Stochastic Unit Commitment and Optimal Power Trading Incorporating PV Uncertainty

Unit Commitment (UC) is an essential decision taken by ISO to ensure reliable and economic operation of the power system. Renewable energy penetration is increasing in a power system due its inexhaustive and environment friendly nature. Renewable energy poses some challenges to the present power systems due to its high uncertainty. In addition to this, the impact of contingencies on the power system also cannot be ignored. Both renewable energy and contingencies make the power system more prone to uncertain behaviour which can affect the economics as well as reliability of the power system. In this paper, UC is solved using deterministic and stochastic approaches. Deterministic UC considers forecasted wind data and Stochastic UC considers uncertain scenarios of the wind. Practically the power system is more prone to uncertainty because of renewable energy penetration and contingencies. Thus, this paper discusses how a UC decision varies as more uncertainties arises. Mixed Integer Linear Programming (MILP) is used for obtaining the UC decision results for IEEE 30-bus system. The results of UC, power dispatch and generation costs obtained with the two approaches have been compared.

As an attempt to reduce reliance on fossil fuels to satisfy electricity demand, the penetration of renewable sources like wind or solar power has experienced rapid growth in recent years. Due to their intermittent nature, the exact contribution of renewable sources to electricity supply is at least partly unknown. In order to be able to accommodate this uncertainty in real-time, sufficient capacities in the form of thermal and hydro power plants must be available. On that account, power system operators solve the so-called unit commitment problem after bidding in the day-ahead market closes to derive schedules for their power plants which can ensure system reliability at low costs. In literature, two approaches have mainly been studied in this context: Robust and stochastic unit commitment. Being a worst-case formulation, robust unit commitment puts its focus on reliability. A common drawback of this approach is that it tends to deliver over-conservative schedules. Stochastic unit commitment on the other hand creates more cost-effective schedules by preparing for the expected case, but either fails to guarantee system reliability or puts a high workload on the CPU. The limitations of known formulations have sparked interest in so-called hybrid approaches, which aim at combining the ideas of robust and stochastic unit commitment in a favorable way. This paper reports a novel hybrid approach to solve the unit commitment under uncertainty, which yields both robust and cost-efficient schedules. The new method respects the continuous nature of uncertainties and is thus in particular favorable for applications in power systems with high penetration of volatile renewable sources. By merging the ideas of robust and stochastic unit commitment, the proposed hybrid formulation minimizes the expected worst-case dispatch costs. Our method relies on partitioning the continuous range of the uncertainties into subsets. By means of the number of partitions, the solution can be adjusted between the conservative robust and the cost-efficient stochastic unit commitment in a user-friendly manner. A Benders decomposition algorithm is derived to solve the hybrid unit commitment efficiently. Finally, a case study confirms the superior performance of the proposed method.

As more wind power and other renewable resources are being integrated into the electric power grid, the forecast uncertainty brings operational challenges for the power system operators. In this report, different operational strategies for uncertainty management are presented and evaluated. A comprehensive and consistent simulation framework is developed to analyze the performance of different reserve policies and scheduling techniques under uncertainty in wind power. Numerical simulations are conducted on a modified version of the IEEE 118-bus system with a 20% wind penetration level, comparing deterministic, interval, and stochastic unit commitment strategies. The results show that stochastic unit commitment provides a reliable schedule without large increases in operational costs. Moreover, decomposition techniques, such as load shift factor and Benders decomposition, can help in overcoming the computational obstacles to stochastic unit commitment and enable the use of a larger scenario set to represent forecast uncertainty. In contrast, deterministic and interval unit commitment tend to give higher system costs as more reserves are being scheduled to address forecast uncertainty. However, these approaches require a much lower computational effort Choosing a proper lower bound for the forecast uncertainty is important for balancing reliability and system operational cost in deterministic and interval unit commitment. Finally, we find that the introduction of zonal reserve requirements improves reliability, but at the expense of higher operational costs.

