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A power system’s operating cost needs to be minimized by satisfying varying load demand while taking into account the prevailing constraints in a multiple unit electrical power system. In this study, by using genetic algorithms (GA), a short-term thermal unit commitment problem was solved and an economical generating unit schedule was made with the solution obtained. Taking into account the negative effects of emissions due to the use of fossil fuels, emission costs were added to the objective function together with fuel and start-up costs. The GA chromosome structure was formed by binary encoding, new generations were selected by roulette wheel selection mechanism and single point crossover was applied. The representation, formulation and the simulation results of the problem for a 5-unit test system during the scheduling hours of the period are presented. The number and the operating hours of the generating units to be committed were determined by satisfying the prevailing constraints. During the planning period, 13360 MW of power demand was met by 755 MW of spinning reserve. Total operating cost was calculated as $430330. Of the total operating cost, 32% consists of emission costs.

As an important application in the power system operation and electricity market clearing, the network-constrained unit commitment (NCUC) problem is usually executed by Independent System Operators (ISO) in an open-looped predict-then-optimize (O-PO) process, in which an upstream prediction (e.g., on renewable energy sources (RES) and loads) and a downstream NCUC are executed in a queue. However, in the O-PO framework, a statistically more accurate prediction may not necessarily lead to a higher NCUC economics against actual RES and load realizations. To this end, this paper presents a closed-loop predict-and-optimize (C-PO) framework for improving the NCUC economics. Specifically, the C-PO leverages structures (i.e., constraints and objective) of the NCUC model and relevant feature data to train a cost-oriented RES prediction model, in which the prediction quality is evaluated via the induced NCUC cost instead of the statistical forecast errors. Therefore, the loop between the prediction and the optimization is closed to deliver a cost-oriented RES power prediction for NCUC optimization. Lagrangian relaxation is adopted to accelerate the training process, making the C-PO applicable for real-world systems. Case studies with real-world data show that the proposed C-PO can effectively improve the NCUC economics as compared to the traditional O-PO.

The widespread presence of contingent generation, when coupled with the resulting volatility of the chronological net-load (i.e., the difference between stochastic generation and uncertain load) in today's modern electricity markets, engender the significant operational risks of an uncertain sufficiency of flexible energy capacity. In this article, we address several operational flexibility concerns that originate from the increase in generation variability captured within a security-constrained unit commitment (SCUC) formulation in smart grids. To quantitatively assess the power grid operational flexibility capacity, we first introduce two reference operation strategies based on a two-stage robust SCUC, one through a fixed and the other via an adjustable uncertainty set, for which the state-of-the-art techniques may not be always feasible, efficient, and practical. To address these concerns and to account for the effects of the uncertainty cost resulting from dispatch limitations of flexible resources, a new framework centered on the adjustable penetration of stochastic generation is proposed. Our hypothesis is that if the SCUC is scheduled with an appropriate dispatch level of stochastic generation, the system uncertainty cost will decrease, and subsequently, the system's ability to accommodate additional uncertainty will improve. Numerical simulations on a modified IEEE 73-bus test system verify the efficiency of the suggested assessment techniques.

We propose an approach to solving the AC network-constrained unit commitment problem (AC-NCUC) of large-scale power systems. This approach relies on solving convex (continuous and mixed-integer) optimization problems. First, we formulate a second-order conic relaxation of the original optimization problem, which renders a mixed-integer second-order conic optimization problem. To solve this problem, we use Benders' decomposition, which decomposes it into a master problem, which is mixed-integer linear, and a subproblem, which is continuous and second-order conic. To improve the convergence of the Benders' algorithm, we add several linear feasibility constraints to the master problem. Since the second-order relaxation of the original problem cannot guarantee AC feasibility of the solution found, we ensure such feasibility by solving a sequence of continuous convex optimization problems. We numerically validate the proposed approach using a Texas 2000-bus system.

