Unit Commitment Research Articles

RoCoF Constrained Unit Commitment Considering Spatial Difference in Frequency Dynamics

The post-disturbance rate of change of frequency (RoCoF) is a critical index for low-inertia power system frequency stability. This paper proposes a RoCoF constrained unit commitment model so as to enhance the frequency stability in operation time-scale, where the spatial difference in frequency dynamics is considered and the RoCoF constraint is enforced for each node. The maximum of node RoCoF is approximated by two terms, i.e., the initial post-disturbance node RoCoF and the maximum of the center of inertia (COI) RoCoF. Analytical expressions of the node initial RoCoF under typical disturbances are derived. Then, a tractable relationship between the node initial RoCoF and the working status of generators is obtained by the piecewise linearization approach. Simulation results carried out on the IEEE 39-bus system demonstrate the proposed model can limit the node RoCoF in an economic and accurate manner. The adaptability to renewable power generation and online application are also discussed.

Multi-area Frequency-constrained Unit Commitment for Power Systems with High Penetration of Renewable Energy Sources and Induction Machine Load

Multi-area Frequency-constrained Unit Commitment for Power Systems with High Penetration of Renewable Energy Sources and Induction Machine Load

Transient Stability-Constrained Unit Commitment Using Input Convex Neural Network.

This article proposes a transient stability-constrained unit commitment (TSC-UC) model using input convex neural networks (ICNNs). An ICNN is trained to learn the transient function that maps prefault operation conditions (e.g., generator power output) to the transient stability index (TSI), which can be further utilized to identify the transient status (e.g., stable or unstable). Transient stability evaluation is conducted using the learned ICNN, without discretizing differential-algebraic equations (DAEs) or interacting with the time-domain simulation tools. Based on the convexity of ICNNs, the trained ICNN is exactly encoded as a linear programming (LP) model and integrated into conventional UC models to form a TSC-UC model. To impose transient stability constraints and expedite the solution process, the proposed TSC-UC model is decomposed into a UC master problem and two subproblems (i.e., network feasibility check subproblems and transient stability check subproblems). The decomposed problem is then iteratively solved using the Benders decomposition. Simulation tests are conducted in the New England 39-bus test system and IEEE 118-bus test system to verify the validity of the proposed approach.

A potential framework for cross-zonal reserve procurement on European power exchanges based on robust optimization

In order to prepare for unexpected events in the power system, regulation reserves are routinely procured in advance. Economic considerations dictate that it is advantageous to perform reserve procurement and energy allocation on a joint market platform using a single clearing algorithm. Furthermore, it is also beneficial if the option exists to allocate resources between different bidding zones to alleviate local shortages and corresponding price pressures. The present paper proposes a solution algorithm for this task in a European market environment without unit commitment and uplift payments to non-convex bidders. The main challenge of cross-zonal reserve allocation arises from the fact that deployment decisions are not yet known, therefore the actual deployment flows are uncertain at the time of procurement. The proposed algorithm handles this issue with robust optimization techniques and provides a guarantee of feasible transmission limits for deployment i.e. reserve deliverability. The clearing model is formalized as a computationally efficient Mixed Integer Linear Problem; its exact equations are presented along with case studies for the purpose of demonstration. The research is part of the FARCROSS H2020 project of the European Union.

Power System Operation Mode Calculation Based on Improved Deep Reinforcement Learning

Power system operation mode calculation (OMC) is the basis for unit commitment, scheduling arrangement, and stability analyses. In dispatch centers at all levels, OMC is usually realized by manually adjusting the parameters of power system components. In a new-type power system scenario, a large number of new energy sources lead to a significant increase in the complexity and uncertainty of a system structure, thus further increasing the workload and difficulty of manual adjustment. Therefore, improving efficiency and quality is of particular importance for power system OMC. This paper first considers generator power adjustment and line switching, and it then models the power flow adjustment process in OMC as a Markov decision process. Afterward, an improved deep Q-network (improved DQN) method is proposed for OMC. A state space, action space, and reward function that conform to the rules of the power system are designed. In addition, the action mapping strategy for generator power adjustment is improved to reduce the number of action adjustments and to speed up the network training process. Finally, 14 load levels under normal and N-1 fault conditions are designed. The experimental results on an IEEE-118 bus system show that the proposed method can effectively generate the operation mode under a given load level, and that it has good robustness.

