Stochastic Wind Power Generation Research Articles

CAVOA: A chaotic optimization algorithm for optimal power flow with facts devices and stochastic wind power generation

AbstractThe study proposes a modified version of African Vultures Optimization Algorithm (AVOA) to address the optimal power flow (OPF) issue. The developed optimizer is called Chaotic AVOA (CAVOA). Prior to applying CAVOA to the problem at hand, its accuracy is evaluated using 23 benchmark functions. The production powers of WTs that are interrupted are predicted using Weibull probability density functions (PDFs). Two additional costs, namely penalty cost and reserve cost, are incorporated into the goal function of the OPF. The simulation results of CAVOA are compared with those of the original AVOA to solve the OPF. The proposed OPF technique and its solution methodology are verified on the IEEE 30‐bus test system, taking into account the flexible alternating current transmission systems (FACTS) devices, which have several benefits such as reducing active power transmission loss, regulating power flow, and improving voltage stability/profile. The research's simulation results demonstrate that CAVOA is more effective in identifying the OPF's optimal solution by reducing the overall power cost and power losses. The results indicate that the CAVOA algorithm outperforms AVOA as a metaheuristic optimization algorithm due to its superior capability in addressing challenging OPF problems with a minimal convergence rate. For example, when comparing the two algorithms, CAVOA achieved a significant improvement. It successfully reduced the cost function by approximately 0.023% in Case I and 0.035% in Case II, while also decreasing power loss by 2.57% in Case II and 0.57% in Case I. Additionally, CAVOA exhibited a remarkable reduction of 5.36% in voltage deviation compared to AVOA in Case I. Furthermore, in Case III, CAVOA demonstrated a decrease of 0.64% in gross cost when compared to AVOA.

Stochastic Wind Power Generation Planning in Liberalised Electricity Markets within a Heterogeneous Landscape

Spatially separated locations may differ greatly with respect to their electricity demand, available space, and local weather conditions. Thus, the regions that are best suited to operating wind turbines are often not those where electricity is demanded the most. Optimally, renewable generation facilities are constructed where the maximum generation can be expected. With transmission lines limited in capacity though, it might be economically rational to install renewable power sources in geographically less favourable locations. In this paper, a stochastic bilevel optimisation is developed as a mixed-integer linear programme to find the socially optimal investment decisions for generation expansion in a multi-node system with transmission constraints under an emissions reduction policy. The geographic heterogeneity is captured by using differently skewed distributions as a basis for scenario generation for wind speeds as well as different opportunities to install generation facilities at each node. The results reinforce that binding transmission constraints can greatly decrease total economic and emissions efficiency, implying additional incentives to enhance transmission capacity between the optimal supplier locations and large demand centres.

Assessment of the wind power generation uncertainty on the steady-state operation of electric power systems

Nowadays, the large-scale integration of wind energy conversion systems in transmission networks is one of the most effective and practical options for generating electricity from renewable sources. However, the increase in wind energy penetration causes the operation of electrical power systems to become more dependent and vulnerable to variations in wind speed. Within this context, it is necessary to perform probabilistic power flow (PPF) studies to maintain system integrity in the face of stochastic wind power generation. This paper describes and implements a power flow method that considers the uncertainties that arise from wind generation behavior. This PPF approach, based on a point estimation technique, is validated against thousands of Monte Carlo simulations.

Nash equilibria in electricity pool markets with large-scale wind power integration

This work investigates the interaction between power producers with conventional and wind generation portfolios participating in a network-constrained pool-based market. A stochastic bi-level problem is introduced to model the strategic behavior of each single producer. The upper-level problem maximizes the producers’ expected profits and the lower-level problem optimizes the jointly cleared energy and balancing market under economic dispatch. Market participants’ offers are modeled using linear stepwise curves, and the stochastic wind power generation is realized through a set of plausible wind scenarios. The bi-level problem is recast into a single-level mathematical problem with equilibrium constraints with primal-dual formulation using the Karush-Kuhn-Tacker first order optimality conditions and the strong duality theorem. The joint solution of all strategic producers’ problems constitutes an equilibrium problem with equilibrium constraints. The latter is reduced into an equivalent mixed integer linear program by using disjunctive constraints. Different objective functions are applied to the final program to define the range of market equilibria, and a single-iterate diagonalization process is used to justify those equilibria that are meaningful. The model addresses several cases considering different types of market competition, transmission line congestions, and different levels of wind power penetration and volatility.

