Correlated Wind Power Research Articles

Optimal offering strategy for wind-storage systems under correlated wind production

This paper formulates the offering problem for a cluster of wind-storage systems in the day-ahead energy market using a risk-constrained stochastic programming approach that anticipates different operating conditions in the real-time energy market. Wind-storage systems can be jointly operated as a cluster so as to achieve higher profitability. However, a meaningful positive correlation among the production provided by wind farms located in the cluster results in a higher level of uncertainty that imposes additional risk. A key issue is how this correlation influences the operation of the cluster in the energy markets. In order to study this subject, this paper presents the uncertainties involved by means of a number of correlated scenarios including: (i) the correlated prices in the day-ahead and the real-time markets, and (ii) the correlated wind power production of multiple wind farms jointly generated using an innovative scenario generation methodology. The comparative statistical analysis validates the good accuracy of the method proposed in order to capture the spatio-temporal correlation among the wind farms. The results of a realistic case study are, moreover, compared with those obtained by considering that the scenarios are generated individually for each wind farm. Upon considering the latter, the variability of wind power production is underestimated, which has a negligible impact on the expected profit; however, the profit risk modeled using the conditional value-at-risk is significantly overestimated. The overestimation error particularly concerns a less risk-averse operator of the cluster in the case of low wind power production.

Data-driven Based Uncertainty Set Modeling Method for Microgrid Robust Optimization with Correlated Wind Power

Data-driven Based Uncertainty Set Modeling Method for Microgrid Robust Optimization with Correlated Wind Power

Probabilistic optimal power flow calculation method considering sequential features and correlations of multi-uncertain source-load scenarios

In order to accurately evaluate the influence of the correlation and sequential feature of wind power, PV power, and load on the economic operation of a power system, a sequential probabilistic optimal power flow calculation method based on multi-uncertain source-load scenarios generated by a multi-generative adversarial network (MGAN) is proposed. First, the historical datasets of wind power, PV power, and load in adjacent areas were collected, and their probability distributions in 24 time periods were analyzed. The results showed that the probability distribution of different periods had obvious differences, which were defined as time sequence differences in this paper. Second, a novel neural network called MGAN for scenario generation was designed. Based on the historical data of each time period, the correlated wind power, photovoltaic (PV) power, and load scenarios were generated by MGAN. Finally, in the modified IEEE 118-bus system, in which two wind power sources, two PV power sources, and two loads with correlation were integrated, probabilistic optimal power flow calculations were carried out for 24 periods with the goal of the lowest power generation cost of thermal power units. The experimental results showed that the power generation cost fluctuation ranges that considered the time sequence difference were reduced by 60% on average compared with the nonconsidered. The proposed method can effectively reduce the power generation cost budget.

Probabilistic Forecasting Based Sizing and Control of Hybrid Energy Storage for Wind Power Smoothing

With the increasing wind power integration, the security and economy of the power system operations are greatly influenced by the intermittency and fluctuation of wind power. Due to the flexible operational modes for charging/discharging, the hybrid energy storage system (HESS) is composed of battery energy storage system and super-capacitor can effectively mitigate the wind power uncertainty. This paper proposes a probabilistic forecasting-based HESS sizing and control scheme to cost-effectively smooth wind power fluctuations. First, probabilistic wind power forecasting is combined with multivariate Gaussian copula to generate temporally correlated wind power scenarios. Then, an adaptive variational mode decomposition (VMD) method is proposed to extract the frequency components of each wind scenario and determine the pre-scheduled power of wind-HESS system adaptively. Finally, a two-stage stochastic optimization model is constructed to determine the capacity and correct the pre-scheduled power of HESS with the objective of minimizing total cost. Case studies based on actual data from a Danish wind farm demonstrate that the proposed HESS sizing and control scheme can significantly reduce the installation cost and operation cost of HESS and prominently smooth wind power fluctuations.

Addressing the Conditional and Correlated Wind Power Forecast Errors in Unit Commitment by Distributionally Robust Optimization

In this paper, a study of the day-ahead unit commitment problem with stochastic wind power generation is presented, which considers conditional, and correlated wind power forecast errors through a distributionally robust optimization approach. Firstly, to capture the characteristics of random wind power forecast errors, the least absolute shrinkage, and selection operator (Lasso) is utilized to develop a robust conditional error estimator, while an unbiased estimator is used to obtain the covariance matrix. The conditional error, and the covariance matrix are then used to construct an enhanced ambiguity set. Secondly, we develop an equivalent mixed integer semidefinite programming (MISDP) formulation of the two-stage distributionally robust unit commitment model with a polyhedral support of random variables. Further, to efficiently solve this problem, a novel cutting plane algorithm that makes use of the extremal distributions identified from the second-stage semidefinite programming (SDP) problems is introduced. Finally, numerical case studies show the advantage of the proposed model in capturing the spatiotemporal correlation in wind power generation, as well as the economic efficiency, and robustness of dispatch decisions.

