Unit Commitment Solution Research Articles

Hybrid quantum annealing decomposition framework for unit commitment

Quantum computing is an emerging and promising technology that has overwhelming quantum advantages compared to its classical counterparts. Unit commitment (UC) is a critical issue in the power system, and it becomes more challenging with the integration of intermittent renewable energy. Therefore, this paper proposes an innovative decomposition and coordination optimization framework to accelerate the solution of UC, in which the interaction between an adiabatic quantum computer and a classical computer is designed to harness the immense computational power of quantum computers effectively. First, decomposition methods considering the requirements of quantum computers are introduced to decompose UC into small-scale models. Then, the paper presents a quadratic unconstrained binary optimization modeling method to transform UC problems into the form of quantum computing. Furthermore, due to the limitations of quantum computing resources, a reductive variable technique is proposed to reduce the number of slack variables in the optimization model and ensure that it remains feasible for quantum computers. Case studies conducted in test systems with a quantum annealing simulator and a real quantum annealing computer illustrate the feasibility and effectiveness of the method and demonstrate its potential in the era of quantum computing.

Exact mixed-integer quadratic formulation and solution for large-scale thermal unit commitment

Abstract Thermal unit commitment (UC) is a nonlinear combinatorial optimization problem that minimizes total operating costs while considering system load balance, on/off restrictions and other constraints. Successfully solving the thermal UC problem contributes to a more reliable power system and reduces thermal costs. This paper presents an exact mixed-integer quadratic programming (EMIQP) method for large-scale thermal UC problems. EMIQP revolutionizes the landscape by seamlessly translating the intricate nonlinear combinatorial optimization problem of UC into an exact mixed-integer quadratic formulation. This approach also elegantly reimagines on/off constraints as mixed-integer linear equations, employing both the sum and respective approaches. Our case studies unequivocally demonstrate the exceptional prowess of the EMIQP method, consistently securing the global optimum. Moreover, the mathematical-based EMIQP method produces identical results at each run, which is extremely important for UC in the real world.

Distributionally robust optimization model considering deep peak shaving and uncertainty of renewable energy

In order to achieve the goal of carbon neutrality, the capacity of renewable power generation is continuously expanding while thermal power units are transitioning from main power source to auxiliary power source. To alleviate the peak shaving burden of thermal power units under the uncertainty of renewable energy and improve the absorption level of renewable energy, a two-stage distributionally robust optimization (DRO) model considering deep peak shaving and the uncertainty of renewable energy is proposed. The day-ahead unit commitment solutions are determined in the first stage, and the detailed scheduling strategies are obtained in the second stage. Column-and-constraint generation (C&CG) algorithm is applied to solve the model, and the master problem and subproblem are reformulated as duality-free mixed integer linear programming problems. The results show that the scheduling strategy obtained based on the model can alleviate the peak shaving burden brought by the uncertainty of renewable energy and reduce the abandonment rate of wind resources and solar resources, and the proposed DRO model provides a good trade-off between economy and robustness compared to stochastic optimization (SO) and robust optimization (RO).

Random Furrowing for a Stochastic Unit Commitment Solution

The Unit Commitment Problem involves the inherent difficulty of obtaining optimal combinatorial power generation schedules over a future short term period. The formulation of the generalized Unit Commitment Schedule formulation involves the specific combination of generation units at several de-rated capacities during each hour of the planning horizon, the load demand profile, load indeterminateness and several other operating constraints. This largely deterministic schedule continues to find favor with several plant operators, keeping in mind the close operating time-periods involved. However, the deterministic nature of the load profile is sought to be phased out by a stochastic pattern that is realistic and mirrors real-life situations, owing to modern trends in Demand side management. This shift is in tune with the ongoing power restructuring activities of electricity power reforms. The stochastic profile is obtained by a suitably tuned 2-parameter Weibull distribution that uses appropriate shape and scale parameters. The resulting band of generated load profiles are used to evaluate net power and penal costs associated with a set of pervasive randomized probability indices. The exact UCS comprises of a specific unit absolute state corresponding to a certain time period within the planning horizon. Subsequently, regression analysis is applied to establish the correlation between the absolute states and the cumulative randomized load demand against the intervals within the planning horizon. This method is analogous to random furrowing of probabilistic demand profile.

