Uncertain Wind Power Research Articles

Deep neural network accelerated-group African vulture optimization algorithm for unit commitment considering uncertain wind power

The unit commitment (UC) of power systems serves to plan out the starting and shutdown of units and the power generation of units for a future period of time. However, the UC problem for large-scale systems faces the problems of long solution time and insufficiently accurate solution. Uncertainty in wind power generation poses a great challenge in solving the unit combination problem. This work proposes a deep neural network accelerated-double layer optimization method (DNNA-DOM) to improve the solution efficiency, accuracy, and economy of UC. The outer layer of DNNA-DOM utilizes the proposed deep neural network accelerated-group African vulture optimization algorithm (DNNA-GAVOA) to optimize the on-off condition of conventional coal-fired power units. The inner layer of DNNA-DOM adopts quadratic programming to optimize the solution of the economic dispatch problem of load distribution. The GAVOA optimizes the simulated African vultures in four groups to obtain the optimal solution after diverse exploration, exploitation, and exploitation activities, with low complexity and high accuracy. This work first evaluates the performance of GAVOA by solving seven unimodal functions. Furthermore, the 10-unit simulation by incorporating wind power curves and related constraints is optimized through the DNNA-DOM. The results show that GAVOA outperforms the African vulture optimization algorithm (AVOA) and traditional metaheuristics like the particle swarm algorithm and gray wolf algorithm in terms of lower operating cost and optimization stability. The DNNA-DOM combined with DNNA-GAVOA in the outer layer results in an average daily cost reduction of $36.30 and a 45.1997 % speed increase compared to AVOA in the outer layer.

Probabilistic Small Signal Stability Analysis with Wind Power Based on Maximum Entropy Theory

The probability parameters for the small signal stability in a system are studied to quantify the impact of uncertain wind power on system stability. With the increase in the scale of wind power access systems, how to more efficiently and accurately obtain the probability of small signal stability is worthy of further investigation. Therefore, this work proposes an analysis method of probabilistic small signal stability (PSSS) based on maximum entropy (ME) theory for studying power systems with uncertain wind power from doubly fed induction generators (DFIGs). Firstly, the sensitivity of the eigenvalues to the variable power is obtained by linearization. Then, when the probability characteristic for wind is known, the probability characteristic for the system critical eigenvalues is approximated using the ME method and the derived sensitivity. The proposed ME method is used in the analysis of the PSSS for power systems with different wind power penetration scales in case studies. Compared to the probability function for the eigenvalue obtained by the conventional series expansion method, the proposed method has excellent accuracy and sufficient efficiency in analysing the PSSS for a system with uncertain wind power.

Analysis of power dispatching decisions with energy storage systems using the optimal probability distribution model of renewable energy

Effectively managing the inherent unpredictability and fluctuation attributes of renewable energy sources within scheduling systems has emerged as a critical matter demanding immediate attention. The incorporation of energy storage technology offers notable advantages by mitigating fluctuations in wind power generation and curtailing peak shaving costs in scheduling systems through economical utilization of energy storage. This study employs the adjustment of energy storage’s reserve capacity function to modify the economic gains and losses arising from fixed spinning reserve. This approach tailors the reserve capacity function by formulating the uncertainty inherent in wind power generation. The paper presents an enhanced selection method for calculating optimal bandwidth within the framework of least squares approximation probability density function scenarios. The fusion of least squares approximation and optimal bandwidth computation permits precise refinement of bandwidth in non-parametric kernel density estimation approaches. Consequently, the study puts forth a comprehensive model for coordinated scheduling and regulation of a multi-scale energy storage power system. Finally, the stability and economy of the proposed method in the scheduling operation process were verified through simulation, and the research results can provide a theoretical basis for future uncertain wind power scheduling.