SLIME MOULD ALGORITHM FOR PRACTICAL OPTIMAL POWER FLOW SOLUTIONS INCORPORATING STOCHASTIC WIND POWER AND STATIC VAR COMPENSATOR DEVICE

Purpose. This paper proposes the application procedure of a new metaheuristic technique in a practical electrical power system to solve optimal power flow problems, this technique namely the slime mould algorithm (SMA) which is inspired by the swarming behavior and morphology of slime mould in nature. This study aims to test and verify the effectiveness of the proposed algorithm to get good solutions for optimal power flow problems by incorporating stochastic wind power generation and static VAR compensators devices. In this context, different cases are considered in order to minimize the total generation cost, reduction of active power losses as well as improving voltage profile. Methodology. The objective function of our problem is considered to be the minimum the total costs of conventional power generation and stochastic wind power generation with satisfying the power system constraints. The stochastic wind power function considers the penalty cost due to the underestimation and the reserve cost due to the overestimation of available wind power. In this work, the function of Weibull probability density is used to model and characterize the distributions of wind speed. Practical value. The proposed algorithm was examined on the IEEE-30 bus system and a large Algerian electrical test system with 114 buses. In the cases with the objective is to minimize the conventional power generation, the achieved results in both of the testing power systems showed that the slime mould algorithm performs better than other existing optimization techniques. Additionally, the achieved results with incorporating the wind power and static VAR compensator devices illustrate the effectiveness and performances of the proposed algorithm compared to the ant lion optimizer algorithm in terms of convergence to the global optimal solution.

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.

Optimal Power Flow Incorporating FACTS Devices and Stochastic Wind Power Generation Using Krill Herd Algorithm

This paper deals with investigating the Optimal Power Flow (OPF) solution of power systems considering Flexible AC Transmission Systems (FACTS) devices and wind power generation under uncertainty. The Krill Herd Algorithm (KHA), as a new meta-heuristic approach, is employed to cope with the OPF problem of power systems, incorporating FACTS devices and stochastic wind power generation. The wind power uncertainty is included in the optimization problem using Weibull probability density function modeling to determine the optimal values of decision variables. Various objective functions, including minimization of fuel cost, active power losses across transmission lines, emission, and Combined Economic and Environmental Costs (CEEC), are separately formulated to solve the OPF considering FACTS devices and stochastic wind power generation. The effectiveness of the KHA approach is investigated on modified IEEE-30 bus and IEEE-57 bus test systems and compared with other conventional methods available in the literature.

Robust Dispatch of High Wind Power-Penetrated Power Systems Against Transient Instability

High-level wind power integration can dramatically affect a power system's dynamic performance and introduce significant uncertainties to system's operation. This paper proposes a robust dispatch method to optimize the power system's operation state while sustaining its transient stability with highly variable and stochastic wind power generation. The problem is first modeled as an augmented optimal power flow model with uncertain variables and differential-algebraic equations. Then, the stability constraints are converted to approximately-equivalent algebraic equations based on one-machine-infinite-bus equivalence technique and trajectory sensitivity analysis. Next, the uncertain wind power generation is represented by a small number of strategically selected testing scenarios. Finally, a decomposition-based computation strategy is developed to divide the original model into a master problem and a series of slave problems which are solved iteratively. Using industry-grade system dynamic models and simulation software, the proposed method is tested on the New England 39-bus system and Nordic32 system, showing high performance on economic optimality, stability robustness, and computational efficiency.

Reactive Power Reserve Assessment Scheme Considering Stochastic Wind Power Generation

Abstract This paper presents a reactive power “VAR” reserve assessment tool considering the extended capability curve of the doubly fed induction generator (DFIG) based wind farm. The problem is formulated such that the VAR reserve amount is determined taking into account the wind power forecast errors by addressing their possible scenarios for both the base case and a presumed severe disturbance. The model is stated as an optimization problem, aiming to optimize simultaneously three objective functions representing the expected values of the energy cost corresponding to the base case, corrective control cost under the most severe contingency, and the VAR reserve from the committed conventional synchronous generators. The total objective function is achieved while satisfying, for each addressed scenario, a set of operating constraints including explicitly the probable active power output of DFIG wind turbine and its relevant VAR capability limits as well as voltage stability margin.

Vector ordinal optimization theory based large‐scale multi‐objective unit commitment considering stochastic wind power

The unit commitment problem of a large power system with the popularity of large‐scale wind power is complex and difficult to solve. Vector ordinal optimization (VOO) is a new method to solve multi‐objective optimization problems with complex calculation burdens which can obtain a satisfactory solution at a high enough probability. Our objective is to develop a new technique for optimal design with stochastic wind power. In this paper, we select coal consumption, power purchase costs and SO2 emissions as the objective functions. Based on the scenario method, the stochastic wind power generation is taken into account. A real provincial power system with a large‐scale wind farm is taken as a numerical example, in which hydropower, nuclear power, biomass energy, gas turbines, thermal power and other complex power structures are considered. The results show that the VOO based method proposed in this paper is effective in solving large‐scale multi‐objective unit commitment problems considering stochastic wind power. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Dynamic stochastic optimal power flow of wind power and the electric vehicle integrated power system considering temporal-spatial characteristics

