Stochastic Unit Commitment Model Research Articles

A multi-objective two-stage stochastic unit commitment model for wind and battery-integrated power systems

This paper presents a mathematical programming framework for modeling the operations of power systems with high wind power penetration and BESS, accounting for wind and power demand uncertainties. For this, we introduce a multi-objective two-stage stochastic unit commitment model aimed at constructing on/off schedules that balance operating costs and CO2 emissions. Under the realistic limitations imposed by BESS high variable operating cost, we focus on assessing and analyzing the operational impact of BESS for two different integration schemes: wind farm-coupled and stand-alone. The proposed method of solution consists in an augmented ϵ-constrained algorithm with an integrated normalized euclidean distance-based bisection routine to produce more equispaced Pareto optimal solutions. We applied the proposed framework to a modified version of the New England IEEE-39 bus test system for three disjoint cases of analysis: without BESS integration, with BESS integrated into a wind farm, and with a stand-alone BESS integrated into the grid. The results demonstrate the efficacy of the proposed framework and show substantial benefits in terms of CO2 emissions reductions, particularly in the stand-alone configuration, which, although limited in extent of use, promotes the direct injection of wind power into the grid, the decommitment of polluting thermal units, enhance the use of free or low emissions technologies, and contributes as a provider of spinning reserves.

Reliability based computational model for stochastic unit commitment of a bulk power system integrated with volatile wind power

Reliable and economic operation of transmission systems is one of the most onerous problems faced by the grid operators as a penetration rate of wind energy is on rise. It is a crucial carbon-free source and alleviates dependency upon the conventional resources, though its stochastic and unpredictable nature can cause the risk of random component failures. Therefore, reliability evaluation of the system under wind power is of paramount importance and is suggested as the proposed study. A Reliability based Stochastic Unit Commitment (RSUC) model is proposed for a bulk power system integrated with volatile wind power. It is formulated using Mixed Integer Linear problem considering networks and spinning reserve constraints. The volatility of wind speed is modeled by generating different scenarios using K-means clustering approach with computation of correlation among them using autocorrelation factor and their transition probabilities is proposed using Markov Chain (MC). Further, the system's reliability is evaluated using Loss of Load Probability (LOLP) and Expected Energy Not Supplied (EENS). The proposed approach is investigated on the IEEE 24 Reliability Test System (RTS) under the various overloading and random component outage conditions. Further, its results effectiveness is compared and validated with the other existing approaches.

Unit Commitment Considering Long-term Supply Risk of Natural Gas Pipeline Network

As the coupling degree of the natural gas pipeline network (NGPN) and the power system increase, unreliable gas supply risk related to random failures in NGPN has threatened the operation security of the power system. However, present studies seldom discuss the effect of natural gas supply reliability on power system operation. In this manner, a stochastic unit commitment model is presented with the consideration of long-term gas supply risk in NGPN. Firstly, with the combination of the Monte Carlo simulation (MCS) technique and the maximum-flow algorithm, the failure scenario set corresponding to gas supply risk can be obtained. Then, a two-stage model for unit commitment is established considering gas supply uncertainty based on the stochastic optimization model. Finally, case studies have shown that the power operation reliability has been improved with the increased reliability indices.

Two-stage stochastic unit commitment for renewable energy integrated power systems considering dynamic capacity-increase technologies of transmission lines

Dynamic capacity-increase technologies (DCITs), as a solution to reduce the stress of transmission networks, avoid long-term constructions and update the maximum transmitted capacities based on real-time environment factors and the maximum allowable operation temperatures (MAOTs), which provide flexibility in optimizing the operation modes for power systems. This paper proposes a detailed two-stage stochastic unit commitment model considering the physical processes of heat transfer as well as the uncertainties of renewable energy. The dynamic thermal rating (DTR) is calculated based on the heat balance of transmission lines in the steady state, including radiated and convective heat loss and gain from the solar heat and power flows. To simulate the uncertainties from renewable energy outputs, this paper applies the Latin hypercube sampling method to generate output scenarios in stochastic optimization. Finally, the proposed model is verified on a modified IEEE-24-bus test system. The effectiveness of DCITs is illustrated through the case study.

