Power Forecast Errors Research Articles

A novel wind power forecast diffusion model based on prior knowledge

AbstractTo improve the forecast accuracy of wind power, diffusion model based on prior knowledge (DMPK) is proposed. Different from the traditional diffusion model (DM), where the noise perturbation in the diffusion or generation process is random, the noise added in DMPK is modified aiming to the characteristics of wind power signals. The distribution of wind power forecast errors is not a standard Gaussian. Wind power forecast errors are related to forecast methods, weather conditions, and other factors, containing both random signals and certain regularity. This paper adapts the Gaussian distribution to fit the historical forecast error to represent the prior knowledge of wind power. Then, the sampling distribution is derived from its relationship with the fitted prior distribution to replace the standard Gaussian in DM. Taking the prior knowledge into account during the process of noise sampling, the data in the forward process of DMPK can be guided by the distribution of historical errors for diffusion, while the generated result by the reverse process is more consistent with the actual wind power signal. Finally, the superiority of the proposed method is verified by using the wind power data from two real‐world wind farms.

Addressing Wind Power Forecast Errors in Day-Ahead Pricing With Energy Storage Systems: A Distributionally Robust Joint Chance-Constrained Approach

Addressing Wind Power Forecast Errors in Day-Ahead Pricing With Energy Storage Systems: A Distributionally Robust Joint Chance-Constrained Approach

Effect of PV power forecast error on the frequency of a standalone microgrid system

Effect of PV power forecast error on the frequency of a standalone microgrid system

Energy and reserve procurement in integrated electricity and heating system: A high-dimensional covariance matrix approach based on stochastic differential equations

The integration of stochastic renewable energy sources into energy systems presents challenges due to flexibility insufficiency and uncertainty modeling inaccuracy. To address these challenges, this paper explores a high-dimensional covariance matrix approach based on stochastic differential equations (SDEs) for energy and reserve co-dispatch in integrated electricity and heating systems. By capturing the long-term correlation of wind power forecast errors, the SDE model simultaneously models point forecasts and high-dimensional positive-definite covariance matrices, resulting in a compact uncertainty set. To ensure computational efficiency, we employ duality theory to transform the stochastic co-dispatch problem with the high-dimensional uncertainty set into deterministic convex programming. Additionally, a virtual heat storage model is introduced for the district heating network, leveraging the thermal inertia of the network to enhance reserve capacity. Simulations validate the calibration and sharpness of the proposed high-dimensional uncertainty set. The results demonstrate that co-dispatch using the SDE-based uncertainty set reduces operational costs by 4.9% compared to a set that does not consider the long-term correlation of wind power, under a 95% coverage rate. Moreover, the storage capabilities of district heating pipelines and smart buildings provide cost-free reserves, saving the operational costs of the two test systems by 2.8% and 1.3%, respectively.

Interval evaluation of wind power prediction based on skew-slash t distribution

Wind resources have characteristics of stochastic volatility, resulting in wind power forecast errors greatly. The short and medium-term wind power forecast error distribution of the actual wind farm operating system is analyzed, and a sharp peak and thick tail, with heavy tail and skewness characteristics, are presented. A skew-slash t distribution (SST distribution) is proposed to describe the error distribution of short-term wind power prediction, and the parameter estimation is carried out by probability density curve fitting. The fitting results of the wind power forecast error historical data of the Wind power plant based on SST distribution, t distribution, and t Location-slash distribution (TLS distribution) are obtained, and the fitting goodness and prediction accuracy are compared. The results show that the SST distribution can more effectively estimate the wind power prediction interval.

Distributed optimal operation of PV-storage-load micro-grid considering renewable and load uncertainties

Micro-grid is one of the important carriers for renewable energy integration. Optimizing the operation mode of micro-grid can improve economic benefits and reduce risks brought by uncertainties. To maximize the economic benefits of photovoltaic-storage-load micro-grid, a chance-constrained optimal operation model considering renewable and load uncertainties is proposed in this paper. Firstly, the photovoltaic (PV) power and load forecast error distribution function based on fitting method is obtained. Then, a probabilistic power balance constraint based on chance constrained theory is established to reflect risks brought by uncertainties. To protect the information privacy of different entities, the alternating direction multiplier method (ADMM) with self-adaptive parameters is used to the proposed optimal model in a distributed way. Case study demonstrates that the proposed model can achieve a profit and risk balance of micro-grid scheduling by setting different confidence levels, and the information privacy of micro-grid operator and users is well protected.

