Two-stage Robust Unit Commitment Research Articles

Robust Unit Commitment With Decision-Dependent Uncertain Demand and Time-of-Use Pricing

Two-stage robust unit commitment (UC) is nowadays an effective decision-making model to support power system operations under uncertainty. This study extends the classical robust UC model to a novel formulation where the set of uncertain demand endogenously depends on the first-stage price decisions. We employ a generic time-of-use (ToU) pricing scheme, in a regulated system, to determine the optimal peak and off-peak price rates and periods of individual load buses. To exactly compute such ToU-based robust UC with decision-dependent demand, we customize and implement a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">parametric</i> variant of the column-and-constraint generation method to handle this complex program with a changing uncertainty set. The proposed model and the computational performance of the solution method are illustrated on two typical systems, and experimental results are discussed with a set of novel insights.

Two-Stage Robust Unit Commitment Problem With Complex Temperature and Demand Uncertainties

In this paper, we present and study a robust unit commitment model and some variants that consider complex temperature and demand uncertainties. Since there is a strong relationship among the efficiency of gas generators, demand, and temperature in practical systems, our robust models have both left- and right-hand-side (LHS and RHS, respectively) uncertainties. Unlike many existing robust models with RHS uncertainty only, the introduction of LHS uncertainty imposes a huge challenge in computing robust solutions. For those complex formulations, we analyze their structures, derive important properties, and design exact and fast approximation solution strategies under the column-and-constraint generation framework. Numerical experiments are conducted on typical IEEE test systems, which showcase the great performance of our solution methods and demonstrate a clear impact of complex and correlated uncertainties in system operations.

A fast linearized AC power flow-constrained robust unit commitment approach with customized redundant constraint identification method

The large-scale integration of renewable energy resources in the power system challenges its economic and secure operation. Particularly, the increasing penetration of renewable energy will result in insufficient system voltage regulation and reactive power support capabilities, and may cause high risks of nodal voltage and branch flow violations. Therefore, to hedge the operational risks under the worst realization of uncertainties of renewable energy sources, a two-stage robust unit commitment (UC) model is developed. Meanwhile, the convexified AC power flow model is incorporated in the robust UC model to more accurately characterize the real-time operating status of power systems. On this basis, an AC power flow-constrained robust unit commitment (ACRUC) model is formulated. A circular linearization method is then adopted to handle the quadratic constraints in the original AC power flow model, transforming them into tractable linear constraints. Furthermore, to reduce the computational complexity caused by the large-scale newly-added constraints after the linearization process, a customized redundant constraint identification (RCI) method is developed, in which two different modes (i.e., cold and warm start modes) are designed considering the difference in base case system operating condition for linearizing branch losses. Then, the redundant network security constraints could be identified by solving a series of relatively simple optimization subproblems. Numerical results on the modified NERL-118 test system indicate that the proposed model could accurately depict actual operation and scheduling conditions, and also verify that the proposed customized RCI method could effectively reduce the problem scale and improve the solution efficiency.

Two-stage robust unit commitment with the cascade hydropower stations retrofitted with pump stations

Cascade hydropower stations are excellent flexible resources to regulate the drastic fluctuations of wind and photovoltaic power generation in the hybrid energy system. By constructing pump stations between two adjacent upstream and downstream reservoirs, the conventional cascade hydropower stations can be transformed into a cascade pumped hydro energy storage (CPHES) system, which further can promote the integration of clean energy resources. In this paper, a two-stage robust unit commitment model for the cascade hydropower stations retrofitted with pump stations is established to address the renewable energy uncertainties. A short-term scheduling framework is proposed for the hybrid energy system including CPHES, which coordinates the operating cost and clean energy curtailment. Besides, a modified nested column-and-constraint algorithm is employed to solve the two-stage robust optimization problem with integer resources. Numerical tests performed on a modified IEEE 24-bus system and a large-scale practical power system verify the effectiveness of the proposed scheduling model and algorithm.