Reducing uplift payments has been a challenging problem for most wholesale markets in the U.S. The main difficulty comes from the discrete decision-making and non- linear objective function in the unit commitment (UC) problem. Recently, the convex hull pricing approach has shown promises to reduce the uplift payments, in which efficient algorithms are available when i) the convex hull description for each unit and ii) the convex envelope for the objective function are available. Following this framework, in this paper, we provide network-flow-based compact extended formulations for each UC considering ramping constraints, different initial statuses, and maximum start-up restrictions. Meanwhile, by using a piece-wise linear approximation of a quadratic cost curve in the objective function, we show that the corresponding piece-wise linear convex envelope converges to the quadratic envelope as the number of pieces increases in the convex hull pricing problem. The final computational experiments on a revised IEEE 118-bus system indicates the effectiveness of the proposed approach. The trade-off between the cost-saving and computational time improvement is also reported as a reference for further usage.

The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that is feasible to a carefully chosen number of scenarios. A crucial step in the scenario approach is to compute the cardinality of essential sets, which is the smallest subset of scenarios that determine the optimal solution. This paper addresses the challenge of efficiently identifying essential sets. For convex problems, we demonstrate that the sparsest dual solution of the scenario problem could pinpoint the essential set. For non-convex problems, we show that two simple algorithms return the essential set when the scenario problem is non-degenerate. Finally, we illustrate the theoretical results and computational algorithms on security-constrained unit commitment (SCUC) in power systems. In particular, case studies of chance-constrained SCUC are performed in the IEEE 118-bus system. Numerical results suggest that the scenario approach could be an attractive solution to practical power system applications.

To ensure powersupply–demand balance under the increasing penetration of wind power, the existing nonanticipative robust unit commitment models (NRUCs) co-optimize the commitment status and the dispatch policy of power sources. Exploiting the fact that the wind power uncertainty reduces over time, this article proposes an NRUC where determining the dispatch policy is delayed until the uncertainty decreases. The proposed NRUC features three decision-making problems sequentially solved under different degrees of uncertainty. The first decision-making problem is formulated as an intractable three-stage robust optimization problem. To solve this problem, a suboptimal approach is developed where a constraint is imposed on the dispatch policy so that the transmission capacity constraint is met regardless of the dispatch level. Results of simulations on a 24-bus and a 300-bus test system show that the proposed NRUC outperforms existing NRUCs regarding feasibility and optimality under currently severe but decreasing wind power uncertainty.

This paper proposes a new model of scenario-based security-constrained unit commitment (SCUC with BESSs. By formulating such a model as a mixed-integer programming (MIP) problem, we can obtain the optimal control strategy of units and BESSs to reduce the operating cost. To solve this MIP with the proposed model, we propose a new learning-based approach to solve the security-constrained unit commitment (SCUC) problem. The proposed deep neural network (DNN)-based SCUC algorithm (DSCUC) has two main stages. First, DSCUC trains a DNN to obtain the binary unit commitment decisions. Then, the continuous variables corresponding to unit power outputs are solved by a small-scale convex optimization problem. In contrast to the existing work, the DSCUC algorithm eliminates the need of explicitly considering the scenario-based security constraints in the optimization problem, and thus greatly reduces the computational complexity. The average gap to the optimal solution is as small as 0.0964%. The algorithm is scalable in the sense that the computational time is reduced from about 1300 seconds to about 0.7 second in a 10-unit and 200-scenario system. Besides, the computation time remains almost constant when the number of scenarios increases. More than 4.70% operating cost is reduced by incorporating BESSs in the system.

Rapid growth of gas-fired generators strengthens the interdependency of electricity and natural gas markets. To meet the uncertainty challenge, a robust day-ahead market clearing framework for the integrated electricity and natural gas system (IEGS) is presented. First, a robust security-constrained unit commitment (SCUC) model is built considering the joint dispatch of ancillary services. Regulation-up/down reserve is scheduled to balance electrical load/wind power uncertainties, spinning reserve is to manage N-1 generator outage, and natural gas reserve is to withstand gas load uncertainty and provide fuel for gas-fired electrical reserve. The SCUC model is a two-stage mixed-integer nonlinear optimization problem so that a sequential linear approximation-based Column & Constraint Generation (SLA-based C&CG) algorithm is proposed. Then, according to SCUC solutions, an economic dispatch model is derived to obtain market clearing and pricing results. Based on locational marginal pricing, novel definitions of electrical energy, natural gas and multiple ancillary service prices are proposed, which can reflect network limits and uncertainty effects. Numerical cases on two test IEGSs and a provincial-level IEGS demonstrate the high accuracy of proposed SLA-based C&CG algorithm and the impact of uncertainties on market clearing.