The intermittent volatility of wind power integrated into the grid poses a great threat to the stable operation of power systems on the supply side. Conversely, large-scale charging of electric vehicles (EVs) also brings new challenges to dispatch on the demand side. In response, the randomness and temporal-spatial correlations of stochastic wind power generation are considered in this paper. Additionally, the EV charging infrastructure is studied. A dynamic stochastic optimal power flow (DSOPF) for wind farms and EVs integrated power system based on the chance-constrained programming model is proposed. An optimal dispatch scheme is obtained by solving the dynamic optimal power flow. After that, dynamic probabilistic power flow based on cumulants is performed under the scheme to obtain the probability distribution of state variables. The upper and lower bounds of chance constraints are adjusted according to the probability distribution function until they are all satisfied. Illustrative examples demonstrate the effectiveness of DSOPF for firming the variable wind energy, and EV charging is performed on the Institute of Electrical and Electronics Engineers systems. On this basis, different EV charging modes and the temporal-spatial correlations are specifically discussed.

Thermal behavior of power cables in offshore wind sites considering wind speed uncertainty

A novel method for sizing power cables that connect offshore wind parks to the grid is presented. The followed methodology consists of two different and independent tasks: The stochastic wind power generation of the wind park is estimated based on historical data and, then, the cooling effect of high wind speeds on the temperature of the cable's aerial part is evaluated. In contrast to the IEC60287 standard, the effect of the variable heat transfer coefficient (h) caused by the variable wind speeds, is taken into account following a Finite Element Method approach which leads to a different thermal behavior than the expected one. Higher h values are caused by high wind speeds increasing, therefore, the current carrying capacity of the cable. The results of this study lead to a more efficient way of sizing power cables, avoiding power curtailment in periods with particularly high wind speeds, leading to a more cost efficient cable design.

Operating reserve policies with high wind power penetration

The rapid increase in installed wind generation capacity in the United States has raised concerns about electricity system reliability because of the intermittent and variable nature of the wind power. To help manage the wind power variability new ways of determining the amount of operating reserve capacity that must be kept available are necessary. A two-stage stochastic programming approach for the unit commitment problem had been introduced to mimic the short-term power operation decision process, i.e., day-ahead unit commitment and hour-ahead economic dispatch. Within this framework, a new formulation is proposed to determine the spinning and non-spinning reserve levels for large-scale systems over a 24-h optimization horizon with economic considerations. The proposed model is then applied to a large-scaled California test system. Simulation results illustrate the impact of stochastic wind power generation behavior and increased installed wind capacity on operating reserve requirements and the system cost as a whole.

Robust <i>H</i><sub>∞</sub> Control for Stochastic Wind Power Generation Systems

This paper studies the design of robust H∞ controller for stochastic wind power generation systems. Assuming the system is convex uncertain，this article presents the H∞ performance criterion for uncertain stochastic system , deduces sufficiency conditions of the existence of H∞ controller with state feedback, and expresses them into a form of the linear matrix inequality (LMI), then utilizes schur complement lemma to transform them into LMIs which can be solved. At last we utilize standard digital software to get the disturbance attenuation level and the state feedback matrix.

ARIMA-Based Time Series Model of Stochastic Wind Power Generation

This paper proposes a stochastic wind power model based on an autoregressive integrated moving average (ARIMA) process. The model takes into account the nonstationarity and physical limits of stochastic wind power generation. The model is constructed based on wind power measurement of one year from the Nysted offshore wind farm in Denmark. The proposed limited-ARIMA (LARIMA) model introduces a limiter and characterizes the stochastic wind power generation by mean level, temporal correlation and driving noise. The model is validated against the measurement in terms of temporal correlation and probability distribution. The LARIMA model outperforms a first-order transition matrix based discrete Markov model in terms of temporal correlation, probability distribution and model parameter number. The proposed LARIMA model is further extended to include the monthly variation of the stochastic wind power generation.

퐁력전원이 피크타임과 발전설비구성에 미치는 영향분석: 제3차 신재생에너지 기술개발 및 이용.보급 기본계획 기준

Although renewable power is regarded a way to active response to climate change, the stability of whole power system could be a serious problem in the future due to its uncertainties such as indispatchableness and intermittency. From this perspective, the peak time impact of stochastic wind power generation is estimated using simulation method up to year 2030 based on the 3rd master plan for the promotion of new and renewable energy on peak time. Result shows that the highest probability of wind power impact on peak time power supply could be up to 4.41% in 2030. The impact of wind power generation on overall power mix is also analyzed up to 2030 using SCM model. The impact seems smaller than expectation, however, the estimated investment cost to make up such lack of power generation in terms of LNG power generation facilities is shown to be a significant burden to existing power companies.