Hidden power system inflexibilities imposed by traditional unit commitment formulations

In traditional electricity market unit commitment (UC) is done only for the reduction of operating cost. In the deregulated electricity market, for a secure and economical hourly generation schedule of the day ahead market, independent system operator (ISO) executes the security constrained unit commitment (SCUC) problem. The objective of the paper is to develop scheduling algorithm using hybrid particle swarm optimization (PSO) for electric generation that accounts directly for system security requirements. The proposed SCUC formulation includes constraints, such as hourly power demand, system reserves, ramp up/down limits, minimum ON/OFF duration limits. The innovation of our approach is to capture the system security requirements within a network flow sub-problem that is solved in conjunction with the unit commitment problem. To solve such SCUC model, a binary coded particle swarm optimization (BPSO) is used for unit commitment master problem and real coded particle swarm optimization (RPSO) is used for the economic dispatch sub-problem. The effectiveness of the suggested method to solve the SCUC problem is validated on different test systems.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, in this paper we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations.

We present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually nondominated solutions. We study the impact of aggregation on two large-scale UC instances: one from the academic literature and the other based on real-world operator data. Our computational tests demonstrate that, when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Furthermore, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.

An improved multi-area unit commitment and economic dispatch algorithm is proposed. The approach supplements the traditional dynamic programming unit commitment with heuristic adjustments to refine the commitment schedule in each area. A global economic dispatch scheme coordinates the transactions between areas. A new tie-line constraint checking is included which is simple and effective. The overall algorithm can be implemented on an IBM-PC, which can process a fairly large system in a reasonable period of time. Experimental results show the application potential of this method to general multi-area power generation scheduling problems.

The paper describes a procedure developed to assist a generating company in choosing the most convenient bidding strategies for a day-ahead electricity energy market. According to the proposed method, the profit maximization problem is transformed into a minimization problem that can be solved by a traditional hydro-thermal unit commitment program after implementing a few modifications. The paper describes the modifications introduced in a unit commitment program based on the Lagrangian relaxation approach and on a disaggregated Bundle method for the solution of the dual problem. It also presents some results obtained for a realistic data set of hydrothermal power plants. The results are discussed in order to emphasize how the method can be applied to assess the bidding strategy choice of a given company.

The ramp rate of a combined cycle (CC) unit varies significantly with its generation level. In current unit commitment (UC) formulations, ramp rates of CC units are usually modeled as constants. Reserve capabilities may thus be significantly overestimated, causing serious consequences when reserves are needed. When generation-dependent ramp rates are considered, the performance of existing approaches decreases drastically and is not stable. This paper is on effective modeling and resolution of generation-dependent ramp rates in look-ahead UC problems. New ramp and reserve capability functions are established, and the UC formulation is further improved based on existing tight single-unit formulations. Testing results by using branch-and-cut (B&C) show that the solution quality and computational efficiency are improved and the performance is stable. These modifications can be directly incorporated in existing solvers. To exploit the tightened single-unit formation, the problem is also solved by the integration of our recent decomposition and coordination approach with B&C. Testing results show that time-consuming branching operations are much reduced as compared with those of B&C and the coordination is effective, demonstrating great potentials for complicated mixed-integer linear programming problems.

Decision models used in wholesale electricity markets are advancing to manage adequately distributed storage on the grid and grapple with increasing stochasticity and variability in net-load. The goal of this paper is to address these three issues jointly, by introducing a continuous-time stochastic multi-stage reserve unit commitment. Compared to the conventional unit commitment (UC) formulation, the one we propose a) accommodates storage devices with limited energy capacity, b) addresses load uncertainty through a multi-variate scenario tree, and c) models, through a piece-wise polynomial approximation, continuous-time changes in load and generation. In numerical simulations, we compare the system operating cost of our approach relative to relaxations of our proposed formulation, including the conventional UC. The comparisons show the relative impact of the three modeling pillars of our formulation, aimed at capturing storage constraints, uncertainty, and ramping events with inter-hourly variations.

Unit commitment is important in economy and security of power system operation. However, Large penetration of wind power integrated into power system increases the uncertainty on unit commitment. How to efficiently accommodate the uncertainty has been researched widely. In this paper, a new interval unit commitment (UC) formulation based on interval optimization is proposed in which the uncertain wind power is described as fluctuant intervals. Then, the interval UC with uncertainty is transformed into a deterministic form by using order relation of interval number and degree of satisfaction. The transformed model is a two-stage and multi-objective optimization problem. Therefore, the intergeneration projection genetic algorithm is developed to deal with the transformed deterministic model. Finally, the case study with IEEE 39-bus system demonstrated the effectiveness and advantages of the proposed model.

