Hybrid Robust/Stochastic Unit Commitment With Iterative Partitions of the Continuous Uncertainty Set

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 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.

This paper focuses on the optimal unit commitment (UC) scheme along with optimal power trading for the Northeast Power System (NEPS) of Afghanistan with a penetration of 230 MW of PV power energy. The NEPS is the biggest power system of Afghanistan fed from three main sources; 1. Afghanistan’s own power generation units (three thermal units and three hydro units); 2. imported power from Tajikistan; 3. imported power from Uzbekistan. PV power forecasting fluctuations have been handled by means of 50 scenarios generated by Latin-hypercube sampling (LHS) after getting the point solar radiation forecast through the neural network (NN) toolbox. To carry out the analysis, we consider three deterministic UC and two stochastic UC cases with a two-stage programming model that indicates the day-ahead UC as the first stage and the intra-day operation of the system as the second stage. A binary-real genetic algorithm is coded in MATLAB software to optimize the proposed cases in terms of thermal units’ operation costs, import power tariffs, as well as from the perspective of the system reliability risks expressed as the reserve and load not served costs. The results indicate that in the deterministic UC models, the risk of reserve and load curtailment does exist. The stochastic UC approaches including the optimal power trading are superior to the deterministic ones. Moreover, the scheduled UC costs and reserves are different from the actual ones.

The use of renewable energy sources (RES) has increased exponentially worldwide, as an alternative to the indiscriminate use of fossil fuels and to mitigate their effects on the environment. Cuba is not lagging behind in this development since the government’s plan until 2030 includes the contribution of renewable sources as a fundamental component in the national energy mix. This paper models possible scenarios based on 2019 statistics for achieving a 25% and 100% penetration of renewable sources by 2030 in the Isla de la Juventud’s (an island south of the main island of Cuba) electrical power system (EPS). This modeling is carried out utilizing and open source Excel-based accounting framework Long-range Integrated Development Analysis (LINDA). For this purpose, international and national trends in the use and development of renewable energy sources and the influence of the characteristics of each renewable source (wind, solar, biodiesel, battery storage) were analyzed. The analysis of Isla de la Juventud’s electrical power system was based on the characteristics of its energy mix, the possibilities of renewable energy penetration and the current and future energy demand by sector. Based on the analysis, two probable scenarios were modeled with LINDA model: a 25% renewable energy-based scenario (RENES) and a 100% renewables-based scenario (MAXRES). Results from RENES and MAXRES scenarios show high penetration of renewable energy sources in electricity generation is theoretically possible with the abundance of renewable energy resources, and thus it is possible for Cuba to move towards 100% renewable energy mix. However, the choices regarding the best fit energy mix need to be carefully analyzed in order to design a least cost system that answers the needs of the future demand.

We develop a Design and Analysis of the Computer Experiments (DACE) approach to the stochastic unit commitment problem for power systems with significant renewable integration. For this purpose, we use a two-stage stochastic programming formulation of the stochastic unit commitment-economic dispatch problem. Typically, a sample average approximation of the true problem is solved using a cutting plane method (such as the L-shaped method) or scenario decomposition (such as Progressive Hedging) algorithms. However, when the number of scenarios increases, these solution methods become computationally prohibitive. To address this challenge, we develop a novel DACE approach that exploits the structure of the first-stage unit commitment decision space in a design of experiments, uses features based upon solar generation, and trains a multivariate adaptive regression splines model to approximate the second stage of the stochastic unit commitment-economic dispatch problem. We conduct experiments on two modified IEEE-57 and IEEE-118 test systems and assess the quality of the solutions obtained from both the DACE and the L-shaped methods in a replicated procedure. The results obtained from this approach attest to the significant improvement in the computational performance of the DACE approach over the traditional L-shaped method.

Managing solar uncertainty in microgrid systems with stochastic unit commitment

Wind power forecasting uncertainty and unit commitment

High renewables penetrated power systems would be greatly influenced by the uncertainty of variable renewable energy such as wind power and photovoltaic power. Unlike wind and photovoltaic plant, concentrating solar power with thermal energy storage has similar dispatchable characteristics as conventional thermal unit. Besides, thermal energy storage could support the coordinated operation of concentrating solar power with an electrical heater, which can be employed to convert surplus electricity in the grid into thermal power stored in thermal energy storage for further utilization. In this paper, concentrating solar power is incorporated into a chance-constrained two-stage stochastic unit commitment model. The model considers the energy and reserve services of concentrating solar power and the uncertainty of renewables. The proposed method is employed to assess the role of a concentrating solar power station with thermal energy storage and an electrical heater to provide grid flexibility in high renewables penetrated power systems. Numerical studies are performed on a modified IEEE 24-bus system to validate the viability of the proposed method for the day-ahead stochastic scheduling. The results demonstrate the economic and reliable value of concentrating solar power station to the improvement of unit commitment schedule, to the mitigation of wind uncertainty and photovoltaic uncertainty, and to the reduction of traditional unit reserve requirement. It is concluded that concentrating solar power with thermal energy storage and an electrical heater is effective in promoting the further penetration of renewables.

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

To enhance the resilience of transmission systems with offshore wind farms before the advent of typhoons, a proactive unit commitment scheme is proposed. A novel scenario tree is proposed to quantify the uncertain impacts of typhoons on offshore wind farms, transmission lines, and system states, where the inertia support from offshore wind farms and random system state are in‐cooperated. The frequency security constraint is captured by a multi‐variative piece‐wise linear function, where the frequency nadir are simulated under varying inertia and disturbance combinations. The unit commitment problem is formulated as a two‐stage stochastic optimisation problem with nonlinear recourse. This problem is solved by a multi‐cuts Benders decomposition algorithm with finite iteration convergence property. Simulations are conducted on a modified IEEE‐RTS 79 test system with offshore wind farms. Results verify the effectiveness of the proposed model regarding the load shedding and frequency nadir enhancement.

We present a distributed asynchronous algorithm for solving two-stage stochastic mixed-integer programs (SMIP) using scenario decomposition, aimed at industrial-scale instances of the stochastic unit commitment (SUC) problem. The algorithm is motivated by large differences in run times observed among scenario subproblems of SUC instances, which can result in inefficient use of distributed computing resources by synchronous parallel algorithms. Our algorithm performs dual iterations asynchronously using a block-coordinate subgradient descent method which allows performing block-coordinate updates using delayed information, while candidate primal solutions are recovered from the solutions of scenario subproblems using heuristics. We present a high performance computing implementation of the asynchronous algorithm, detailing the operations performed by each parallel process and the communication mechanisms among them. We conduct numerical experiments using SUC instances of the Western Electricity Coordinating Council system with up to 1000 scenarios and of the Central Western European system with up to 120 scenarios. We also conduct numerical experiments on generic SMIP instances from the SIPLIB library (DCAP and SSLP). The results demonstrate the general applicability of the proposed algorithm and its ability to solve industrial-scale SUC instances within operationally acceptable time frames. Moreover, we find that an equivalent synchronous parallel algorithm would leave cores idle up to 80.4% of the time on our realistic test instances, an observation which underscores the need for designing asynchronous optimization schemes in order to fully exploit distributed computing on real world applications.

We introduce a two stage stochastic unit commitment formulation in which the second stage recourse actions include possible reconfiguration of the power grid topology through transmission line switching. We conduct numerical test on IEEE 118 system to demonstrate the benefits of such adaptive topology control. Our results show that such recourse capability in response to realized uncertainty of intermittent renewable resources can mitigate such adverse variability and significantly improve unit commitment efficiency.

A deep generative model for probabilistic energy forecasting in power systems: normalizing flows

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.