1 Abstract-- 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. Index Terms--ARIMA processes, Markov processes, stochastic processes, time series, wind power generation. I. INTRODUCTION HE high integration of wind power into electrical systems calls for new methods and simulation tools that can assist electric utilities in analyzing the impact of stochastic wind power generation on power system operation and planning [1]. Such analyses usually require a probabilistic approach, which commonly relies on sequential Monte Carlo simulations [2]. The sequential Monte Carlo simulations consider both the probability distribution and chronological characteristics of wind power generation, load profiles, and transition states of all the system components [2]. Furthermore, the sequential Monte Carlo simulations usually require a large number of simulation runs to obtain statistically reliable results, for instance to capture rare events such as extreme wind situations. Thus, stochastic wind power models that are able to capture both the probability distribution and temporal correlation of the wind power generation are needed. As depicted in Fig. 1, existing approaches for the stochastic modeling of the wind power generation fall into two categories: the wind speed approach [3]-[8] and the wind This work was supported by the Danish Agency for Science Technology and Innovation, under the project of 2104-05-0043. P. Chen, B. Bak-Jensen and Z. Chen are all with the Department of Energy Technology, Pontoppidanstraede 101, Aalborg University, Aalborg, 9220 Denmark (e-mail: pch@iet.aau.dk, zch@iet.aau.dk, bbj@iet.aau.dk). T. Pedersen is with the Department of Electronic Systems, Section Navigation and Communications, Aalborg University, Fredrik Bajers Vej 7, Aalborg, 9220 Denmark (e-mail: troels@es.aau.dk). power approach [9]. Both approaches are based on wind speed measurements. The former approach requires a wind speed model. The available wind speed models include the autoregressive moving average (ARMA) model [3], [4], the discrete Markov model [5]-[7], and the wavelet-based model [8]. In contrast, the latter approach requires a wind power model. The available wind power model in [9] uses a transition matrix based discrete Markov model. The two approaches can be applied to planning of future wind farms in the power system. However, both approaches entail wind speed measurements and an accurate wind farm model, which is usually unavailable. The accurate wind farm model is not needed in the case where wind power measurements are available. In fact, electric utilities measure and record wind power flowing into their networks. Thus, they have direct access to these wind power data. In this case, as shown in Fig. 1, wind power measurements can be directly used to build a wind power model, which may be used for system planning involving already operating wind farms. In addition, the need for wind speed measurements is alleviated. Proposed approach Wind speed approach Ref. [3]-[8] Wind power approach Ref. [9] Fig. 1. Alternative approaches for modeling wind power time series. In the case that only wind speed measurements are available, either approaches may be applied. One disadvantage of the wind power approach is that wind power generation has both lower and upper limits and does not follow a standard probability distribution. These make it more challenging to apply standard statistical models. On the other hand, one drawback of the wind speed approach is that an error, e.g. of 3%, in wind speed modeling may cause an error of around 9% in wind power. This is because wind power varies with cube of wind speed when the speed is between cut in and rated value. In brief, the challenges of building the stochastic wind power model are that the wind power generation is a ARIMA-Based Time Series Model of Stochastic Wind Power Generation Peiyuan Chen, Student Member, IEEE, Troels Pedersen, Student Member, IEEE, Birgitte Bak-Jensen, Member, IEEE, Zhe Chen, Senior Member, IEEE T