Power Forecast Errors Research Articles

Optimal sizing of energy storage considering the spatial‐temporal correlation of wind power forecast errors

Energy storage is considered as an effective approach to deal with the power deviation that caused by the stochastic wind power forecast error. Because of the spatial-temporal correlation of forecast errors for wind farms, which locate close to each other and integrate into the same regional power grid, energy storage could be deployed effectively and economically. Therefore, this study proposes an optimisation method to size the capacity of energy storage system (ESS) considering the spatial-temporal correlation of forecast errors for multiple nearby wind farms. The copula theory based correlation model of high-dimensional forecast errors is built to capture the spatial-temporal characteristics of forecast error. Then, according to multiple scenarios technique, an optimal ESS sizing model is established to minimise the investment and operation costs of the ESS. Meanwhile, an operation strategy considering the trend of prediction and correlation of errors is used to implement rolling operation strategy of ESS. The case studies demonstrate the effectiveness of the new method and illustrate the significant impact of the correlation of forecast error on the capacity of ESS.

A Distributed Probabilistic Modeling Algorithm for the Aggregated Power Forecast Error of Multiple Newly Built Wind Farms

The extensive penetration of wind farms (WFs) presents challenges to the operation of distribution networks (DNs). Building a probability distribution of the aggregated wind power forecast error is of great value for decision making. However, as a result of recent government incentives, many WFs are being newly built with little historical data for training distribution models. Moreover, WFs with different stakeholders may refuse to submit the raw data to a data center for model training. To address these problems, a Gaussian mixture model (GMM) is applied to build the distribution of the aggregated wind power forecast error; then, the maximum a posteriori (MAP) estimation method is adopted to overcome the limited training data problem in GMM parameter estimation. Next, a distributed MAP estimation method is developed based on the average consensus filter algorithm to address the data privacy issue. The distribution control center is introduced into the distributed estimation process to acquire more precise estimation results and better adapt to the DN control architecture. The effectiveness of the proposed algorithm is empirically verified using historical data.

Virtual Power Plant Operation with Solar Power Forecast Errors and Demand Response

Intermittent renewable energy production, determined by weather conditions, is increasing in power markets. Their efficient integration calls for flexible participants in smart power grids. It has been acknowledged that a huge underutilized flexibility resource lies on the electricity consumer-side. The activation of this demand flexibility is, however, a big challenge. Despite the recently risen interest towards demand flexibility, there is a gap in the literature investigating the incentives for consumers to offer their flexibility to power markets. It has been proposed that there needs to be a third-party operator aggregating and controlling this flexibility. In this paper we examine a concept of virtual power plant, which simultaneously optimizes the response of controllable electric hot water heaters to solar power forecast error imbalances. Uncertainty is included in the optimization in terms of solar power day-ahead forecast errors and balancing power market conditions. We show that the virtual power plant can add value from optimizing the combination of these resources. The results indicate that while the total profits are increasing, the marginal revenues are diminishing with the number of participating households. From a policy perspective, our results imply that market efficiency can be increased by allowing the aggregated resources to participate more freely in the markets.

Impacts of wind power forecast errors on the real‐time balancing need: a Nordic case study

As the share of wind power increases in the power system, also the share of uncertain generation increases. This, in turn, increases the total balancing energy, real-time balancing power requirements and ramping of the balancing generation. In this study, the impact of wind power forecast errors on the real-time balancing need was investigated for different shares of wind energy (4-30%) in Finland and the Nordic region (comprising Denmark, Finland, Norway and Sweden). The size of the aggregation area of the net imbalances has an impact on the net imbalance volumes. The larger the size of the area is, the smaller the normalised net imbalance volumes are. In Finland, the impact of wind forecast errors on the net imbalance volumes and the largest net imbalances is almost two times as large as the impact of wind power forecast errors in the Nordic region. A shorter forecast horizon has an impact of similar magnitude both on reducing the net imbalance volumes and the largest net imbalances and on aggregating imbalances from large spatial areas. When day-ahead forecasts are not corrected intraday (ID) the impact on the net imbalance volumes and the largest net imbalances is twice as large as when ID forecasts are used.