Two-stage AGC Control Method for Wind Farm Considering Power Forecast and Theoretical Power Error

With the large-scale wind farm connected to the power system, the uncertainty and fluctuation of its output bring challenges to the power grid dispatching and operation, especially in the automatic generation control. The problem of inaccurate theoretical power upper limit and power forecast has always been prominent. Therefore, this paper proposes a two-stage AGC control method for wind farms. In the first stage, the power control target value of the wind turbine group is determined by comprehensively considering the grid connection point of the station, the power consumption of the station, the loss in the station, and the theoretical power error. In the second stage, the power control of the wind turbine group is divided according to the proportion of the maximum power generation capacity and sent to the wind turbine, to realize the closed-loop control. Based on the measured data of a typical wind farm in Jiangsu province, the calculation results show that the control strategy proposed in this paper is effective and can greatly improve the response speed and accuracy of wind farm AGC.

Probabilistic load margin assessment considering forecast error of wind power generation

The increasing integration of wind power in power systems necessitates the probabilistic assessment of various uncertain factors. In operational planning, modeling short-term scale uncertainties, i.e., wind power forecast errors, plays an important role. In this paper, according to the different forecast values, the corresponding probability distributions of wind power forecast errors are developed using a data-driven manner. Then, the polynomial chaos expansion surrogate is developed to facilitate the probabilistic load margin assessment considering wind power forecast errors. The effectiveness of the forecast error model is verified using the historical data of realistic wind power plants. The results show that the probability distributions of forecast errors vary with the level of forecast values. Moreover, the performance of the polynomial chaos expansion surrogate in estimating probabilistic load margin is validated in the IEEE 30-bus system. The results demonstrate that the versatile forecast error distributions significantly impact the characteristics of load margin. Moreover, the polynomial chaos expansion surrogate can accelerate the load margin assessment compared to the Monter Carlo simulation while retaining the same accuracy.

Impacts of the Aerosol Representation in WRF-Solar Clear-Sky Irradiance Forecasts over CONUS

Abstract Aerosol optical depth (AOD) is a primary source of solar irradiance forecast error in clear-sky conditions. Improving the accuracy of AOD in NWP models like WRF will thus reduce error in both direct normal irradiance (DNI) and global horizontal irradiance (GHI), which should improve solar power forecast errors, at least in cloud-free conditions. In this study clear-sky GHI and DNI was analyzed from four configurations of the WRF-Solar model with different aerosol representations: 1) the default Tegen climatology, 2) imposing AOD forecasts from the GEOS-5 model, 3) imposing AOD forecasts from the Copernicus Atmosphere Monitoring Service (CAMS) model, and 4) the Thompson–Eidhammer aerosol-aware water/ice-friendly aerosol climatology. More than 8 months of these 15-min output forecasts are compared with high-quality irradiance observations at NOAA SURFRAD and Solar Radiation (SOLRAD) stations located across CONUS. In general, WRF-Solar with GEOS-5 AOD had the lowest errors in clear-sky DNI, while WRF-Solar with CAMS AOD had the highest errors, higher even than the two aerosol climatologies, which is consistent with validation of the four AOD550 datasets against AERONET stations. For clear-sky GHI, the statistics differed little between the four models, as expected because of the lesser sensitivity of GHI to aerosol loading. Hourly average clear-sky DNI and GHI were also analyzed, and they were additionally compared with CAMS model output directly. CAMS irradiance performed competitively with the best WRF-Solar configuration (with GEOS-5 AOD). The markedly different performance of CAMS versus WRF-Solar with CAMS AOD indicates that CAMS is apparently less sensitive to AOD550 than WRF-Solar is. Significance Statement Particles in the atmosphere called aerosols, which can include dust, smoke, sea salt, sulfates, black carbon, and organic carbon, absorb and scatter incoming sunlight. Improving the representation of aerosols in numerical weather prediction models reduces forecast errors in solar irradiance at ground level, particularly direct normal irradiance, during cloud-free conditions. This in turn should result in improved accuracy of solar power forecasts, especially for concentrated solar power (CSP) plants. CSP plants tend to be built in more arid, less cloudy regions that are also prone to dust loading, so accurate aerosol forecasts are particularly relevant. Comparing four representations of aerosols in the WRF-Solar model over eight months of forecasts across the United States reveals substantial differences in clear-sky irradiance forecast skill.