Solving the unit commitment (UC) problem is one of the most complicated issues in power systems that its exact solving can be calculated by perfect counting of entire possible compounds of generative units. UC is equated as a nonlinear optimization with huge size. Purpose of solving this problem is to programming the optimization of the generative units to minimize the full action cost regarding problem constraints. In this article, a modified version of ant colony optimization (MACO) is introduced for solving the UC problem in a power system. ACO algorithm is a powerful optimization method which has the capability of fleeing from local minimums by performing flexible memory system. The efficiency of proposed method in two power system containing 4 and 10 generative units is indicated. Comparison of obtained results from the proposed method with results of the past well-known methods is a proof for suitability of performing the introduced algorithm in economic input and output of generative units.

Bulk integrated electricity and gas systems (IEGSs) introduce complex coupling relations and induce synergistic operation challenges. The growing uncertainty arising from the renewable power generation in the IEGS further aggravates the synergistic problems. Considering the availability of historical wind power generation data, this paper adopts a two-stage sample robust optimization (SRO) model, which is equivalent to the two-stage distributionally robust optimization (DRO) model with a ${\text{type}} - \infty $ Wasserstein ambiguity set, to address the wind power penetrated unit commitment optimal energy flow (UC-OEF) problem for the IEGS. Compared to the equivalent DRO model, the two-stage SRO model can be approximately transformed into a computationally efficient form. Specifically, we employ linear decision rules to simplify the proposed UC-OEF model. Moreover, we further enhance the tractability of the simplified model by exploring its structural features and, accordingly, develop a solution method. Simulation results on two IEGSs validate the effectiveness of the proposed model and solution method.

In this paper, a Frequency Stability Constrained Unit Commitment (FSCUC) model is presented. The on/off status of generating units, generation levels and operating reserves are optimized to minimize the operational daily costs. The frequency stability constraints are included in the proposed FSCUC model to guarantee the safety of System Frequency Response (SFR) under sudden generation outages. A new multi-area SFR model is proposed to capture the regional dynamics of system frequency with considering the impacts of transmission network. An SFR model is developed for each electric region and then the resulted regional SFRs are coupled via a set of constraints. In order to enhance the primary SFR and keep the daily operating point at its economic schedule, Flywheel Energy Storage (FES) devices are utilized in the proposed FSCUC model. The proposed multi-area SFR model allows the optimal allocation of operating reserve and the accurate modeling of FESs in FSCUC model. The proposed FSCUC model is formulated as a Mixed Integer Linear Programming (MILP) problem and is applied over the IEEE 118-bus test system to show the accuracy of the proposed multi-region SFR and the impact of FES in frequency support. The developed MILP model is solved using CPLEX in GAMS.

In this paper, we propose a novel hybrid algorithm based on MAX-MIN Ant System version of ant colony optimization coupled with quadratic programming (MMAS-QP). Quadratic programming is used to optimize the Economic Dispatching process and MMAS for planning the switching schedule of a set of production units. The algorithm is implemented in MATLAB software environment for two systems, one is 4 generating units running for 8 hours, and the other is 10 generating units running for 24 hours. The impact of heuristic parameters on the behavior of the algorithm is highlighted through the parameters setting. Results obtained shows improved solution compared to several methods such as Modified Ant Colony Optimization (MACO), particle Swarm Optimization combined with Lagrange Relaxation (PSO-LR), Swarm and Evolutionary Computation (SEC), Particle Swarm Optimization combined with Genetic Algorithm (PSO-GA). The proposed method improves sufficiently the quality of the solution as well as the execution time.

This paper proposes a three-stage unit commitment model for the market operation of transmission and distribution coordination under the uncertainties of renewable generation and demand variations. The first stage is for the independent system operator (ISO) that determines the commitment decisions of the transmission-level generators and the distribution-level system reconfiguration; the second stage optimizes the transmission economic dispatch; then distribution system operators (DSOs) in the third stage perform their economic dispatch and exchange information with the ISO at the boundary nodes. Between the transmission and distribution networks, not only conventional thermal generators but renewables and variable demands are considered, which are tackled via a multi-stage stochastic programming approach. The model adopts a convexified AC branch flow formulation in the distribution system. We devise a generalized nested L-shaped algorithm to solve the proposed framework in an efficient manner. Numerical experiments on multi-scale test systems corroborate the efficacy of this strategy.