Integration of Solar Photovoltaic Plant in the Eastern Sumba Microgrid Using Unit Commitment Optimization

Integrating renewable energy sources (RES) into island microgrids is usually done to provide a cost-effective electricity supply. The integration process is carried out by scheduling generating unit operations with a unit commitment (UC) scheme to ensure low system operating costs. This article discusses developing a UC optimization method for integrating solar photovoltaic plants in Indonesia’s Eastern Sumba microgrid power system. The scope of this study is the optimization algorithm of the UC, which consists of a priority list (PL) for the UC stage and an economic dispatch (ED) that relies on a genetic algorithm (GA) to minimize total operating costs (TOC). The results show that the PL-GA algorithm performs better than the extended priority list (EPL), and combinations of genetic algorithm and Lagrange, by applying continuous problem dispatch and improved binary GA hourly dispatch to meet ramping constraints. The application of RES incentive programs, such as carbon taxes and incentives for RES generation in calculating the TOC, shows an improvement in the financial feasibility analysis of the internal rate of return (IRR) and net present value (NPV) of actual projects in Indonesia.

Operation of Energy and Regulation Reserve Markets in the presence of Virtual Power Plant Including Storage System and Distributed Generation based on Unit Commitment Model

Operation of Energy and Regulation Reserve Markets in the presence of Virtual Power Plant Including Storage System and Distributed Generation based on Unit Commitment Model

Optimal Unit Commitment and Generation Scheduling of Integrated Power System with Plug-In Electric Vehicles and Renewable Energy Sources

The integration of wind energy sources and plug-in electric vehicles is essential for the efficient planning, reliability, and operation of modern electric power systems. Minimizing the overall operational cost of integrated power systems while dealing with wind energy sources and plug-in electric vehicles in integrated power systems using a chaotic zebra optimization algorithm (CZOA) is described. The proposed system deals with a probabilistic forecasting system for wind power generation and a realistic plug-in electric vehicle charging profile based on travel patterns and infrastructure characteristics. The objective is to identify the optimal scheduling and committed status of the generating unit for thermal and wind power generation while considering the system power demand, charging, and discharging of electric vehicles, as well as power available from wind energy sources. The proposed CZOA adeptly tackles the intricacies of the unit commitment problem by seamlessly integrating scheduling and the unit’s committed status, thereby enabling highly effective optimization. The proposed algorithm is tested for 10-, 20-, and 40-generating unit systems. The empirical findings pertaining to the 10-unit system indicate that the amalgamation of a thermal generating unit system with plug-in electric vehicles yields a 0.84% reduction in total generation cost. Furthermore, integrating the same system with a wind energy source results in a substantial 12.71% cost saving. Notably, the integration of the thermal generating system with both plug-in electric vehicles and a wind energy source leads to an even more pronounced overall cost reduction of 13.05%. The outcome of this study reveals competitive test results for 20- and 40-generating unit systems and contributes to the advancement of sustainable and reliable power systems, fostering the transition towards a greener energy future.

Quantifying Sustainable Urban Energy Solutions: Statistical Analysis of Renewable Adoption, Economic Viability, and Technological Innovations

In the context of quantifying sustainable and reliable urban microgrid energy solutions economic feasibility, and technological innovation, this study investigates the potential advantages of hybrid AC-DC microgrids (HMGs) over traditional AC microgrids by eliminating the need for voltage inverters and mitigating energy losses associated with AC-DC converters. We propose a probabilistic strategy for economic feasibility and optimizing the unit commitment of HMGs while considering the integration of renewable energy sources and batteries. To account for uncertainties stemming from load demand fluctuations, energy market price variations, and renewable energy source output power variability, we introduce a stochastic power flow model based on the 2 m point estimation method for economic feasibility and technological innovation of HMGs. Furthermore, we present a novel and robust hybrid optimization approach that combines the harmony search optimization method and genetic algorithm to explore the problem space and identify optimal solutions. This hybrid optimization method incorporates a unique two-stage modification technique, enhancing its search capabilities while preventing convergence to local optima. To assess the performance of our proposed method, we apply it to the IEEE test system. The results demonstrate the effectiveness of our approach in achieving optimal management of the microgrid system, emphasizing its relevance to the quantification of sustainable and reliable urban microgrid energy solutions.