Fuzzy semi-entropy based downside risk to low-carbon oriented multi-energy dispatch considering multiple dependent uncertainties

Increasing deployment of wind power into integrated energy system becomes a critical pathway for deep decarbonizing the power sector. It is imperative to investigate the impacts of uncertain wind power on integrated power system as the result of the heavy interdependencies among different types of energy in supplying the requirements of economy, low carbon and risk aversion. Here, the concept of fuzzy semi-entropy is presented to quantify the downside risk of uncertain wind power. After that, a mean-semi-entropy model for low-carbon oriented electrical-gas-heat energy system including carbon emission, carbon capture and carbon trading is proposed. In particular, the dependence of wind power outputs from different wind turbines is investigated by the multivariate Gaussian Copula. Results obtained from case studies demonstrate the feasibility of the proposed model in achieving a balanced trade-off among system economy, low carbon emission and operation risk properly. The proposed model enables the reduction in total cost and carbon emission by 2.29% and 5.18% in comparison to these of traditional cost minimization model. In addition, the accommodation level of wind power with multivariate Gaussian Copula improves by 2.17% compared to that without considering coupling.

Hybrid Reinforcement Learning for Power Transmission Network Self-Healing Considering Wind Power.

Transmission network self-healing considering uncertain wind power becomes crucial with increasing penetration of wind power. A hybrid reinforcement learning (HRL) method combining offline self-learning with online Monte Carlo tree search (MCTS) is designed to deal with the strong uncertainty induced by wind power restoration. The HRL method trains a policy network with offline self-learning based on historical wind and transmission system data. It then applies the policy network to guide MCTS to realize step-by-step transmission network self-healing based on real-time and forecast data in different wind power scenarios. Besides, a model predictive control method for active power dispatch is proposed to improve wind power generation credibility during self-healing. Simulation results of both test and real-life power systems demonstrate that the proposed method can realize online transmission system self-healing reliably. Comparisons among different reinforcement learning methods indicate that the number of scenarios dominated by HRL is more than twice that dominated by MCTS and a dozen times that dominated by deep Q-network. Meanwhile, the online method is more flexible in uncertain wind power scenarios than optimization methods.

Security-constrained Transmission Expansion Planning with N-k Security Criterion and Transient Stability

The integration of large-scale wind power into the power system is a global trend in response to climate change, however, the intermittent nature of wind power presents new challenges for planners. Conventional transmission expansion planning (TEP) methods, which only consider N-1 static security, may not ensure the security of multiple contingencies and transient stability in a large-scale wind power integration scenario. Incorporating N-k-based static constraints and dynamic constraints, such as differential-algebraic-equations-(DAEs)-based transient stability constraints, into TEP can result in a heavy computational burden and render the TEP model intractable. This paper proposes a tractable mathematical model (S&DSTEP) for joint consideration of static and dynamic security in TEP with wind power. The uncertain wind power generation is captured through selected scenarios and the model is divided into a TEP master problem and multiple sub-problems for evaluating static security and transient stability. Static security is determined by the use of fault chain theory (FCT), avoiding the need for enumerating all N-k contingencies, thus reducing the computational burden. Transient stability is analyzed through the use of stabilizing cuts generated from the extended equal-area criteria (EEAC) rather than dynamic constraints expressed as DAEs. The proposed model is verified on the modified New England 39-bus system and IEEE 118-bus system, demonstrating its ability to consider transient stability while being more computationally efficient compared to the robust method that directly incorporates all contingency scenarios.

A two‐stage adaptive‐robust optimization model for active distribution network with high penetration wind power generation

AbstractHigh penetration of uncertain wind power generation brings challenges to power system operational security and economy. Here, an adjustable box uncertainty set is first presented to characterize the spatiotemporal correlation of multiple wind power generations. Afterward, a two‐stage risk‐adjusted robust energy dispatching model is established as a min‐max‐min optimization problem for active distribution networks operating with high penetration wind power generation. Then a three‐layer Nest Column and Constraint Generation (NCCG) decomposition approach is designed to efficiently solve the proposed model. Finally, the proposed two‐stage adaptive robust optimization model and NCCG approach are validated by a distribution network with uncertain wind power generations, and the simulation results indicate the distribution network operation economy could be compromised with robustness by adjusting the conservative regulation parameter.

Robust stochastic low-carbon optimal dispatch of park-integrated energy system with multiple uncertainties from source and load

To realize the cascaded utilization of energy, improve the effective utilization of energy, and further reduce the carbon emissions of integrated energy systems a robust stochastic low-carbon optimal dispatch model with economy, environmental protection and reliability is developed for a park-integrated energy system wherein the multiple uncertainties brought by source and load are fully considered. First, a two-stage robust optimization algorithm is employed to handle uncertain wind power generation. A multi-case analysis method for the uncertainties of photovoltaics and load is proposed based on an improved centralized reduction algorithm. Then, considering the depreciation of the weighted average of the comprehensive operation cost, carbon emissions, and energy undersupply rate, a robust stochastic optimal dispatch model can be derived and efficiently solved by using a multi-objective fuzzy optimization algorithm with an improved membership function. Finally, by comparing the four cases, the simulation results show that the computational complexity and calculation time of the system can be reduced, the trimming result errors can be decreased, and a balance between economy, environmental protection, reliability, and robustness can be achieved.

