Network-constrained Unit Commitment Problem Research Articles

Maximizing wind energy utilization in smart power systems using a flexible network-constrained unit commitment through dynamic lines and transformers rating

Wind power generations as renewable and sustainable energies are widely integrated into electric power systems due to their technical, environmental, and economic advantages. This integration affects the power system operation and planning studies. Network-constrained unit commitment (NCUC) is one of important operation studies of electric power systems in which the aim is to schedule the generating units for the next 24-h period with the minimum operating cost considering the constraints of generating units and transmission network. One of the essential constraints influencing the results of NCUC is thermal rating of lines and transformers. In most of the previous studies, static ratings have been used for this equipment. The static ratings are conservative values leading to non-optimal use of real capacity of lines and transformers and increasing the system's operational costs. This issue is highlighted when there exist wind energy generations in system. A new NCUC problem is addressed in this paper that considers dynamic line rating (DLR) and dynamic transformer rating (DTR) in the presence of wind power generations. The proposed approach has been implemented on the 24-bus IEEE-RTS system in the GAMS environment in different experiments. The simulation results demonstrate effectiveness of the conducted model in reducing the operational costs and maximizing the usage of wind energy.

AC Network-Constrained Unit Commitment via Relaxation and Decomposition

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.

AC network-constrained unit commitment via conic relaxation and convex programming

To address the AC network-constrained unit commitment problem, we propose an effective three-step solution approach. We first solve a DC (mixed-integer linear) approximation of the original problem to identify an initial solution and the set of transmission lines likely to be congested. Secondly, with the linear solution as a starting point, we solve a mixed-integer second-order conic relaxation of the original problem using an active set strategy regarding transmission constraints. Finally, using the solution of the relaxed problem as a starting point, we solve a set of increasingly accurate continuous convex optimization problems to ensure full AC feasibility. We show the effectiveness of the proposed approach using the IEEE 24-bus test system and an Illinois 200-bus system with 49 generators and 245 lines.

Techno-economic evaluation of transportable battery energy storage in robust day-ahead scheduling of integrated power and railway transportation networks

In recent years, the use of renewable energy (RE) sources has an upward trend due to the environmental and economic reasons. However, finding a solution method to manage the fluctuating nature of these sources and more efficient utilization of total generation capacity are challenging problems, especially when there is a high penetration of REs in power systems. On the other side, the network congestion in power grids is another obstacle that inhibits the full utilization of REs. Battery-based energy storage transportation using a railway network leads to emerging high-efficiency technology called transportable battery-based energy storage (TBES) system. TBES technology is a practical and economical option to reduce transmission congestion and increase the utilization of the energy storage systems’ (ESSs’) capacity by providing additional facility to transfer power. As a flexible resource, TBES can adapt to the load profile of the system at peak-load hours and result in cost reduction and more prudent management of wind power variations. The demand response (DR) program is another solution to deal with wind power uncertainty and has a considerable impact on reducing power network congestion and total operation cost by peak-load shaving. Hence, to overcome the mentioned challenges and obstacles, this paper focuses on solving a robust network constrained unit commitment (NCUC) with TBES and DR programs. To manage the wind power uncertainty, an information gap decision theory (IGDT)-based robust optimization technique is proposed to obtain maximum robustness against the wind power uncertainty. The advantage of the presented model is that neither probability distribution functions (PDFs) nor scenario generation are required. The 6-bus power system coordinated with the 3-station railway network is applied as the test system. Numerical studies pointed out that integrating TBES technology in IGDT-based robust NCUC problems and considering the DR program has improved the power system’s flexibility and uncertainty management of wind power, alleviated the congestion, and reduced the optimized cost. Simulation results revealed a 6.5% cost reduction by applying TBES and also 11.3% cost decrement by developing coordinated TBES and DR.

Risk-Based Networked-Constrained Unit Commitment Considering Correlated Power System Uncertainties

The forecast errors for distributed energy resources (DERs) and hourly demands have contributed to power system uncertainties and additional risks in the day-ahead scheduling of electricity markets. In this paper, a risk-based approach is introduced to determine the stochastic solution of network-constrained unit commitment (NCUC) when additional uncertainties are embedded in the power system scheduling. The historical power market transaction data are used to model nodal injection uncertainties and reserve capacity requirements are considered to assess the solution of the risk-based NCUC. The proposed NCUC problem is formulated as a single-stage second order cone program which is a convex algorithm. The proposed approach provides an efficient solution for large-scale stochastic problems and helps accommodate the DER variabilities in secure and economic operations of power systems. The proposed stochastic algorithm is tested and the results are analyzed for the IEEE RTS-96 and IEEE 300-bus test systems.