Formulating a quadratic frequency nadir constraint in unit commitment based on energy conservation law

This paper proposes a quadratic formulation for the frequency nadir constraint (FNC) based on the energy conservation law. Incorporating the formulation into the unit commitment (UC) model, a mixed-integer quadratically constrained programming (MIQCP) model for frequency nadir constrained UC can be obtained, which can be solved efficiently by the MIQCP solver. The distinct feature of the formulation is that it considers the inertia difference among generators, which has a significant effect on the on/off schedule of generators. Besides, the formulation has a clear physical meaning and does not have to be linearized. The test on the WSCC 3-machine 9-bus benchmark system validates the accuracy of the formulation, and the case studies on a New England 10-machine 39-bus system confirm the effectiveness of the proposed formulation.

Self-Unit Commitment of Combined-Cycle Units with Real Operational Constraints

This paper highlights the importance of accurately modeling the operational constraints of Combined-Cycle Gas Turbines (CCGTs) within a unit-commitment framework. In practice, in Colombia, when given an initial dispatch by the Independent System Operator, CCGT plants are operated according to the results of heuristic simulation codes. Such heuristics often omit technical operating constraints, including hot, warm, or cold startup ramps; the minimum operation hours required for a gas turbine to start a steam turbine; the relationship between the dispatched number of steam and gas turbines; the load distribution among gas turbines; and supplementary fires. Most unit-commitment models in the literature represent standard technical constraints like startup, shutdown, up/down ramps, and in some cases, supplementary fires. However, they typically overlook other real-life CCGT operating constraints, which were considered in this work. These constraints are crucial in integrated energy systems to avoid equipment damage, which can potentially put CCGT plants out of service and ultimately lead to lower operating costs.

A novel scheduling approach of stochastic cogeneration model in power system environment using improved civilized swarm search algorithm to reduce cost and carbon emission

This study explores a cogeneration system's optimal commitment and generation scheduling while considering power and heat demand uncertainty. The deterministic model corresponding to the Cogeneration Based Unit Commitment Problem (CBUCP) cannot express the uncertainties related to input data and energy demand. In the present work, the stochastic Multi-Objective Cogeneration Based Unit Commitment Problem (MO-CBUCP) aims to obtain the optimal generation schedule at minimum operational cost and emission, considering uncertainties in the heat and power demand. To deal with continuous and binary variables of MO-CBUCP and obtain an optimal solution, an effective combination of nature-inspired techniques such as Civilized Swarm Search Algorithm (CSSA) and Binary Particle Swarm Optimization (BPSO) is employed for the cogeneration-based test system. To improve the exploration ability of CSSA, the predator and seasonal effect has been incorporated, as the movement of particles is affected by weather changes. Improved CSSA effectively balances the exploration and exploitation during the optimization. The results of the proposed technique are compared with other optimization techniques to show efficacy. The comparative analysis shows that the cogeneration plant significantly affects operating cost and emission for the deterministic and stochastic models.