Transmission impedance control impacts on carbon emissions and renewable energy curtailment

Increased levels of renewable energy penetration have created new congestion patterns in recent years. Since the grid is not designed for the new patterns, the operators may need to curtail renewable energy to maintain transmission flows within acceptable limits. Transmission line impedance control, using flexible ac transmission system (FACTS) devices, has been proposed as an approach to relieve congestion in transmission systems and enhance renewable energy utilization. In this paper, we conduct a comprehensive study to provide insights on FACTS implementation’s impact on renewable energy integration and carbon emission reduction. The study considers variations in renewable energy penetration level, system loading patterns, location of renewable generation, and location of FACTS devices. Furthermore, generation mix data from prominent regional transmission organizations (RTO) are used to achieve more realistic results. Simulations studies are carried out on a modified RTS-96 system with a two-stage stochastic unit commitment model. The results show that, even though impedance control is effective in cost reduction, it has limitations in facilitating renewable energy integration in systems with prominent cheap fossil fuel power plants.

Multi-objective two-stage stochastic unit commitment model for wind-integrated power systems: A compromise programming approach

In this paper, we introduce a compromise programming (CP) framework for solving a multi-objective two-stage stochastic unit commitment problem characterized by high penetration of wind power. The proposed framework aims at finding best-compromise Pareto efficient on/off schedules, accounting for wind and power demand uncertainties: such solutions must trade off the three objectives of operating cost, CO2 emissions, and wind power curtailment in accordance to the decision maker preferences. To achieve this, we introduce a practical procedure to compute the ideal and Nadir points associated to the multi-objective two-stage stochastic unit commitment problem and propose a linearized ℓ1 norm-based compromise program to design best-compromise on/off schedules that correspondingly minimize and maximize their weighted distances to the ideal point and to the Nadir point, considering the preference weights assigned by the decision maker to each of the three objective functions. The proposed CP framework is applied to a case study related to the New England IEEE-39 bus test system. The results show that, compared to the schedule obtained through the traditional minimization of operating cost, the designed best-compromised schedules considerably improve CO2 emissions reduction and wind power curtailment performance by conservatively sacrificing operating cost performance.

Inertia Pricing in Stochastic Electricity Markets

Maintaining the stability of renewable-dominant power systems requires the procurement of virtual inertia services from non-synchronous resources (e.g., batteries, wind turbines) in addition to inertia traditionally provided by synchronous resources (e.g., thermal generators). However, the pricing of inertia provision has not been studied in a stochastic electricity market, where the uncertainty characteristics of renewable energy sources (RES) are considered. To fill in this research gap, this paper formulates a chance-constrained stochastic unit commitment model with inertia requirements and computes equilibrium energy, reserve and inertia prices using convex duality. Numerical experiments on an illustrative system and a modified IEEE 118-bus system show the performance of the proposed pricing mechanism. By allowing new virtual inertia providers to contribute to system inertia requirements, the total operating cost reduces. Moreover, the proposed stochastic electricity market internalizes RES uncertainty, which yields additional cost reductions by co-optimizing energy, reserve and inertia procurement.

Pricing Information in Smart Grids: A Quality-Based Data Valuation Paradigm

With the development of Internet technology, information has become an increasingly important asset for the operation and planning of power systems. However, the existing studies and practices pay little attention to information value evaluation, i.e., the potential for information to be converted into actual economic benefits. To this end, this paper designs an information market framework and proposes a generalized information valuation model to help price data in smart grids efficiently. Here we analyze the information value of photovoltaic (PV)-related data in a power system operation problem. Specifically, we examine how additional meteorological and PV power data help to improve day-ahead forecasting accuracy, thus enhancing unit commitment (UC). In this paper, information quality is captured by two indices of a set of PV-related data, i.e., Shannon entropy and non-noise ratio. Then a neural network-based engine is employed to predict day-ahead hourly solar power on the premise of input datasets with different information quality. Here we define forecasting accuracy as information utility, and discover an exponential relationship between such utility and information quality. Finally, a two-stage stochastic UC model is formulated to quantify the contributions of different PV-related datasets, in which real-time solar power deviation is penalized. In this instance, the economic value of PV-related data is measured as the operational cost reduction induced by forecasting accuracy improvement, which we find can be estimated by information quality. Case studies based on the IEEE 30- and 118-bus systems validate the effectiveness of the proposed paradigm and method.