Network-constrained unit commitment with RE uncertainty and PHES by using a binary artificial sheep algorithm

With increasing share of renewable energy (RE) in power system, the unit commitment of hybrid power system have become more complicated due to network security demand and integration of pumped hydro energy storage (PHES). In this paper, a network-constrained unit commitment (NCUC) problem considering RE uncertainty and modulation of PHES has been raised. The NCUC model, with AC network security constraints and environmental constraints as well as traditional terms of constraints, is complicated to be solved. A novel Binary Artificial Sheep Algorithm (BASA) is used to solve the NCUC model. In the frame of BASA, the NCUC problem is decomposed as a master UC problem to determine start/stop status and economic load dispatch and a sub problem to check the AC network constraints. Based on the NCUC model and the solving method, the joint impacts of RE uncertainty and PHES have been studied. Test systems with different size have been adopted to verify the feasibility and effectiveness of the BASA. It is seen that the BASA has achieve an overall competitive performance on terms of operation cost and convergence speed by comparing it with existing methods. A modified IEEE 30-bus system with wind and photovoltaic power stations has been designed to reveal the impacts of RE and PHES. The results demonstrate that uncertainty of RE affects operation cost and security of the hybrid power system, and the adverse impact would aggravate as the RE forecasting error increase. The results also confirm the significant effect of PHES in restraining the negative influence of RE uncertainty.

Efficient period elimination Benders decomposition for network‐constrained AC unit commitment

Recent complexities in interconnected power system operation call for more efficient and fast approaches for operational problems including network-constrained unit commitment (NCUC). In this study, an algorithm called period-elimination Benders decomposition (PEBD) is proposed to enhance the computational efficiency of AC NCUC problems. After linearising the AC NCUC, two subproblems (SPs) are defined to ensure power balance at buses as well as constraints of branches and inter-regional transactions. In the classical Benders decomposition (BD), all time periods are solved at all iterations up to convergence. However, in the proposed PEBD, a time period that satisfies a SP in an iteration is eliminated from the solution procedure of that SP at next iterations. After both SPs are satisfied for all time periods, the solution is checked for interrelation constraints and a few more iterations may be needed to finalise the solution. The efficiency and accuracy of the proposed PEBD method are verified by examining it on two test systems. It is found that the PEBD greatly enhances the speed of NCUC, especially in larger power systems due to eliminating unnecessary calculations for satisfied time periods.

Decentralized Implementation of Unit Commitment With Analytical Target Cascading: A Parallel Approach

This paper presents a decentralized solution algorithm for network-constrained unit commitment (NCUC) in multiregional power systems. The proposed algorithm is based on our previous work in which a local NCUC was formulated for each control entity (i.e., region) and an analytical target cascading (ATC) based distributed but partially parallelized algorithm requiring a central coordinator was presented. The primary objective of this paper is to present a decentralized approach that relaxes the need for any form of central coordinator in ATC and allows fully parallelized solutions of the local NCUCs. To achieve this objective, we formulate a bilevel optimization problem for each control entity. While the upper level solves the NCUC problem of the control entity, the lower level seeks to coordinate the control entity with its neighboring regions. The lower level is a convex optimization, which can be further replaced in the upper level problem by the Karush–Kuhn–Tucker conditions. The control entities communicate directly with each other and synchronously solve their local NCUCs. Having no need for any form of central coordinator, the proposed algorithm is potentially less vulnerable to cyber-attacks and communication failures than the distributed methods utilizing a coordinator.

A Two-Stage Approach for Network Constrained Unit Commitment Problem With Demand Response

This paper proposes a two-stage formulation for the day-ahead energy scheduling problem with demand response (DR). The first stage solves a network-constrained unit commitment problem with DR, to determine the hourly net demand changes (i.e., difference between final and initial demand values) happening at each DR bus 1 along with the unit commitment schedule and ac load flow solution. Here, the objective is to maximize the social welfare which is expressed as the total utility of the demand side minus the total generation cost. The second stage solves an incentive or penalty minimization problem to determine the demand shifting and demand curtailment across the 24-h period at each DR bus, offering DR, based on the hourly net demand changes obtained during the first stage. The proposed formulation shows how demand shift and demand curtailment happening at different DR buses can be traced back to the hourly net demand changes occurring at the system level. The results, presented for a six-bus system and IEEE 118 bus system, show the benefits of including DR into the network-constrained unit commitment problem according to the proposed formulation. 1 Any bus which is capable of offering DR will be referred to as DR bus. It should not be mistaken for PQ bus referred in the load flow analysis.