Multi-stage robust optimization of a multi-energy coupled system considering multiple uncertainties

As an effective means to improve the efficient use of energy, multi-energy coupled systems have indicated the important direction for the development of Energy Internet in the foreseeable future. However, the uncertainties that exist in various energy networks present severe challenges to the implementation of this innovative system. In this regard, this paper proposed a multi-stage robust optimization model for the coordinated operation of an electricity-gas-transportation coupled system, which simultaneously considered the uncertainties of traffic demands, wind power, and gas fuel consumption by gas-fired units. To conform to the non-anticipative sequential decision-making process for power system scheduling, the multi-stage robust unit commitment (UC) problem was established and considered as the master problem, which was solved by introducing a linear affine rule and the robust counterpart method. The gas network operation feasibility checks in each period were then addressed as the subproblems, and the generalized benders decomposition-based decoupling-coordination strategy was developed to solve the above master-subproblems iteratively. Simulation results demonstrate that the proposed multi-stage robust UC model can achieve a scheduling solution with superior economic performance and reduced conservativeness compared to the two-stage robust UC model. Furthermore, the effectiveness of the decoupling-coordination solving strategy was verified for the multi-energy coupled system.

A Multi-Timescale Two-Stage Robust Grid-Friendly Dispatch Model for Microgrid Operation

Uncertainty in renewable energy generation and load consumption is a great challenge for microgrid operation, especially in islanded mode as the microgrid may be small in size and has limited flexible resources. In this paper, a multi-timescale, two-stage robust unit commitment and economic dispatch model is proposed to optimize the microgrid operation. The first stage is a combination of day-ahead hourly and real-time sub-hourly model, which means the day-ahead dispatch result must also satisfy the real-time condition at the same time. The second stage is to verify the feasibility of the day-ahead dispatch result in worst-case condition considering high-level uncertainty in renewable energy dispatch and load consumptions. In the proposed model, battery energy storage system (BESS) and solar PV units are integrated as a combined solar-storage system. The BESS plays an essential role to balance the variable output of solar PV units, which keeps the combined solar-storage system output unchanged on an hourly basis. In this way, it largely neutralizes the impact of solar uncertainty and makes the microgrid operation grid friendly. Furthermore, in order to enhance the flexibility and resilience of the microgrid, both BESS and thermal units provide regulating reserve to manage solar and load uncertainty. The model has been tested in a controlled hardware in loop (CHIL) environment for the Bronzeville Community Microgrid system in Chicago. The simulation results show that the proposed model works effectively in managing the uncertainty in solar PV and load and can provide a flexible dispatch in both grid-connected and islanded modes.

A mixed-integer SDP solution approach to distributionally robust unit commitment with second order moment constraints

A power system unit commitment (UC) problem considering uncertainties of renewable energy sources is investigated in this paper, through a distributionally robust optimization approach. We assume that the first and second order moments of stochastic parameters can be inferred from historical data, and then employed to model the set of probability distributions. The resulting problem is a two-stage distributionally robust unit commitment with second order moment constraints, and we show that it can be recast as a mixed-integer semidefinite programming (MI-SDP) with finite constraints. The solution algorithm of the problem comprises solving a series of relaxed MI-SDPs and a subroutine of feasibility checking and vertex generation. Based on the verification of strong duality of the semidefinite programming (SDP) problems, we propose a cutting plane algorithm for solving the MI-SDPs; we also introduce a SDP relaxation for the feasibility checking problem, which is an intractable biconvex optimization. Experimental results on a IEEE 6-bus system are presented, showing that without any tunings of parameters, the real-time operation cost of distributionally robust UC method outperforms those of deterministic UC and two-stage robust UC methods in general, and our method also enjoys higher reliability of dispatch operation.

Feasibility Identification and Computational Efficiency Improvement for Two-Stage RUC With Multiple Wind Farms

The increasing penetration level of wind power challenges robust unit commitment with feasibilities and high computational burden. To meet these challenges, we propose two-fold advances for the two-stage robust unit commitment (TS-RUC), aiming at providing feasible solution and efficient decision tool for the TS-RUC with multiple wind farms. First, the feasibility identification method is proposed to ensure the tractability of the TS-RUC. The feasibility boundaries are determined based on values of two sets of introduced slack variables, the wind power curtailment and load shedding. Second, the disjunctive programming is used to improve the computational efficiency of the max-min problem, which is reformulated with convex hull relaxation (CHR) method to reduce constraints embedding binary uncertainty variables. Simulation results on the modified IEEE-118 bus system and Henan power grid demonstrate that the proposed improvement for the TS-RUC can be implemented for power systems with multiple wind farms and significant wind power. The feasibility identification can guarantee a feasible solution and the use of the CHR can improve computational efficiency.

