Transmission Constrained Unit Commitment Research Articles

Accelerating transmission-constrained unit commitment via a data-driven learning framework

As a fundamental task in power system operations, transmission-constrained unit commitment (TCUC) decides ON/OFF state (i.e., commitment) and scheduled generation for each unit. Generally, TCUC is formulated as a mixed-integer linear programming (MILP) and must be resolved within a limited time window. However, due to the NP-hard property of MILP and the increasing complexity of power systems, solving the TCUC within a limited time is computationally challenging. Regarding the computation challenge, the availability of historical TCUC data and the development of the machine learning (ML) community are potentially helpful. To this end, this paper designs an ML-aided framework that can leverage historical data in enabling computation improvement of TCUC. In the offline stage, ML models are trained to predict the commitments based on historical TCUC data. In the online stage, the commitments are quickly predicted using the well-trained ML. Furthermore, a feasibility checking process is conducted to ensure the commitment feasibility. As a result, only a reduced TCUC with fewer binary variables needs to be solved, leading to computation acceleration. Case studies on an IEEE 24-bus and a practical 5655-bus system show the effectiveness of the presented framework.

A Data-driven Variable Reduction Approach for Transmission-constrained Unit Commitment of Large-scale Systems

This paper presents a data-driven variable reduction approach to accelerate the computation of large-scale transmission-constrained unit commitment (TCUC). Lagrangian relaxation (LR) and mixed-integer linear programming (MILP) are popular approaches to solving TCUC. However, with many binary unit commitment variables, LR suffers from slow convergence and MILP presents heavy computation burden. The proposed data-driven variable reduction approach consists of offline and online calculations to accelerate computational performance of the MILP-based large-scale TCUC problems. A database including multiple nodal net load intervals and the corresponding TCUC solutions is first built offline via the data-driven and all-scenario-feasible (ASF) approaches, which is then leveraged to efficiently solve new TCUC instances online. On/off statuses of considerable units can be fixed in the online calculation according to the database, which would reduce the computation burden while guaranteeing good solution quality for new TCUC instances. A feasibility proposition is proposed to promptly check the feasibility of the new TCUC instances with fixed binary variables, which can be used to dynamically tune parameters of binary variable fixing strategies and guarantee the existence of feasible UC solutions even when system structure changes. Numerical tests illustrate the efficiency of the proposed approach.

Ac Transmission-Constrained Unit Commitment with Data-Based Linear Power Flow

Ac Transmission-Constrained Unit Commitment with Data-Based Linear Power Flow

Capacity expansion planning for wind power and energy storage considering hourly robust transmission constrained unit commitment

The installed capacity of renewable energy in power systems is rising rapidly in recent years due to environmental pressure. And as the main asset of mitigating renewable output fluctuations, energy storage (ES) also has been greatly developed with the increase of renewable capacity. To this end, the capacity planning of renewables and ESs has drawn much attention and many methods have been proposed. In the formulations of capacity planning problems, more detailed and complicated operation constraints mean more accurate planning results, which is the consensus of many researchers. However, to guarantee the problem formulation tractable, the actual multistage operation process of power system is not properly considered in existing planning methods. Therefore, in this paper, a new capacity expansion planning method for wind power and ESs is proposed considering the actual multistage operation process of power system. Specially, the hourly robust transmission constrained unit commitment (TCUC) and economic dispatch (ED) are involved in this planning method and thus, it could accurately evaluate the operational cost under certain planning decision. Besides, to guarantee the solvability and computational efficiency of planning method, a parallel horizon-splitting method is improved to solve the long-time-horizon hourly robust TCUC problem, and a genetic algorithm nested gradient descent method is established to accelerate the solving of planning problem. With the actual multistage operation process, a more reasonable expansion planning decision is obtained and the computational efficiency is greatly improved by the proposed acceleration algorithm. Numerical tests verify the efficacy of proposed method.