A Unit Commitment Model Considering Feasibility of Operating Reserves under Stochastic Optimization Framework

Grid integration of renewable resources such as solar and wind energy can significantly raise the level of uncertainty in power systems, making the scheduled operation of generating units difficult. Therefore, the importance of operating reserves is more emphasized to prevent disruption by sudden changes in outputs of generators. In this paper, a stochastic unit commitment (UC) model to reflect uncertainty due to a large amount of renewable resources is proposed, in which upward and downward operating reserves are deployed simultaneously, and feasibility of the reserves is examined to make the deployed reserves supplied reliably. Uncertain parameters considered in the model are wind power availability, solar direct normal irradiance, and electric load. Two-stage stochastic programming is applied to the mathematical formulation, where UC decisions including dispatch are modeled as non-anticipative variables at the first stage, and redispatch decisions to serve realized electric demand are made at the second stage as recourse. By solving the UC problem, feasible and reliable stochastic UC and dispatch solutions can be provided to power system operators.

Decomposed Modeling of Controllable and Uncontrollable Components in Power Systems with High Penetration of Renewable Energies

The high penetration of variable renewable energies requires the flexibility from both the generation and demand sides. This raises the necessity of modeling stochastic and flexible energy resources in power system operation. However, some distributed energy resources have both stochasticity and flexibility, e.g., prosumers with distributed photovoltaics and energy storage, and plug-in electric vehicles with stochastic charging behavior and demand response capability. Such partly controllable participants pose challenges to modeling the aggregate behavior of large numbers of entities in power system operation. This paper proposes a new perspective on the aggregate modeling of such energy resources in power system operation. Specifically, a unified controllability-uncontrollability-decomposed model for various energy resources is established by modeling the controllable and uncontrollable parts of energy resources separately. Such decomposition enables the straightforward aggregate modeling of massive energy resources with different controllabilities by integrating their controllable components with linking constraints and uncontrollable components with dependent discrete convolution. Furthermore, a two-stage stochastic unit commitment model based on the proposed model for power system operation is established. The proposed model is tested using a three-bus system and real Qinghai provincial power grid of China. The result shows that this model is able to characterize at high accuracy the aggregate behavior of massive energy resources with different levels of controllability so that their flexibility can be fully explored.

Decision-Dependent Uncertainty Modeling in Power System Operational Reliability Evaluations

The integration of the variable renewable energies makes the operation conditions of the power system ever-changeable. Consequently, the power system operational reliability evaluation is increasingly important. This paper introduces the concept of decision-dependent uncertainty (DDU) in the operational reliability evaluation. Unlike the exogenous uncertainties, DDU reveals that the decisions of the system operation could significantly affect the resolution of the uncertainties which influence the reliability metrics. In this paper, the proposed DDU modeling method links the device reliability indices, i.e., the forced outage rate, and the operational-decision variables. The impacts of DDU on operational reliability are analyzed based on a reliability-constrained stochastic unit commitment (UC) model. An adaptive reliability improvement UC (ARIUC) algorithm is proposed to efficiently solve the problem. Case studies underline the necessity of considering DDU in power system operational reliability evaluations.

Stochastic Optimization for Residential Demand Response With Unit Commitment and Time of Use

As compensation to power generation dispatch, demand response (DR) enables demand controllability by changing the consumers' electricity usage patterns, which can be used to reduce electricity cost, integrate renewable energy, and provide ancillary services. To reveal the benefits from residential DR, this study develops the following two approaches: optimal load aggregation under augmented time-of-use (TOU) pricing; and active DR participation in unit commitment (UC) under rewards. We have shown that plain TOU pricing is not a promising DR policy if residential customers are equipped with home energy management systems (EMSs). We, therefore, propose an augmented TOU by radial basis functions. With a 60% participation level, the proposed optimal load aggregation model under the augmented TOU can reduce the power generation cost by 24% and decrease the standard deviation of the load profile by 42%. However, these results can be affected by the customer's participation level, which is also quantitatively studied. Specifically, when the participation level exceeds 80%, this method becomes less efficient. The second proposed approach, a two-stage stochastic UC model with DR flexibility, reduces the power generation cost by 20% and decreases the standard deviation of the load profile by 77%. In addition, the inconvenience of DR participation is quantitatively evaluated, and a Pareto surface is developed, which can be used as a baseline for residential customers to set up the home EMS for DR implementation. Both the proposed mechanisms can be used to improve the energy efficiency by uncovering the residential DR potential.