Unit Commitment Problem with Energy Storage Under Correlated Renewables Uncertainty

Unit Commitment Problem with Energy Storage Under Correlated Renewables Uncertainty” introduces a novel approach to address the challenges of renewable integration. The study acknowledges the growing variability and correlation in power availability due to renewable generation and proposes a day-ahead unit commitment (UC) problem formulation that incorporates energy storage and considers multistage correlated uncertainty. Using a variant of the stochastic dual dynamic programming (SDDP) method, which can handle temporal correlations effectively, the researchers solve the complex UC problem. Results obtained from the IEEE 118-bus system demonstrate the significant advantages of considering multistage uncertainty and correlations. Applying their approach to the Chilean power system, the researchers present superior UC solutions that adapt generation to changing uncertainty at a lower cost. Additionally, they propose a more efficient deterministic UC solution that outperforms current industry practices. These advancements promise to enhance the integration of renewable energy sources, enabling a more sustainable and environmentally friendly future.

Deep reinforcement learning based model-free optimization for unit commitment against wind power uncertainty

Solving the unit commitment (UC) problem in a computationally efficient manner has become increasingly crucial, especially in the context of high renewable energy penetration. This paper tackles this challenge by employing the offline training of a model-free deep reinforcement learning (DRL) framework, thereby enhancing the optimization efficiency of the UC problem. The complex modeling of random variables is avoided by reformulating the UC problem as a Markov decision process, where the DRL-based method extracts knowledge regarding wind output forecasting errors from historical data. Finally, a discrete proximal policy optimization (PPO-D) algorithm is developed to generate UC solutions under the discrete action spaces necessitated by unit start-up/shut-down variables. Simulation results on the 5-unit system demonstrate that the proposed DRL-based UC model can yield an optimal solution with higher computational efficiency compared to the conventional mathematical optimization methods, while hedging against the wind power uncertainty. In addition, the case study on the IEEE 118-bus system involving 31 testing days further validates the generalization ability of the proposed DRL-based UC model.

Online Learning of Stable Integer Variables in Unit Commitment Using Internal Information

In a set of similar unit commitment (UC) problems, a variable is called a stable integer variable (SIV) if its optimal value is 0 or 1 on a regular basis, which reflects an inherent pattern in UC solutions. The computational complexity can be significantly reduced by fixing SIVs with a minor chance of accuracy loss. To identify SIVs, this letter proposes a method to collect internal solution information from the initial branch-and-bound process of artificial mixed-integer programming problems generated from the given problem. A distinct advantage of this method is that because no prior offline training is needed, learning is instance-specific and has no dependency on the training set. With identified SIVs, machine learning-based acceleration is achieved. Based on 50 test cases from publicly available and practical data, the proposed method improves the percentage of solved problems within the clearing time window from 68% to 96% compared with commercial solvers, counting the total time of data collection, prediction, and optimization.

Cost-Driven Screening of Network Constraints for the Unit Commitment Problem

In an attempt to speed up the solution of the unit commitment (UC) problem, both machine-learning and optimization-based methods have been proposed to lighten the full UC formulation by removing as many superfluous line-flow constraints as possible. While the elimination strategies based on machine learning are fast and typically delete more constraints, they may be over-optimistic and result in infeasible UC solutions. For their part, optimization-based methods seek to identify redundant constraints in the full UC formulation by exploring the feasibility region of an LP-relaxation. In doing so, these methods only get rid of line-flow constraints whose removal leaves the feasibility region of the original UC problem unchanged. In this paper, we propose a procedure to substantially increase the line-flow constraints that are filtered out by optimization-based methods without jeopardizing their appealing ability of preserving feasibility. Our approach is based on tightening the LP-relaxation that the optimization-based method uses with a valid inequality related to the objective function of the UC problem and hence, of an economic nature. The result is that the so strengthened optimization-based method identifies not only redundant line-flow constraints but also inactive ones, thus leading to more reduced UC formulations.