Day-ahead energy and reserve scheduling under correlated wind power production

Empirical reports validate significant correlation among adjacent wind farms. However, in practice, the market operator schedules the amounts of energy and reserve in the day-ahead market without considering the correlation. This paper develops a computational framework, which allows the market operator to clear the day-ahead market under the correlated wind power production, and evaluate how the energy and reserve schedules may change due to ignoring the correlation. To accomplish this task, a scenario generation methodology is proposed to provide correlated scenarios of wind production in the daily horizon. Through the methodology, a multivariate model presents the power production of each wind farm as a nonlinear function of wind speed and autoregressive moving average model. The multivariate models of wind farms are coupled through their cross-correlation matrix. The methodology is applied to the real-world data of wind farms located at diverse geographic regions in United States. The scenarios are considered as input data for clearing a joint energy and reserve market, which is formulated as a two-stage stochastic model. The potential impact of significant correlation among wind farms is investigated through 6-bus and IEEE 118-bus test systems for different wind penetration levels. The results show that for higher correlation, the policy adopted by the market operator is to schedule less wind energy in the day-ahead market, at the expense of greater energy and reserve capacity allocated to conventional generating units. By ignoring the correlation, the market operator underestimates the reserve capacity that may threaten system security and impose additional cost on the real-time operation.

Robust transmission constrained unit commitment under wind power uncertainty with adjustable conservatism

This study proposes a novel robust transmission-constrained unit commitment model with adjustable conservatism (denoted as RAC-TCUC). Ellipsoidal uncertainty set (EUS) is adopted in this model to well fit the spatial-temporal correlated wind power. The affine policy is utilised in the generation dispatch process of the model for the sake of computational tractability. To reduce the conservatism, a novel criterion for budget value selection of the EUS is presented. Moreover, this study discusses a crucial, yet barely addressed issue in the literature: the feasibility of the solution against the realisation of uncertainties beyond the prescribed EUS. To prove the validity of the criterion, an analytical relationship between the budget value of the EUS and the actual probability of solution's feasibility against all possible scenarios of uncertainties is presented. Finally, the testing results demonstrate the effectiveness and economic benefits of the proposed method.

Enhancing Hosting Capacity of Uncertain and Correlated Wind Power in Distribution Network With ANM Strategies

To settle the large-scale integration of wind power, it is necessary to enhance the wind power hosting capacity of distribution network. To this end, this paper proposes a stochastic mixed-integer linear programming (MILP) model to enhance the hosting capacity of distribution network with active network management (ANM) strategies. The considered ANM strategies include power factor control, reactive power compensation and network reconfiguration. The coordination of these strategies enables the distribution network to accommodate more wind power without violating its constraints. The proposed model relaxes the original nonlinear power flow equations into linear format, so that a near optimal solution can be obtained with moderate computational burden. The wind power and load demand are inherently variable due to the influence of various factors. Moreover, the output powers of multiple wind turbines (WTs) located at adjacent sites of a wind farm are spatially correlated. To represent the uncertain loads, the roulette wheel mechanism is used to generate the load samples. In addition, a combined method of inverse transformation and Nataf transformation is established to deal with the uncertain and correlated wind power. Then, scenario combination and reduction are conducted to generate representative scenarios. Finally, the feasibility and accuracy of the proposed method are verified via numerical tests on the modified IEEE 33-bus test system.

Robust Bidding Strategy and Profit Allocation for Cooperative DSR Aggregators With Correlated Wind Power Generation

Aggregation is an effective way of collective management of demand-side resources (DSRs). As an independent entity in electricity market, DSR aggregator can participate in both the energy and ancillary services markets. The DSR aggregator's optimal bidding strategy is subject to market price uncertainties and resource variability. In this paper, spatial correlation of wind power generation is considered in developing a robust DSR bidding strategy which takes into account individual and cooperative aggregators. The proposed model is transformed into and solved as a mixed integer second order cone programming (MISOCP) problem. The Aumann–Shapley procedure is applied in this paper to allocate the payoff among cooperative DSR aggregators considering potential uncertainties. By replacing binary variables with their optimal values, the original MISOCP is transformed into a second order cone programming (SOCP) problem and Lagrange multipliers are employed for the implantation of a discrete Aumann–Shapley procedure. Case studies verify the feasibility and effectiveness of the proposed bidding model and payoff allocation procedure.