Optimal dispatch of modern power systems often entails efficiently solving large-scale optimization problems, especially when generators have to respond to the fast fluctuation of renewable generation. This paper develops a method to learn the optimal strategy from a mixed-integer quadratic program with time-varying parameters, which can model many power system operation problems such as unit commitment and optimal power flow. Different from existing machine learning methods that learn a map from the parameter to the optimal action, the proposed method learns the map from the parameter to the optimal integer solution and the optimal basis, forming a discrete pattern. Such a framework naturally gives rise to a classification problem: the parameter set is partitioned into polyhedral regions; in each region, the optimal 0-1 variable and the set of active constraints remain unchanged, and the optimal continuous variables are affine functions in the parameter. The outcome of classification is compared with analytical results derived from multi-parametric programming theory, showing interesting connections between traditional mathematical programming theory and the interpretability of the learning-based method. Tests on a small-scale problem demonstrate the partition of the parameter set learned from data meets the theoretical outcome. More tests on the IEEE 57-bus system and a real-world 1881-bus system validate the performance of the proposed method with a high-dimensional parameter for which the analytical method is intractable.

Energy storage unit (ESU) is playing an increasingly important role in load shifting and uncertainty mitigation. This paper aims to quantify the value of ESU in the unit commitment (UC) with renewable generation. By treating the power and energy capacities of ESU as continuous parameters, the stochastic UC problem is cast as a multi-parametric mixed-integer linear program (mp-MILP), whose optimal value function (OVF) gives the relation between storage capacity and the daily UC cost in an analytical manner. It encompasses abundant sensitivity information, and its surface can be easily visualized. The reduced cost compared with the benchmark case without storage can be regarded as the value of ESU. As a potential application, the OVF is used to formulated an optimal storage sizing problem that maximizes the ratio between the reduced operation cost and the investment cost, ensuring the minimum time of cost recovery. The solution consists of two steps: the first step constructs the OVF parameterized in storage capacity; the second step reformulates the fractional storage sizing program into an MILP, leveraging the expression of the OVF and variable transformations. Case studies conducted on the IEEE 9-bus system and IEEE 118-bus system illustrate how the OVF offers useful reference for power system operation and planning. The proposed optimal sizing model shows advantages in efficient utilization of investment in terms of payback time and rate of return.

This paper presents an algorithm to solve the unit commitment problem in a power system. The proposed algorithm employs the Salp swarm algorithm technique to search the optimum unit schedule for a particular daily demand pattern and specific time horizon. Different constraints are taken into consideration, transition cost (start-up and shut down )cost, mean-up time, mean-down time, spinning reserve, and power balance. The proposed algorithm is applied to 10-units and 26-unit. The obtained results are compared with other methods. It reveals the robustness of the proposed algorithm in terms of minimizing overall running costs.

Generation expansion planning (GEP) is one of the most important decision making activities in electric utilities. The electric power industry in the United States is being restructured with the passage of regulation by the Federal Energy Regulatory Commission. Least‐cost GEP is to determine the minimum‐cost capacity addition plan that meets forecasted demand within a pre‐specified reliability criterion over a planning horizon. A global optimization technique using genetic algorithm (GA) has been successfully applied to various areas of power system such as economic dispatch, unit commitment, reactive power planning, and power plant control. The GA‐based approaches for least‐cost GEP have several advantages. Optimal GEP is traditionally focused on minimizing the total investment and satisfying operation constraints. Solving a least‐cost GEP problem is equivalent to finding a set of optimal decision vectors over a planning horizon that minimizes an objective function under several constraints.

The Unit Commitment (UC) problem is a combinatorial optimization problem in power system operation with the key focus on achieving optimum commitment schedule of the generators for forecasted demand and spinning reserve. The computational complexity to determine a solution for the UC problem grows exponentially with the number of generators and system constraints. In this paper, the UC problem is formulated as a mixed-integer optimization problem and solved using novel Adaptive Binary Salp Swarm Algorithm by considering minimum up/down time limits, prohibited operating zones, spinning reserve, valve-point effect, and ramp rate limits. The proposed algorithm is tested for efficiency on the standard 10-unit system, 26-unit RTS system, 54-unit IEEE 118-bus system, 20, 40, 60, 80, and 100-unit systems. Additionally, an Adaptive Multi-Objective Binary Salp Swarm Optimization Algorithm is proposed for resolving the bi-objective emission constrained UC problem and tested using a 10-unit system. The obtained results are analyzed for positive differences against other algorithms from the literature. The statistical analysis exhibits the efficiency of the proposed method for large scale real-time systems.