In recent years, high penetration of variable generating sources, such as wind power, has challenged independent system operators (ISO) in keeping a cheap and reliable power system operation. Any deviation between expected and real wind production must be absorbed by the power system resources (reserves), which must be available and ready to be deployed in real time. To guarantee this resource availability, the system resources must be committed in advance, usually the day-ahead, by solving the so-called unit commitment (UC) problem. If the quantity of committed resources is extremely low, there will be devastating and costly consequences in the system, such as significant load shedding. On the other hand, if this quantity is extremely high, the system operation will be excessively expensive, mainly because facilities will not be fully exploited. This thesis proposes computationally efficient models for optimal day-ahead planning in (thermal) power systems to adequately face the stochastic nature of wind production in the real-time system operation. The models can support ISOs to face the new challenges in short-term planning as uncertainty increases dramatically due to the integration of variable generating resources. This thesis then tackles the UC problem in the following aspects: Power system representation: This thesis identifies drawbacks of the traditional energy-block scheduling approach, which make it unable to adequately prepare the power system to face deterministic and perfectly known events. To overcome those drawbacks, we propose the ramp-based scheduling approach that more accurately describes the system operation, thus better exploiting the system flexibility. UC computational performance: Developing more accurate models would be pointless if these models considerably increase the computational burden of the UC problem, which is already a complex integer and non-convex problem. We then devise simultaneously tight and compact formulations under the mixed-integer programming (MIP) approach. This simultaneous characteristic reinforces the convergence speed by reducing the search space (tightness) and simultaneously increasing the searching speed (compactness) with which solvers explore that reduced space. Uncertainty management in UC: By putting together the improvements in the previous two aspects, this thesis contributes to a better management of wind uncertainty in UC, even though these two aspects are in conflict and improving one often means harming the other. If compared with a traditional energy-block UC model under the stochastic (deterministic) paradigm, a stochastic (deterministic) ramp-based UC model: 1) leads to more economic operation, due to a better and more detailed system representation, while 2) being solved significantly faster, because the core of the model is built upon simultaneously tight and compact MIP formulations. To further improve the uncertainty management in the proposed ramp-based UC, we extend the formulation to a network-constrained UC with robust reserve modelling. Based on robust optimization insights, the UC solution guarantees feasibility for any realization of the uncertain wind production, within the considered uncertainty ranges. This final model remains as a pure linear MIP problem whose size does not depend on the uncertainty representation, thus avoiding the inherent computational complications of the stochastic and robust UCs commonly found in the literature.

Power reserves are usually scheduled in day-ahead unit commitment (UC) to minimize operating costs while maintaining system security. In applying basic UC (bUC) after a contingency, the system frequency may fall upon the activation of the load-shedding global control (under-frequency load-shedding or UFLS) limits. Small isolated microgrids are more sensitive to this issue due to their lack of inertia. Including dynamic considerations into the bUC problem can minimize UFLS activation and also avoid the need for the operator to later check the short-term feasibility of a bUC solution. These proposals are known as Frequency-Constrained UC (FCUC), although the implementation are very time-consuming. FCUC implementation will increase the system’s operational costs, which should be calculated to estimate remuneration to the safety service based on the additional reserve provision. The electrical system of Gran Canaria island has suffered several episodes of greater blackouts in recent years. Shortly, there will be 242 MW of wind generation installed (26% of the thermal power installed on Gran Canaria). The main objective of this work is to improve the island system reliability by means of an FCUC formulation applied by the system operator in practice, including renewable sources. The results show that the frequency values remained within the admissible boundaries, but the system’s operational costs increased by around 13%.

