midcontinent Independent System Operator (MISO) data. [ABSTRACT FROM AUTHOR]

With the introduction of high voltage direct current (HVDC)-system, especially the voltage source converter (VSC)-based implementation, new degrees of freedom have been made accessible for system operation and for ensuring system security where they can be utilized either in the form of preventive or curative actions. This work presents an optimization model meant to determine a set of preventive and curative relief measures. Thereby, both methods are not calculated in a successive approach, but the optimization of the curative actions is nested into the preventive optimization. By doing so, a feedback can be given in cases the preventive optimization is evolving in regions where no feasible curative actions can be provided. A numerical case study is conducted, where the calculation of the curative set-points is performed with a linearized power flow model. Thereby, an effect is shown, where preventive insecure contingencies appear as curative feasible as the linearized model does not show any violated constraints. [ABSTRACT FROM AUTHOR]

The environmental-economic dispatch (EED) is a bi-objective optimization problem. The Nash bargaining theory provides one way to determine a compromising solution without a clear carbon tax or carbon cap, or any subjective attitudes on both objectives, which yields a non-convex program. This letter proposes a convex formulation for Nash bargaining based EED and a linear programming (LP) based algorithm. Case studies show its scalability on real-world large-scale power systems. [ABSTRACT FROM PUBLISHER]

Due to the variability of renewable resources, the ISO tries to identify do-not-exceed (DNE) limits, which are the maximum renewable generation ranges that the power system can accommodate without sacrificing system reliability. The problem is formulated as an optimization problem whose objective is to find the largest operating ranges of variable resources such that the system remains feasible under any generation realizations within the range. Computing the DNE limits can be conceptually translated into finding the largest uncertain set of a robust optimization problem. Depending on the assumptions on how the system responds to the uncertainty of renewable resources, three alternative approaches are developed to convert the nonstandard robust optimization problem into linear programming, bilinear programming and two-stage robust optimization problems, respectively. Although the linear programming problem is easier to solve as compared to the other two alternatives, its resulting DNE limits are the most conservative. Therefore, the trade-off needs to be considered when deciding which approach is the most appropriate in real-time operation. A 5-bus system and the ISO New England power system are used to test the proposed approaches. [ABSTRACT FROM PUBLISHER]

We propose a probabilistic framework to design an N-1 secure day-ahead dispatch and determine the minimum cost reserves for power systems with wind power generation. We also identify a reserve strategy according to which we deploy the reserves in real-time operation, which serves as a corrective control action. To achieve this, we formulate a stochastic optimization program with chance constraints, which encode the probability of satisfying the transmission capacity constraints of the lines and the generation limits. To incorporate a reserve decision scheme, we take into account the steady-state behavior of the secondary frequency controller and, hence, consider the deployed reserves to be a linear function of the total generation-load mismatch. The overall problem results in a chance constrained bilinear program. To achieve tractability, we propose a convex reformulation and a heuristic algorithm, whereas to deal with the chance constraint we use a scenario-based-approach and an approach that considers only the quantiles of the stationary distribution of the wind power error. To quantify the effectiveness of the proposed methodologies and compare them in terms of cost and performance, we use the IEEE 30-bus network and carry out Monte Carlo simulations, corresponding to different wind power realizations generated by a Markov chain-based model. [ABSTRACT FROM PUBLISHER]