Analysis of Unit Commitment of Coal-fired Units in a Power Base of Cross-area DC Transmission Lines Under Dual Carbon Targets

China has announced achieving a carbon peak before 2030 and neutralization by 2060. Cross-area UHVDC transmission provides a feasible way for the new energy base to transmit power to the load center on a large scale. Usually, the dispatching of coal power units of DC transmission line power base is divided according to the equal proportion of unit capacity, this paper takes all the units as a group and proposes a unit commitment solution to realize lower carbon emission. As the capacity of new energy in the power base increases, this paper also considers the generation margin for new energy to do the optimization simulation. The results show that by operating coal-fired units as a group, it operates in a more economic and environmentally friendly way.

A linear AC unit commitment formulation: An application of data-driven linear power flow model

Unit commitment is an important schedule procedure in power system daily operations, and an ideal version is to combine the unit commitment with the optimal power flow, thereby, it achieves an AC-power-flow-constrained unit commitment problem, which is referred to as the AC unit commitment. The AC unit commitment is quite benefit for system operation, however, the AC unit commitment problem is intractable since it is generally a large-scale non-convex and nonlinear program.To overcome this difficulty, this paper proposes a linear AC unit commitment model, which achieves a high-accuracy solution that is close to the solution of the exact AC unit commitment, while it keeps the problem from getting into a huge computational burden. To achieve a high accuracy, the recent data-driven linear power flow model is adopted, and for making the data-driven linear power flow model applicable for the unit commitment problem, a chance-constrained support vector regression approach is proposed to the replace the common least-squares regression in former data-driven linear power flow models, and physical models are used to deduce aid formulations to make the data-driven linear power flow model more robust.The resultant linear unit commitment model is tested on several standard systems, including a 2000-bus system, and the results verify the effectiveness of the proposed method, and show that the accuracy of the proposed data-driven linear power flow model improved about two-folds compared with the classical one.

Converter-driven stability constrained unit commitment considering dynamic interactions of wind generation

With increasing penetration of renewable energy in power systems, conventional unit commitment (UC) focusing on static constraints may fail to meet dynamic constraints, such as converter-driven stability. This paper proposes a practical paradigm to perform UC considering the requirement of converter-driven stability in wind generation penetrated power systems. First, wind generation is regarded as a constant source, and a regular UC problem is solved without considering the dynamic impact of wind generation. Second, converter-driven stability analysis is employed to evaluate the stability margin of the UC solution. Different wind penetration levels and dynamic interaction conditions are investigated to account for the dynamic impact of wind generation. In several time horizons, especially heavy loading periods, the stability margin may be very limited or negative, and a modification to the UC solution should be carried out. Thus, a power sensitivity-based power dispatch method is elaborated to enhance the stability margin as well as update the UC solution. It is substantiated that in strong interaction cases, the system has more unstable operating regions (e.g., 1.33 times of those in weak interaction cases) and greatly affects the feasibility of the UC solution, but can be effectively tackled with the proposed power dispatch method.

A Unit Commitment Model Considering Feasibility of Operating Reserves under Stochastic Optimization Framework

Grid integration of renewable resources such as solar and wind energy can significantly raise the level of uncertainty in power systems, making the scheduled operation of generating units difficult. Therefore, the importance of operating reserves is more emphasized to prevent disruption by sudden changes in outputs of generators. In this paper, a stochastic unit commitment (UC) model to reflect uncertainty due to a large amount of renewable resources is proposed, in which upward and downward operating reserves are deployed simultaneously, and feasibility of the reserves is examined to make the deployed reserves supplied reliably. Uncertain parameters considered in the model are wind power availability, solar direct normal irradiance, and electric load. Two-stage stochastic programming is applied to the mathematical formulation, where UC decisions including dispatch are modeled as non-anticipative variables at the first stage, and redispatch decisions to serve realized electric demand are made at the second stage as recourse. By solving the UC problem, feasible and reliable stochastic UC and dispatch solutions can be provided to power system operators.