Box-Based Temporal Decomposition of Multi-Period Economic Dispatch for Two-Stage Robust Unit Commitment

To ensure the feasibility of a unit commitment (UC) schedule under uncertainty, most existing two-stage robust UC methods formulate their second-stage problems as a multi-period economic dispatch (ED) problem with dynamic constraints, which does not properly model real-time ED where dynamic constraints relevant to the future operation are not certifiable. This paper proposes a two-stage robust UC method where a UC schedule and a box in a feasible operation set of each power source as its new feasible operation set are determined. As the multi-period ED problem with the refined feasible set at the second stage has no dynamic constraint, it is identical to a series of single-period ED problems. By modeling real-time ED as the single-period ED problems whose solutions depend only on uncertainties at the corresponding timeslots, the proposed method presents a practical framework of non-anticipative robust UC. Simulation results with a 118-bus system demonstrate the performance of the proposed method.

Two-Stage Robust Unit Commitment for Co-Optimized Electricity Markets: An Adaptive Data-Driven Approach for Scenario-Based Uncertainty Sets

Two-stage robust unit commitment (RUC) models have been widely used for day-ahead energy and reserve scheduling under high renewable integration. The current state of the art relies on budget-constrained polyhedral uncertainty sets to control the conservativeness of the solutions. The associated lack of interpretability and parameter specification procedures, as well as the high computational burden exhibited by available exact solution techniques call for new approaches. In this work, we use an alternative scenario-based framework whereby uncertain renewable generation is characterized by a polyhedral uncertainty set relying on the direct specification of its vertexes. Moreover, we present a simple, yet efficient, adaptive data-driven procedure to dynamically update the uncertainty set vertexes with observed daily renewable-output profiles. Within this setting, the proposed data-driven RUC ensures protection against the convex hull of realistic scenarios empirically capturing the complex and time-varying intra-day spatial and temporal interdependences among renewable units. The resulting counterpart features advantageous properties from a computational perspective and can be effectively solved by the column-and-constraint generation algorithm until $\epsilon$-global optimality. Out-of-sample experiments reveal that the proposed approach is capable of attaining efficient solutions in terms of cost and robustness while keeping the model tractable and scalable.

Multistage Multiresolution Robust Unit Commitment With Nondeterministic Flexible Ramp Considering Load and Wind Variabilities

This paper investigates the impacts of integrating nondeterministic flexible ramp reserves in a multistage multiresolution day-ahead robust unit commitment to cope with variability of renewable energy sources. While the common literature considers deterministic forms of flexible ramp reserves, the proposed affinely adjustable robust UC model considers explicit endogenous up and down subhourly ramp reserve deployment to effectively allocate flexible ramp capacities. In addition, unlike the conventional noncausal two-stage robust unit commitment models that immunize solutions against worst economic scenario with the dependency of decisions on the future information of uncertainty, the current nonconservative multistage model optimizes hourly commitment and dispatch scheduling for the base-case scenario, while ensuring that the specified subhourly causal ramp reserves can be adaptively adjusted. Moreover, dimensionality limitations of the conventional duality-based affinely adjustable robust optimizations are resolved. The effectiveness of the proposed model compared with conventional robust unit commitment frameworks is extensively illustrated on the IEEE 24-bus reliability test system and the IEEE 118-bus test system.

Risk–Based Admissibility Analysis of Wind Power Integration into Power System With Energy Storage System

The increasing high penetration of wind power will further increase the uncertainty in power systems, and three key issues should be addressed: 1) determining the maximum accommodation level of wind power without sacrificing system reliability; 2) quantifying the potential risk when the wind generation realization is beyond the prescribed uncertainty sets; and 3) how to reduce the risk loss. Motivated by these, a risk-based two-stage robust unit commitment (RUC) model is proposed to analyze the admissibility of wind power. In this model, the electricity storage system (ESS) is utilized for managing the wind power uncertainty to reduce the risk loss. Different from a determined uncertainty set in the previous RUC, the proposed method can flexibly adjust the uncertainty set by optimizing the operational risks including the wind spillage risk and load shedding risk. Conditional Value-at Risk (CVaR) is adopted to describe the risk loss when the real wind power output is beyond the predefined uncertainty set. Meanwhile, the low-probability, high-influence events are taken into the account based on CVaR to determine the optimal acceptable wind generation considering the tradeoff between reliability and economics. The proposed model is solved effectively by the modified column and constraint generation method. Case studies on two benchmark systems illustrate that the ESS can reduce the risk loss of power system and improve the ability to accommodate the uncertainty of wind generation.