Multistage Transmission-Constrained Unit Commitment With Renewable Energy and Energy Storage: Implicit and Explicit Decision Methods

Generation scheduling decision-making of power systems with renewable energy and energy storage (ES) is a multistage stochastic programming problem in nature, in which unit commitment (UC) decisions have to be made one day ahead before uncertainties are revealed, and hourly economic dispatch (ED) decisions are successively determined when real uncertainty realizations are observed gradually (i.e., nonanticipativity). To this end, inappropriate ED decisions at current hour may cause infeasibility of future ED decisions (i.e., robustness). Thus, how to properly schedule thermal unit outputs and ES charging/ discharging power against uncertainties becomes an important and urgent issue. In this paper, two mixed-integer linear programming (MILP) methods are proposed to solve the scheduling problem of thermal units and ESs with uncertainties while ensuring solution robustness and nonanticipativity: explicit and implicit decision methods. Specifically, explicit decision method directly assumes affine policies between decision variables and uncertainty realizations; implicit decision method explores safe ranges of thermal unit outputs and ES state-of-charge (SOC) levels to guarantees feasibility of future ED solutions. Both methods can guarantee the nonanticipativity and robustness of multistage solutions. Numerical tests illustrate effectiveness of the proposed methods.

Robust transmission constrained unit commitment: a column merging method

With rapid integration of power sources with uncertainty, robustness must be carefully considered in the transmission constrained unit commitment (TCUC) problem. The overall computational complexity of the robust TCUC methods is closely related to the vertex number of the uncertainty set. The vertex number is further associated with 1) the period number in the scheduling horizon as well as 2) the number of nodes with uncertain injections. In this paper, a column merging method (CMM) is proposed to reduce the computation burden by merging the uncertain nodes, while still guar-anteeing the robustness of the solution. By the CMM, the transmission constraints are modified, with the parameters obtained based on an analytical solution of a uniform approximation problem, so that the computational time is negligi-ble. The CMM is applied under a greedy-algorithm based framework, where the number of merged nodes and the ap-proximation error can be well balanced. The CMM is designed as a preprocessing tool to improve the solution efficiency for robust TCUC problems and is compatible with many solution methods (like two-stage and multi-stage robust optimi-zation methods). Numerical tests show the method is effective.

Data-Driven Screening of Network Constraints for Unit Commitment

The transmission-constrained unit commitment (TC-UC) problem is one of the most relevant problems solved by independent system operators for the daily operation of power systems. Given its computational complexity, this problem is usually not solved to global optimality for real-size power systems. In this paper, we propose a data-driven method that leverages historical information to screen out network constraints in the TC-UC problem. First, past data on demand and renewable generation throughout the network are used to learn the congestion status of transmission lines. Then, we infer the lines that will not become congested for upcoming operating conditions based on such learning and disregard their capacity constraints. This way, we formulate a reduced TC-UC problem that is easier to solve. Numerical results on a medium- and a large-size power system show that the proposed approach outperforms existing ones by significantly reducing the computational time while obtaining solutions that are equal or close to the one obtained with the original TC-UC problem. Furthermore, the purely data-driven method we propose can be seamlessly complemented with a constraint generation procedure to guarantee that the optimal solution to the original TC-UC problem is eventually recovered.

Robust transmission constrained unit commitment under wind power uncertainty with adjustable conservatism

This study proposes a novel robust transmission-constrained unit commitment model with adjustable conservatism (denoted as RAC-TCUC). Ellipsoidal uncertainty set (EUS) is adopted in this model to well fit the spatial-temporal correlated wind power. The affine policy is utilised in the generation dispatch process of the model for the sake of computational tractability. To reduce the conservatism, a novel criterion for budget value selection of the EUS is presented. Moreover, this study discusses a crucial, yet barely addressed issue in the literature: the feasibility of the solution against the realisation of uncertainties beyond the prescribed EUS. To prove the validity of the criterion, an analytical relationship between the budget value of the EUS and the actual probability of solution's feasibility against all possible scenarios of uncertainties is presented. Finally, the testing results demonstrate the effectiveness and economic benefits of the proposed method.