This paper is concerned with the problem of Security-Constrained Unit Commitment (SCUC) which is a long-standing challenge in power system engineering faced by system operators and utility companies on a daily basis. We consider a detailed variant of this problem that suffers from complexities posed by the presence of binary variables, the uncertainty of renewable sources and security constraints. A convex relaxation is formulated which is capable of finding feasible solutions within a provable distance from global optimality. We demonstrate the performance of this approach on detailed and challenging instances of SCUC with IEEE and PEGASE benchmark cases from Matpower . The proposed approach is able to handle over 12,000 binary variables and 2 million continuous variables with significant improvement in solution quality over commonly-used off-the-shelf solvers and other methods of convex relaxation.

We study decomposition methods for two-stage data-driven Wasserstein-based DROs with right-hand-sided uncertainty and rectangular support. We propose a novel finite reformulation that explores the rectangular uncertainty support to develop and test five new different decomposition schemes: Column-Constraint Generation, Single-cut and Multi-cut Benders, as well as Regularized Single-cut and Multi-cut Benders. We compare the efficiency of the proposed methods for a unit commitment problem with 14 and 54 thermal generators whose uncertainty vector differs from a 24 to 240-dimensional array.

This paper applies the sine cosine algorithm to the operation planning of wind-penetrated thermoelectric systems considering wind-related uncertainties, which is a mixed-integer nonlinear programming problem often referred to as thermal unit commitment with power integration. The proposed method, denominated hybrid sine cosine algorithm (HSCA), is based on heuristic information derived from sensitivity indexes obtained from priority lists and power dispatch evaluations regarding the thermoelectric system operation. Wind uncertainty was managed by two methodologies, which are extensions of the HSCA, through a set of predicted generation scenarios. One is based on the median wind power generation (M-HSCA), whereas the other is based on the probability distribution matrix (PDM-HSCA). Results have shown that the proposed method is reliable since it guarantees the attendance of all constraints. Furthermore, concerning the operational cost values obtained, it proved itself competitive when compared to other methods found in the literature.

This paper proposes a resilient and secure configuration for coastal distribution grids by integrating the security constraint unit commitment (SCUC) and mobile marine microgrids (MMMGs). In the proposed configuration, MMMGs can be connected to the coastal distribution grids in both normal and post-disaster operations. It is assumed that both MMMGs and SCUC networks include both dispatchable (e.g., gas turbines and diesel generators) and nondispatchable generators (e.g., photovoltaics and wind turbines). The proposed problem consists of realistic formulations that seek to minimize the total MMMGs and SCUC operation costs, while maximizing distribution grid resiliency. A heuristic technique, known as the collective decision optimization algorithm, is employed to address the complexity and nonlinearity of the formulated problem. Moreover, the unscented transform technique is adopted to model the uncertainties associated with renewable energy sources output and load demand. To show the effectiveness and merits of the proposed configuration, the IEEE 69-bus distribution network is selected and tested for both normal and post-disaster operations.

In centralized approaches for the network-constrained unit commitment problem, the dominant way to formulate the linearized power flow problem is based on sensitivity factors such as power transfer distribution factors (PTDF formulation), instead of using phase-angle variables (b-theta formulation). The PTDF formulation enables various exploits of the problem structure, and those exploits grow in importance with the problem size. While these exploits exist for centralized approaches, new challenges arise for distributed approaches that are based on regional decomposition. In distributed approaches, additional constraints for tie lines need to be added to the PTDF formulation. At the same time, the advantages of the PTDF formulation diminish, since a distributed approach often solves smaller-sized unit commitment (UC) problems for each region in an iterative manner until convergence is achieved. This paper explores the performance of distributed algorithms for network-constrained UC problems based on two ways of formulating the linearized power flow problem for the power grid: PTDF-based and phase-angle-based. The performance of the two mathematical models is analyzed at different degrees of decomposition. Numerical simulations are performed to solve 24-h unit commitment problems for a Polish 3012-bus system. The results show that when the number of buses in each subproblem is large and binary constraints are enforced, the PTDF formulation performs better. The results also show that partitioning into more regions may take more iterations to reach desired solution quality, although each iteration takes less time. This trade-off need to be considered in the application of distributed unit commitment algorithms.

