Physics-Informed AI Surrogates for Day-Ahead Wind Power Probabilistic Forecasting with Incomplete Data for Smart Grid in Smart Cities

Due to the high inherent uncertainty of renewable energy,probabilistic day-ahead wind power forecasting is crucial for modeling and controlling the uncertainty of renewable energy smart grids in smart cities.However,the accuracy and reliability of high-resolution day-ahead wind power forecasting are constrained by unreliable local weather prediction and incomplete power generation data.This article proposes a physics-informed artificial intelligence(AI)surrogates method to augment the incomplete dataset and quantify its uncertainty to improve wind power forecasting performance.The incomplete dataset,built with numerical weather prediction data,historical wind power generation,and weather factors data,is augmented based on generative adversarial networks.After augmentation,the enriched data is then fed into a multiple AI surrogates model constructed by two extreme learning machine networks to train the forecasting model for wind power.Therefore,the forecasting models’accuracy and generalization ability are improved by mining the implicit physics information from the incomplete dataset.An incomplete dataset gathered from a wind farm in North China,containing only 15 days of weather and wind power generation data withmissing points caused by occasional shutdowns,is utilized to verify the proposed method’s performance.Compared with other probabilistic forecastingmethods,the proposed method shows better accuracy and probabilistic performance on the same incomplete dataset,which highlights its potential for more flexible and sensitive maintenance of smart grids in smart cities.

Day-ahead scheduling based on reinforcement learning with hybrid action space

Driven by the improvement of the smart grid,the active distribution network(ADN)has attracted much attention due to its characteristic of active management.By making full use of electricity price signals for optimal scheduling,the total cost of the ADN can be reduced.However,the optimal dayahead scheduling problem is challenging since the future electricity price is unknown.Moreover,in ADN,some schedulable variables are continuous while some schedulable variables are discrete,which increases the difficulty of determining the optimal scheduling scheme.In this paper,the day-ahead scheduling problem of the ADN is formulated as a Markov decision process(MDP)with continuous-discrete hybrid action space.Then,an algorithm based on multi-agent hybrid reinforcement learning(HRL)is proposed to obtain the optimal scheduling scheme.The proposed algorithm adopts the structure of centralized training and decentralized execution,and different methods are applied to determine the selection policy of continuous scheduling variables and discrete scheduling variables.The simulation experiment results demonstrate the effectiveness of the algorithm.

基于风电场功率特性的日前风电预测误差概率分布研究

风电功率预测误差的分布对电力系统调度决策、备用安排等有着重要的影响。基于风电场日前功率预测"从风速到功率"的实际过程,提出了确定日前风电功率预测误差分布的分析方法。首先,使用最小二乘法拟合风电场的功率特性,分析风电场功率特性拟合误差及其对日前风电功率预测误差的影响;其次,通过模拟日前风速的预测误差,研究风速预测误差对日前风电功率预测误差的影响;最后,使用蒙特卡罗双层抽样技术模拟上述2种误差的共同作用,并使用最大似然估计技术,确定各风速区间对应的日前功率预测误差所服从的分布。基于实际风电场历史数据的算例分析结果表明,所提出的误差分析方法能够准确描述风电场在不同预测风速下的功率预测误差概率分布,并能够确定各分布的适用范围,可为优化调度方案的制定提供参考。

间歇式电源发电功率的不确定度模型

为了定量刻画间歇式电源功率不确定性的统计规律,定义了不确定度概念,建立了关于不确定度与预测超前时间关系的α函数模型体系。首先,用α函数α（t）描述风电场和太阳能电站发电功率的不确定性;其次,将电网的全部α函数合成为多时间常数的α和函数αΣ（t）;第三,将α和函数降阶为单时间系数函数的等值α函数α[t,τ（t）];最后,将单时间系数函数定常,等值α函数被化简为单时间常数的廓线α函数α（t,τ0）。基于幅值和时间常数是两个数字特征,α函数廓线式地刻画了间歇式电源功率不确定性的统计规律。提出和证明的4个数学命题保证了α函数模型体系的严谨性。

Resource-specific Orders in European Day-ahead Market Under Different Pricing Rules