Two-Layer Robust Distributed Predictive Control for Load Frequency Control of a Power System under Wind Power Fluctuation

The frequency stability of interconnected power systems becomes quite challenging when incorporating renewable energy sources (mostly wind power). Distributed model predictive control (DMPC) is an effective method to maintain stable grid frequency and realize power system load frequency control (LFC). This paper proposes a two-layer robust DMPC for the LFC of an interconnected power system. In the scheme, the wind power penetrating the power grid is largely affected by the environment condition, and it is taken as an uncertain disturbance to the power system. The two-layer robust DMPC consists of a nominal DMPC controller and an ancillary DMPC controller. The nominal DMPCs coordinate with each other in achieving the systemwide LFC objective, where the systemwide objective is a strict convex combination of the local LFC objectives. The nominal optimization problems are solved supposing the wind power fluctuation is zero. The ancillary DMPC generates the actual control signal for each generation unit based on signals which are transmitted from the nominal DMPC controller. The simulation on a four-area interconnected power system demonstrates the effectiveness of the proposed algorithm in alleviating the frequency deviation caused by varying the load and uncertain wind power fluctuation.

Peak shaving and short-term economic operation of hydro-wind-PV hybrid system considering the uncertainty of wind and PV power

With uncertain wind and PV power integrated into the grid, the difficulty of peak shaving is exacerbated. Therefore, the peak shaving operation of hydropower has become one of the most important problems in power system. In this paper, an optimal operation strategy of hydro-unit level coordinated peak shaving and economic operation in hydro-wind-PV hybrid system under uncertain conditions of wind and PV power is proposed. Firstly, the uncertainty of wind and PV power is described based on Latin hypercube sampling and scenario reduction methods. Secondly, a two-layer optimization model considering wind and PV uncertainty is established. And then, the synchronous peak shaving strategy and the improved lambda flow iteration strategy are proposed to solve the model. A case study is performed with the HWPHS in the Yarlung Zangbo River basin of China. The results show that (1) The residual load of power system fluctuates steadily under the condition of wind and PV uncertainty, and the peak shaving rate is 95.53%. (2) Compared with the DP algorithm, the proposed algorithm can increase the economic efficiency by 0.89% when solving the lower-layer model. (3) The V3 shaped mapping function proved to be superior to other functions.

Rolling dispatch framework of integrated electricity-gas system considering power-to-gas facilities and natural gas network dynamics: Modelling and case studies

Rolling dispatch strategy is widely used in power systems to handle the uncertainty and volatility of renewable energy. Meanwhile, flexible gas-fired units and emerging power-to-gas (P2G) facilities integrate the power system and natural gas system as an integrated electricity-gas system (IEGS). Hence, rolling dispatch should be applied to the whole IEGS. This paper designs the rolling dispatch framework in the IEGS and proposes the partial-differential-equations-involved (PDEs) mathematical models that accurately formulate the natural gas network dynamics and the operation properties of P2G facilities to retain the facticity of the IEGS in the rolling dispatch process (e.g., the linepack characteristics of natural gas networks and the physical limits of the P2G facilities). The impact of uncertain wind power on the IEGS operation is also considered. In order to reduce the computational burdens, this paper employs a combination of implicit difference method and the technique of linearization to transform the original rolling dispatch model with PDEs and chance constraints into mixed-integer linear programming which is solvable by off-the-shelf solvers. The results of the case studies demonstrate that the proposed rolling dispatch strategy promotes renewable energy accommodation, enhances the flexibility, security, and efficiency of the IEGS, and mitigates the impact of renewable energy's uncertainty and volatility on the IEGS.