Wind power system reliability sensitivity analysis by considering forecast error based on non-standard third-order polynomial normal transformation method

The impact of the wind power forecast error (WPFE) on the reliability of the wind power system may be quantified by using the sensitivity, which is difficult to calculate because the distribution of the WPFE is unknown. The assumption that the WPFE follows the normal distribution is often impractical. The non-standard third-order polynomial normal transformation (NSTPNT) method is newly proposed. And the analytical expressions of the probability weighted moments (PWMs) of the normal random variable are newly derived to directly calculate the polynomial coefficients. The non-normal WPFE is resembled by a non-standard normal random variable using the NSTPNT method, which ensures the accuracy of the reliability assessment and the convenience for calculating sensitivities. Combining the NSTPNT method and the discrete WPFE, the reliability sensitivities of the wind power system respect to the distribution parameters, expectation, and standard deviation, of the WPFE following the non-normal distributions are established respectively. In numerical results, the accuracy of the NSTPNT method and the sensitivities are verified. Different reserve capacities with high level of the wind power penetration are examined. The effects of the reserve capacity and the standard deviation of the forecast error on the reliability sensitivities are analyzed.

Extreme wind power forecast error analysis considering its application in day‐ahead reserve capacity planning

Accurate wind power forecasting is crucial for setting reserve dimensions of a power system. From the perspective of power grid dispatcher, one of the most critical issues of dealing with the uncertainty brought by wind power forecast error (WPFE) is to analyse its extreme value to decide the new reserve requirements induced by variable wind power. This study targets at predicting the daily maximum of day-ahead WPFE via extreme value analysis approach considering its application of operating reserve planning. Non-stationary block maxima method (NS-BMM) is applied to model the probabilistic characteristic of daily maxima WPFE via fitting the non-linear relationship between distribution parameters and the covariates. To better shape the non-stationarity, a conditional NS-BMM (CNS-BMM) via partition according to wind conditions is proposed. Moreover, indicators to evaluate the quality of applying NS-BMMs in the day-ahead reserve plan are also discussed. Finally, a case study based on the operational data from a typical wind farm in northern China is carried out. Results show that CNS-BMM offers a better model of daily maximum WPFE compared to not only traditional quantile regression but also non-CNS-BMM, and applying the estimate of daily maximum WPFE on reserve plan demonstrates an advantage over conventional three-sigma method.

Multi-Objective based Optimal Generation Scheduling Considering Wind and Solar Energy Systems

Abstract This paper presents an optimum day-ahead scheduling of thermal and renewable (wind and solar photovoltaic) power generation as a multi-objective optimization (MOO) problem considering the uncertainty. System operating cost (i.e. cost of thermal, wind, solar PV and battery), reliability and emission cost are considered to be optimized simultaneously. The uncertainties due to the generator outages, wind, solar PV power and load forecast errors are incorporated in the proposed optimization problem using the Loss Of Load Probability (LOLP) and Expected Unserved Energy (EUE) reliability indices. In the proposed approach, the amount of spinning reserves (SRs) required are scheduled based on the desired level of system reliability. The proposed multi-objective optimization problem is solved using NSGA-II algorithm. Different case studies are performed considering different objective functions that may be selected by system operator (SO) based on the preference.

Modelling wind power spatial-temporal correlation in multi-interval optimal power flow: A sparse correlation matrix approach

