APPLICATION OF FUZZY LOGIC IN MATHEMATICAL MODELING OF VOLTAGE REGULATION IN SPINNING MILLS

ABSTRACT

In the article power quality indicators are considered as key parameters of electric energy. Regulation of voltage and frequency deviations, harmonic distortions, and load imbalance, as well as correction of short-term deviations of supply system voltage from the nominal value, are carried out directly on the basis of controlling these parameters. The control process itself is implemented through mathematical modeling. A number of modern methods of mathematical modeling exist, and this scientific article is devoted to voltage regulation based on fuzzy logic. By employing type-II fuzzy logic, the fuzzification process is performed, and based on the Gaussian membership function, the function of the input parameter - the active power load of the spinning mill (P_k) - is formed.  

АННОТАЦИЯ

В статье показатели качества электроэнергии рассматриваются как ключевые параметры электрической энергии. Регулирование отклонений напряжения и частоты, гармонических искажений и дисбаланса нагрузок, а также коррекция кратковременных отклонений напряжения системы электроснабжения от номинального значения осуществляются непосредственно на основе управления данными параметрами. Сам процесс управления реализуется посредством математического моделирования. Существует ряд современных методов математического моделирования, и данная научная статья посвящена регулированию напряжения на основе нечеткой логики. Применяя нечеткую логику второго типа, выполняется процесс фаззификации, и на основе гауссовской функции принадлежности формируется функция входного параметра — активной мощности нагрузки прядильного предприятия (P_k).

Keywords: Textile enterprise, electric power quality, active power, fuzzy logic, membership function, Gaussian function, mathematical model, nominal voltage value. Textile enterprise, electric power quality, active power, fuzzy logic, membership function, Gaussian function, mathematical model, nominal voltage value.

Ключевые слова: Текстильное предприятие, качество электрической энергии, активная мощность, нечеткая логика, функция принадлежности, гауссова функция, математическая модель, номинальное значение напряжения.

INTRODUCTION

Mathematical modeling of the quality of electric energy, which is considered the primary source of energy today, and its indicators contributes to stabilizing the operation of modern power supply systems, enhancing their reliability, and improving their economic efficiency. Modeling of voltage regulation devices, which represent a key indicator of electric power quality, plays an important role not only in ensuring stable and high-quality power supply to industrial enterprises, but also in improving overall energy efficiency. The design and mathematical modeling of voltage regulation devices in spinning mills are considered necessary for the following reasons:

• deviations of voltage values from the nominal level in power supply systems may cause interruptions and shutdowns in the production process;
• The occurrence of malfunctions in the operation of electric motors and electronic devices;
• It leads to an increase in conditions of unreliability with respect to the quality of electrical energy and the power supply system.

In order to eliminate the aforementioned conditions, this article addresses the problem of controlling voltage sag based on fuzzy logic, which is considered a modern method of mathematical modeling.

In the power supply systems of spinning mills, short-term rapid voltage sags are phenomena that occur on a millisecond scale. Because the exact time of occurrence, operating conditions, duration, and the depth of deviation from the nominal voltage are unknown, among modeling approaches fuzzy logic describes this state more accurately than other methods (neural networks, digital twins, and hybrid approaches). This conclusion is examined in detail in the scientific article [1] using SWOT and PESTEL analyses.

METOD

Fuzzy logic is a logical approach that, instead of operating with strict boundaries (‘yes/no’), represents outcomes within intervals expressed by real numbers. Each event or property is represented by a membership function within the range of 0…1 (μ∈[0,1]). Fuzzy logic encompasses uncertainties and nonlinearities in the real-time domain (such as the depth, duration, and recurrence of short-term voltage sags) [2].

For modeling the operation of a particular object, two types of fuzzification processes are available [2].

The first type of fuzzy logic is considered reliable in processes where the input data are precise and the membership functions are predefined, and where the procedure is simple and the final inference needs to be obtained quickly and efficiently.

                                        (1)

Here, the possible membership values for Jx are within the interval Jx⊆[0,1], where u — the membership function — varies within Jx [5].

The second type of fuzzy logic is considered appropriate to apply in modeling processes where both the input data and the membership functions are variable, and where uncertainties are present in the system [3,5].

After the fuzzification process in fuzzy logic, the decision-making step is of key importance and is concluded based on the graph of the membership function (Figure 1). In this procedure, the membership function is first selected for the given problem, and subsequently its graph is constructed. Since fuzzy logic provides several types of membership functions, and considering that the mitigation of short-term voltage sags is treated as a nonlinear process in this study, the Gaussian membership function is employed.

