Uncertain Renewable Resources Research Articles

A hybrid data-driven and model-based approach for computationally efficient stochastic unit commitment and economic dispatch under wind and solar uncertainty

Stochastic unit commitment (UC) and economic dispatch (ED) are imperative in dealing with uncertainty in renewable forecast for power system operation and planning such that the overall expected production cost is minimized over the planning horizon. However, accurate calculation of the expected production cost requires assessment of a very large number of different scenarios of uncertain renewable resources, such as solar and wind, which is practically infeasible to simulate in real time. This article proposes a hybrid data-driven and physics-based model-predictive paradigm to efficiently solve for stochastic unit commitment and economic dispatch considering uncertainty in wind and solar power forecasts. The novelty of the approach lies in decoupling the production cost estimation from the unit commitment and economic dispatch optimization problems under uncertainty without compromising on the fidelity of the solutions. A data-driven machine learning model is first developed to predict the mean optimal production cost. A physics-based inverse problem is then solved to get the stochastic UC and ED profiles from the expected cost. The presented approach considers, for the first time, solar uncertainty in UC/ED determination and enables efficient and accurate propagation of wind and solar uncertainty to estimate the statistics of the production cost. The effectiveness of the developed approach is demonstrated systematically on a stylized RTS-GMLC single-node system. The overall framework predicts the expected cost 62.5% more accurately than the existing state-of-the-art, on unforeseen days during the entire year, and yields, for the first time, the associated physically consistent UC and ED profiles. The solutions are also shown to be flexible in providing adequate daily reserves to address any statistical deviations from probabilistic power forecasts. The computational time associated with the presented method is only about 10 s compared to over 24 h needed for a conventional stochastic UC/ED determination under uncertainty on an Intel Core i9 processor with 32 GB of RAM.

Online ADMM for Distributed Optimal Power Flow via Lagrangian Duality

At present, the power system has the characteristics of mutual independence but interconnection, and the interconnection between the various subsystems brings certain challenges to the distributed computing of the power grid. In addition, a substantial amount of naturally uncertain renewable resources are incorporated into the power system, which will impose volatile dynamics on the grid. In this paper, an alternating direction multiplier method (ADMM) is proposed for the power system with real-time renewables to tackle the online optimal power flow (OPF) problem. Due to the adoption of the Lagrangian duality, the proposed distributed ADMM scheme utilizes consensus ADMM to solve the dual OPF problem, which only discloses boundary coupling via the Lagrangian multiplier and further reduces the amount of information communication. Given the natural uncertainty of distributed energy resources (DER), the algorithm avoids the double-loop implementation or the uncertainty of traditional distributed methods of using the boundary information as equality constraints caused by dynamic DER. It is thus capable of providing a provable performance guarantee and is inherently developed to cope with the dynamic OPF problem with renewables in an online fashion. Taking the IEEE 30-bus system as a test feeder, the simulation results verify the efficiency and robustness of the proposed algorithms in solving both the static and dynamic OPF problems; in addition, the online method can effectively avoid the violent fluctuations of the conventional generator output copying with renewables rapid variation in comparison with the offline algorithms.

Learning to solve DCOPF: A duality approach

The optimal power flow (OPF) problem is a fundamental tool in power system operation and control. Because of the increase in uncertain renewable resources, solving OPF problems fast and accurately provides significant values because of a large number of load and generation scenarios need to be accounted for. Recent works have focused on using neural networks to replace iterative solvers to speed up the computation of OPF problems. A critical challenge is to ensure solutions satisfy the hard constraints in the OPF problem, which is difficult to do in end-to-end machine learning. In this work, by leveraging the rich theory of duality and physical interpretations of OPF, we design a learning-based approach that has theoretical characterizations of constraint satisfaction. This approach is an order of magnitude faster than standard solvers, and performs much better than other learning methods in terms of feasibility and optimality.

Multi-objective energy management for modern distribution power systems considering industrial flexibility mechanisms

Increasing energy generation from variable and uncertain renewable resources leads to high demand for flexibility procurement from different energy sectors to maintain supply/demand balance in distribution power systems. Industrial energy systems are rapidly emerging as the primary contributor in providing the bulk of said flexibility to the electrical power systems due to their energy capacity, reliable infrastructure, and potential financial benefits. However, there is a lack of available energy management models that help integrate industrial flexibility into the fold and can solve for an optimal operation of the distribution power system. This paper proposes an efficient energy management model that solves a distributed multi-objective optimal power flow for a modern distribution grid, including industrial prosumers and distributed generation resources. We generate two distinct kinds of flexible industrial load profiles: one uses optimal peak shaving with an energy storage system, and the other employs process optimization in the industrial grid. The obtained results show that the proposed energy management model can solve for optimal operation of all involved participants while maintaining data privacy between them. Industrial prosumers save up to 4.85% in financial expenses and 18.6% in energy exchange with the grid. Further, the grid operator can reduce its CO2 emissions by 4.6%.