Balanced Standalone Clustering Unit Commitment Solution for Smart Grid Using Probability Algorithms

ABSTRACT For a smart grid system operating with clustered generating units, the challenge usually lies in the optimal scheduling of energy resources. Thus, the improvement of a unit commitment problem gains importance in the present power network. In this paper, a novel probability algorithm is proposed for solving the unit commitment problem, in which five separate units from a four-cluster group are operated for one day. This is done with the aim of optimizing the characteristics such as optional units, generation, operating, and marginal cost. Being a multi-objective function, the other factors such as cost response, unit commitment of supply clustering units, clustering of combined operational units, and CO2 emissions are also included. For this study, an RLC load is mathematically modeled in the cluster system, whereas the Unit Control is provided by a Converter and Battery Management Unit. The clustering model developed along with the Unit demand aims to increase the optional units (from 20 to 100 units), decrease the average demand (from 99 to 93 percentage), and lower the generating and marginal costs (from Rs.23,881 to Rs.21,079, Rs.43,082 to Rs.42,111, Rs.71,162 to Rs.64,955, Rs.83,169 to Rs.81,694, Rs.104,104 to Rs.102,928). The suggested algorithm is simulated for a comprehensive smart grid system and the response for marginal cost, CO2 emissions are obtained. In comparison to conventional schemes, the results of the proposed optimization approach show a reduction in the Carbon dioxide emission (in the range of 100 to 400 kg) and in the losses after adding working units with cluster spans of 0.5 to 1.5 kW.

Impact of battery degradation on energy cost and carbon footprint of smart homes

Optimal energy management in residential buildings with battery storage devices largely relies on the implementation of accurate battery degradation models. A proper wear model to use for the battery scheduling at homes should be universally applicable to different battery technologies and precisely model the impact of the major parameters that contribute to the capacity loss. In this work, a technology-agnostic battery wear model has been proposed to address the degradation caused by the irregular cycling of batteries in residential buildings. The proposed wear model provides the DoD-associated degradation for charging/discharging events between random SoCs only by employing the lifecycle curve of batteries which is usually provided by battery manufactures. This model has been formulated in the framework of mixed-integer programming (MIP) such that it can be directly incorporated into MIP optimization models to provide optimal unit commitment solutions without sacrificing other objectives of the problem. To facilitate the implementation of the nonlinear wear coefficient in MIP models, a curve-fitted version of the wear coefficient is used in the MIP problem. A comprehensive study on the costs and carbon footprint of a smart home has been carried out in this paper by producing a MIP problem that incorporates the proposed battery wear model. The problem has been solved with different approaches to minimize costs, capacity loss, and emissions of the system. The optimization results show that the application of the presented wear model managed to lower the cost, carbon footprint, and battery degradation by 78%, 30%, and 81% respectively.

Unit Commitment Solution Based on Improved Particle Swarm Optimization Method

This paper presents an algorithm to solve the unit commitment problem using the intelligence technique based on improved Particle Swarm Optimization (IPSO) for establishing the optimal scheduling of the generating units in the electric power system with the lowest production cost during a specified time and subjected to all the constraints. The minimum production cost is calculated based on using the Lambda Iteration method. A conventional method was also used for solving the unit commitment problem using the Dynamic Programming method (DP). The two methods were tested on the 14-bus IEEE test system and the results of both methods were compared with each other and with other references. The comparison showed the effectiveness of the proposed method over other methods.

Short‐term nodal load forecasting based on machine learning techniques

This paper introduces an advanced Short-term Nodal Load Forecasting (STNLF) method that forecasts nodal load profiles for the next day in power systems, based on the combined use of three machine learning techniques. Least Absolute Shrinkage and Selection Operator (LASSO) is employed to reduce the number of features for a single nodal load forecasting. Principal Component Analysis (PCA) is used to capture the features of historical loads in low-dimensional space compared to the original high-dimensional load space where features are barely possible to depict. Bayesian Ridge Regression (BRR) is utilized to decide the parameters of the prediction model from a statistics perspective. Tests based on modified PJM load data demonstrate the effectiveness of the proposed STNLF method compared to the state-of-the-art General Regression Neural Network (GRNN) method. Moreover, the reliability of the day-ahead Unit Commitment (UC) solution is shown to have been improved, based on the forecasted load data using the proposed STNLF method.