Probabilistic load flow with correlated wind power sources using a frequency and duration method

Probabilistic load flow (PLF) is an important tool in power system planning and operation. One limitation of conventional PLF is that only the probability information of random variables is obtained as a reference for related analyses. Frequency and duration information often plays an important role in power system assessment. In this study, a frequency and duration method for PLF with correlated wind power sources and loads is proposed based on Latin hypercube sampling (LHS), Nataf transformation, and Markov chains. In the proposed method, the spatial and temporal correlations among wind power sources and loads are addressed using Nataf transformation and Markov chains, which are incorporated into the LHS framework to solve the PLF problem with frequency and duration quantities. With the proposed method, not only the probability information but also the frequency and duration information of the random output variables in a PLF problem can be efficiently and accurately obtained. The performance of the proposed PLF method is verified using comparative tests on three modified test systems.

Robust coalitional game theoretic optimisation for cooperative energy hubs with correlated wind power

As the development of the energy industry, the integration and complementary of various energy resources will be trends of future multiple energy systems. Energy hub (EH) plays an important role in allocating energy resources efficiently. This study proposes a robust coalitional game theoretic optimisation model to execute the cooperative operation of multiple EHs with correlated wind power. First, an EH model with wind power generation is established. It considers both uncertainties and correlations of wind power. Then, coalitional game theory is introduced to solve the cooperation problem of multiple EHs. Distributed coalition formation algorithm called merge-split rule is developed to form coalitions of EHs. Furthermore, the robust optimisation method is presented to cope with the uncertainties of wind power. Scenarios of correlated historical data are covered by minimum volume enclosing ellipsoid and solved by Khachiyan's first-order algorithm. Numerical results are given to verify the feasibility and efficiency of our proposed models and methods.

Second‐order cone robust AC–DC DOPF considering correlation of wind power

Due to the increasing penetration, intermittent renewable energy sources (RESs), such as wind power, have added additional uncertainties to AC–DC power system operation. The strong correlation between wind power will bring larger computational errors. It makes generation dispatching incompatible with the current single-period optimal power flow practice. This study presents an AC–DC affinely adjustable robust dynamic optimal power flow (AARDOPF) model. Ellipsoidal uncertainty set is adopted to well fit the spatial-temporal correlated wind power. Affine policies are utilised in the re-dispatch process. To apply AC–DC AARDOPF, the base-point generation is calculated and determined to match the power with forecasted RES output. And once the uncertainty is revealed, generators reschedule its output through participation factors responding to the uncertain fluctuation of RES output to ensure a feasible solution for all realisations of RES output. Then original non-linear models are transformed into SOCP models. Finally, GUROBI is used to solve this model. Numerical results are obtained on modified AC–DC IEEE 30-bus and 118-bus system to minimise the expected operational cost. Comparing with stochastic dynamic optimal power flow (DOPF), this model is proved to be more practical and effective.

Stochastic optimal transmission switching considering the correlated wind power

Optimal transmission switching (OTS) is widely used in mitigating transmission congestion and reducing power losses. However, with large-scale renewable energy integration to the grid, making a decision for the randomness characteristic of renewable energy (e.g. wind and solar power) is complicated in OTS. In this study, a novel stochastic optimal power flow-based point estimation method (PEM) is presented to model the uncertainties of wind power and load in OTS. Polynomial normal transformation is introduced to handle the correlations between random variables, and percentile matching method is employed to obtain the coefficients of polynomial normal transformation, which can avoid the integral operation. Moreover, the expected value of power flow obtained by the PEM is applied to the presented model to control the line overload risk. Two indexes, namely, population sample mean and mean of population sample standard deviation, are proposed to investigate the effect of correlations on OTS strategies. The proposed model is finally transformed into a mixed-integer second-order cone programming to consider bus voltage and reactive power, and the modified IEEE RTS 24-bus system and IEEE 118 system are presented to test the model.

Data-Driven Risk-Averse Two-Stage Optimal Stochastic Scheduling of Energy and Reserve With Correlated Wind Power

This paper proposes a data-driven optimization method to solve the integrated energy and reserve dispatch problem with variable and correlated renewable energy generation. The proposed method applies the kernel density estimation to establish an ambiguity set of continuous multivariate probability distributions and the optimization model for the integrated dispatch is formulated as a combination of stochastic and robust optimization problems. First, a risk-averse two-stage stochastic optimization model is formulated to hedge the distributional uncertainty. Next, the second-stage worst case expectation is evaluated, using the equivalent model reformulation, as a combination of conditional value-at-risk (CVaR) and the extreme cost in the worst case scenario. The CVaR is calculated using a scenario-based stochastic optimization problem. After describing the wind power correlation in ellipsoidal uncertainty sets, the robust optimization problem for finding the worst case cost is cast into a mixed-integer second-order cone programming problem. Finally, the column-and-constraint generation method is employed to solve the proposed risk-averse two-stage problem. The proposed method is tested on the 6-bus and IEEE 118-bus systems and validated by comparing the results with those of conventional stochastic and robust optimization methods.