This paper addresses two issues that concern the electricity market participants under the European day-ahead market(DAM)framework,namely the feasibility of the attained schedules and the non-confiscation of cleared volumes.To address the first issue,new resource-specific orders,i.e.,thermal orders for thermal generating units,demand response orders for load responsive resources,and energy limited orders for storage resources,are proposed and incorporated in the existing European DAM clearing problem.To address the second issue,two approaches which lead to a non-confiscatory market are analyzed:①discriminatory pricing with side-payments(U.S.paradigm);and②non-discriminatory pricing excluding out-ofmoney orders(European paradigm).A comparison is performed between the two approaches to investigate the most appropriate pricing rule in terms of social welfare,derived revenues for the sellers,and efficiency of the attained results.The proposed model with new resource-specific products is evaluated in a European test system,achieving robust solutions.The feasibility of the attained schedules is demonstrated when using resource-specific orders compared with block orders.Finally,the results indicate the supremacy of discriminatory pricing with side-payments compared with the current European pricing rule.

A novel pure data-selection framework for day-ahead wind power forecasting

Numerical weather prediction(NWP)data possess internal inaccuracies,such as low NWP wind speed corresponding to high actual wind power generation.This study is intended to reduce the negative effects of such inaccuracies by proposing a pure data-selection framework(PDF)to choose useful data prior to modeling,thus improving the accuracy of day-ahead wind power forecasting.Briefly,we convert an entire NWP training dataset into many small subsets and then select the best subset combination via a validation set to build a forecasting model.Although a small subset can increase selection flexibility,it can also produce billions of subset combinations,resulting in computational issues.To address this problem,we incorporated metamodeling and optimization steps into PDF.We then proposed a design and analysis of the computer experiments-based metamodeling algorithm and heuristic-exhaustive search optimization algorithm,respectively.Experimental results demonstrate that(1)it is necessary to select data before constructing a forecasting model;(2)using a smaller subset will likely increase selection flexibility,leading to a more accurate forecasting model;(3)PDF can generate a better training dataset than similarity-based data selection methods(e.g.,K-means and support vector classification);and(4)choosing data before building a forecasting model produces a more accurate forecasting model compared with using a machine learning method to construct a model directly.

Storing Freshwater Versus Storing Electricity in Power Systems with High Freshwater Electric Demand

We consider a power system whose electric demand pertaining to freshwater production is high(high freshwater electric demand),as in the Middle East,and investigate the tradeoff of storing freshwater in tanks versus storing electricity in batteries at the day-ahead operation stage.Both storing freshwater and storing electricity increase the actual electric demand at valley hours and decrease it at peak hours,which is generally beneficial in term of cost and reliability.But,to what extent?We analyze this question considering three power systems with different generation-mix configurations,i.e.,a thermal-dominated mix,a renewable-dominated one,and a fully renewable one.These generation-mix configurations are inspired by how power systems may evolve in different countries in the Middle East.Renewable production uncertainty is compactly modeled using chance constraints.We draw conclusions on how both storage facilities(freshwater and electricity)complement each other to render an optimal operation of the power system.

Day-ahead Optimization Schedule for Gas-electric Integrated Energy System Based on Second-order Cone Programming

This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES.

Robust coordination of interdependent electricity and natural gas systems in day-ahead scheduling for facilitating volatile renewable generations via power-to-gas technology

The increasing interdependency of electricity and natural gas systems promotes coordination of the two systems for ensuring operational security and economics.This paper proposes a robust day-ahead scheduling model for the optimal coordinated operation of integrated energy systems while considering key uncertainties of the power system and natural gas system operation cost. Energy hub,with collocated gas-fired units, power-to-gas(Pt G) facilities, and natural gas storages, is considered to store or convert one type of energy(i.e., electricity or natural gas)into the other form, which could analogously function as large-scale electrical energy storages. The column-andconstraint generation(C&CG) is adopted to solve the proposed integrated robust model, in which nonlinear natural gas network constraints are reformulated via a set of linear constraints. Numerical experiments signify the effectiveness of the proposed model for handling volatile electrical loads and renewable generations via the coordinated scheduling of electricity and natural gas systems.