A fully distributed asynchronous approach for multi-area coordinated network-constrained unit commitment

This paper discusses a consensus-based alternating direction method of multipliers (ADMM) approach to solve the multi-area coordinated network-constrained unit commitment (NCUC) problem in a distributed manner. Due to political and technical difficulties, it is neither practical nor feasible to solve the multi-area coordination problem in a centralized fashion, which requires full access to all data of individual areas. In comparison, in the proposed fully-distributed approach, local NCUC problems of individual areas can be solved independently, and only limited information is exchanged among adjacent areas for facilitating multi-area coordination. Furthermore, as traditional ADMM can only guarantee convergence for convex problems, this paper discusses several strategies to mitigate oscillations, enhance convergence performance, and derive good-enough feasible solutions, including: (i) A tie-line power flow based area coordination strategy is designed to reduce the number of global consensus variables; (ii) Different penalty parameters \r{ho} are assigned to individual consensus variables and are updated via certain rules during the iterative procedure, which would reduce the impact of initial values of \r{ho} on convergence performance; (iii) Heuristic rules are adopted to fix certain unit commitment variables for avoiding oscillations during the iterative procedure; and (iv) An asynchronous distributed strategy is studied, which solves NCUC subproblems of small areas multiple times and exchanges information with adjacent areas more frequently within one complete run of slower NCUC subproblems of large areas. Numerical cases illustrate effectiveness of the proposed asynchronous fully-distributed NCUC approach, and investigate key factors that would affect its convergence performance.

Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage optimization-based bounds tightening, second-order cone relaxations, and piecewise outer approximations to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

Accelerating NCUC Via Binary Variable-Based Locally Ideal Formulation and Dynamic Global Cuts

This paper presents tighter formulations and dynamic global cutting plane solution approaches for accelerating network-constrained unit commitment (NCUC) problems, as the computational bottleneck of NCUC problems is always a concern to independent system operators (ISOs)/regional transmission owners (RTOs). Specifically, this paper explores tighter mixed-integer linear programming (MILP)-based NCUC formulations, via locally ideal reformulation for piece-wise linear cost functions of generators and valid cover inequalities by linking system load balance/power flow constraints with generation capacity limits. The paper also discusses an enhanced solution approach by dynamically generating global cutting planes at infeasible/suboptimal nodes of the branch-and-cut (BAC) tree, which would prevent similar infeasible/suboptimal nodes from being explored repeatedly. Since the major computational complexity of NCUC is caused by the large number of binary UC variables, the proposed strategies, being directly related to binary UC variables, could quickly identify infeasible/suboptimal binary solutions, reduce the search space in the BAC tree, and in turn improve the computational performance. Numerical case studies show that the proposed approach could significantly reduce the overall computational time as compared to the traditional NCUC approach.

A tight MIP formulation of the unit commitment problem with start-up and shut-down constraints

This paper provides the convex hull description of the single thermal Unit Commitment (UC) problem with the following basic operating constraints: (1) generation limits, (2) start-up and shut-down capabilities, and (3) minimum up and down times. The proposed constraints can be used as the core of any unit commitment formulation to strengthen the lower bound in enumerative approaches. We provide evidence that dramatic improvements in computational time are obtained by solving the self-UC problem and the network-constrained UC problem with the new inequalities for different case studies.

Tight MIP formulations of the power-based unit commitment problem

This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are (1) generation limits and (2) minimum up and down times. Apart from this, the startup and shutdown processes are also modeled, using (3) startup and shutdown power trajectories for slow-start units, and (4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, power schedules are used to represent the staircase energy schedule; however, this simplification leads to infeasible energy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-based UC formulation drawing a clear distinction between power and energy. The proposed constraints can be used as the core of any power-based UC formulation, thus tightening the final mixed-integer programming UC problem. We provide evidence that dramatic improvements in computational time are obtained by solving different case studies, for self-UC and network-constrained UC problems.

