• Combined systems [30].

The ARIMA models are the most commonly used class of models for stationary signal forecasting (or a signal that can be made stationary). These models support random walk, seasonal trend, non-seasonal exponential smoothing, and autoregressive models.

Lags of the stationarized series in the forecasting equation are called "autoregressive" terms, while "moving average" terms describe the lags of the forecast errors. A time series, which needs to be differenced to be made stationary, is said to be an "integrated" version of a stationary series. Random-walk and random-trend models, autoregressive models, and exponential smoothing models are all considered special cases of ARIMA models.

The learning and encoding of signal temporal features are enabled by the RNN. This is an ideal approach to forecast signals, which are reasonably predictable based on past events. LSTM networks are recurrent networks that can overcome some of the historic challenges related to the training of recurrent networks, such as the vanishing gradients problem. This study will not go into the detail of evaluating and comparing forecasting models and will adopt the LSTM model due to its universally accepted ability to predict wind speed and load and perform predictive diagnostics of equipment condition.

Wind power plant output forecasts are based both on weather conditions and the power curves of the turbines. Moreover, at least one numerical weather forecast model should be integrated into the model being developed. These weather models will help to predict global weather patterns and their effects on local conditions. The numerical weather model (NWM) used to consider information other than data from local station observations is the NEMS4 model [31]. This model is provided free of charge by MeteoBlue (meteoblue AG, Basel, Switzerland) for a given date range and station. The data are provided in raw format.

The weather data prediction unit is connected to the icing prediction unit. When operating a wind turbine in a cold climate, additional power losses occur due to several types of icing: heavy frosting of the blades (in temperatures below −25 ◦C), sedimentary (cloudy) icing, and atmospheric icing (Figure 3).

Modern wind turbines include proven technical solutions to enable their operation in temperatures as low as −35 ◦C [32]. However, it is not only temperature that is important but also the duration of icing. For areas with long winter seasons, it is important to strengthen the control system by adding an icing prediction unit. This will make it possible to effectively use the existing systems to protect against ice, which can grow intensively on the surface of the blades.

According to the Makkonen theory [33], the functionality of the icing intensity indicator depends on the predicted weather parameters. Based on these calculations, a decision is made to turn on the protection system. The intensity of icing is determined by the following equation:

$$\mathbf{I} = \mathbf{a} \times \boldsymbol{\upbeta} \times \mathbf{v} \times \mathbf{LWC} \times \mathbf{v} \times \mathbf{A},\tag{1}$$

where α is the collision efficiency factor; β is the coefficient of sticking efficiency; γ is the coefficient of efficiency of growth (accretion); LWC is the liquid water content in the air (mass particle concentration), kg/m3; v is the speed of incoming airflow (particle velocity), m/s; A is the cross-sectional area of the wind turbine blade (relative to the direction of the airflow velocity vector), m2. LWC values and alpha coefficients depend on the weather parameters (pressure, temperature, humidity, specific water content in the environment, etc.). In this article, the prediction of the onset of atmospheric icing is based on the occurrence of the conditions presented in Table 1.

**Table 1.** Conditions for atmospheric icing (adopted from [34]).


To protect the blades from ice, special anti-icing and de-icing systems are used, as described in detail in [32,35]. In the icing prediction unit, the input data are acquired from meteorological instruments (weather data), wind measuring systems (wind speed, data correlation for the "heated–unheated anemometer" system), and directly from the wind turbine (power). When the output power from the wind turbine drops and there are conditions for atmospheric icing (Table 1), the system produces a signal to turn on the anti-icing system.

All icing protection systems are divided into two types: active and passive. Active systems require additional power from their own system (these include all anti-icing systems installed inside or outside the blade). Passive systems do not incur additional costs when operating the wind turbine (de-icing systems, for example, painting the blades in black). The pitch-control system for wind turbines with a capacity of more than 1 MW is categorized as a passive system since it is preinstalled and does not incur substantial additional costs to be operated. However, for wind turbines of a maximum 1 MW capacity, a feasibility study concerning the application of the regulation system is required.

In the case of a pitch-control in a lower capacity turbine, it is necessary to compare cost and effectiveness. The possible effect can be estimated based on the power output increase. Figure 4 shows how the turbine power coefficient changes due to icing based on the airfoil data reported by Homola et al. [36]. The calculations are based on Wilson's equation [37] and involve different angles of attack and tip-to-speed ratios. It is noticeable that, when icing occurs, the changes in the ratio of the lift and drag forces influence performance but so do changes in the tip-to-speed ratio.

In the development of a pitch-control-based approach, optimal drag-to-lift ratios from several references including airfoil performance data for both clean and icing conditions [32,33,35–39] are used. The data used include several wind speeds, as seen in Table 2. Wilson's equation [37] with different angles of attack and tip-to-speed ratios is used to predict the maximum power coefficient of a wind turbine. The results under four conditions are presented: 1. clean turbine, 2. turbine under icing conditions, 3. turbine under icing conditions with pitch control, and 4. turbine under icing conditions with combined pitch and tip-to-speed ratio control. The results for different wind speeds are summarized in Table 2. This analysis reveals that the pitch control can overcome some of

the icing effects, but the combined pitch and tip-to-speed ratio control has even higher loss reduction potential. Therefore, the potential of the combined pitch and tip-to-speed ratio control is examined more closely in the following section.

**Figure 4.** Effects of tip-to-speed ratio and angle of attack on turbine power coefficient for (**a**) clean turbine and (**b**) during icing based on the drag to lift data (adopted from [34]).

**Table 2.** Results summary of the performance analysis for a wind turbine with and without icing (adopted from [34]). The results are presented for a clean turbine (Cpclean), a turbine under icing conditions (Cpicing), a turbine under icing conditions with pitch control (Cpα), and a turbine under icing conditions with pitch and tip-to-speed ratio control (Cpαλ).

