Security-constrained Unit Commitment Problem Research Articles

Linearization Method for Large-Scale Hydro-Thermal Security-Constrained Unit Commitment

Security-constrained unit commitment (SCUC) is one of the most fundamental optimization problems in power systems. The objective of SCUC is to minimize the operating cost while respecting both system-wide and generator-specific constraints. It leads to a large-scale and mixed-integer programming (MIP) model with a large number of binary decision variables which is difficult to solve. This paper, based on the convex hull theory of single-unit, proposes a linearization method for the hydro-thermal SCUC problem with decoupled thermal units and variable-head hydro units. Then, the strategy of embedding two types of convex hulls in a multi-unit commitment and the heuristic method of constructing a feasible solution are designed, by which the multi-UC is approximated from large-scale mixed-integer programming to linear programming that can be solved in polynomial time. Finally, we theoretically prove that the optimal solution of the proposed LP model is always better than that of the Lagrangian Relaxation model. Numerical experiments on several large-scale test systems demonstrate the effectiveness and efficiency of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper proposes a linear programming model for the SCUC problem by lifting up to a higher-dimensional space. It realizes an important innovation in reducing the computational complexity of SCUC from the perspective of linearization. The proposed method can be well applied to large-scale long-term unit commitment problems. To better use this method, the following two properties should be highlighted: 1) the error of the proposed method is less than the Lagrangian relaxation method and decreases with the increasing system scales and 2) the computational efficiency of the proposed method is 10-100 times faster than that of the MIP model. We have tested many practical power systems and find that the error of the proposed LP model is usually very small compared with the precise MIP while the computational performance is significantly improved. In some practical cases, the decision makers usually do not want to find the precise optimal solution while only an approximation under a fast speed, because the boundary condition is imprecise. The proposed method is useful. Besides, for the cases that need the precise optimal solution, the proposed method can provide a high-quality initial solution for the MIP model to accelerate the convergence.

A fast ES-based method for solving SCUC problem

Security-Constrained Unit Commitment (SCUC) is the foundation for the safe and stable operation of the power system. However, existing methods for solving SCUC problems are either computationally expensive or inaccurate. An Encoding Strategy SCUC (ES-SCUC) approach that consists of a classifier and a linear system solution is proposed in this paper. First, the classifier predicts the ES, including tight constraints and on/off values, and then the ES is substituted into the Linear system to get an approximate solution. Experimental results show that the ES-SCUC solves for case300 SCUC problems within milliseconds. Compared to the state-of-the-art solver, it achieves speedups of two orders of magnitude with high accuracy.

Faster identification of redundant security constraints in SCUC

One of the main reasons why it has long been difficult to solve the security-constrained unit commitment (SCUC) problem is that there are a large number of security constraints in SCUC such as transmission constraints in the base case and N-1 criterion constraints, and adding all of them to the model will make the solution of the problem very challenging. Related research shows that most of these security constraints are redundant for solving SCUC, so identifying and eliminating most of the redundant security constraints in the model will greatly improve the speed of solving SCUC. In this paper, a fast and efficient algorithm is proposed for identifying redundant security constraints in SCUC. The proposed algorithm introduces parameters in the basic transmission constraints to additionally limit the transmission capacity. In the N-1 constraints based on Line Outage Distribution Factor (LODF), more redundant constraints are identified and removed in the model by comparing the upper limit of transmission line capacity with the maximum transmission power flow that may occur in the line when the system is running. More importantly, the proposed algorithm does not need to solve additional auxiliary optimization problems or iteratively solve multiple models, and only needs to identify a large number of redundant security constraints through a quick calculation and logical judgment in the early stage of model establishment. It has been tested on the IEEE 30-bus system and the IEEE 118-bus system. The numerical experimental results show that the algorithm can identify 98.52% and 99.3% of redundant security constraints, and the computational speed is 1.63 times and 17.85 times of the full model, respectively. Compared with other methods in the literature, it has more advantages in computational efficiency.