Day-ahead Scheduling of Multi-carrier Energy Systems with Multi-type Energy Storages and Wind Power

The integration of large-scale wind power brings challenges to the operation of integrated energy systems(IES).In this paper,a day-ahead scheduling model for IES with wind power and multi-type energy storage is proposed in a scenario-based stochastic programming framework.The structure of the IES consists of electricity,natural gas,and heating networks which are all included in the model.Operational constraints for IES incorporating multi-type energy storage devices are also considered.The constraints of the electricity network,natural gas network and heating network are formulated,and non-linear constraints are linearized.The calculation method for the correlation of wind speed between wind farms based on historical data is proposed.Uncertainties of correlated wind power were represented by creating multiple representative scenarios with different probabilities,and this was done using the Latin hyper-cube sampling(LHS)method.The stochastic scheduling model is formulated as a mixed integer linear programming(MILP)problem with the objective function of minimizing the total expected operation cost.Numerical results on a modified PJM 5-bus electricity system with a seven-node natural gas system and a six-node heating system validate the proposed model.The results demonstrate that multi-type energy storage devices can help reduce wind power curtailments and improve the operational flexibility of IES.

Day-ahead scheduling of large numbers of thermostatically controlled loads based on equivalent energy storage model

Due to their heat/cool storage characteristics, thermostatically controlled loads(TCLs) play an important role in demand response programmers. However, the modeling of the heat/cool storage characteristic of large numbers of TCLs is not simple. In this paper, the heat exchange power is adopted to calculate the power instead of the average power, and the relationship between the heat exchange power and energy storage is considered to develop an equivalent storage model, based on which the time-varying power constraints and the energy storage constraints are developed to establish the overall day-ahead schedulingmodel. Finally, the proposed scheduling method is verified using the simulation results of a six-bus system.

An economic and low-carbon day-ahead Pareto-optimal scheduling for wind farm integrated power systems with demand response

Demand response(DR)and wind power are beneficial to low-carbon electricity to deal with energy and environmental problems.However,the uncertain wind power generation(WG)which has anti-peaking characteristic would be hard to exert its ability in carbon reduction.This paper introduces DR into traditional unit commitment(UC)strategy and proposes a multi-objective day-ahead optimal scheduling model for wind farm integrated power systems,since incentive-based DR can accommodate excess wind power and can be used as a source of system spinning reserve to alleviate generation side reserve pressure during both peak and valley load periods.Firstly,net load curve is obtained by forecasting load and wind power output.Then,considering the behavior of DR,a day-ahead optimal dispatching scheme is proposed with objectives of minimum generating cost and carbon emission.Non-dominated sorting genetic algorithm-II(NSGA-II)and satisfaction-maximizing method are adopted to solve the multi-objective model with Pareto fronts and eclectic decision obtained.Finally,a case study is carried out to demonstrate that the approach can achieve economic and environmental aims and DR can help to accommodate the wind power.

Approximating Nash Equilibrium in Day-ahead Electricity Market Bidding with Multi-agent Deep Reinforcement Learning

In this paper,a day-ahead electricity market bidding problem with multiple strategic generation company(GEN-CO)bidders is studied.The problem is formulated as a Markov game model,where GENCO bidders interact with each other to develop their optimal day-ahead bidding strategies.Considering unobservable information in the problem,a model-free and data-driven approach,known as multi-agent deep deterministic policy gradient(MADDPG),is applied for approximating the Nash equilibrium(NE)in the above Markov game.The MAD-DPG algorithm has the advantage of generalization due to the automatic feature extraction ability of the deep neural networks.The algorithm is tested on an IEEE 30-bus system with three competitive GENCO bidders in both an uncongested case and a congested case.Comparisons with a truthful bidding strategy and state-of-the-art deep reinforcement learning methods including deep Q network and deep deterministic policy gradient(DDPG)demonstrate that the applied MADDPG algorithm can find a superior bidding strategy for all the market participants with increased profit gains.In addition,the comparison with a conventional-model-based method shows that the MADDPG algorithm has higher computational efficiency,which is feasible for real-world applications.