The convergence of the electric power industry toward the competitive framework throughout the world has led to a market environment replacing the traditional monopolistic scenario. It has given rise to more efficient production and distribution of electricity, provided a better choice to market participants while maintaining the security and reliability of the power supply. Earlier power utilities had been producing electrical power with the objective to minimize the costs and demand, as well as reserves, were met. Under the new structure, generation companies (GENCOs) schedule their generators to maximize profit. This paper uses a new approach to deal with profit-based unit commitment (PBUC), considering the conditions of power and reserve. The proposed method allows GENCO to decide how much power and reserve should be sold in the markets to achieve maximum profit. For the PBUC problem, three computational techniques, namely ANTIGONE, COUENNE, and BARON in general algebraic modeling system (GAMS), have been applied on three test case studies comprising three, ten, and hundred thermal units in a day-ahead power market. The uncertainty in the energy spot price has been considered using Monte Carlo simulation approach. The various diversified constraints such as system energy load, spinning reserve, ramp rate, unit up and downtime imposed on the PBUC problem have been considered while solving the problem. Simulation results demonstrate that the BARON method has provided better results and has outperformed over the ANTIGONE and COUENNE methods and previously existing techniques reported in the literature in terms of solution quality, the satisfaction of constraints, and an ability to solve large-scale test system.

The main objective of the paper is to minimize the use of conventional generators and optimize the fuel cost. To minimize the use of conventional generators, solar thermal power plant (STPP) is proposed in this paper. An approach for optimal location of STPP is also proposed in this paper. To minimize the fuel cost, firstly unit commitment (UC) is applied in conventional generators. Then genetic algorithm (GA) is used to optimize the fuel cost of committed generators. The suggested method is tested on an IEEE 14 bus test system for 24 hr. schedule with variable load. The effectiveness of the proposed methodology is illustrated in three cases. Case 1 is used to identify the STPP location to reduce the fuel cost of conventional generator. In Case 2, unit-commitment is applied to save considerable fuel input and cost. In order to optimize the committed fuel cost, a genetic algorithm is applied in Case 3.

There is a continuous need to improve the computational efficiency of the Unit Commitment (UC) in the power system and electricity market operations. Studies show that most of the transmission constraints are inactive in the UC. If the inactive constraints can be identified and curtailed from the model, the computational time can be significantly reduced. A redundant and nonbinding transmission constraints identification method combining the economic and physical insights of the UC is proposed in this paper. The economic insights are reflected in the cost-based schedule without transmission constraints, which is solved as the base result. The output and power flow transfer caused by congestion management, which shows the physical insight, are simulated based on the cost-based schedule to identify the inactive constraints. The inactive constraints can be efficiently identified by solving the problem without transmission constraints once instead of using several iterations. A case study shows that the proposed method can identify many inactive constraints that cannot be identified by the CPLEX presolving process, which can significantly improve the computational efficiency.

The unit commitment problem with uncertainty is considered one of the most challenging power system scheduling problems. Different stochastic models have been proposed to solve the problem, but such approaches have yet to be applied in industry practice because of computational challenges. In practice, the problem is formulated as a deterministic model with reserve requirements to hedge against uncertainty. However, simply requiring a certain level of reserves cannot ensure power system reliability as the procured reserves may be nondispatchable because of transmission limitations. In this paper, we derive a set of feasibility cuts (constraints) for managing the unit commitment problem with uncertainty. These cuts eliminate unreliable scheduling solutions and reallocate reserves in the power system; they are induced by the extreme rays of a polyhedral dual cone. This paper shows that, with the proposed reformulation, the extreme rays of the dual cone can be characterized by combinatorial selections of transmission lines (arcs) and buses (nodes) of the power system. As a result, the cuts can then be characterized using engineering insights. The unit commitment problem with uncertainty is formulated as a deterministic model with the identified extreme ray feasibility cuts. Test results show that, with the proposed extreme ray feasibility cuts, the problem can be solved more efficiently, and the resulting scheduling decision is also more reliable.