Impact of implementing a price-based demand response program on the system reliability in security-constrained unit commitment problem coupled with wind farms in the presence of contingencies

Large scale penetration of highly intermittent wind energy sources has caused new challenges to the reliable operation of power systems. To address these challenges, demand response program is considered as an efficient solution to manage shift-able loads. In this paper, the impact of demand response on power system reliability has been evaluated by developing a two-stage stochastic security constraint unit commitment that considers both the wind volatility and line outages at the same time. The allocation of ramping products and spinning reserves to cover these uncertainties has also been modeled. wind curtailment and load shedding are considered as alternative strategies, and an optimal exchange between them and the use of spinning reserves and flexible ramping products has been modeled in the objective function. To assess the system reliability, the expected load not served (ELNS) index was evaluated in different cases. The proposed scheme as a mixed-integer linear programming problem was solved by a scenario-based two-stage stochastic programming method. The IEEE test systems 6-bus, modified 24-bus, and 118-bus were examined numerically. The results show that the simultaneous consideration of demand response and flexible ramping product coordinated with wind energy has adequate flexibility to reduce the reliability index and system operational cost.

Large-Scale Preventive Security-Constrained Unit Commitment Considering N-k Line Outages and Transmission Losses

This paper presents a new formulation for the preventive security-constrained unit commitment problem modeling <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> line outages and transmission losses. The pre- and post-contingency transmission constraints, representing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> line outages, are explicitly included by using generalized generation distribution factors. To account for security, a contingency selection procedure based on line outage distribution factors finds a list of worst-case contingencies. Transmission losses are incorporated using piecewise linear expressions. The proposed model is formulated as an instance of mixed-integer linear programming. The effectiveness of the proposed approach is illustrated with the IEEE 57-bus system and the 1,354-bus portion of the European transmission system. As empirically evidenced, the explicit consideration of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N-k</i> line outages and transmission losses leads to different decisions in the generation scheduling and dispatch, ensuring secure power system operation.

Security Constrained Unit Commitment Based on Modified Line Outage Distribution Factors

The N-1 criterion is universally taken as the security constrains in the security-constrained unit commitment (SCUC) problem. The line outage distribution factors (LODF) is widely used in the N-1 continency for its state independence and computational efficiency. However, the LODF based model fails to consider reactive power and voltage magnitude. This paper closes this gap by deriving modified line outage distribution factors (MLODF) based on a linear power flow model. The proposed model, though state-independent, provides high-quality approximation of voltage magnitudes. Then, we apply this model to formulate the SCUC problem and propose an iterative solution process based on MLODF post-contingency filter to set up the contingency constraints. The simulation results of the benchmark test systems verify the accuracy of proposed MLODF. The six-bus and IEEE 118-bus systems show that the MLODF based model can provide a more accurate and secure generation schedule comparing with the traditional LODF based model while ensuring the AC feasibility for most N-1 continency.

Security-Constrained Unit Commitment for Hybrid VSC-MTDC/AC Power Systems With High Penetration of Wind Generation

This paper presents the solution to the security-constrained unit commitment (SCUC) problem for hybrid voltage source converter (VSC) based multi-terminal DC/AC (VSC-MTDC/AC) power systems with high penetration of wind generation. The formulated SCUC model presents a detailed representation of the VSCs with two different VSC control strategies considered, constant DC voltage control (master-slave control) and DC voltage droop control. In addition, Grid Code for wind farm connection is considered. Benders decomposition is used to solve the formulated SCUC problem by decomposing it into a master problem for solving unit commitment (UC) and hourly transmission security check subproblems. The final SCUC solution provides an economic and secure operation and control strategy for the meshed MTDC/AC system. Numerical tests illustrated the efficiency of the proposed SCUC model.

Sizing and Siting of Battery Energy Storage Systems: A Colombian Case

This paper presents a mixed-integer linear programming (MILP) formulation for sizing and siting of battery energy storage systems (BESSs). The problem formulation seeks to minimize both operation costs and BESS investment. The proposed model includes restrictions of the conventional security-constrained unit commitment problem, a piece-wise linear approximation to model power losses, and a linear model of hydro generation units. The proposed model is tested in a 6-bus test system and a 15-bus system representing the Colombian power system. For the two studied systems, simulation results show that the reduction of operation costs due to the installation of BESSs compensates the investments, under some of the considered technical cost cases. Additionally, results show that adequate sizing and siting of BESSs reduce renewable energy curtailment in the Colombian power system with high penetration of fluctuating renewable generation.