The significantly increasing deployment of wind power necessitates that system operation considers the spatial-temporal correlation of power forecast from different wind power plants. How to model this spatial-temporal correlation in the actual system dispatch is challenging. In this paper, a sparse correlation matrix is utilized to efficiently model the spatial-temporal correlation of wind power forecast in the generation dispatch model. A novel, adjustable, and distributionally-robust chance-constrained multi-interval optimal power flow (ADRCC-MIOPF) model is proposed to obtain reliable economic dispatch (ED) solutions. The spatial-temporal correlation of wind power plants power forecasts is represented by the sparse correlation covariance matrix obtained from historical, time series wind power forecast error data. The chance constraints in the ADRCC-MIOPF model are transformed into a set of second-order-cone (SOC) constraints in which an adjustable coefficient in the chance constraints controls the robustness of the ADRCC-MIOPF model to the wind power forecast errors distribution. Case studies performed on the PJM 5-bus system and IEEE 118-bus system verify the proposed method to improve the system security and reduce the cost especially under the high wind penetration levels. All the cases can be solved within several minutes for both the small and large cases which validates the efficiency of the proposed sparse matrix model. In addition, considering the spatial-temporal correlation of wind power forecast and the distributional robustness of wind power forecast error leads to a more reliable economic dispatch with lower system violations.

Multi-Time Scale Rolling Economic Dispatch for Wind/Storage Power System Based on Forecast Error Feature Extraction

This paper looks at the ability to cope with the uncertainty of wind power and reduce the impact of wind power forecast error (WPFE) on the operation and dispatch of power system. Therefore, several factors which are related to WPFE will be studied. By statistical analysis of the historical data, an indicator of real-time error based on these factors is obtained to estimate WPFE. Based on the real-time estimation of WPFE, a multi-time scale rolling dispatch model for wind/storage power system is established. In the real-time error compensation section of this model, the previous dispatch plan of thermal power unit is revised according to the estimation of WPFE. As the regulating capacity of thermal power unit within a short time period is limited, the estimation of WPFE is further compensated by using battery energy storage system. This can not only decrease the risk caused by the wind power uncertainty and lessen wind spillage, but also reduce the total cost. Thereby providing a new method to describe and model wind power uncertainty, and providing economic, safe and energy-saving dispatch plan for power system. The analysis in case study verifies the effectiveness of the proposed model.

Power System Day-Ahead Unit Commitment Based on Chance-Constrained Dependent Chance Goal Programming

In the context of large-scale renewable energy integrated into an electrical power system, the effects of power forecast errors on the power balance equation of the power system unit commitment model is considered. In this paper, the problem of solving the power balance equation with uncertain variables was studied. The unit commitment model with random variables in the power balance equation was solved by establishing a power system day-ahead optimisation unit commitment model based on chance-constrained dependent chance goal programming. First, to achieve the solution of the power balance equation with random variables, the equality constraint is loosened into an inequality constraint, and the power balance equation constraint is transformed into a dependent chance programming model aimed at maximising the probability of occurrence of random events in an uncertain environment. Then, the dependent chance programming model is proposed to ensure the economy and security of the scheme, and the goal programming model is introduced to facilitate an efficient solution. By combining dependent chance programming and goal programming, a power system day-ahead unit commitment model based on chance-constrained dependent chance goal programming is established. Finally, an example is discussed to demonstrate the effectiveness of the proposed model.

Generation of Time-Coupled Wind Power Infeed Scenarios Using Pair-Copula Construction

Wind power forecasts for an aggregation of wind farms have become pivotal to many user groups, e.g., system operators and market actors. However, deviations from these forecasts impact system stability and energy prices in power systems with a high share of installed wind power. Hence, modeling such deviations with probabilistic wind power forecasting approaches has become more relevant. Most methods account for different look-ahead timestamps separately and neglect the temporal propagation of wind power forecast errors. This paper presents a new approach that applies the so-called pair-copula constructions or vine copulae to generate time-coupled wind power infeed scenarios for an aggregation of wind farms. By using a copula approach, the modeling of the temporal dependence structure can be separated from the modeling of the wind power uncertainty in each timestamp. A D-vine structure is proposed and compared with a C-vine and a Gaussian copula in a case study on Belgian offshore wind farms. Different pair-copula selections and estimation procedures are tested. The evaluation results appear promising, especially for D-vines.