A Convex Neural Network Solver for DCOPF With Generalization Guarantees

The dc optimal power flow (DCOPF) problem is a fundamental problem in power systems operations and planning. With high penetration of uncertain renewable resources in power systems, DCOPF needs to be solved repeatedly for a large amount of scenarios, which can be computationally challenging. As an alternative to iterative solvers, neural networks are often trained and used to solve DCOPF. These approaches can offer orders of magnitude reduction in computational time, but they cannot guarantee generalization, and small training error does not imply small testing errors. In this work, we propose a novel algorithm for solving DCOPF that guarantees the generalization performance. First, by utilizing the convexity of the DCOPF problem, we train an input convex neural network. Second, we construct the training loss based on Karush–Kuhn–Tucker optimality conditions. By combining these two techniques, the trained model has provable generalization properties, where small training error implies small testing errors. In experiments, our algorithm significantly outperforms other machine learning methods.

Reliability assessment and congestion management of power system with energy storage system and uncertain renewable resources

The high penetration of Renewable Energy Sources (RES) makes the power system unreliable due to its uncertain nature and to deal with this uncertainties installation of an Energy Storage System (ESS) is suggested. In this paper, the quantifying impact of ESS capacity on power system network reliability and relieving the congestion is analyzed. The proposed reliability assessment and congestion relief problem is formulated by considering generation cost and demand interruption cost for N-1 contingency criteria. The proposed algorithm manages the optimal charging and discharging of ESS to mitigate the uncertainties associated with RES and relieving the congestion. The impact of ESS capacity on reliability indices Expected Energy not Supplied (EENS) and Expected interruption Cost (ECOST) for Generating Companies (GENCOs), Transmission Companies (TRANSCOs), customers, and entire power system are calculated. The appropriate size of ESS is selected by the trade-off between investment cost of ESS and percentage change in EENS and ECOST value for the entire power system, GENCOs, TRANSCOs, and customers. The effectiveness of the proposed approach is tested on the modified IEEE RTS 24 bus system. The problem is modeled in the Generic Algebraic Solver (GAMS) environment and solved using CONOPT as an NLP solver.

Day-ahead energy market as adjustable robust optimization: Spatio-temporal pricing of dispatchable generators, storage batteries, and uncertain renewable resources

We present modeling and analysis of day-ahead spatio-temporal energy markets in which each competitive aggregator aims at making the highest profit by managing a complex mixture of different energy resources, such as conventional generators, storage batteries, and uncertain renewable resources. First, we develop an energy market model in terms of an adjustable robust convex program. This market modeling is novel in the sense that the prosumption cost function of each aggregator, which evaluates the cost to realize an amount of spatio-temporal energy prosumption, is a multi-variable function resulting from a "parameterized" max-min program, in which the variable of the prosumption cost function is involved as a continuous parameter and the variable of dispatchable resources is involved as an adjustable variable for energy balance. This formulation enables to reasonably evaluate a reward for intertemporal dispatchability enhancement and a penalty for renewable energy uncertainty in a unified way. In addition, it enables to enforce a market regulation in which every aggregator is responsible for absorbing his renewable energy uncertainty by managing his own dispatchable energy resources. Second, in view of social economy as well as personal economy, we conduct a numerical analysis on the premise of several photovoltaic penetration levels. In this numerical analysis, we demonstrate that renewable generators do not always have priority of energy supply higher than conventional generators due to their uncertainty and limited dispatchability, meaning that the merit order of conventional and renewable generators can reverse. Furthermore, we analyze long-term evolution of competitive energy markets demonstrating that there can be found a social equilibrium of battery penetration levels, at which maximum personal profit with respect to battery system enhancement is attained.

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.

A parallel multi-scenario learning method for near-real-time power dispatch optimization

Power dispatch problems become more complex when the weight of uncertain renewable resources in the power system gradually increases in recent years. To make use of renewable energy, such as wind energy, more adequately, wisely and intelligently, higher requirements are placed on the level of inter-region power dispatch coordination. In the context, solving the problem of power dispatch on a large scale in near-real-time (5 min in this paper) becomes more important. In this paper, the power dispatch was treated as a sequential decision-making problem and Deep Reinforcement Learning (DRL) with continuous control was introduced to offer a smarter solution. In this way, we designed a novel interactive learning environment based on the economic power dispatch model for the DRL algorithm and we proposed two feasible implementations to handle the different application scenarios. As a result, DRL with a continuous control method has a great performance in our proposed implementations. Moreover, we found that dispatching data richness has a significant influence on the generalization of the learned policy.