Robust Transient Stability Emergency Control Considering Wind Power Uncertainties

Transient stability emergency control (TSEC) enhances power system transient stability during large disturbances but faces challenges in the high-penetration wind power grid where the wind power forecast error still cannot be ignored even with state-of-the-art forecasting methods. In this paper, the TSEC problem is modeled as robust nonlinear programming with the objective of maintaining rotor angle stability by generator tripping and load shedding while the uncertain wind power outputs are regarded as intervals. Interval programming is employed to solve the robust TSEC problem where the trajectory sensitivity analysis is applied to approximate the bounds of transient stability constraints. Numerical results on two test systems demonstrate that the proposed method improves computational efficiency and shows good performance on robustness.

Time-coupled day-ahead wind power scenario generation: A combined regular vine copula and variance reduction method

Advanced stochastic programming-based power system operations planning requires wind power forecast in the form of scenarios. Generating wind power scenarios reflecting the intertemporal dependence over the forecast horizon is paramount for multi-period operations planning routines. Yet, less attention has been given to such time-coupled (temporal) wind power scenario generation (SG). Recent literature shows that copula-based SG methods are suitable for typical operations planning routines like economic dispatch and unit commitment. This work proposes a new and efficient data-driven temporal wind power SG framework using regular vine copula with variance reduction. The proposed SG puts forth two contributions to improve the quality of the temporal scenarios. The first contribution is to introduce the regular vine copula to model the temporal dependence structure of the wind power forecast error, which is shown to fit the real-world data better than the existing copula models. The second contribution is to propose a uniform design-based vine copula sampling algorithm, which benefits the downstream operations planning applications with improved convergence and accuracy of the solutions. A detailed multivariate scenario evaluation using multiple metrics shows that the proposed SG improves the quality of the temporal scenarios compared to the existing benchmarks. The Diebold-Mariano statistical test also verifies the significant improvement in the quality of the wind power scenarios.

Normal-transformation-based probabilistic load flow with correlated wind and load forecast errors

With aggressive government policies driving the electric power systems around the globe towards high renewable energy penetration, methodologies for considering forecast uncertainties in power system analysis and planning are gaining relevance. Probabilistic load flow (PLF) is a useful tool to carry out risk-based power system analysis and planning. This article discusses the need and philosophy of Normal-transformations, elaborating on Nataf transformation and polynomial normal transformation (PNT), to solve PLF and presents a unified approach for representation. Through detailed statistical modeling, the Gaussian mixture (GM) model is found to fit the historical wind and load power forecast error data better compared to widely used parametric models. Sampling of correlated marginal distributions, for scenario generation in PLF, requires the quantile function of the GM distribution, which is not available in a closed expression. A strategy, using quantile functions of Gaussian component sampling and interpolation, to approximate the GM’s quantile function is presented. The presented approximation enables the use of GM for solving PLF with correlated marginals, which is not addressed in the literature. This work also contributes to prevailing research questions by two new performance comparisons: between various higher-order PNT embedded to point estimate methods (PEMs) for PLF, and between PEM and Quasi-Monte Carlo (QMC) methods for PLF analysis. When PEMs are employed for PLF, there is no improvement observed in going for higher than third order PNT (3PNT). Results show that estimating the first four moments of the output variables through QMC-PLF is more accurate compared to PEM-PLF. Formulae useful for implementation of various higher-order PNT, for QMC and PEM, are derived and presented for direct use. Finally, the impact of correlated non-normal modeling of inputs on PLF output variables’ distribution is demonstrated.

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

We present a robust approximation of joint chance constrained DC optimal power flow in combination with a model-based prediction of uncertain power supply via R-vine copulas. It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in. This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (Eur J Oper Res (2022) https://doi.org/10.1016/j.ejor.2021.10.051). The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets. The resulting robust optimization problem has a known equivalent tractable reformulation. To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes. The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model. Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts. The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas. We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.