Optimal electric vehicles charging scheduling for energy and reserve markets considering wind uncertainty and generator contingency

Decarburization of electrical systems encourage high wind power into electric power systems and the electrification of transport sectors through electric vehicles (EVs). The increasing penetration of uncertain wind power generation and transportation networks via EV charging stations has introduced challenges for system operators to manage power systems and market operations. In this context, this paper presents a stochastic AC security-constrained unit commitment (SCUC) model to clear day-ahead energy and reserve markets considering transportation–electricity networks through EV charging stations in the presence of uncertain wind power and generator contingency. Pre-contingency ranking is a common strategy for reducing the time of the SCUC problem, but it provides high-impact outages. To address this issue, generator outages ranked first are identified using the post-contingency generator response ranking approach. The main contribution of this paper is the development of a structure with the most effective outages in the presence of uncertain wind power and transportation networks. The stochastic optimization approach is modeled through scenarios with corresponding probabilities to manage the wind uncertainty. The computationally complex proposed model is solved by a prominent bender decomposition approach. Case studies are shown on a modified IEEE 118-bus system with 26 nodes and 74 connected links of the electricity transportation network. The results show that optimal EV travel scheduling can optimize the transportation network and a sufficient energy reserve, confirming the security of the power system with minimum operating cost.

Multi-objective Mathematical Programming to Simultaneously Control SCUC and OUPFC to Improve Power System Controllability

ABSTRACT Security-Constrained Unit Commitment (SCUC) problem and subsequently employing Flexible AC Transmission Systems (FACTS) controllers including Optimal Unified Power Flow Controller (OUPFC) play a crucial role in power systems operation and control in terms of increasing the security of energy transmission networks. The principal objective of the SCUC problem is to acquire the minimum operating cost simultaneously maintaining the security of the system. In this paper, significant attention is paid particularly to simultaneously control SCUC and OUPFC, since energy loss reduction and transmission lines capacity release can be effectively achieved with incorporating SCUC and OUPFC, and subsequently setting the effective variables. In this regard, the SCUC problem with the presence of OUPFC is solved as Nonlinear Programming with Discontinuous Derivatives (DNLP) framework and the proposed algorithm is implemented on two IEEE 14-bus and IEEE 30-bus systems using General Algebraic Modeling System (GAMS) software in order to optimize the total fuel cost, power losses and cost of OUPFC installation as objective functions in the multi-objective framework. The simulation results show the capability of the proposed algorithm to simultaneously determine the optimal location of the OUPFC and its settings in the SCUC problem and to improve the controllability of the power system operation.

A New Affinely Adjustable Robust Model for Security Constrained Unit Commitment under Uncertainty

Currently, optimization models for the safe and reliable operation of power systems deal with two major challenges: the first one is the reduction of the computational load when considering N−1 contingencies; the second one is the adequate modeling of the uncertainty of intermittent generation and demand. This paper proposes a new affinely adjustable robust model to solve the security constrained unit commitment problem considering these sources of uncertainty. Linear decision rules, which take into account the forecasts and forecast errors of the different sources of uncertainty, are used for the affine formulation of the dispatch variables, thus allowing the tractability of the model. Another major novelty is that the evaluation of the N−1 security constraints is performed by incorporating a novel method, proposed in the literature, based on the user-cuts concept. This method efficiently and dynamically adds only the binding N−1 security constraints, increasing the computational efficiency of the model when transmission line contingencies are considered. Finally, Monte Carlo simulations on the post-optimization results were run to demonstrate the effectiveness, feasibility and robustness of the solutions provided by the proposed model.

Simultaneous optimal short term SCUC solution and power system redesign with real gap decomposition technique

In this work, firstly, a decomposition technique is proposed and applied to solve the Security Constrained Unit Commitment problem (SCUC). A recently developed model for optimal short term programming of power generation in thermoelectric plants including transmission constraints is adopted. Real gap is computed at the final solution. Secondly, a method to analyze results and redesign the system structure is also proposed. By applying this method, critical lines and generators can be detected, and then, network improvements can be suggested by either eliminating or duplicating lines or generators. With the aim of studying the efficiency of the proposed method, two systems of different sizes are considered. The efficiency of the proposed technique is compared with the direct resolution of the original model and a linearly approximate model. The proposed decomposition technique presents a good performance: optimal solutions are obtained within small real gaps and efficient computing times. In power systems, the SCUC problem is solved every 60 minutes or less; therefore, the resolution time sought must be much less than that. Without applying the decomposition technique, the resolution of the SCUC problem takes several hours to reach an acceptable gap; and instead, when applying the decomposition technique; smaller gaps can be obtained in a few minutes.

