Contingency-Constrained Unit Commitment Research Articles

Uncertainty Integration of the Hybrid Energy Storage System Frequency Response in the Contingency Constrained Unit Commitment

Uncertainty Integration of the Hybrid Energy Storage System Frequency Response in the Contingency Constrained Unit Commitment

N-1-1 contingency-constrained unit commitment with renewable integration and corrective actions

N-1-1 contingency-constrained unit commitment with renewable integration and corrective actions

A robust contingency-constrained unit commitment with an [formula omitted] security criterion

We propose a generalized N-k security criterion, which is called N-αk, and applies it to a robust contingency-constrained unit commitment (CCUC) model. In the previous works, the N-k security criterion takes into account the simultaneous loss of up to k components. However, a robust solution of N-k CCUC model may be over-conservative in most cases. To mitigate this over-conservativeness, we propose a robust N-αk CCUC model which guarantees N-2 security criterion throughout the service hours and adopts N-k security criterion only for a few hours. The operational information is used to define an uncertainty set of N-αk security criterion. In addition, we introduce a constant, which we denote as Δ, to control the conservativeness of the N-αk security criterion. We propose a mixed-integer linear programming formulation for the robust N-αk CCUC problem. The proposed N-αk CCUC model can provide cost savings as well as the robustness of the solutions with a proper criterion setting. Benders decomposition (BD) type cutting plane algorithm is used to solve the proposed model, and maximum feasible subsystem cuts are additionally generated at each BD iteration to improve the performance of the BD algorithm. Numerical case studies on a modified IEEE 118-bus system illustrate the effectiveness of the proposed robust N-αk CCUC model and provide some guidelines for α criterion setting.

Day-Ahead Contingency-Constrained Unit Commitment With Co-Optimized Post-Contingency Transmission Switching

This paper addresses the incorporation of transmission switching in the contingency-constrained unit commitment problem within the context of co-optimized electricity markets for energy and reserves. The proposed generation scheduling model differs from existing formulations due to the joint consideration of four major complicating factors. First, transmission switching actions are considered both in the pre- and post-contingency states, thereby requiring binary post-contingency variables. Secondly, generation scheduling and transmission switching actions are co-optimized. In addition, the time-coupled operation of generating units is precisely characterized. Finally, practical features of modern power systems, such as uncertain nodal net injections and the operation of energy storage, are also considered. The proposed model is cast as a challenging mixed-integer program for which the off-the-shelf software customarily used for simpler models may lead to intractability even for moderately-sized instances. In order to circumvent this computational issue, this paper presents an enhanced and novel application of an exact nested column-and-constraint generation algorithm featuring the inclusion of valid constraints to improve the overall computational performance. Numerical simulations based on the IEEE 118- and 300-bus systems demonstrate the effective performance of the proposed approach as well as its economic and operational advantages over existing models disregarding post-contingency transmission switching.

Interval based transmission contingency-constrained unit commitment for integrated energy systems with high renewable penetration

As the reliance on natural gas to meet electric generation requirements increases, additional operational measures and risks must be considered to better understand the implications of the complex interdependency between the natural gas system and the power system. This paper develops a novel interval optimization framework of contingency-constrained unit commitment for integrated energy systems. Uncertainties in contingencies are captured by interval numbers, which reduces the computational burden compared with other uncertainty representations. Moreover, we incorporate the risk preferences of decision makers in the framework to alleviate the conservativeness of solutions. It is observed that power-to-gas technology can reduce renewable curtailment and offer auxiliary services. Numerical results demonstrate the economic value of power-to-gas in integrated energy systems.

Robust N – k CCUC model considering the fault outage probability of units and transmission lines

Robust optimisation has been applied to the dispatching problem considering fault outage of power systems. The traditional fault outage uncertainty set are too conservative. To solve this problem, a robust contingency constrained unit commitment (CCUC) model considering the outage probability of units and transmission lines is proposed. The proposed model has the following characteristics: (i) the outage probability of units is determined by normal operation time and fault repair time, whereas the outage probability of transmission lines is determined by length and load rate; (ii) based on the probability criterion of unit outage contingencies, the outage probabilities of units and transmission lines are both incorporated into the modelling of uncertainty sets; (iii) the robust CCUC model obtains UC decision of base case and the UC decision under uncertainty scenarios can adjust the output of units by spinning reserve capacity to cope with stochastic fault outage scenarios. The proposed robust CCUC model is solved with Benders-column and constraint generation (C&CG) method combined with Benders decomposition method and C&CG method. Simulations on the modified IEEE-RTS-79 system and IEEE-RTS-96 system demonstrate the effectiveness and reliability of the proposed robust CCUC model.

Distributionally Robust Contingency-Constrained Unit Commitment

This paper proposes a distributionally robust optimization approach for the contingency-constrained unit commitment problem. In our approach, we consider a case where the true probability distribution of contingencies is ambiguous, i.e., difficult to accurately estimate. Instead of assigning a (fixed) probability estimate for each contingency scenario, we consider a set of contingency probability distributions (termed the ambiguity set) based on the $N-k$ security criterion and moment information. Our approach considers all possible distributions in the ambiguity set, and is hence distributionally robust. Meanwhile, as this approach utilizes moment information, it can benefit from available data and become less conservative than the robust optimization approaches. We derive an equivalent reformulation and study a Benders’ decomposition algorithm for solving the model. Furthermore, we extend the model to incorporate wind power uncertainty. The case studies on a 6-Bus system and the IEEE 118-Bus system demonstrate that the proposed approach provides less conservative unit commitment decisions as compared with the robust optimization approach.