Optimization of orderly charging strategy of electric vehicle based on improved alternating direction method of multipliers

When it comes to solving the optimization problem of wind power and large-scale electric vehicle (EV) synergistic access to the power grid, issues like the difficulty of accurately predicting wind power, the massive amount of information communication, the difficulty of handling EV constraints, and the privacy leakage of EV owners are critical. A distributed framework based on power grids, EV load aggregates, and single EV is established in this paper. Based on this framework, an EV rolling real-time optimization model considering wind power forecast errors and EV forecast information has been established. An improved alternating direction multiplier approach is utilized to solve the model, and a small amount of information is transmitted between the two agents in each iteration to achieve the parallel solution of each agent's optimization goals. Without requiring global coordination, the proposed architecture can achieve the goal of synchronous iteration. Finally, an example of a regional power grid is used, with EVs divided into three regions. The improved ADMM algorithm now has seven multipliers, and the problem is solved, with the load variation, wind power consumption, and EV before and after optimization compared. To evaluate the effectiveness and convergence of the improved ADMM algorithm, as well as the impact of prediction information, electricity power sales price, and vehicle owner preference coefficient on dispatching outcomes, the operator's operational cost and the EV owner's charging satisfaction are examined. The example's simulation results show that the developed model achieves the goal of cutting peaks and filling valleys to absorb wind power, reducing operating costs and improving EV owner satisfaction.

Impact of the tilt angle, inverter sizing factor and row spacing on the photovoltaic power forecast accuracy

The growth of the installed photovoltaic (PV) capacity calls for accurate power forecasts, which are commonly calculated from irradiance forecasts using physical model chains. This study analyses the impact of the PV plant design parameters on the additional error of the irradiance-to-power conversion using three approaches. First, PV power curves are plotted for different design parameters to illustrate the amplification of errors and to enhance the understanding of the presented phenomena. Second, six forecast accuracy metrics are calculated as a function of the design parameters for the irradiance observation and forecast data of ten stations from five climate zones and two forecast providers. Third, the Pareto-optimal tradeoff between the annual energy production and the absolute forecast errors are obtained by the NSGA-II multi-objective optimization algorithm. The results reveal that the design parameters highly influence the PV power forecast errors, which is important to consider in all studies presenting PV power forecast verification. A tilt angle of 45° increases the error metrics up to 49% compared to a horizontal plane, and undersizing the inverters by a 1.5 sizing factor lead to an average error decrease up to 25%. Including the expected forecast errors as an objective during their design optimization process is important to maximize the net revenues of PV plants, especially if the unit imbalance costs are more than 50% of the electricity prices.

Wind–Thermal power generation scheduling with predictive transmission security margin

Optimal scheduling of generation and transmission resources in the day-ahead market is vital for the assurance of operational reliability in the case of with high wind penetration. To mitigate the ramifications of wind power uncertainty, this paper presents a risk-averse approach for the unit commitment (UC) model in a two-settlement market. A newly defined concept of predictive transmission security margin (PTSM) is formulated in the UC, which provides a measure for the risk margin of transmission congestion while accounting for wind power forecast error and contingencies. These procured PTSMs on each line are dynamically characterized based on the statistics of ex-post line flows in the real-time re-dispatch. The proposed framework is formed as a bi-level optimization problem, and is transformed into a mixed integer programming formulation using Karush–Kuhn–Tucher (KKT) optimality conditions for computational tractability. The effectiveness of the proposed method is tested using various case scenarios on a modified IEEE RTS 24-bus and a 118-bus system in terms of key performance metrics, including the total operation cost, congestion hours, and required and undelivered generation reserves. The results show that the proposed method can effectively reduce the total operation costs by suppressing congestion risk and improving reserve deliverability.

Sustainable power systems operations under renewable energy induced disjunctive uncertainties via machine learning-based robust optimization