Low-carbon electric power systems are often characterized by high shares of renewables, such as wind power. The variable nature and limited predictability of some renewables will require novel system operation methods to properly size and cost-efficiently allocate the required reserves. The current state-of-the-art stochastic unit commitment models internalize this sizing and allocation process by considering a set of scenarios representing the stochastic input during the unit commitment optimization. This results in a cost-efficient scheduling of reserves, while maintaining the reliability of the system. However, calculation times are typically high. Therefore, in this paper, we merge a state-of-the-art probabilistic reserve sizing technique and stochastic unit commitment model with a limited number of scenarios in order to reduce the computational cost. Results obtained for a power system with a 30% wind energy penetration show that this hybrid approach allows to approximate the expected operational costs and reliability of the resulting unit commitment of the stochastic model at roughly one thirtieth of the computational cost. The presented hybrid unit commitment model can be used by researchers to assess the impact of uncertainty on power systems or by independent system operators to optimize their unit commitment decisions taking into account the uncertainty in their system.

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, in this paper we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations.

Integration of renewable generation uncertainties into stochastic unit commitment considering reserve and risk: A comparative study

Data-adaptive robust unit commitment in the hybrid AC/DC power system

Stochastic unit commitment in microgrids: Influence of the load forecasting error and the availability of energy storage

To enhance controllability, flexibility, and economic performance, this approach develops a dynamic model for the joint optimization of unit commitment (UC) and optimal transmission switching (OTS), considering grid topology changes. This mixed‐integer nonlinear problem sees computational complexity rise sharply with system size. A consensus‐based distributed quantum decomposition algorithm (QDA) is proposed, splitting the problem into locally relaxed sub‐problems (SPs) and consensus‐constrained master problems (MPs). Multi‐stage strategy is employed to iteratively refine solutions by incorporating cutting planes. For MPs, quadratic unconstrained binary optimization Hamiltonians are designed to be compatible with quantum computing, their complexity is simplified by inserting up/down constraint Hamiltonians that eliminate auxiliary binary variables. Leveraging quantum annealing and a photonic quantum computer, these Hamiltonians are efficiently solved to explore optimal UC and grid topology. Results on the 6‐Bus System validate the centralized QDA, while the consensus‐based distributed QDA outperforms Gurobi9 in operational costs and solution time for the IEEE RTS 24‐Bus System. The joint UC‐OTS optimization reduces costs compared to static networks’ UC, demonstrating the mutual influence of unit and topology optimization. This approach won the Grand Prize of the 2024 “Challenge and Leadership Selection” Special Competition of the 19th National Challenge Cup Competition.

Due to their uncertain and variable nature, the large-scale integration of wind and solar power poses significant challenges to the generator scheduling process in power systems. To support this process, system operators require using repeatedly updated forecasts of the best possible quality for renewable power. Motivated by this, the present work aims to study the benefits of incorporating spatiotemporal dependence and seasonalities into probabilistic forecasts for the intraday unit commitment (UC) process. With this purpose, a highly efficient forecasting-optimization scheme is proposed, which is composed of a detrended periodic vector autoregressive model and a technology-clustered interval UC model. The proposed approach is tested on a 120-GW power system with 210 conventional generators using real wind and solar measurements and compared to existing deterministic and stochastic UC techniques alongside standard forecasting methods. Extensive computational experiments show that the incorporation of spatiotemporal dependence and seasonalities into forecasts translates in a reduction of up to 1.55% in operational costs for a daily UC relative to standard practice, the application of intraday instead of daily UC runs further reduces operational costs in up to 1.51%, and the proposed forecasting-optimization scheme takes less than 10 h to simulate a whole year.

This paper presents centralized control for a wind farm using model predictive control (MPC) method. In order to solve intra-day unit commitment (UC) problem, the UC problem is solved by using the MPC method with short-term wind power forecasting. We introduce a new dynamics model for the UC with some constraints to utilize the benefits of the MPC method. The objective function considering the operation and maintenance costs is formulated by adding a new variable in order to average the operating time of each wind turbine (WT) within the whole time. The proposed method could solve the UC problems on-line using the prediction time horizon that could be selected flexibly considering time horizon based on wind power forecasting errors. From the simulation study using 10 WTs, we observed that the proposed dynamics model of UC effectively provided the optimal solution to each scenario. Numerical study will validate that the proposed method can be applied to solving the UC problem of a large scale wind farm by aggregating WTs.

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.

Wind power forecasting uncertainty and unit commitment