Aggregating Correlated Wind Power With Full Surplus Extraction

We study the problem of designing profit-maximizing mechanisms for an aggregator who aggregates wind power from a group of wind power producers (WPPs). The WPPs have more refined forecasts of the wind power generation than the aggregator. Such forecasts are their private information, which also give the reservation utilities of the WPPs. The goal of the aggregator is to elicit the private information truthfully, while paying them as little as possible. Inspired by the fact that those forecasts are typically correlated due to the geographical proximity of the WPPs, we formally define the full correlation condition, which holds ubiquitously in practice. Under that condition, we construct an optimal mechanism which yields the truthful elicitation, while extracting the full surplus (i.e., with minimum payments equal to the reservation utilities) in expectation. Finally, we conduct a case study based on the real-world data, which empirically validates the results.

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 nonlinear 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 hypercube 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.

Comparison of Different Methods in Stochastic Power Flow with Correlated Wind Power Generation

Abstract As increasing penetration of renewable energy, stochastic power flow method becomes an essential tool to analyze the randomness and variation in power system. Conventional methods cannot count in the correlation between input random variables, which will lead to obvious error in most cases. Consequently, it’s necessary to study enhanced methods, and also conduct comparisons among them to provide criteria for method selection. This paper builds up the basic frame of stochastic power flow methods considering correlation and compares them, especially two typical cumulant methods in aspects of accuracy, efficiency and complexity. Useful conclusions are obtained for further study and application.

Generation Adequacy Analysis of Multi-Area Power Systems With a High Share of Wind Power

There is growing concern regarding generation adequacy within the power system industry. The ever-increasing injection of intermittent renewable resources makes it harder than before to estimate the reliability of modern power systems using traditional approaches. This paper develops a framework for estimating the reliability of modern power systems that have considerable levels of wind power generation. Monte Carlo simulation is applied using a very efficient importance sampling technique based on the cross-entropy method as well as the Copula theory. Tailor-made importance sampling functions for conventional generation, load, and wind power generation drastically reduce the number of samples required to estimate reliability parameters of interest. The methodology enables simulation of multi-area power systems with considerable amount of correlated wind power generation in each of the different areas. Simulation results confirm the efficiency as well as the accuracy of the proposed method and show that it is orders of magnitude faster than crude Monte Carlo simulation.

Available transfer capability evaluation in a deregulated electricity market considering correlated wind power

Evaluation of available transfer capability (ATC) is a complicated process involving the determination of the total transfer capability (TTC) and the existing transfer commitments (ETC). Considering the uncertain renewable generation such as wind power will bring more challenge to this process. Previously the uncertainty of wind power is considered either in the ED model or the following TTC calculation, but not included in two process simultaneously. Therefore, the ATC output may not be accurate since the uncertainty impact two problem simultaneously. To consider the uncertainty and correlation of wind power in both ISO's ED and ATC evaluation, this paper proposes a bi-level optimization framework in which the ATC evaluation is formulated as the upper level problem and the ED is the lower level. The bi-level model is first converted to a mathematic program with equilibrium constraints (MPEC) by recasting the lower level problem as its Karush-Kuhn-Tucker (KKT) optimality conditions, and then transformed to a mixed-integer linear programming (MILP) problem which can be solved by existing optimization tools. Case studies on the PJM 5-bus and IEEE 118-bus systems are presented to verify the proposed methodology and the impacts of correlation of wind power on ATC are analysed.

Chance-Constrained Economic Dispatch With Non-Gaussian Correlated Wind Power Uncertainty

Extending traditional deterministic economic dispatch to incorporate significant stochastic wind power is an important but challenging task in today's power system decision making. In this paper, this issue is formulated as a chance-constrained economic dispatch (CCED) problem. Usually, in the presence of non-Gaussian correlated random variables, both the objective function and constraints are difficult to handle. To address this issue, this paper provides a novel method dealing with non-Gaussian random variables. First, the Gaussian mixture model is adopted to represent the joint probability density function of power output for multiple wind farms. Then, analytical formulae are derived that can be used for fast computation of partial derivatives of the objective function and transformation of chance constraints into linear ones. Thereafter, the CCED can be solved as a deterministic linear convex optimization with a global optimal solution. The effectiveness and efficiency of the proposed methodology are validated via a case study with a modified IEEE 39-bus system.