Risk-constrained non-probabilistic scheduling of coordinated power-to-gas conversion facility and natural gas storage in power and gas based energy systems

Abstract Increasing environmental concerns related to fossil fuels has led to an increased desire to utilize renewable energy in the power system. Wind power resources as clean energy have an important role in the long-term energy landscape. However, the probabilistic nature of these resources will make several challenges from the integration point of view with the modern power system. Power-to-gas (P2G) technology as an emerging storage system by converting the power generated from the wind power into natural gas (NG) plays a significant role in integrating more and more wind power into the power system. Besides, the NG-fired (NGF) units have received much attention due to faster response, higher efficiency, and far lower pollution emissions. The emergence of P2G and NGF units has led to the interdependency of NG and electrical networks. This interconnection requires the simultaneous optimization and operation of both networks considering all relevant restrictions. Therefore, this paper presents a developed security-constrained unit commitment (SCUC) problem for integrated power and NG networks in the presence of P2G, NG storage, and wind power resources. The main objective of the proposed problem is to minimize the operation cost by considering all the characteristics and interconnections between the power and NG networks. To handle the uncertainty related to wind power, the information gap decision theory (IGDT)-based non-probabilistic robust approach is applied. The proposed model is implemented on the integrated 6-bus electrical and 6-node NG networks and integrated 24-bus electrical and 10-node NG networks for different cases and numerical results reveal the effectiveness of the proposed approach.

A clearing mechanism for joint energy and ancillary services in non-convex markets considering high penetration of renewable energy sources

This paper introduces a day-ahead clearing model for the simultaneous energy and ancillary services market in high penetration of renewable energy sources (RESs) considering fast-start generators’ behaviors as non-spinning reserve providers. For managing the uncertainties of RESs, the system operator takes the advantages of the stochastic model of security-constrained unit commitment (SCUC) problem considering plausible scenarios. The non-convexities due to the startup costs, minimum power outputs, and commitment variables make the stochastic SCUC problem and market-clearing non-convex. Meanwhile, with traditional market-clearing methods for energy and ancillary services based on marginal costs or dual variables, the net profit of some generators may become negative. In this situation, more financial losses will be imposed on fast-start generators since they are marginal/intermittent units for managing the uncertainties of RESs. Using a duality gap minimization and profit insurance, this paper presents a pricing model to solve these issues. The proposed market-clearing model leads to uniform prices for ancillary services and nodal prices for energy guaranteeing the non-negative net profit of all generators. The results of the 3-buses system and IEEE 118-buses system are analyzed to illustrate the applications of the proposed pricing approach.

Graph computing based security constrained unit commitment in hydro-thermal power systems incorporating pumped hydro storage

This paper proposes a graph computing based mixed integer programming (MIP) framework for solving the security constrained unit commitment (SCUC) problem in hydro-thermal power systems incorporating pumped hydro storage (PHS). The proposed graph computing-based MIP framework considers the economic operations of thermal units, cascade hydropower stations and PHS stations, as well as their technical impacts towards the network security. First, the hydro-thermal power system data and unit information are stored in a graph structure with nodes and edges, which enables nodal and hierarchical parallel computing for the unit commitment (UC) solution calculation and network security analysis. A MIP model is then formulated to solve the SCUC problem with the mathematical models of thermal units, cascade hydropower stations and PHS stations. In addition, two optimization approaches including convex hull reformulation (CHR) and special ordered set (SOS) methods are introduced for speeding up the MIP calculation procedure. To ensure the system stability under the derived UC solution, a parallelized graph power flow (PGPF) algorithm is proposed for the hydro-thermal power system network security analysis. Finally, case studies of the IEEE 118-bus system and a practical 2749-bus hydro-thermal power system are introduced to demonstrate the feasibility and validity of the proposed graph computing-based MIP framework.

Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift.Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

A novel robust security constrained unit commitment model considering HVDC regulation

To further improve the robustness and economic efficiency of the conventional security-constrained unit commitment (SCUC) problem when confronting system uncertainties, we propose a novel robust SCUC model considering the prompt and flexible controllability of high voltage direct current (HVDC) in asynchronous interconnected systems. Unlike the conventional method, the proposed model minimizes the total cost of pre-day commitment for the base case and real-time dispatch under extreme uncertainties when guaranteeing the generation units and HVDC can be adjusted adaptively and securely. The robustness and economic efficiency of the model are enhanced by optimizing their trade-off when integrating HVDC regulation. As the method involves unit commitment, short-term dispatch, and power rescheduling, an improved tri-level Benders decomposition algorithm is developed according to the structure of the model to solve this mixed-integer nonlinear programming problem. In computational experiments, the effectiveness of the proposed model was validated in a two-area HVDC interconnected asynchronous system under various uncertainties. Additionally, the superior cooperation between a day-ahead commitment plan and real-time dispatch in the novel SCUC model with HVDC regulation was verified.

A Novel Strategy to Reduce Computational Burden of the Stochastic Security Constrained Unit Commitment Problem

The uncertainty related to the massive integration of intermittent energy sources (e.g., wind and solar generation) is one of the biggest challenges for the economic, safe and reliable operation of current power systems. One way to tackle this challenge is through a stochastic security constraint unit commitment (SSCUC) model. However, the SSCUC is a mixed-integer linear programming problem with high computational and dimensional complexity in large-scale power systems. This feature hinders the reaction times required for decision making to ensure a proper operation of the system. As an alternative, this paper presents a joint strategy to efficiently solve a SSCUC model. The solution strategy combines the use of linear sensitivity factors (LSF) to compute power flows in a quick and reliable way and a method, which dynamically identifies and adds as user cuts those active security constraints N − 1 that establish the feasible region of the model. These two components are embedded within a progressive hedging algorithm (PHA), which breaks down the SSCUC problem into computationally more tractable subproblems by relaxing the coupling constraints between scenarios. The numerical results on the IEEE RTS-96 system show that the proposed strategy provides high quality solutions, up to 50 times faster compared to the extensive formulation (EF) of the SSCUC. Additionally, the solution strategy identifies the most affected (overloaded) lines before contingencies, as well as the most critical contingencies in the system. Two metrics that provide valuable information for decision making during transmission system expansion are studied.

Hierarchical and Robust Scheduling Approach for VSC-MTDC Meshed AC/DC Grid With High Share of Wind Power

This paper proposes a novel hierarchical and robust scheduling paradigm for the emerging voltage source converter (VSC) based multiterminal high voltage direct current (VSC-MTDC) meshed AC/DC hybrid system with high share of wind power. Considering the multilevel structure of the VSC-MTDC meshed AC/DC system, the scheduling problem is decomposed into three interactive levels according to the hierarchical analytical target cascading (ATC) technique. The low level is a two-stage adaptive robust security-constrained unit commitment problem for the AC system, which is solved by the column-and-constraint generation (C&CG) algorithm; the middle level is a day-ahead power transmission optimization problem for the VSC stations, where a day-ahead operation model for the VSC station is presented to fully use its flexible and controllable power adjustment capability to promote wind power accommodation; and the high level is a multi-period optimal power flow problem for the DC grid. An integrated ATC and C&CG algorithm is proposed to enable the hierarchical and robust scheduling. The parallel solution is used to accelerate the hierarchical scheduling. Simulations show that this formulation is effective in dealing with wind power uncertainty, promoting wind power accommodation, and improving the calculation efficiency.

Optimal scheduling of reconfigurable grids considering dynamic line rating constraint

Power system automation is an effective tool from both economical and technical aspects to improve the optimal operation of power generators. In this regard, Security Constrained Unit Commitment (SCUC) incorporating Dynamic Thermal Line Rating (DTLR) of overhead transmission lines can boost the system security effectively. Using Transmission Switching (TS) tool in SCUC problems leads to cost reduction. Still, one of the main challenges arisen in TS problems is the excessive number of switching in lines, which decreases the lifespan of power switches. In this paper, an Improved Linear AC Optimal Power Flow (ILACOPF) is proposed by using TS and considering Heat Balance Equation (HBE) as a security constraint. Merging dynamic thermal line rating (considering the weather conditions) in SCUC with TS, besides decreasing the number of switching and increasing the lifespan of power switches, causes a remarkable reduction in operating costs. In this power flow, system losses are modeled by linear formulations. Moreover, a linear approximation of the heat losses due to power flow through lines is proposed. To solve the proposed model, Benders' decomposition approach is applied. The performance of the proposed framework has been evaluated on 6-bus and 118-bus IEEE test systems.