A Chance-Constrained Stochastic Electricity Market

Efficiently accommodating uncertain renewable resources in wholesale electricity markets is among the foremost priorities of market regulators in the US, UK and EU nations. However, existing deterministic market designs fail to internalize the uncertainty and their scenario-based stochastic extensions are limited in their ability to simultaneously maximize social welfare and guarantee non-confiscatory market outcomes in expectation and per each scenario. This article proposes a chance-constrained stochastic market design, which is capable of producing a robust competitive equilibrium and internalizing uncertainty of the renewable resources in the price formation process. The equilibrium and resulting prices are obtained for different uncertainty assumptions, which requires using either linear (restrictive assumptions) or second-order conic (more general assumptions) duality in the price formation process. The usefulness of the proposed stochastic market design is demonstrated via the case study carried out on the 8-zone ISO New England testbed.

Demand response based congestion management of power system with uncertain renewable resources

In this paper, the combined approach of rescheduling of generators and demand-side management using various demand response programme (DRP) for congestion management is analysed. The uncertainties of wind and solar output power are modelled by Rayleigh and Beta distribution function. These uncertainties result in a large number of scenarios which increases the computational burden. The k-means clustering algorithm is applied to reduce the number of scenarios. This system is analysed by using Monte Carlo simulation. The impact of various DRPs on technical and economic characteristics of the load profile is investigated. The priority of DRPs for the reduction in rescheduling cost and a bill is derived. The result has shown that all DRPs are not profitable for minimising rescheduling cost compared to without DRPs. The best preferred DRP for congestion management is determined among all DRPs. The proposed approach is modelled in GAMS environment and solved by using CONOPT solver.

Congestion management of power system with uncertain renewable resources and plug‐in electrical vehicle

The study describes the quantifying impact of plug-in electrical vehicles (PEVs) and renewable energy sources (RES) for congestion management of power system. The proposed congestion management problem is formulated considering uncertainties of wind, solar, number of PEVs and load condition over a day. The uncertainty modelling of solar, wind and PEVs is presented using beta, Rayleigh and normal distribution functions, respectively. The PEVs uncertainty is dependent on its number and increases with escalation in number. The degree of uncertainties of RES is dependent on corresponding variable (wind and solar). These uncertainties result in large number of scenarios which increases the computational burden. The k-means clustering algorithm is applied to reduce the number of scenarios. The objective function is formulated to minimise generation cost, rescheduling cost and PEV cost for congestion management. This system is analysed by using Monte Carlo simulation. The proposed methodology relieves the congestion and reduces the generation cost, total power generation, total loss with increasing number of PEVs. The test result indicates that PEVs not only act as small storage unit but it also provides power during peak hours. The proposed approach is modelled in GAMS environment and implemented on modified IEEE 39-bus system.

Adaptive robust unit commitment considering distributional uncertainty

To reduce the conservativeness of robust optimization-based unit commitment methods, an uncertainty set is usually prespecified with respect to the distributions of uncertain renewable resources, i.e., wind power. However, since the law of large numbers does not always work in practice, the obtained probability distribution may be unreliable. In this paper, a data-driven adaptive robust optimization method for the unit commitment of bulk power systems with high-level wind power integration is proposed. Different from the conventional robust unit commitment methods, the distributional uncertainty of wind power is well respected in the proposed approach. An imprecise-Dirichlet-model-based method is developed to construct the ambiguity set of wind power, which incorporates all possible probability distributions confirmed by historical data. The set can dynamically change with the data, i.e., the more valid data we have, the smaller the ambiguity set will become. With respect to the bounds of the ambiguity set, a polyhedron uncertainty set of wind power is constructed. By tuning the parameters of the uncertainty set, a balance between operational efficiency and risk can be achieved. An adaptive, robust unit commitment model is constructed based on the uncertainty set. By using the duality principle and big-M method, the formulations are converted into a mixed integer linear programming problem and solved using a column and constraint generation algorithm. Case studies on two benchmark systems illustrate the effectiveness and efficiency of the proposed method.

A profitability investigation into the collaborative operation of wind and underwater compressed air energy storage units in the spot market

Abstract Nowadays, the integration of uncertain renewable resources has been accelerated, which encounters the operational scheduling of power system with some challenges for achieving optimal operation schedule. Hence, uncertain resources will be penalized if they create an imbalance in power generation. Both of the positive and negative imbalances will lead to a decrease in the uncertain resources' profitability. In the market environment, when the time is close to the real operation, the excess generation could not be sold. In some markets, the system operator buys the excess renewable generation by penalty factors. Furthermore, the insufficient generation must be compensated through buying from the spot market which has higher prices. The owners of uncertain resources want to have coordinated operation with storage units to mitigate the risk of commitment in the electricity market and to be protected from high prices of the spot market in case of their inaccurate forecasting. Hence, a contract model is proposed to satisfy both renewable and energy storage generating companies. Hence, a state-of-the-art storage technology which is called UWCAES is incorporated. The uncertain resources cannot be effectively profited of participation in the wholesale electricity market without collaborative operation. The results show the effectiveness of the proposed model.