A real-time energy management system for smart grid integrated photovoltaic generation with battery storage

Abstract This paper proposes a real-time energy management system (EMS) suitable for rooftop PV installations with battery storage. The EMS is connected to a smart grid where the price signals indirectly control the power output of the PV/battery system in response to the demand variation of the electricity networks. The objective of the EMS is to maximize the revenue over a given time period while meeting the battery stored energy constraint. The optimization problem is solved using the method of Lagrange multipliers. The uniqueness of the proposed EMS remains in the reactive real-time control mechanism that compensates for the PV power forecast error. The proposed EMS requires only forecasting the average PV power output over the total optimization period. This is in contrast to the predictive power scheduling techniques that require accurate instantaneous PV power forecast. The proposed EMS method is verified by benchmarking against the predictive brute-force dynamic programming (DP) approach. The simulation analysis considers days with varying solar irradiance profiles. The simulation analysis shows the proposed EMS operating under practical assumptions, where the battery storage capacity is subject to constraints and the PV power output is not known a priori.

Two-Stage Optimization of Battery Energy Storage Capacity to Decrease Wind Power Curtailment in Grid-Connected Wind Farms

As wind power makes an increasing contribution to power systems, the problems associated with wind power curtailment have become a concern in recent years. Battery energy storage (BES) can reduce the effects of wind power curtailment by peak shaving and wind power forecast error compensation. Accordingly, the operational constraints of power systems and wind power uncertainty should be considered in the optimization of BES capacity installed at wind farms. This paper proposes a two-stage method to determine the optimal power and capacity of BES in systems including thermal plants, wind farms, and BES. In the first stage, the unit commitment of thermal generators and scheduled wind farm output are optimized with ac power flow constraints modeled by second-order cone programming. Time series of the wind farm output generated by Monte Carlo simulations are used for BES optimization. In the second stage, operational strategies for BES are designed. The simulation results indicate that cooperation between the BES and wind farm using the proposed method can reduce the costs of both wind farms and thermal plants. Finally, a sensitivity analysis is performed to assess the influence of the BES unit cost and wind power penetration on the optimal power and capacity of BES.

CorClustST—Correlation-based clustering of big spatio-temporal datasets

Increasing amounts of high-velocity spatio-temporal data reinforce the need for clustering algorithms which are effective for big data processing and data reduction. As currently applied spatio-temporal clustering algorithms have certain drawbacks regarding the comparability of the results, we propose an alternative spatio-temporal clustering technique which is based on empirical spatial correlations over time. As a key feature, CorClustST makes it easily possible to compare and interpret clustering results for different scenarios such as multiple underlying variables or varying time frames. In a test case, we show that the clustering strategy successfully identifies increasing spatial correlations of wind power forecast errors in Europe for longer forecast horizons. An extension of the clustering algorithm is finally presented which allows for a large-scale parallel implementation and helps to circumvent memory limitations. The proposed method will especially be helpful for researchers who aim to preprocess big spatio-temporal datasets and who intend to compare clustering results and spatial dependencies for different scenarios.

Wind power variability and power system reserves in South Africa

Variable renewable generation, primarily from wind and solar, introduces new uncertainties in the operation of power systems. This paper describes and applies a method to quantify how wind power development will affect the use of short-term automatic reserves in the future South African power system. The study uses a scenario for wind power development in South Africa, based on information from the South African transmission system operator (Eskom) and the Department of Energy. The scenario foresees 5% wind power penetration by 2025. Time series for wind power production and forecasts are simulated, and the duration curves for wind power ramp rates and wind power forecast errors are applied to assess the use of reserves due to wind power variability. The main finding is that the 5% wind power penetration in 2025 will increase the use of short-term automatic reserves by approximately 2%.