A probabilistic technique is presented to evaluate the effect of standby units, interruptible load, postponable outages and margin time on the response well-being of a generation system. The well-being of the system is quantified in terms of system health and margin, in addition to the system risk index. A procedure is presented which utilises a least costly adjustment to determine how far the acceptable load dispatch must be displaced from the most economic one. A given load dispatch is considered to be acceptable if the response criterion is satisfied. Reliable power system operation requires that a generation system has high healthy state probability in both unit commitment and response studies. The concepts of unit commitment and response well-being are described pictorially to make them more understandable.

In a competitive and deregulated power scenario, the utilities try to maintain their real electric power generation in balance with the load demand, which creates a need for the precise real time generation scheduling (GS). In this paper, the GS problem is solved to perform the unit commitment (UC) based on frequency prediction by using artificial neural network (ANN) with the objective to minimize the overall system cost of the state utility. The introduction of availability-based tariff (ABT) signifies the importance of frequency in GS. Under-prediction or over-prediction will result in an unnecessary commitment of generating units or buying power from central generating units at a higher cost. Therefore, an accurate frequency prediction is the first step toward optimal GS. The dependency of frequency on various parameters such as actual generation, load demand, wind power and power deficit has been considered in this paper. The proposed technique provides a reliable solution for the input parameter different from the one presented in the training data. The performance of the frequency predictor model has been evaluated based on the absolute percentage error (APE) and the mean absolute percentage error (MAPE). The proposed predicted frequency sensitive GS model is applied to the system of Indian state of Tamilnadu, which reduces the overall system cost of the state utility by keeping off the dearer units selected based on the predicted frequency.

The power system inertia is gradually decreasing with the growing share of variable renewable energy (VRE). This may jeopardize the frequency dynamics and challenges the secure operation of power systems. In this paper, the concept of frequency security margin is proposed to quantify the system frequency regulation ability under contingency. It is defined as the maximum power imbalance that the system can tolerate while keeping frequency within the tolerable frequency range. A frequency constrained unit commitment (FCUC) model considering frequency securitymargin is proposed. Firstly, the analytical formulation of system frequency nadir is derived while considering both the frequency regulation characteristics of the thermal generators and the frequency support from VRE plants. Then, the frequency security margin is analytically formulated and piecewise linearized. A novel FCUC model is proposed by incorporating linear frequency security constraints into the traditional unit commitment model. Case studies on a modified IEEE RTS-79 system and HRP-38 system are provided to verify the effectiveness of the proposed FCUC model. The impacts of VRE penetration on system frequency security are analyzed using frequency security margin.

The environmental concerns are having a significant impact on the operation of power systems. The traditional Unit Commitment problem, which to minimizes the fuel cost is inadequate when environmental emissions are also considered in the operation of power plants. This paper presents a Biased Random Key Genetic Algorithm (BRKGA) approach combined with non-dominated sorting procedure to find solutions for the unit commitment multiobjective optimization problem. In the first stage, the BRKGA solutions are encoded by using random keys, which are represented as vectors of real numbers in the interval [0,1]. In the subsequent stage, a nondominated sorting procedure similar to NSGA II is employed to approximate the set of Pareto solution through an evolutionary optimization process. The GA proposed is a variant of the random key genetic algorithm, since bias is introduced in the parent selection procedure, as well as, in the crossover strategy. Test results with the existent benchmark systems of 10 units and 24 hours scheduling horizon are presented. The comparison of the obtained results with those of other Unit Commitment (UC) multiobjective optimization methods reveal the effectiveness of the proposed method.

Due to deregulation of power industries, generation companies strive to attain maximum profit without any compulsion of satisfying consumer's demand. For generation companies, unit commitment is an optimizing task of scheduling units to acquire maximum profit with minimum operation cost. This paper proposes Gbest Artificial Bee Colony algorithm to solve profit based unit commitment (PBUC). The competence of proposed algorithm is endorsed on IEEE 26 unit test system. The simulation results confirm that PBUC has drawn more profit compared to traditional unit commitment.

A novel projected two-binary-variable formulation for unit commitment in power systems