For sustainable and reliable power systems operations integrating variable renewable energy, it is essential to incorporate the uncertain intermittent power outputs. A novel robust unit commitment framework with data-driven disjunctive uncertainty sets is proposed for sustainable energy systems with volatile renewable wind power, assisted by machine learning. The approach can flexibly identify the uncertainty space based on renewable power forecast error data with disjunctive structures. Specifically, the uncertainty data are grouped using K-means and density-based spatial clustering of applications with noise (DBSCAN) following the optimal cluster number determined by the Calinski-Harabasz index. Disjunctive uncertainty sets are constructed accordingly as the union of multiple basic uncertainty sets, including conventional box and budget uncertainty sets, and data-driven uncertainty sets using Dirichlet process mixture model, principal component analysis coupled with kernel density estimation, and support vector clustering. Subsequently, the problem is formulated into a two-stage adaptive robust unit commitment model with data-driven disjunctive uncertainty sets and with a multi-level optimization structure. To facilitate the solution process, a tailored decomposition-based optimization algorithm is developed. The effectiveness and scalability of the proposed framework are illustrated with two case studies investigating sustainable operations scheduling based on IEEE 39-bus and 118-bus systems, considering the integration of intermittent renewable energy. Results show that the proposed framework can reduce the price of robustness by 8–48% compared to the conventional “one-set-fits-all” robust optimization approaches. Benchmarking with stochastic programming indicates that the proposed framework can achieve the same or better economic performance for sustainable operations with over 75% less computational time.

A Method of Probability Distribution Modeling of Multi-Dimensional Conditions for Wind Power Forecast Error Based on MNSGA-II-Kmeans

How to consider both the influence of weather and wind power in the modeling process of probability distribution of wind power forecast error (WPFE), and to emphasize the application value of conditional modeling, is rarely studied at present. This paper proposes a novel method of conditional probability distribution modeling for WPFE. This method uses a proposed MNSGA-II-Kmeans algorithm to perform multi-objective clustering of multi-dimensional influencing factors (MDIF), including weather and wind power. It can maximize the difference between the probability distributions of each MDIF mode’s WPFE while clustering, thus ensuring the application value of the conditional modeling way. Based on the clustering results, by using the versatile distribution to simulate the probability distribution of WPFE and the support vector machine to realize the recognition of MDIF modes, the specific conditional probability distribution function of WPFE can be provided to stochastic economic dispatch by identifying the forecast MDIF data. A wind plant of north China with historical data is selected for calculation. The results verify the effectiveness of the proposed method, and by comparison with the non-conditional probability distribution of WPFE that does not consider MDIF, it can effectively increase the wind power consumption of the power system.

Reliability evaluation of a composite power system in the presence of renewable generations

Power system reliability evaluation plays a vital role in the planning and operation studies by reflecting the system safety level. In this paper, a combination of a non-sequential Monte Carlo simulation (MCS)-based model and an improved Estimation of Distribution Algorithm (EDA) is exploited for evaluating the reliability of the composite power systems considering variability and uncertainty of wind farms (WFs) and Photovoltaic (PV) units. Variability of these resources is defined as the random fluctuation of wind speed and solar irradiation caused by changes in the atmosphere, while their uncertainty results from output power forecast errors. In the proposed model, the states of traditional generating units, transmission lines, WFs, and PV units are constructed using non-sequential MCS. These states can be achieved based on the component failure probability for dispatchable traditional generators and transmission lines along with the Probability Distribution Functions (PDFs) of renewable generations. To enhance the computational efficiency of the MCS in the sampling step, the improved EDA upgraded with the Population-Based Incremental Learning (PBIL) algorithm is employed. The proposed mathematical model for reliability evaluation of composite power system is applied to the IEEE RTS 24-bus system, and numerical studies are performed under several case studies. The simulation results confirm the proficiency of the proposed method to improve the computational efficiency, while the high accuracy of reliability evaluation of the composite power system is attained.

Short term wind energy prediction model based on data decomposition and optimized LSSVM

The uncertainty and instability of wind power make it difficult to develop wind energy, wind farm grid connection, and power system stability, so accurate forecasting of wind power is very important. How to reduce wind power forecast errors and improve wind power forecast accuracy has become an urgent problem to be solved. The combined model proposed in this paper uses fast filtering algorithm (FCBF) and variational mode decomposition (VMD) to extract features of wind resource data, and uses least squares support vector machine (LSSVM) to predict short-term wind speed. Finally, according to the point prediction results and the prediction error, the wind speed range is estimated. In this paper, three groups of wind speed data at different times and regions are used for experiments. The experimental results show that the prediction error of the model designed in this paper is significantly less than that of the comparison model. The results show that the prediction system proposed in this paper is superior to all comparative prediction schemes, which can reduce the fluctuation risk and improve the stability and security of wind power system.