Multivariate wind power curve modeling using multivariate adaptive regression splines and regression trees

PLOS ONE RESEARCH ARTICLE Multivariate wind power curve modeling using multivariate adaptive regression splines and regression trees Khurram Mushtaq ID1, Runmin Zou1, Asim Waris ID2*, Kaifeng Yang ID3, Ji Wang1, Javaid Iqbal2, Mohammed Jameel4 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 1 School of Automation, Central South University, Changsha, China, 2 School of Mechanical and Manufacturing Engineering, National University of Sciences & Technology, Islamabad, Pakistan, 3 School of Informatics, Communications and Media, University of Applied Sciences Upper Austria, Hagenberg, Austria, 4 Department of Civil Engineering, College of Engineering, King Khalid University, Asir, Abha, Saudi Arabia * Abstract OPEN ACCESS Citation: Mushtaq K, Zou R, Waris A, Yang K, Wang J, Iqbal J, et al. (2023) Multivariate wind power curve modeling using multivariate adaptive regression splines and regression trees. PLoS ONE 18(8): e0290316. https://doi.org/10.1371/journal. pone.0290316 Editor: AL MAHFOODH, UNITEN: Universiti Tenaga Nasional, MALAYSIA Received: June 20, 2023 Accepted: August 6, 2023 Published: August 28, 2023 Copyright: © 2023 Mushtaq et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: This research is carried out using two different publicly available SCADA system datasets. The first dataset can be accessed through the Kaggle repository (https:// www.kaggle.com/datasets/berkerisen/windturbine-scada-dataset). The second dataset can be accessed through the Kaggle repository (https:// www.kaggle.com/datasets/theforcecoder/windpower-forecasting). Funding: The authors extend their appreciation to the deanship of scientific research at King Khalid Wind turbine power curve (WTPC) serves as an important tool for wind turbine condition monitoring and wind power forecasting. Due to complex environmental factors and technical issues of the wind turbines, there are many outliers and inconsistencies present in the recorded data, which cannot be removed through any pre-processing technique. However, the current WTPC models have limited ability to understand such complex relation between wind speed and wind power and have limited non-linear fitting ability, which limit their modelling accuracy. In this paper, the accuracy of the WTPC models is improved in two ways: first is by developing multivariate models and second is by proposing MARS as WTPC modeling technique. MARS is a regression-based flexible modeling technique that automatically models complex the nonlinearities in the data using spline functions. Experimental results show that by incorporating additional inputs the accuracy of the power curve estimation is significantly improved. Also by studying the error distribution it is proved that multivariate models successfully mitigate the adverse effect of hidden outliers, as their distribution has higher peaks and lesser standard deviation, which proves that the errors, are more converged to zero compared to the univariate models. Additionally, MARS with its superior non-linear fitting ability outperforms the compared methods in terms of the error metrics and ranks higher than regression trees and several other popular parametric and non-parametric methods. Finally, an outlier detection method is developed to remove the hidden outliers from the data using the error distribution of the modeled power curves. Introduction As the world population increases, energy consumption is increasing by each day. However, to meet these demands, the use of fossil fuels causes severe damage to the environment, leading to global warming. To meet the challenge of decreasing the use of fossil fuel, the world is moving towards renewable resources for electrical power generation. Among many renewable energy technologies, wind energy generated through wind turbines is among the fastest- PLOS ONE | https://doi.org/10.1371/journal.pone.0290316 August 28, 2023 1 / 25 PLOS ONE University for funding this work through large group project under grant number (RGP. 2/94/44). Competing interests: The authors have declared that no competing interests exist. Multivariate wind power curve modeling using MARS growing electricity generation source [1]. Wind energy is cheap, clean, unlimited, sustainable and extensively distributed [2]. Wind power produced more than 6 percent of global electricity in 2020 with 743 GW of global capacity as stated in the Global Wind Report 2021 [3]. In order to make wind energy competitive with non-renewable energy sources, there is a need to reduce the maintenance cost of the wind turbine. However, to reduce the maintenance cost, early fault detection should be made possible, because it speeds up the repair process, which reduces the non-operational time of the turbine and the resulting loss of energy. Hence, tracking the performance of a turbine plays a crucial role in early fault detection and helps in reducing the cost of mounting additional sensors on the turbine [4, 5]. Since wind energy is stochastic and non-linear in nature, hence to increase the use of wind power in the power grid, accurately predicting the power generated by wind turbines is necessary. Accurately predicting the power can help the power system to plan and manage accordingly and make energy management much easier. The wind turbine power curve (WTPC), which shows the non-linear relationship between wind speed and wind power [6], serves as an important tool for performance monitoring and obtaining accurate forecasts of future wind power [7]. A power curve model depicts the performance and behavior of a wind turbine in normal operating conditions. Hence, the performance of the wind turbine can be monitored by comparing the expected wind power on WTPC with the actual (measured) power, and anomalies and faults can be detected. WTPC can be used for wind power prediction if the corresponding forecasted wind speed value is available. Several methods are available for wind speed forecasting, such as the ones proposed by [8–10]. Furthermore, accurate WTPC models also help in wind energy potential estimation of the area and selection of a wind turbine [11]. Theoretical power curves which are given by wind turbine manufacturers based on the International Electrotechnical Commission (IEC) standard, cannot accurately depict the wind turbine performance because they are estimated under ideal environmental conditions [11, 12]. Wind turbines, on the other hand, are hardly used in ideal conditions, and real power curves may differ significantly from theoretical ones because they do not take into account complicated variables like the air density, wind field, wind direction, yaw, and pitch misalignment, shading effects from surrounding obstacles, mechanical and control issues, location (...truncated)