Hidden Markov Models for Wind Farm Power Output

Abstract

The reliability of the transmission grid is challenged by the integration of intermittent renewable energy sources into the grid. For model-based reliability studies, it is important to have suitable models available of renewable energy sources like wind and solar power. In this study, we investigate to what extent the power output of wind farms can be modeled with discrete Hidden Markov Models (HMMs). The parameters of the HMMs are inferred from measurement data from multiple turbines in a wind farm. We use these models both for individual turbine output and for total aggregated power output of multiple turbines. When modeling individual turbine output, the hidden process in the HMM is instrumental in capturing the dependencies between the output of the different turbines. It is important to account for these dependencies in order to correctly capture the upper quantiles (90%, 95%, 99%) of the distribution of the wind farm aggregated power output. We show that despite their simple structure, HMMs are able to reproduce important features of the power output of wind farms. This opens up possibilities to model and analyze these features with methods and techniques stemming from the field of Markov models and stochastic processes. Index Terms-Wind farm power generation, data models, power system modeling, time series analysis, hidden Markov models.

Mixed Copula-Based Uncertainty Modeling of Hourly Wind Farm Production for Power System Operational Planning Studies

“…Remark 1: In this paper, the Frank, Clayton and Gumbel copulas are considered for modeling the temporal dependence, as shown in (15). For Clayton and Frank copulas, h −1 , the inverse function of ( 16), is given in ( 17) and (18), respectively [63], [64].…”

“…There exist other models based on Markov chain and GAN, which offer high flexibility in modeling the correlations between the power productions of different turbines within a farm. As an example, in [18], the dependence between the output power of different turbines of a wind farm is captured with the help of hidden Markov chains. The output power of each wind turbine is divided into several levels of production, which are used to estimate the transition probabilities and stochastic matrices of the Markov chain models.…”

“…The proposed HMCM produces scenarios of wind farm production with a significant reduction in the total number of copula parameters that need to be estimated. The HMCM is able to capture non-linear temporal dependence among wind time-series data (unlike [10]- [13]), while being a computationally tractable algorithm (unlike [14], [15], [18]) and an effective probabilistic wind modeling for large dimensions (unlike [16], [17]). In addition, the proposed model has a simple structure and does not require training (unlike [19], [20]).…”

Short‐term photovoltaic power dynamic weighted combination forecasting based on least squares method

“…P Rt = c 1t P R1t + c 2t P R2t + · · · + c it P Rit + · · · + c nt P Rnt (11) 4. According to (8), the objective function of the LS method is…”

“…Then, a frog leaping algorithm was proposed to find the optimal parameters, and, finally, the PV power could be forecast. Reference studied the degree to which the power output of winds farm can be modeled using a discrete hidden Markov chain (HMM). When simulating the output of a single turbine, the hidden process of a HMM helps in capturing the dependence between the output of different turbines.…”