Data-driven nested robust optimization for generation maintenance scheduling considering temporal correlation

Traditional power grids are gradually transitioning to smart grids with high penetration of renewable energy, which can realize the efficient utilization of power resources and low carbon emissions. However, the uncertainties of renewable energy (e.g., wind power) and load demand pose considerable challenges to secure operation and cost-effective planning in smart grids, such as generation maintenance scheduling (GMS). In this context, conventional methods including stochastic optimization and robust optimization are adopted to cope with the uncertainties and formulate the GMS plan. Unfortunately, these methods fail to consider the temporal information in uncertain variables, which can introduce extra operational costs brought by the uncertainties. To address this issue, we consider the temporal correlation of the uncertain wind power and load demand, and develop a data-driven two-stage nested robust optimization (NRO) approach for GMS to minimize the total costs of power system operation under uncertain scenarios. In our proposed approach, a temporal correlation Dirichlet process mixture model (TCDPMM) is developed to investigate the temporal information in the wind power and load demand datasets. Then, variational Bayesian inference (VBI) is employed to construct the data-driven uncertainty set, in which the temporal information for the uncertain variables and the correlations between the uncertain variables are considered. Subsequently, combined with this uncertainty set, a two-stage GMS problem is converted to a “min–max-max–min” optimization problem which is solved by the parallel Benders’ decomposition algorithm. The effectiveness and superiority of the proposed approach are demonstrated with a six-bus power system and a practical power system in China.

Distributionally robust optimal dispatching method of integrated electricity and heating system based on improved Wasserstein metric

This paper proposed a distributionally robust optimal dispatching (DROD) method of integrated electricity and heating system based on an improved Wasserstein metric, for dispatching problems to manage the risk from uncertain wind power forecasted errors and operating characteristics of electric vehicles (EVs). The ambiguity set employed in the distributionally robust formulation for wind power forecasted error is the Wasserstein ball centered at the empirical distribution and an adjustable uncertainty set of EV operating characteristics is proposed in this model to quantify the uncertainty of EVs more flexibly and intuitively. The proposed framework minimizes the generating cost, EV operating cost, and the expected generation units adjustable cost under the worst-case distribution in the uncertainty set. To improve the computational efficiency of the proposed DROD model, an improved Wasserstein metric based on extreme scenarios DROD (WMES-DROD) model is proposed to construct the ambiguity set of wind power forecasted error. The comparison between the Wasserstein metric-based DROD and WMES-DROD indicates that the proposed WMES-DROD model can obtain optimal results with less time. The out-of-sample analysis with the IEEE 118-bus test system confirms the excellent robustness and computational superiority of the proposed model.

Reliability-based Multi-objective Optimization with Uncertain Wind Power

The unpredictability for wind power interprets the critical factor limiting its large-scale penetration in microgrids. Gaussian and Cauchy distributions describe both the arbitrary and vague characteristics of wind power to evaluate wind power unpredictability. Afterward, the wind power is presumed an undefined arbitrary variable, and a multi-objective optimization model concerning the credibility density function is developed to balance the economics and the reliability of microgrids. For the solution of the model, the NSGA-II algorithm is applied to seize the Pareto front. By fully deliberating the cognitive uncertainty of the dispatchers, the evidence-theory-based decision-making is employed to drive the eventual scheduling from the Pareto set. The emulation performances substantiate the appropriateness and efficacy of the proffered model with unpredictable wind power by providing a compromise scheme between economics and reliability.

A New Technique for Investigating Wind Power Prediction Error in the Multi-Objective Environmental Economics Problem

This paper develops a novel multi-objective evolutionary algorithm (MOEA), namely an enhanced multi-objective exchange market algorithm (EMEMA), to solve the multi-objective problems in the presence of uncertainty. In this paper, Quasi-Monte Carlo (QMC) simulation is implemented for the first time to address the overestimation and underestimation caused by the uncertain wind power generation. In QMC, instead of pseudorandom numbers, some samples are generated to reduce the computational burden using the Sobol sequences. In addition, a new procedure is introduced to increase the spread and maintain the diversity of solutions. The effectiveness of the EMEMA is tested on two well-known benchmark functions and Taiwan's well-known 40-unit test system in two different scenarios, with and without considering the uncertainty. Also, four different measurements are employed to scrutinize the algorithm performance. The results prove the superiority of the proposed method compared to the state-of-art algorithms. Finally, the robustness of the EMEMA is studied using parametric and non-parametric statistical tests. The statistical analysis corroborates the robustness of the proposed method.