Fast solution method for TCUC with long time horizon based on horizon splitting

Long-term transmission constrained unit commitment (LT-TCUC) is an important tool in generation expansion planning and has got much attention in recent years. When traditional Lagrangian relaxation (LR) and mixed integer programming (MIP) based methods are used to solve LT-TCUC problems, serious challenges related with the solution efficiency are encountered. This paper proposes a fast method for solving TCUC with long time horizon based on horizon splitting. The basic idea is to partition the whole horizon into several short time intervals, and then relax the coupling constraints between consecutive intervals (ramp rate constraints and minimum up/down time constraints). Sub-TCUC problem in each time interval is then solved independently (in parallel) with CPLEX and the solutions are further adjusted based on MIP to satisfy the relaxed coupling constraints. In this way, the feasibility of the solution is guaranteed and the solutions to the sub-TCUC problems are connected. Salient features of the method include that the solution efficiency is guaranteed and the solution quality can be estimated based on the optimality gap. The proposed method is tested on the modified IEEE 24-bus system, 118-bus systems, and a regional grid in China with one-month or one-year time horizon. Numerical results show that the solution method is efficient.

Multi-stage robust transmission constrained unit commitment: A decomposition framework with implicit decision rules

With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment problem. Among all methods, two-stage and multi-stage robust optimization-based methods are the most widely adopted ones. In the two-stage methods, non-anticipativity of economic dispatch (ED) decisions are not considered. While in multi-stage methods, explicit decision rules (like affine decision rules) are adopted to guarantee non-anticipativity of ED decisions, the computational burden can be heavy and the optimality of the solution is affected. In this paper, a multi-stage robust TCUC formulation with implicit decision rules is proposed, as well as a decomposition framework to solve it. The solutions are proved to be multi-stage robust and non-anticipativity of ED decisions is guaranteed. Meanwhile, a computationally efficient time-decoupled solution method for the feasibility check subproblems is also proposed, such that the method is suitable for large-scale TCUC problems with uncertain power injections. Numerical tests are conducted on IEEE 118-bus system and Polish 2383-bus system. The proposed method outperforms the multi-stage robust method with explicit decision rules in solution’s economic performances, and is more computationally efficient than the all-scenario-feasible method. The effectiveness of time-decoupled solution method is also verified.

Using Generalized Generation Distribution Factors in a MILP Model to Solve the Transmission-Constrained Unit Commitment Problem

This study proposes a mixed-integer linear programming (MILP) model to figure out the transmission-constrained direct current (DC)-based unit commitment (UC) problem using the generalized generation distribution factors (GGDF) for modeling the transmission network constraints. The UC problem has been reformulated using these linear distribution factors without sacrificing optimality. Several test power systems (PJM 5-bus, IEEE-24, and 118-bus) have been used to validate the introduced formulation. Results demonstrate that the proposed approach is more compact and less computationally burdensome than the classical DC-based formulation, which is commonly employed in the technical literature to carry out the transmission network constraints. Therefore, there is a potential applicability of the accomplished methodology to carry out the UC problem applied to medium and large-scale electrical power systems.

Transmission Constrained UC With Wind Power: An All-Scenario-Feasible MILP Formulation With Strong Nonanticipativity

To deal with the difficulties caused by uncertainty of renewable energy sources in solving transmission constrained unit commitment (TCUC), robust optimization (RO) and scenario-based stochastic optimization (SO) methods have gained popularity in recent years. However, RO formulations have a multilevel (min-max-min or min-max) structure and the solution methods are usually complicated. On the other hand, when SO-based formulation is adopted, a careful balance is often required between accuracy and scale of the formulation, since they are conflicting with each other when determining the number of scenarios. Moreover, nonanticipative constraints on economic dispatch (ED) decisions are sometimes not considered in two-stage stochastic UC formulation. An example is given in this paper to show that this may have a serious consequence. The motivation of this paper is to establish a TCUC formulation that can address the above concerns. In summary, the proposed formulation has three features including: it is single-level rather than multilevel, it is established based on very limited scenarios while the solution is feasible to all scenarios, and finally, nonanticipativity of both UC and ED decisions is guaranteed by the formulation. Numerical testing is also performed and the results show that the proposed formulation is effective.