Role of optimal transmission switching in accommodating renewable energy in deep peak regulation-enabled power systems

Due to the shortage of fossil energy and the pollution caused by combustion of fossil fuels, the proportion of renewable energy in power systems is gradually increasing across the world. Accordingly, the capacity of power systems to accommodate renewable energy must be improved. However, integration of a large amount of renewable energy into power grids may result in network congestion. Hence, in this study, optimal transmission switching (OTS) is considered as an important method of accommodating renewable energy. It is incorporated into the operation of a power grid along with deep peak regulation of thermal power units, forming an interactive mode of coordinated operation of source and network. A stochastic unit commitment model considering deep peak regulation and OTS is established, and the role of OTS in promoting the accommodation of renewable energy is analyzed quantitatively. The results of case studies involving the IEEE 30-bus system demonstrate that OTS can enable utilization of the potential of deep peak regulation and facilitate the accommodation of renewable energy.

Robust risk‐averse unit commitment with solar PV systems

A challenge for energy market operators (EMOs) is to render a cost-effective generation schedule, known as unit commitment (UC), for the power system with intermittent renewable power generations. Consolidating the risk management concept and robustness into the UC not only helps EMO to maintain the secure operation of power systems but also informs the EMO about the tail-risk cost. Based on this motivation, the authors have proposed a model for UC with worst-case conditional value-at-risk (UC-WCVaR) with intermittent solar generations and loads. Unlike intractable risk-averse stochastic UC models, this model minimises the worst-case CVaR of the dispatch cost over an ambiguity set of the probability distributions. This robust tractable model relies on the historical data that can partially characterise the underlying probability distributions of solar photovoltaic (PV) systems and loads. They solved this model by its equivalent tractable robust counterpart using linear decision rules. The tests conducted on the IEEE 118-bus test system demonstrate that: (i) UC-WCVaR solution matches the results derived from normally distributed solar samples; (ii) the UC-WCVaR is less conservative than the classic robust unit commitment. Also, the computation time is directly proportional to the number of uncertain resources and inversely proportional to the number of stages.

Stochastic Unit Commitment in Low-Inertia Grids

In this paper, the Unit Commitment (UC) problem in a power network with low levels of rotational inertia is studied. Frequency-related constraints, namely the limitation on Rate-of-Change-of-Frequency (RoCoF), frequency nadir and steady-state frequency error, are derived from a uniform system frequency response model that incorporates dynamics and controls of both synchronous generators and grid-forming inverters. These constraints are then included into a stochastic UC formulation that accounts for wind power and equipment contingency uncertainties using a scenario-tree approach. In contrast to the linear RoCoF and steady-state frequency error constraints, the nadir constraint is highly nonlinear. To preserve the mixed-integer linear formulation of the stochastic UC model, we propose a computationally efficient approach that allows to recast the nadir constraint by introducing appropriate bounds on relevant decision variables of the UC model. This method is shown to be generally more accurate and computationally more efficient for medium-sized networks than a piece-wise linearization method adapted from the literature. Simulation results for a modified IEEE RTS-96 system revealed that the inclusion of inertia-related constraints significantly influences the UC decisions and increases total costs, as more synchronous machines are forced to be online to provide inertial response.

Reserve Model of Energy Storage in Day-Ahead Joint Energy and Reserve Markets: A Stochastic UC Solution

With many favorable advantages including fast response ability in particular, utility-level energy storage systems (ESS) are being integrated into energy and reserve markets to help mitigate uncertain renewable resources and fluctuant demands. This paper discusses a stochastic unit commitment (UC) model to explore capabilities of ESSs in providing valuable grid services by simultaneously joining energy and reserve markets. The proposed reserve model of ESSs presents the following features: (i) two constraints are proposed to formulate ESS's reserve provision ability in each hour via six operation modes, namely increasing/reducing the level of charge, switching to discharge, increasing/reducing the level of discharge, switching to charge; (ii) as an energy-limited asset, constraints on ESS's reserve deliverability across multiple hours is introduced to hold enough state of charge (SOC) headroom and floor room, guaranteeing that reserves cleared in individual hours are continuously deliverable over multiple successive hours without violating operation limits. Moreover, a scenario-based UC model, which addresses uncertainties of renewables and demands, is adopted to evaluate reserves provided by ESSs and generators. To effectively solve the stochastic UC problem, the progressive hedging algorithm with heuristic approaches is discussed. A 6-bus system and a modified IEEE 118-bus system are used to illustrate effectiveness of the proposed approaches.