Research on Highway Self-Consistent Energy System Planning with Uncertain Wind and Photovoltaic Power Output

Highways are a critical consumer of energy. The integration of the highway and the energy system (ES) is a proven method towards carbon neutrality. The increasing energy demands of highway transportation infrastructure and the development of distributed energy and energy storage technologies drive the coupling between the highway system (HS) and the energy supply network, which is becoming tighter than ever before. Many scholars have explored the mode and path of integrated transportation and energy development. However, the energy and transportation systems’ coupling relationship and the collaborative planning scheme have not been thoroughly studied. Facing the increasing interconnection between transportation and energy networks, as well as addressing the demand for clean energy in highway transportation effectively, this paper proposes a highway self-consistent energy system (HSCES) planning model integrating uncertain wind and photovoltaic (PV) power output, so as to analyze the energy supply mode of the HS and determine the multi-energy capacity configuration of the self-consistent energy system (SCES). Firstly, the mathematical model related to each micro-generator of the SCES and the load aggregation scenario of the HS is established. Secondly, considering the uncertainty of renewable energy, this paper focuses on wind and PV power generation, and abatement technology, under uncertain conditions to ensure the best solution for reliability. Thirdly, taking the economy, reliability and the renewable energy utilization rate of the system into account, the system planning model is established under the condition of ensuring the system correlation constraints. Finally, the proposed method is validated using a section of the highway transportation system in western China. The results show that the hybrid energy storage planning scheme can cause the system’s renewable energy utilization rate to reach 99.61%, and the system’s power supply reliability to reach 99.74%. Therefore, it is necessary to carry out coordinated planning while considering the characteristics of the HS and the ES, which can minimize the planning cost of a HSCES, reduce the waste of wind and solar energy, and ensure the reliability of the power supply for the HS.

Optimal allocation of phase shifting transformer with uncertain wind power based on dynamic programming

Phase Shifting Transformer (PST) can help improve the power flow distribution of the transmission section, which can increase the wind power consumption of the grid. In order to adapt the PST allocation to the grid evolution, this paper presents a dynamic programming method to allocate PST in each planning stage of the grid optimally. The optimal allocation model of PST under a single grid seeks to maximize the wind power consumption and the Total Transfer Capacity (TTC) between areas. A calculation method for TTC of grids containing PST and wind power is proposed. The Non-Dominated Sorting Genetic Algorithm II (NSGA2) is used to solve the Pareto sets under each planning stage of the grid. Then, the optimal planning path of PST is derived based on dynamic programming. The superiority of the proposed method is demonstrated by comparing the IEEE-118 system results of dynamic and static programming.

Flexibility Exploitation With Nonlinear Integrated Demand Response for Multi-Energy System Against Load Estimation Mistake

Integrated demand response contributes to flexibility improvement in multi-energy system. Yet, the challenge posed by the load estimation mistake needs to be addressed to explore the available flexibility. In this paper, we present a price-based nonlinear integrated demand response for multi-energy microgrid against estimation mistakes of both electricity and gas loads. Among them, we develop a period partition method to describe load characteristics and reach a reasonable time-of-use pricing. Besides, a credibility theory-based risk measurement is presented to evaluate the uncertain wind power. Finally, case studies demonstrate the feasibility and effectiveness of the proposed method in flattening load curve, reducing operation cost and promoting the accommodation of wind power.

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.

Optimal scheduling of a wind energy dominated distribution network via a deep reinforcement learning approach

With the development of clean energy systems, large-scale renewable energy is being connected to the traditional distribution network, which also brings new challenges to the reliable and economic scheduling of the power grid. To address these challenges, this paper proposes an intelligent scheduling strategy for a wind energy dominated distribution network, which aims to reduce the fluctuation caused by the wind energy. First, the energy scheduling model and objective function of the distribution network system are established and the constraints of various types of components are considered. Then, deep reinforcement learning is introduced to realize real-time decision in distribution network to solve the problem of fluctuation caused by the uncertain wind power output. The energy scheduling method is developed into a Markov decision process based on deep deterministic policy gradient (DDPG) algorithm. Finally, the simulation is verified on the IEEE14 node system. The results verify that the proposed approach can effectively reduce power fluctuations in the distribution network. The superiority of the adopted DDPG algorithm is demonstrated by comparing with the deep Q network algorithm.