Power‐based transmission constrained unit commitment formulation with energy‐based reserve

Staircase transmission constrained unit commitment (TCUC) formulations have been used for decades and are considered as energy-based TCUC formulations (EbUC). Recently, it has been reported that EbUC formulations may result in undeliverable energy schedules. Some power-based TCUC formulations (PbUC) have been proposed to address this problem. However, exact continuous time-based power outputs of units are usually approximated in these PbUC formulations and ramp-rate capacities of units are not accurately modelled. Besides, the implicit coupling between ramp-rate constraints and spinning reserves is neglected in both EbUC and PbUC formulations, which may cause that scheduled spinning reserve levels are unavailable in some time periods. To address these problems, a new PbUC formulation is proposed in this study with continuous time-based power outputs. It is found that the formulation can be transformed into an equivalent mathematical program and a Lagrangian relaxation-based approach is presented. Numerical testing is performed for a 10-unit system and an IEEE 24-bus system. Results show that the model and the solution algorithm in this study are effective.

Transmission-Constrained Unit Commitment Considering Combined Electricity and District Heating Networks

Wind power integration could be restricted by inflexible operation of combined heat and power (CHP) units due to the strong linkage between power generation and heating supply in winter. Utilization of the heat storage capacity of existing district heating network (DHN) is a cost-effective measure to enhance power system operational flexibility to accommodate large amounts of variable wind power. In this paper, transmission-constrained unit commitment (UC) with combined electricity and district heating networks (UC-CEHN) is formulated with a linear DHN model to coordinate short-term operation of electric power and district heating systems. The heat storage capacity of the DHN is modeled by capturing the quasi-dynamics of pipeline temperature. Both deterministic and robust models are developed to incorporate UC with the linear DHN model. Case studies are carried out for two test systems to show the potential benefits of the proposed method in terms of wind power integration and efficient operation.

Toward Cost-Efficient and Reliable Unit Commitment Under Uncertainty

Large-scale integration of wind farms causes volatile bus net injections. Although these fluctuations are anticipated, their timing, magnitude and duration cannot be predicted accurately. In order to maintain the operational reliability of the system, this uncertainty must be adequately addressed at the day-ahead generation scheduling stage. The ad-hoc reserve rules incorporated in deterministic unit commitment formulations do not adequately account for this uncertainty. Scenario-based stochastic unit commitment formulations model this uncertainty more precisely, but require computationally demanding simulations. Interval and robust optimization techniques require less computing resources, but produce overly conservative and thus expensive generation schedules. This paper proposes a transmission-constrained unit commitment formulation that improves the performance of the interval unit commitment. The uncertainty is modeled using upper and lower bounds, as in the interval formulation, but inter-hour ramp requirements are based on net load scenarios. This improved interval formulation has been tested using the IEEE RTS-96 and compared with existing stochastic, interval and robust unit commitment techniques in terms of solution robustness and cost. These results show that the proposed method outperforms the existing interval technique both in terms of cost and computing time.