Steady state and transient simulation for electricity‐gas integrated energy systems by using convex optimisation

The increasing interdependence between electric power and natural-gas systems requires integrated simulation tools applicable to the coupled system. Therefore, this study proposes steady-state and transient simulation tools for electricity-gas integrated energy systems (IESs) by using convex optimisation. Steady-state IES simulation is designed for long-term planning studies while transient IES simulation, which includes line-pack storage, is designed for real-time operational research. The proposed convex steady-state gas flow model introduces binary variables to represent gas flow directions, and employs the second-order cone (SOC) to relax non-convex pipeline gas flow equations. As a result, steady-state gas flow analysis is formulated as a mixed integer SOC programming problem. The proposed transient gas flow model employs the implicit finite difference method to transform partial differential equations into algebraic difference equations. Moreover, the short-term gas flow directions are specified and SOC relaxations are used. Simulation results on an integrated IEEE 24-node system and Belgian 20-node gas system verify the effectiveness of the proposed SOC models. The impacts of wind power forecast errors on multi-period gas network operations are also investigated.

A conditional model of wind power forecast errors and its application in scenario generation

In power system operation, characterizing the stochastic nature of wind power is an important albeit challenging issue. It is well known that distributions of wind power forecast errors often exhibit significant variability with respect to different forecast values. Therefore, appropriate probabilistic models that can provide accurate information for conditional forecast error distributions are of great need. On the basis of Gaussian mixture model, this paper constructs analytical conditional distributions of forecast errors for multiple wind farms with respect to different forecast values. The accuracy of the proposed probabilistic models is verified by using historical data. Thereafter, a sampling method is proposed to generate scenarios from the conditional distributions which are non-Gaussian and interdependent. The efficiency of the proposed sampling method is verified.

Modeling the temporal correlation of hourly day-ahead short-term wind power forecast error for optimal sizing energy storage system

Due to the inherent stochastic and intermittent nature of wind generation, it is very difficult to sharply improve the wind power forecasting accuracy. The sizing of energy storage system (ESS) for wind farm can effectively reduce the uncertainty caused by the inevitable forecast error of wind power. However, optimal sizing of ESS is a multi-period decision-making problem and it is the key point that exactly captures the variation magnitude and speed of forecast error. This paper proposes a method to establish the multivariate joint cumulative distribution function (JCDF) of hourly day-ahead short-term multi-period forecast errors using Normal/t copula. Based on the proposed JCDF and multiple scenarios technique, a model of optimal sizing of ESS is proposed in which the temporal correlation relationship between different time period forecast errors and probability distribution of each time period forecast error are both considered. The simulation results verify the effectiveness of the proposed methods and show that if the temporal correlation of wind power short-term forecast error is ignored, the rated energy and power capacity of sizing of ESS will be significantly misestimated.

Parameter Estimation of a Gaussian Mixture Model for Wind Power Forecast Error by Riemann L-BFGS Optimization

With the increasing penetration of wind power into the electricity grid, wind power forecast error analysis plays an important role in operations scheduling. To better describe the characteristics of power forecast error, a probability density function should be established. Compared with the Kernel density estimation method, this paper adopts the Gaussian mixture model (GMM), which is flexible enough to capture different error distribution characteristics, such as bias, heavy tail, multi-peak, and so on. In addition, for GMM parameter estimation, when dealing with a large number of multi-dimensional data sets or unbalanced overlapping mixtures, the expectation maximization (EM) algorithm shows a slower convergence speed and requires a high number of iterations. In this paper, a new L-BFGS optimization method, based on the Riemannian manifold, is used for GMM parameter estimation. Based on actual wind power forecast error data, the suitability of the model and the new optimization algorithm was verified in large, multi-dimensional data sets. The new optimization algorithm has fewer iterations than the EM algorithm, with an improved convergence speed.

Wind power variability and power system reserves in South Africa

Variable renewable generation, primarily from wind and solar, introduces new uncertainties in the operation of power systems. This paper describes and applies a method to quantify how wind power development will affect the use of short-term automatic reserves in the future South African power system. The study uses a scenario for wind power development in South Africa, based on information from the South African transmission system operator (Eskom) and the Department of Energy. The scenario foresees 5% wind power penetration by 2025. Time series for wind power production and forecasts are simulated, and the duration curves for wind power ramp rates and wind power forecast errors are applied to assess the use of reserves due to wind power variability. The main finding is that the 5% wind power penetration in 2025 will increase the use of short-term automatic reserves by approximately 2%.