A hybrid approach for unit commitment with splitting technique and local search

In the modern electricity market, solving the unit commitment (UC) problem becomes more challenging due to its large number of binary variables and coupling constraints. Therefore, the goal of this paper is to obtain nearly optimal solutions for such complex UC problems within specific time limits. To achieve this, a hybrid approach is presented in this paper, which incorporates a splitting technique and a local search for UC. The hybrid approach involves two steps. In the first step, the augmented Lagrange function (ALF) of UC is decomposed using a splitting technique based on the alternating direction method of multipliers (ADMM). The resulting sub-problems can be effectively solved in a distributed manner by utilizing Lagrange duality theory and binary variable characteristics. Additionally, the penalty parameters of the ALF are updated effectively with the sub-gradient method to diminish the influence of the initial penalty parameters on the algorithm. In the second step, the appropriate relaxation unit is selected using the binary variable characteristics in the current solution of ADMM. Further, the high-quality feasibility of the final solution is ensured through local search. The hybrid approach utilizes ADMM to quickly fix most binary variables in the UC model and then leverages the CPLEX solver to solve the mixed-integer linear programming (MILP) formulation of UC by fixing a large number of binary variables. Consequently, the CPLEX solver needs to branch fewer binary variables, reducing the local search time. The hybrid approach is applied to solve several power systems consisting of up to 1000 units. Compared with the CPLEX solver, the solution of the hybrid approach is found to be stable, and the relative gap of the solution is less than 1 %, demonstrating the effectiveness and performance of the proposed approach while meeting the time limit requirements of the power industry dispatching.

Developing a new flexibility-oriented model for generation expansion planning studies of renewable-based energy systems

This paper presents a flexibility-oriented generation expansion planning (GEP) model with the goal of increasing renewable energy penetration. The model incorporates GEP and unit commitment while considering improved reserve requirements. Utilizing GEP and unit commitment results in considering short-term operational constraints. Furthermore, given the increase in renewable portfolio standards (RPS) and the need for accurate reserve requirements determination, it is essential to consider improved reserve requirements in the proposed model. Moreover, this model utilizes a metric that measures power system flexibility deficiency and leads to flexible power system expansion by integrating it into the objective function. The flexibility-oriented GEP model is developed using mixed-integer linear programming and applied to a scaled-sized case study representing the national power system of Iran with a twenty-year planning horizon. The results show that neglecting improved reserve requirements leads to plans short on flexibility, and considering these requirements substantially declines the upward flexibility violation costs by 68% under the base scenario and 87% under increasing non-hydro RPS scenario. Furthermore, using the flexibility metric coupled with improved reserve requirements changes the optimal path for power system expansion and reduces the risk of flexibility deficiency. Also, increasing RPS by 35% would strongly depend on developing fast-response dispatchable generation units in the years before renewable energy resources expansion; however it doesn’t impose a significant extra cost of planning and the total cost will increase just by 9.43%.

Day-ahead reserve determination in power systems with high renewable penetration

We consider the operation of a power system with high renewable penetration and minimal network bottlenecks and provide a technique to determine the appropriate level of reserve to enforce. Within a daily scheduling framework, we model the production uncertainty of renewable units via scenarios and include security constraints per scenario to ensure an uneventful operation in case of failure of key thermal units. The rarely constraining network is modeled via areas with limited capacity at their interfaces. The considered decision-making framework results in a two-stage stochastic programming problem whose first stage decides on the commitment of thermal units and whose second stage reproduces, per scenario, the operation of the system with and without the failure of key thermal units. The optimal unit scheduling obtained from the proposed model implicitly identifies a generating reserve pattern that we compare with common rules used in industry for reserve identification, such as 20% or 30% of the demand. We use the Illinois 200-bus system to illustrate and computationally characterize the methodology proposed.

Profit-based unit commitment models with price-responsive decision-dependent uncertainty

Highlighting the increasing importance of demand elasticity in electricity markets and its impact on the revenues of power generating companies, this paper proposes new profit-based unit commitment models that effectively capture the uncertainty in the willingness-to-pay the price set for the elastic demand. To develop a new revenue scheme for power generating companies, we use a coupling function to model the willingness-to-pay response of the elastic demand as a decision-dependent source of uncertainty. The coupling function reflects how power generating companies’ pricing decisions may influence the market appeal (i.e., the buyer’s willingness-to-pay) and how it affects their revenues. The optimization models are stochastic mixed-integer nonlinear problems with nonconvex continuous relaxations and are not amenable to a numerical solution in their original forms. We devise a convexification reformulation method and derive valid inequalities to strengthen the formulation. We propose a learning framework to parameterize the willingness-to-pay functions and the concept of the value of the decision-dependent solution to quantify the value of the uncertainty modeling approach. Numerical tests on power systems of various sizes, demand portfolios, and price elasticity levels show (i) how the valid inequalities speed up the solution process, (ii) the benefits of properly modeling decision-dependent uncertainty and demand elasticity, and (iii) how the incorporation of decision-dependent uncertainty in demand elasticity can change the power generating companies’ decisions and revenue estimation.