Contingency-Constrained Unit Commitment With Intervening Time for System Adjustments

The $N$ -1-1 contingency reliability criterion considers the consecutive loss of two components in a power system, with intervening time for system adjustments between the two losses. In this paper, we consider the problem of optimizing generation unit while ensuring the $N$ -1-1 criterion. Due to the coupling of time periods associated with consecutive component losses, the resulting problem yields a very large-scale mixed-integer linear optimization model. For efficient solution, we introduce a novel branch-and-cut algorithm using a temporally decomposed bilevel separation oracle. The model and algorithm are assessed using multiple IEEE test systems, and a comprehensive analysis is performed to compare system performance across different contingency criteria. Computational results demonstrate the value of considering intervening time for system adjustments in terms of total cost and system robustness.

Contingency-Constrained Unit Commitment in Meshed Isolated Power Systems

This paper presents a mixed-integer linear optimization problem for unit commitment and economic dispatch of power generators in a meshed isolated power system. The optimization problem is referred to as the optimal reserve planning problem (ORPP). The ORPP guarantees that the system frequency is kept above a predefined limit in the event of a contingency. The minimum frequency constraints are formulated using novel sufficient conditions that take into account the system inertia and the dynamics of the power generators. The proposed sufficient conditions are attractive from both a computational and a modelling point of view. We compare the ORPP to a unit commitment problem that only considers the stationary behavior of the frequency. Simulations based on a Faroe Islands case study show that, without being overly conservative, potential blackouts and power outages can be avoided using the ORPP. In the particular case study, the cost increase associated with the additional security provided by the ORPP is less than 3%.

Transmission Contingency-Constrained Unit Commitment with High Penetration of Renewables via Interval Optimization

Reliability is an overriding concern for power systems that involve different types of uncertainty including contingencies and intermittent renewables. Contingency-constrained unit commitment (CCUC) satisfying the “N – 1 rule” is extremely complex, and the complexity is now compounded by the drastic increase in renewables. This paper develops a novel interval optimization approach for CCUC with N – 1 transmission contingencies and renewable generation. A large number of transmission contingencies are innovatively described by treating corresponding generation shift factors (GSFs) as uncertain parameters varying within intervals. To ensure solution robustness, bounds of GSFs and renewables in different types of constraints are captured based on interval optimization. The resulting model is a mixed-integer linear programming problem. To alleviate its conservativeness and to further reduce the problem size, ranges of GSFs are shrunk through identifying and removing redundant transmission constraints. To solve large-scale problems, Surrogate Lagrangian Relaxation and branch-and-cut (B&C) are used to simultaneously exploit separability and linearity. Numerical results demonstrate that the new approach is effective in terms of computational efficiency, solution robustness, and simulation costs.

Contingency-constrained unit commitment with post-contingency corrective recourse

We consider the problem of minimizing costs in the generation unit commitment problem, a cornerstone in electric power system operations, while enforcing an $$N$$ – $$k$$ – $$\varvec{\varepsilon }$$ reliability criterion. This reliability criterion is a generalization of the well-known $$N$$ – $$k$$ criterion and dictates that at least $$(1-\varepsilon _j)$$ fraction of the total system demand (for $$j = 1,\ldots , k$$ ) must be met following the failure of $$k$$ or fewer system components. We refer to this problem as the contingency-constrained unit commitment problem, or CCUC. We present a mixed-integer programming formulation of the CCUC that accounts for both transmission and generation element failures. We propose novel cutting plane algorithms that avoid the need to explicitly consider an exponential number of contingencies. Computational studies are performed on several IEEE test systems and a simplified model of the Western US interconnection network. These studies demonstrate the effectiveness of our proposed methods relative to current state-of-the-art.

Robust n–k contingency constrained unit commitment with ancillary service demand response program

Today, many Independent System Operators (ISOs) establish programs to manipulate the reserve provided by Demand Response (DR) in ancillary service markets. In this study, Ancillary Service DR (ASDR) programs, recently introduced by Federal Energy Regulatory Commission, is integrated to an n–k Contingency Constrained Unit Commitment problem to investigate the capability of the DR Providers (DRPs), newly added ancillary market participants, in mitigating the impacts of simultaneous multiple contingencies in a power system. In the proposed model, an n–k security criterion by which power balance constraint is satisfied under any contingency state comprising simultaneous outages in generation units is investigated in the presence of the ASDR programs. Demand side reserve is supplied by DRPs, which have the responsibility of aggregating and managing customer responses to offer a bid-quantity to the ISO. The proposed formulation is a Mixed Integer Programming problem based on primal-dual optimisation, reported recently in literature. In addition, a detailed discussion about versatile effects of ASDR programs on n–k security criterion is presented to demonstrate the applicability of the proposed model.

Two-stage robust optimization for N-k contingency-constrained unit commitment

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.

Contingency-Constrained Unit Commitment With $n - K$ Security Criterion: A Robust Optimization Approach

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.