Robust unit commitment with dispatchable wind power

The increasing penetration of uncertain generation such as wind and solar in power systems imposes new challenges to the unit commitment (UC) problem, one of the most critical tasks in power systems operations. The two most common approaches to address these challenges — stochastic and robust optimization — have drawbacks that restrict their application to real-world systems. This paper demonstrates that, by considering dispatchable wind and a box uncertainty set for wind availability, a fully adaptive two-stage robust UC formulation, which is typically a bi-level problem with outer mixed-integer program (MIP) and inner bilinear program, can be translated into an equivalent single-level MIP. Experiments on the IEEE 118-bus test system show that computation time, wind curtailment, and operational costs can be significantly reduced in the proposed unified stochastic–robust approach compared to both pure stochastic approach and pure robust approach, including budget of uncertainty.

Robust Integration of High-Level Dispatchable Renewables in Power System Operation

The increasing penetration of renewable energy sources (RES) requires more flexibility resources (FR), such as thermal units and storages. FR kept in the system can help accommodate the uncertainties from RES. The challenge is how the system can survive when the RES level is very high. In this paper, RESs are considered as full-role market participants. They can bid in the day-ahead market, and the powers they deliver to the market are controllable up to their maximum available powers. Therefore, RESs are effectively dispatchable and can function as FR. To integrate dispatchable renewables, a two-stage robust unit commitment (UC) and dispatch model is established. In the first stage, a base UC and dispatch is determined. In the second stage, all FRs including RESs are used to accommodate the uncertainties, which is a mixed-integer programming (MIP) problem. It is proved that the solution to the max–min problem can be identified directly whether the strong duality holds or not for the inner minimization problem. The solution robustness can be guaranteed by considering only one extra scenario. Numerical results show the effectiveness of the proposed model and its advantages over the traditional robust UC model with high-level RES penetration.

Multistage Adaptive Robust Optimization for the Unit Commitment Problem

The growing uncertainty associated with the increasing penetration of wind and solar power generation has presented new challenges to the operation of large-scale electric power systems. Motivated by these challenges, we present a multistage adaptive robust optimization model for the most critical daily operational problem of power systems, namely, the unit commitment (UC) problem, in the situation where nodal net electricity loads are uncertain. The proposed multistage robust UC model takes into account the time causality of the hourly unfolding of uncertainty in the power system operation process, which we show to be relevant when ramping capacities are limited and net loads present significant variability. To deal with large-scale systems, we explore the idea of simplified affine policies and develop a solution method based on constraint generation. Extensive computational experiments on the IEEE 118-bus test case and a real-world power system with 2,736 buses demonstrate that the proposed algorithm is effective in handling large-scale power systems and that the proposed multistage robust UC model can significantly outperform the deterministic UC and existing two-stage robust UC models in both operational cost and system reliability.

Two-stage robust UC including a novel scenario-based uncertainty model for wind power applications

The complex processes involved in the determination of the availability of power from renewable energy sources, such as wind power, impose great challenges in the forecasting processes carried out by transmission system operators (TSOs). Nowadays, many of these TSOs use operation planning tools that take into account the uncertainty of the wind-power. However, most of these methods typically require strict assumptions about the probabilistic behavior of the forecast error, and usually ignore the dynamic nature of the forecasting process.In this paper a methodological framework to obtain Robust Unit Commitment (UC) policies is presented; such methodology considers a novel scenario-based uncertainty model for wind power applications. The proposed method is composed by three main phases. The first two phases generate a sound wind-power forecast using a bootstrap predictive inference approach. The third phase corresponds to modeling and solving a one-day ahead Robust UC considering the output of the first phase.The performance of proposed approach is evaluated using as case study a new wind farm to be incorporated into the Northern Interconnected System (NIS) of Chile. A projection of wind-based power installation, as well as different characteristic of the uncertain data, are considered in this study.

Modeling Transmission Line Constraints in Two-Stage Robust Unit Commitment Problem

Integration of renewable energy sources and demand response poses new challenges to system operators as they increase the uncertainty of the power supply and demand. Recently, robust optimization techniques are applied to the unit commitment problem with uncertainty as an alternative to the stochastic programming approaches. However, it remains challenging to solve the robust unit commitment model with full transmission line constraints. In this paper, we propose novel acceleration techniques for solving two-stage robust unit commitment problem with consideration of full transmission line constraints. We use 1) the cutting-plane algorithm for the master problem, which dynamically includes critical transmission line constraints, and 2) column-generation methods, including the branch-and-price-and-cut algorithm and heuristic approaches, for the subproblems, which add only necessary transmission line dual variables on the fly. Computational results for the modified IEEE 118-bus system show that the combination of the cutting-plane algorithm and the heuristic column-generation approach greatly reduces the total solution time of the two-stage robust unit commitment problem.