The Gaussian membership function is applied in the modeling of nonlinear and complex technological systems as well as uncertain processes. In particular, the application of the Gaussian membership function is considered highly effective for representing physical processes in which the variation laws of input parameters are uncertain and exhibit a natural exponential character. In this method, the Gaussian curve μÃ(x) is defined as a function of x and depends on three scalar parameters (a, b, c) [4].

RESULT

The sequence of fuzzy logic for voltage control in spinning enterprises is illustrated in Figure 1.

Figure 1. The sequence of fuzzy logic for voltage control in spinning enterprises is illustrated

In Figure 1 above, during the fuzzification process, the occurrence time, the exact moment, and the duration of the short-term rapid voltage sag are considered uncertain. Therefore, the second type of the fuzzification process was employed. According to this type, the active power P_k of the spinning enterprise - which directly influences voltage variation - is taken as the input parameter of the Gaussian membership function [7].

As the research object, the “WBM ROMITEX DIROMM” spinning enterprise was selected, with an active power of 3 MW [6]. In controlling voltage sags in the enterprise’s power supply system, the maximum drop in the enterprise’s active power amounts to 2.42 MW, while the power value under 80% load operation is 2.4 MW. These values are adopted as fuzzy logical variables.

• The active power of the manufacturing enterprise - P_k (MW) for:

JP = {Pk ϵ [2,38; 2,4; 2,45]} – very low. Pmax = 2,4 MW;

P = {Pk ϵ [2,48; 2,5; 2,54]} – lower. Pmax = 2,5 MW;

O` = {Pk ϵ [2,56; 2,6; 2,62]} – average. Pmax = 2,6 MW

Yu = {Pk ϵ [2,66; 2,71; 2,75]} – high. Pmax = 2,71 MW;

O`Yu = {Pk ϵ [2,79; 2,83; 2,88]} – very high. Pmax = 2,83 MW.

The values of the active power of the manufacturing enterprise are expressed as the values of fuzzy linguistic variables as follows:

• For active power:

a) Very low 2,35 M MW≤P_k<2,45 MW when, P_k<2,4 MW it is denoted by the term Very Low (J).

b) 2,45 MW≤P_k<2,54 MW Values approaching within the intervals are denoted by the term ‘Near’ (Ya).

c) P_k>2,88 MW In such cases, it is denoted as ‘Beyond the limit’ (T).

According to the essence of the mathematical modeling problem, the values corresponding to the critical active power in Table 1 were determined through the mathematical expression defining the Gaussian membership function.

Table 1.

Values corresponding to the critical active power

Through Table 1, the possibility is provided to precisely represent, by means of membership functions, the extent to which the active power (Pk) varies during the voltage sag control process. Furthermore, for the critical points indicated in Figure 2, the Gaussian membership function was constructed and differentiated in various colors according to the impact values.

Figure 2. Fuzzy membership function for the active power influencing the control of short-term voltage sag

In Figure 2, within the developed fuzzy logic for controlling short-term voltage sags in spinning enterprises, the active power P_k​ was selected as the input parameter. Based on this, Gaussian-type, piecewise (μ∈ [0,1]) membership functions (JPAQ → PAQ → BPAQ → O‘AQ → NAQ → YuAQ → BYuAQ) were constructed.

DISCUSSION

The main reason for selecting fuzzy logic to address the given problem is that the equipment operating within the technological processes of the spinning enterprise functions under normal conditions and is capable of producing the required output when the voltage is at its nominal value. However, due to internal and external influences affecting the enterprise’s power supply system, deviations and sags in the nominal voltage value occur. If the disturbance occurs suddenly and for a short duration, the voltage in the supply system also drops briefly and then restores to its nominal value. However, during this short interval, certain equipment in the technological process ceases operation, and additional time is required for them to resume functioning. Here, the main requirement for the mathematical modeling of voltage sag control is to represent the response of the equipment to the factors influencing the enterprise’s power supply system, namely ensuring the maintenance of voltage at its nominal level. Due to external or internal influencing factors, the manner, proportion, and timing of changes in the system load, i.e., active power, represent a nonlinear process. A nonlinear process, in contrast, can be effectively modeled by fuzzy logic compared to other methods, particularly when the system behavior is unknown or highly complex, when data are limited, and when real-time requirements are stringent. For this reason, this method has been employed in the present study.

CONCLUSION

The active power of the enterprise, P_k​, is an important indicator influencing voltage variation, and its fuzzy partitioning forms an adaptive and stable response to short-term sags: as P_k decreases, compensation intensifies; the narrow Gaussians in the transition zones respond more rapidly, while the wide Gaussian in the nominal zone ensures the suppression of oscillations. In this way, the control established through fuzzy logic reduces the depth and duration of voltage sags, ensures the continuity of the technological process, and improves the quality indicators of power supply. The modeling sequence presented below is recommended for all digital microprocessor-based regulating devices used in the voltage regulation process within spinning enterprises.

References:

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