Optimizing the hydro unit commitment (HUC) has the potential to increase water use efficiency. However, the large number of variables, along with some nonlinear and non-concave constraints, present a huge challenge to the efficient solution of the HUC problem. For hydropower stations including multiple power plants that have different hydraulic heads, the problem is even more difficult. In this paper, we address this complex HUC problem using a two-layer nested optimization method. First, the total load demand is allocated to each power plant using a novel distribution rate. Thus, in the outer layer, a cuckoo search algorithm optimizes the distribution rate and each unit’s on/off status, while in the inner layer, the load demand of each plant is allocated to online units through dynamic programming. China’s Gezhouba Hydropower Station is selected for a case study. It is shown that: (1) the optimized water consumption is, on average, 1.71% lower than that of actual operations; (2) the optimized status of units vary smoothly with fewer startup/shutdown events; and (3) the optimization performance in non-flood seasons is better than that in flood seasons. These findings verify that the two-layer nested optimization method is an effective means of solving HUC problems for hydropower stations including multiple hydro plants with different hydraulic heads.

In this paper, we tackle the hydro unit commitment problem and scheduling in a hydro valley. We first decompose the problem into several simpler subproblems, one for each reservoir/plant. Then, we model each of them as an optimization problem on graphs with or without resource constraints. We compare our method with a commercial solver for mixed integer linear programming, run on a formulation of the problem and show promising results.

Block orders are increasingly adopted in many electricity markets as they enable power producers to implicitly express their unit commitment characteristics and address price volatility risks. However, previous work on the optimal offering problem of a price-taking producer participating in such markets has only considered the simplest type of block orders (regular block orders-RBO) and has neglected relevant realistic market regulations. This paper addresses these simplifications by proposing a new optimal offering model which also considers the more complex profile block orders (PBO) and linked block orders (LBO). This model is generic in that it can treat the block orders time spans either as fixed parameters (following the modelling approach of previous work) or as endogenous decision variables, which constitutes a completely novel modeling approach. The presented case studies demonstrate that this novel approach yields a tremendously lower number of binary variables and more efficient computational performance, when PBO and LBO are considered. Furthermore, the case studies analyze the physical conditions under which the introduction of different types of block orders increases the examined producers profit.

The power system planning requires the simulation of unit commitment (UC) for long time periods up to multiple years or decades which is conducted with production cost modeling (PCM) and usually ends up solving a number of mixed integer programming problems. The development of concentrating solar power (CSP) raises the computational burden of PCM dramatically due to its complex structural and operational characteristics, small unit capacity and large unit number. To improve the PCM efficiency for power systems with large scale CSP generation, a CSP clustering method is proposed based on a novel CSP unit model where the startup and heat accumulation process is considered to simulate CSP operation properly and avoid infeasible operation schemes. In the CSP clustering method, a series of CSP units are modelled in clusters and the numerous binary variables are replaced by integer ones. The number of the variables can be greatly reduced and so is the problem scale. The case studies on the modified IEEE-RTS 1979 have verified the validity and effectiveness of the proposed model and method. The CSP clustering method well outperforms the aggregated unit model which is introduced for comparison. The solution time for the UC with CSP is dramatically reduced (even by 1–2 orders of magnitude) with high accuracy especially the generation cost whose deviation is usually below 0.1%. The proposed method shows great potential in power system planning and operation with large-scale CSP generation.

Coordination efficiency between different energy sectors with privacy preservation has become a technical bottleneck in distributed operation of the integrated electricity and heat systems (IEHS). This article investigates, for the first time, an equivalent model-based non-iterative solution for this issue. An equivalent model of district heating networks (DHNs) retaining the temperature quasi-dynamics is derived. Based on the equivalence, all the state variables in DHNs are explicitly expressed by the heat power generation, and the feasible region of DHNs is projected on the coupling boundaries of the IEHS. The existence of this equivalent model is proved under a mild sufficient condition. The application of the proposed equivalent model is demonstrated via the distributed unit commitment for IEHS. Case studies of two test systems validate the effectiveness and the efficiency of the solution for distributed IEHS operation.