Value of Point-of-Load Voltage Control for Enhanced Frequency Response in Future GB Power System

The need for Enhanced Frequency Response (EFR) is expected to increase significantly in future low-carbon Great Britain (GB) power system. One way to provide EFR is to use power electronic compensators (PECs) for point-of-load voltage control (PVC) to exploit the voltage dependence of loads. This paper investigates the techno-economic feasibility of such technology in future GB power system by quantifying the total EFR obtainable through deploying PVC in the urban domestic sector, the investment cost of the installment and the economic and environmental benefits of using PVC. The quantification is based on a stochastic domestic demand model and generic medium and low-voltage distribution networks for the urban areas of GB and a stochastic unit commitment (SUC) model with constraints for secure post-fault frequency evolution is used for the value assessment. Two future energy scenarios in the backdrop of 2030 with `smart' and `non-smart' control of electric vehicles and heat pumps, under different levels of penetration of battery energy storage system (BESS) are considered to assess the value of PEC, as well as the associated payback period. It is demonstrated that PVC could effectively complement BESS towards EFR provision in future GB power system.

Modeling flexible generator operating regions via chance-constrained stochastic unit commitment

We introduce a novel chance-constrained stochastic unit commitment model to address uncertainty in renewables’ production in operations of power systems. For most thermal generators, underlying technical constraints that are universally treated as “hard” by deterministic unit commitment models are in fact based on engineering judgments, such that system operators can periodically request operation outside these limits in non-nominal situations, e.g., to ensure reliability. We incorporate this practical consideration into a chance-constrained stochastic unit commitment model, specifically by infrequently allowing minor deviations from the minimum and maximum thermal generator power output levels. We demonstrate that an extensive form of our model is computationally tractable for medium-sized power systems given modest numbers of scenarios for renewables’ production. We show that the model is able to potentially save significant annual production costs by allowing infrequent and controlled violation of the traditionally hard bounds imposed on thermal generator production limits. Finally, we conduct a sensitivity analysis of optimal solutions to our model under two restricted regimes and observe similar qualitative results.

Adaptive Dynamic Programming for Gas-Power Network Constrained Unit Commitment to Accommodate Renewable Energy With Combined-Cycle Units

Due to the fast response capabilities, combined-cycle units could provide valuable flexibilities to cope with uncertainties from the renewable energy resources. However, combined-cycle units intensify the coupling between power and gas networks, so operational constraints of the two networks should be explicitly considered simultaneously. Indeed, neglecting the impact of any network may lead to infeasible solutions that will violate physical operational constraints. Compared with the previous stochastic unit commitment model with only combined-cycle units, this paper establishes a stochastic gas-power network constrained unit commitment model considering both combined-cycle units and gas network. Furthermore, an adaptive dynamic programming (ADP) to prevent the curse of dimensionality is proposed. Numerical results verify the effectiveness of the proposed model.

Stochastic unit commitment with air conditioning loads participating in reserve service

The demand response, providing the reserve service, becomes more and more important in the wind-power-integrated power systems. This study proposes a two-stage stochastic unit commitment model with the air conditioning (AC) aggregators providing the reserve service. A classification compensation scheme is proposed to promote AC users to provide more reserve capacity, which quantifies the users' comfort and their contribution to the system. Besides, a new AC scheduling method with adaptive response capacity (ARC) is proposed to help system operators to determine reasonable reserve capacity with smaller total cost. In addition, the inactive constraints identification is utilised to improve computational performance. Finally, the effectiveness of the proposed method is tested on the modified IEEE 118-bus system with 50 AC aggregators. The simulation results show that the proposed classification compensation scheme and the ARC method can promote more AC response capacity and save the total and reserve costs. The price game between the AC aggregators and the thermal units have a great impact on the decision results. The inactive constraints identification can save the total time by about 70%.