Strategy of constructing virtual peaking unit by public buildings’central air conditioning loads for day-ahead power dispatching

With the gradually widely usage of the air conditioning(AC) loads in developing countries, the urban power grid load has swiftly increased over the past decade.Especially in China, the AC load has accounted for over30% of the maximum load in many cities during summer.This paper proposes a scheme of constructing a virtual peaking unit(VPU) by public buildings’ cool storage central AC(CSCAC) systems and non-CSCAC(NCSCAC)systems for the day-ahead power network dispatching(DAPND). Considering the accumulation effect of different meteorological parameters, a short term load forecasting method of public building’s central AC(CAC) baseline load is firstly discussed. Then, a second-order equivalent thermal parameters model is established for the public building’s CAC load. Moreover, the novel load reduction control strategies for the public building’s CSCAC system and the public building’s NCSCAC system are respectively presented. Furthermore, based on the multiple-rank control strategy, the model of the DAPND with the participation of a VPU is set up. The VPU is composed of large-scale regulated public building’s CAC loads. To demonstrate the effectiveness of the proposed strategy, results of a sample study on a region in Nanjing which involves 22 public buildings’ CAC loads are described in this paper. Simulated results show that, by adopting the proposed DAPND scheme, the power network peak load in the region obviously decreases with a small enough deviation between the regulated load value and the dispatching instruction of the VPU. The total electricity-saving amount accounts for7.78% of total electricity consumption of the VPU before regulation.

Day-ahead optimal charging/discharging scheduling for electric vehicles in microgrids

Microgrid as an important part of smart grid comprises distributed generators(DGs),adjustable loads,energy storage systems(ESSs)and control units.It can be operated either connected with the external system or islanded with the support of ESSs.While the daily output of DGs strongly depends on the temporal distribution of natural resources such as wind and solar,unregulated electric vehicle(EV)charging demand will deteriorate the unbalance between the daily load curve and generation curve.In this paper,a statistic model is presented to describe daily EV charging/discharging behaviors considering the randomness of the initial state of charge(SOC)of EV batteries.The optimization problem is proposed to obtain the economic operation for the microgrid based on this model.In dayahead scheduling,with the estimated power generation and load demand,the optimal charging/discharging scheduling of EVs during 24 h is achieved by serial quadratic programming.With the optimal charging/discharging scheduling of EVs,the daily load curve can better track the generation curve.The network loss in grid-connected operation mode and required ESS capacity in islanded operation mode are both decreased.

Optimal Day-ahead Scheduling of Islanded Microgrid Considering Risk-based Reserve Decision

Due to the lack of support from the main grid,the intermittency of renewable energy sources(RESs)and the fluctuation of load will derive uncertainties to the operation of islanded microgrids(IMGs).It is crucial to allocate appropriate reserve capacity for the economic and reliable operation of IMGs.With the high penetration of RESs,it faces both economic and environmental challenges if we only use spinning reserve for reserve support.To solve these problems,a multi-type reserve scheme for IMGs is proposed according to different operation characteristics of generation,load,and storage.The operation risk due to reserve shortage is modeled by the conditional value-at-risk(CVaR)method.The correlation of input variables is considered for the forecasting error modeling of RES and load,and Latin hypercube sampling(LHS)is adopted to generate the random scenarios of the forecasting error,so as to avoid the dimension disaster caused by conventional large-scale scenario sampling approaches.Furthermore,an optimal day-ahead scheduling model of joint energy and reserve considering riskbased reserve decision is established to coordinate the security and economy of the operation of IMGs.Finally,the comparison of numerical results of different schemes demonstrate the rationality and effectiveness of the proposed scheme and model.