An Improved Decomposition Framework for Accelerating LSF and BD Based Methods for Network-Constrained UC Problems

This paper presents an improved decomposition framework to accelerate the convergence of linear sensitivity factor (LSF) and Benders decomposition (BD) based methods for network-constrained unit commitment (NCUC) problems. Classical LSF and BD methods solve NCUC problems by an iterative procedure between a master UC problem and transmission network evaluation subproblems. Subproblems evaluate the transmission network security of a master UC solution, and feedback violated network constraints or Benders feasibility cuts to the UC problem for seeking a feasible UC solution that could mitigate transmission violations. However, classical methods often converge very slowly and introduce major computational bottlenecks. This paper presents an improved decomposition framework by embedding network evaluation subproblems into the branch-and-bound (BAB)/branch-and-cut (BAC) procedure of the master UC problem. Thus, instead of iteratively solving the UC master problem and network evaluation subproblems, the NCUC problem is solved in one single integrated procedure by performing network evaluations at each BAB/BAC node. The proposed methods reduce the number of BAB/BAC nodes to be solved in the UC problem at the cost of additional network evaluations. Numerical tests demonstrate the efficiency of the proposed decomposition framework. The benefit of the proposed decomposition framework would be significant when a system is heavily congested and a large number of iterations is expected for the classical methods. The proposed decomposition strategy can be extended to other applications for solving large-scale optimization problems in power systems operation, maintenance, and planning.

Two-stage network constrained robust unit commitment problem

For a current deregulated power system, a large amount of operating reserve is often required to maintain the reliability of the power system using traditional approaches. In this paper, we propose a two-stage robust optimization model to address the network constrained unit commitment problem under uncertainty. In our approach, uncertain problem parameters are assumed to be within a given uncertainty set. We study cases with and without transmission capacity and ramp-rate limits (The latter case was described in Zhang and Guan (2009), for which the analysis part is included in Section 3 in this paper). We also analyze solution schemes to solve each problem that include an exact solution approach and an efficient heuristic approach that provides tight lower and upper bounds for the general network constrained robust unit commitment problem. The final computational experiments on an IEEE 118-bus system verify the effectiveness of our approaches, as compared to the nominal model without considering the uncertainty.

Impact of price‐based demand response on market clearing and locational marginal prices

This study quantitatively analyses the impact of price-based demand response (DR) on market clearing and locational marginal prices (LMPs) of power systems using the network-constrained unit commitment (NCUC) model. The price-based DR is formulated via linear price-sensitive demand bidding curves, while considering DR participation levels and energy payback rates. DR is formulated as load shifting as well as load curtailment by adopting different energy payback rates to represent the amount of energy shifted among different hours. The objective is to maximise the system social welfare, which includes the revenue from price-sensitive DR loads minus the energy production costs from generating units. The NCUC problem is formulated as a mixed-integer linear programming (MILP) problem and solved by the commercial MILP solver. Numerical case studies are performed to analyse the impacts of DR on unit commitment, LMPs, energy production costs and DR load payments. Results indicate that with the current market clearing mechanism which maximises the system social welfare, DR dispatch may augment LMPs by displacing less flexible generating units and/or triggering additional transmission congestions and, in turn, increase DR loads' payments, which will ultimately influence the financial stability of DR providers and the sustainable deployment of DR programs.

Accelerating the Benders decomposition for network-constrained unit commitment problems

This paper presents an optimization method by generating multiple strong Benders cuts for accelerating the convergence of Benders Decomposition (BD) when solving the network-constrained generation unit commitment (NCUC) problem. In NCUC, dc transmission network evaluation subproblems are highly degenerate, which would lead to many dual optimal solutions. Furthermore, the classical BD cuts are often low-density which involve only a limited number of decision variables in the master problem. Therefore, the dual optimal solutions and the corresponding Benders cuts are of crucial importance for improving the efficiency of the BD algorithm. The proposed method would generate multiple strong Benders cuts, which are pareto optimal, among candidates from multiple dual optimal solutions. Such cuts would be high-density in comparison with low-density cuts produced by the classical BD. The proposed multiple strong Benders cuts are efficient in terms of reducing the total iteration number and the overall computing time. The high-density cuts may restrict the feasible region of the master unit commitment (UC) problem in each iteration as they incorporate more decision variables in each Benders cut. The multiple strong Benders cuts would accordingly reduce the iteration number and overall computing time. Numerical tests demonstrate the efficiency of the proposed multiple strong Benders cuts method in comparison with the classical BD algorithm and the linear sensitivity factors (LSF) method. The proposed method can be extended to other applications of BD for solving the large-scale optimization problems in power systems operation, maintenance, and planning.