A Bi-level optimization strategy for electric vehicle retailers based on robust pricing and hybrid demand response

The high penetration of electric vehicles (EVs) poses both opportunities and challenges for power systems. EV retailers, playing a critical role in the demand response mechanism, face market risks caused by uncertainties in electricity consumption and prices. To address the operational issues of large-scale EVs and tap the potential of EV retailers, a temporal and spatial domain-based optimization strategy is proposed, which is implemented on bi-level (referring to transmission and distribution grid networks). First, a physical scheduling model of the grid is established, consisting of a novel hybrid demand response mechanism considering the incentives of EV retailers and the retail electricity price of EV users, and a new robust retail electricity pricing strategy handling the uncertainties of EV behavior and the electric market. Then, a bi-level optimization strategy is presented: at the upper level, in the transmission network, based on the robust pricing strategy, a unit commitment model that coordinates the hybrid demand response with other distributed energy resources is designed to optimize load periods of EVs in the time domain; at the lower level, in the distribution network, an optimal power flow model is proposed to spatially dispatch the location of EV loads. The impacts of retail price profile, EV penetration, hybrid demand response mechanism, and EV load location are analyzed in ten tests using the IEEE 33 distribution network. Simulation results indicate that the robust pricing strategy can effectively handle uncertainties, the integration of the hybrid demand response mechanism into scheduling can ensure the benefits of all participants, and the bi-level optimization strategy can accommodate distributed energy resources temporally and spatially.

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).

DC-based security constraints formulation: A perspective of primal-dual interior point method

The DC network security constraints have been extensively studied in numerous power system problems, such as optimal power flow (OPF), security-constrained economic dispatch (SCED), and security-constrained unit commitment (SCUC). Power transfer distribution factors (PTDFs) are widely applied in DC network constraints. However, the PTDF matrix is extremely dense, making it difficult to solve security-constraint optimization problems. This paper investigates the computational inefficiency of PTDF-based security constraints from the perspective of matrix sparsity of primal–dual interior point method (IPM), and proposes a matrix transformation to restore sparsity during IPM iterations. It turns out that the transformation method is equivalent to solving the original optimization problem expressed in pure voltage angle. The regular B-θ formulation is also a variant of the proposed transformation. Numerical studies show that sparsity rather than the size of variables and constraints is the key factor impacting the speed of solving convex quadratic problems, i.e., OPF and SCED problems. The proposed transformation significantly outperforms the PTDF-based approach, achieving a 100x reduction in non-zero elements of the coefficient matrix and a 40x speed increase in barrier processes in a 25,000-bus network.

Adaptive cold-load pickup considerations in 2-stage microgrid unit commitment for enhancing microgrid resilience

In an extended main grid outage spanning multiple days, load shedding serves as a critical mechanism for islanded microgrids to maintain essential power and energy reserves that are indispensable for fulfilling reliability and resiliency mandates. However, using load shedding for such purposes leads to increasing occurrence of cold load pickup (CLPU) events. This study presents an innovative adaptive CLPU model that introduces a method for determining and incorporating parameters related to CLPU power and energy requirements into a two-stage microgrid unit commitment (MGUC) algorithm. In contrast to the traditional fixed-CLPU-curve approach, this model calculates CLPU duration, power, and energy demands by considering outage durations and ambient temperature variations within the MGUC process. By integrating the adaptive CLPU model into the MGUC problem formulation, it allows for the optimal allocation of energy resources throughout the entire scheduling horizon to fulfill the CLPU requirements when scheduling multiple CLPU events. The performance of the enhanced MGUC algorithm considering CLPU needs is assessed using actual load and photovoltaic (PV) data. Simulation results demonstrate significant improvements in dispatch optimality evaluated by the amount of load served, customer comfort, energy storage operation, and adherence to energy schedules. These enhancements collectively contribute to reliable and resilient microgrid operation.