Role of grid and bulk storage in the integration of variable renewable energy resources: Framework for optimal operation-driven multi-period infrastructure planning

This paper presents a unified framework for quantifying the techno-economic value of various technologies in systems with high levels of variable renewables, which is of utter importance in evaluating roadmaps towards an affordable and sustainable future for various energy industry stakeholders. The optimal planning framework is based on integrating the solution of a transmission and generation/storage expansion problem with the solution of unit commitment, with the objective to minimize the total capital and operational expenditures over a selected horizon. The formulation includes, but is not limited to, traditional thermal units, pumped-hydro storage, batteries and transmission technologies. The decision variables include new cross-zonal transmission capacity, bulk energy storage and generation capacity, which are computed over the selected horizon while accounting for the impact of wind and solar variability on hourly (or sub-hourly) basis. A reduced representative version of the European system is used to demonstrate the value of transmission and bulk energy storage for a selected set of future scenarios, including scenarios corresponding to high proliferation of distributed energy storage and e-mobility. Comparative results are presented with emphasis on the renewable energy shares, investment costs, average cost of electricity, and carbon emission targets. Sensitivity analysis is performed considering technology and fuel costs.

Load State Transition Curve Based Unit Commitment for Production Cost Modeling With Wind Power

The production cost modeling (PCM) plays an important role in the mid/long-term power system planning. With the increasing penetration of renewable power, it becomes solving a series of unit commitment (UC) problems for time periods up to one or multiple years. This process is greatly challenged by the UC solution efficiency which hinders its practical use. In this paper, a fast UC method is proposed based on the load state transition curve (LSTC). Firstly, LSTC is proposed and obtained via load clustering. It simplifies the load model as well as maintains the necessary temporal characteristics. Secondly, the LSTC based UC model is developed by accommodating the constraint formulation to LSTC. Compared with the conventional ones, the scale of LSTC-based UC is dramatically reduced. The stochastic and volatile wind power is also taken into consideration. The case studies on the modified IEEE-RTS 1979 have verified the validity and feasibility of the proposed method in which the solution time is reduced from ∼300s to ∼12s with the cost error lower than 0.2%. It provides an efficient tool for the optimal planning and operation of large-scale power systems.

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.

Machine learning approaches to the unit commitment problem: Current trends, emerging challenges, and new strategies

Traditional power system operation and control decision-making processes, such as the unit commitment (UC) problem, primarily rely on the physical models and numerical calculations. With the growing scale and complexity of modern power grids, it becomes more complicated to accurately formulate the physical power system and more difficult to efficiently solve the corresponding UC problems. As a matter of fact, plenty of historical power system operation records as well as real-time data could provide useful information and insights of the underlying power grid. To this end, machine learning methods could be valuable to help understand the relationship of UC performance to power system parameters, reveal the rationality behind such relationship, and finally address UC problems in a more efficient and accurate way. This article discusses the current practices of using machine learning approaches to solve the mixed-integer linear programming based UC problems. The associated challenges are analyzed, and several promising strategies for adopting machine learning approaches to effectively solve UC problems are discussed in this article. In addition, we will also explore machine learning approaches to promptly solve steady-state nonlinear AC power flow and dynamics differential equations, so that they can be integrated into the UC problems to guarantee AC power flow security and dynamic stability of system operations, as compared to the current DC power flow constrained UC practice. Our studies show that machine learning, as model-free methods, is a valuable alternative or addition to the existing model-based methods. As a result, the effective combination of machine learning based approaches and physical model based methods are expected to derive more efficient UC solutions that can improve the secure and economic operation of power systems.