Day-ahead electricity price forecasting using back propagation neural networks and weighted least square technique

This paper proposes the day-ahead electricity price forecasting using the artificial neural networks （ANN） and weighted least square （WLS） technique in the restructured electricity markets. Price forecasting is very important for online trading, e-commerce and power system operation. Forecasting the hourly locational marginal prices （LMP） in the electricity markets is a very important basis for the decision making in order to maximize the profits/benefits. The novel approach pro- posed in this paper for forecasting the electricity prices uses WLS technique and compares the results with the results obtained by using ANNs. To perform this price forecasting, the market knowledge is utilized to optimize the selection of input data for the electricity price forecasting tool. In this paper, price forecasting for Pennsylvania-New Jersey-Maryland （PJM） interconnec- tion is demonstrated using the ANNs and the proposed WLS technique. The data used for this price forecasting is obtained from the PJM website. The forecasting results obtained by both methods are compared, which shows the effectiveness of the proposed forecasting approach. From the simulation results, it can be observed that the accuracy of prediction has increased in both seasons using the proposed WLS technique. Another important advantage of the proposed WLS technique is that it is not an iterative method.

Day-ahead Optimal Dispatch Model for Coupled System Considering Ladder-type Ramping Rate and Flexible Spinning Reserve of Thermal Power Units

In northern China,thermal power units(TPUs)are important in improving the penetration level of renewable energy.In such areas,the potentials of coordinated dispatch of renewable energy sources(RESs)and TPUs can be better realized,if RESs and TPUs connected to the power grid at the same point of common coupling(PCC)are dispatched as a coupled system.Firstly,the definition of the coupled system is introduced,followed by an analysis on its characteristics.Secondly,based on the operation characteristics of deep peak regulation(DPR)of TPUs in the coupled system,the constraint of the ladder-type ramping rate applicable for day-ahead dispatch is proposed,and the corresponding flexible spinning reserve constraint is further established.Then,considering these constraints and peak regulation ancillary services,a day-ahead optimal dispatch model of the coupled system is established.Finally,the operational characteristics and advantages of the coupled system are analyzed in several case studies based on a real-world power grid in Liaoning province,China.The numerical results show that the coupled system can further improve the economic benefits of RESs and TPUs under the existing policies.

Dual Interval Optimization Based Trading Strategy for ESCO in Day-ahead Market with Bilateral Contracts

Being capable of aggregating multiple energy resources, the energy service company(ESCO) has been regarded as a promising alternative for improving power system flexibility and facilitating the consumption of renewable resources in the electricity market. Considering the uncertain variables in day-ahead(DA) market trading, an ESCO can hardly determine their accurate probability distribution functions. Traditional interval optimization methods are used to process these uncertain variables without specific probability distribution functions.However, the lower and upper bounds of the intervals may change due to extreme weather conditions and other emergent events. Hence, a dual interval optimization based trading strategy(DIOTS) for ESCO in a DA market with bilateral contracts(BCs) is proposed. First, we transfer the dual interval optimization model into a simple model consisting of several interval optimization models. Then, a pessimistic preference ordering method is applied to solve the derived model. Case studies illustrating an actual test system corroborate the validity and the robustness of the proposed model, and also reveal that ECSO is critical in improving power system flexibility and facilitating the ability of absorbing renewable resources.

Optimal Operation of Micro-energy Grids Considering Shared Energy Storage Systems and Balanced Profit Allocations

Following the unprecedented generation of renewable energy,Energy Storage Systems(ESSs)have become essential for facilitating renewable consumption and maintaining reliability in energy networks.However,providing an individual ESS to a single customer is still a luxury.Thus,this paper aims to investigate whether the Shared-ESS can assist energy savings for multiple users through Peer-to-Peer(P2P)trading.Moreover,with the increasing number of market participants in the integrated energy system(IES),a benefit allocation scheme is necessary,ensuring reasonable benefits for every user in the network.Using the multiplayer cooperative game model,the nucleolus and the Shapley value methods are adopted to evaluate the benefit allocation between multiple users.Numerical analyses based on multiple micro-energy grids are performed,so as to assess the performance of the Shared-ESS and the proposed benefit allocation scheme.The results show that the micro-energy grid cluster can save as much as 38.15%of the total energy cost with Shared-ESS being equipped.The following conclusions can be drawn:the Shared-ESS can significantly reduce the operating costs of the micro-energy grid operator,promote the consumption of renewable energy,and play the role of peak-shaving and valley-filling during different energy usage periods.In addition,it is reflected that the multiplayer cooperative game model is effective in revealing the interaction between the micro-energy grids,which makes the distribution results more reasonable.