A Hybrid Stochastic/Interval Approach to Transmission-Constrained Unit Commitment

This paper proposes a new transmission-constrained unit commitment method that combines the cost-efficient but computationally demanding stochastic optimization and the expensive but tractable interval optimization techniques to manage uncertainty on the expected net load. The proposed hybrid unit commitment approach applies the stochastic formulation to the initial operating hours of the optimization horizon, during which the wind forecasts are more accurate, and then switches to the interval formulation for the remaining hours. The switching time is optimized to balance the cost of unhedged uncertainty from the stochastic unit commitment against the cost of the security premium of the interval unit commitment formulation. These hybrid, stochastic, and interval formulations are compared using Monte Carlo simulations on a modified 24-bus IEEE Reliability Test System. The results demonstrate that the proposed unit commitment formulation results in the least expensive day-ahead schedule among all formulations and can be solved in the same amount of time as a full stochastic unit commitment. However, if the range of the switching time is reduced, the hybrid formulation in the parallel computing implementation outperforms the stochastic formulation in terms of computing time.

Transmission‐constrained intrahour coordination of wind and pumped‐storage hydro units

This study proposes a coordination methodology for wind and pumped-storage hydro (PS) units in the day-ahead operation planning of power systems. PS units that can store the extra wind energy will improve the dispatchability of variable wind energy for delivering hourly firmed energy to a power grid. With coordination, the PS unit can offset intrahour wind energy imbalances (i.e. deviations from hourly schedules) and minimise wind energy curtailments. The proposed coordination, which is incorporated into the transmission-constrained unit commitment, can be used by a vertically integrated utility or an independent system operator. The concept of intrahour wind energy imbalances and the wind-PS coordination is illustrated using two case studies. The numerical results for the 6-bus and the IEEE 118-bus system include case studies with and without the coordination of PS and wind generation units. The results that include the intrahour variability of real-time wind speed show the applicability of the proposed wind-PS coordination approach to the short-term power system operation.

Network reduction in the Transmission-Constrained Unit Commitment problem

This paper examines a preprocessing technique for a Mixed Integer Linear Programming (MILP) formulation of the Transmission-Constrained Unit Commitment problem (TC-UC). Incorporating transmission constraints into the Unit Commitment problem can significantly increase the size and difficulty of the problem. By examining the structure of the transmission network, variables that have no impact on the quality of the overall solution can be identified and removed. This preprocessing can reduce the time needed to solve the linear programming relaxation of the MILP, and as a result, the MILP itself. Illinois’s transmission network was used to test the benefit of the proposed technique. Preprocessing was able to remove 30% of the buses in the transmission network. This reduction led to a significant decrease in the time needed to solve a 24h TC-UC problem. An added benefit of the preprocessing is that symmetry can be introduced into the problem. Identifying this symmetry and exploiting it can improve overall solution times even further.

Non-Linear Pricing in Transmission Constrained Electricity Markets: A Congestion Rents Application

Based on recent research of non-linear pricing for single-node unit commitment models, this paper proposes a transmission constrained non-linear pricing alternative based coordination functions added to the classic decomposition Lagrangian relaxation algorithm to solve transmission constrained unit commitment models. The new coordination algorithms finds agent’s purchase and sell prices that coordinate the market in the absence of classic equilibrium. Since non-linear prices differ for each agent connected to a transmission node, the value of the congestion rents are redefined so that the new pricing mechanism is taken in to account. The redefinition of congestion rents is necessary so that the implementation of financial transmission rights, in their varied forms, is still possible in order to provide a price hedging mechanism in the nodal spot market.In this study, we propose a solution of unit commitment problem with network constraints and FTR´s using non-linear prices. The proposes prices have been applied to IEEE 14 and 30 test systems with 20 and 35 generators for a single period. The result shows that the proposed prices are capable to obtain satisfactory schedules without any interest conflicts.

A transmission-constrained unit commitment method in power system scheduling

This paper presents a transmission-constrained unit commitment method using a Lagrangian relaxation approach. Based on a DC power flow model, the transmission constraints are formulated as linear constraints. The transmission constraints, as well as the demand and spinning reserve constraints, are relaxed by attaching Lagrange multipliers. A three-phase algorithmic scheme is devised including dual optimization, a feasibility phase and unit decommitment. A large-scale test problem with more than 2200 buses and 2500 transmission lines is tested along with other test problems.