SELECTION OF ARTIFICIAL NEURAL NETWORK PARAMETERS IN COMPLEX OPTIMIZATION FOR OPERATIONAL CONTROL OF POWER SYSTEMS

Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 31 DOI: https://10.5281/zenodo.17618568 SELECTION OF ARTIFICIAL NEURAL NETWORK PARAMETERS IN COMPLEX OPTIMIZATION FOR OPERATIONAL CONTROL OF POWER SYSTEMS Shanazarov A.E. Toshkent State Technical University, PhD, Acting Associate Professor [email protected] АNNOTATSIYA Ushbu maqolada elektr energetika tizimlarining holatlarini operativ boshqarish maqsadida kompleks optimallashtirish usuli sifatida sunʼiy neyron tarmoq (SNT) parametrlarini tanlash va optimallashtirish jarayonlari ko‘rib chiqildi. Tadqiqotning asosiy maqsadi — elektr energetika tizimining dinamik o‘zgarish sharoitlarida ishlash samaradorligini oshirish, barqarorlashgan holatni va ishonchlilikni taʼminlashdan iboratdir. Bu maqsadga erishish uchun SNT modellarining strukturasi, o‘rganish algoritmlari, va giper parametrlarini tanlash usullari tahlil qilindi. Eksperimental modellashtirish va simulyatsiya natijalari asosida optimal parametrlar kombinatsiyasi aniqlandi, bu esa tizimning tezkor va aniq yechimlar qabul qilish qobiliyatini sezilarli darajada yaxshilanishini ko‘rsatdi. Tadqiqot natijalari elektr energetika tizimlarining holat parametrlarini optimallashtirishda sunʼiy neyron tarmoqlaridan samarali foydalanish imkoniyatlarini kengaytirishga qaratilgan yondashuvlarni taqdim etadi. Kalit so‘zlar: elektr energetika tizimlari, operativ boshqarish, sunʼiy neyron tarmoq, parametrlar optimallashtirishi, kompleks optimallashtirish, giper parametr. АННОТАЦИЯ В данной статье рассматриваются процессы выбора и оптимизации параметров искусственных нейронных сетей (ИНС) как комплексного метода оптимизации для оперативного управления состояниями энергосистем. Основной целью исследования является повышение эффективности работы энергосистемы в условиях динамических изменений, обеспечение ее устойчивости и надежности. Для достижения этой цели были проанализированы структура моделей ИНС, алгоритмы обучения и методы выбора гиперпараметров. На основе результатов экспериментального моделирования и имитационного моделирования определено оптимальное сочетание параметров, что существенно улучшило способность системы принимать быстрые и точные Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 32 решения. Результаты исследования дают подходы, направленные на расширение возможностей эффективного использования ИНС при оптимизации параметров состояния энергосистем. Ключевые слова: энергосистемы, оперативное управление, искусственная нейронная сеть, оптимизация параметров, комплексная оптимизация, гиперпараметр. ABSTRACT This article considers the processes of selecting and optimizing artificial neural network (ANN) parameters as a complex optimization method for operational control of power system states. The main goal of the study is to increase the efficiency of the power system in conditions of dynamic changes, ensure its stability and reliability. To achieve this goal, the structure of ANN models, learning algorithms, and methods for selecting hyperparameters were analyzed. Based on the results of experimental modeling and simulation, an optimal combination of parameters was determined, which significantly improved the system’s ability to make quick and accurate decisions. The results of the study provide approaches aimed at expanding the possibilities of effective use of ANNs in optimizing the state parameters of power systems. Keywords: power systems, operational control, artificial neural network, parameter optimization, complex optimization, hyper parameter. INTRODUCTION At present, considering the potential of artificial neural networks (ANNs) in solving a wide range of problems across various fields, their application for the operational control of power system states has been investigated. To solve the given problem, the parameters of the artificial neural networks were selected based on an analysis of their characteristic properties. In the operational control of an electric power system, the main task of complex optimization is to maintain optimality in the control process, even after short-term load scheduling changes. Therefore, taking into account such factors as the large amount of input and output (optimized) data, the existence of nonlinear and complex relationships between them, and the rapidly changing state of the system, the use of cascade-forward neural networks was proposed. This approach allows for efficient system control under varying load schedules, i.e., in the presence of uncertainties or dynamic changes. Cascade-forward neural networks can quickly adapt to different system variations, improve the decisionmaking process, and significantly increase the accuracy of operational control. Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 33 Moreover, using a model based on artificial neural networks makes it possible to forecast load variations and continuously provide adaptive solutions to those changes [1,2]. This process contributes to ensuring the stability and efficiency of the overall control system. MATERIALS AND METHODS The Cascade Forward Neural Network (CFNN) is a type of neural network that differs from the traditional feedforward network by including connections not only between consecutive layers but also from the input and all previous layers to the subsequent ones. In this structure, each hidden layer neuron is connected not only to the neurons of the previous layer but also directly to the input layer (Figure 1) [3–5]. Figure 1. Structure of the Cascade Forward Neural Network (CFNN). As in feedforward networks, two or more layers in a cascade-forward network can learn any finite input–output relationship, provided that a sufficient number of hidden neurons are included. Cascade-forward neural networks can be applied to process various types of input and output data. This model takes into account both linear and nonlinear relationships between the inputs and outputs. The problem of optimizing electric power systems (EPS) is one of such types of problems, since it involves a large number of initial data as well as several tens of parameters to be optimized [4–6]. Therefore, it is important to explore the possibilities of developing algorithms based on cascade-forward neural networks for solving such optimization problems. In this study, the sigmoid activation function was used in the network model (Figure 2). Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 34 𝑓(𝑥)=1 1+𝑒−𝑥 (1) Since this function is nonlinear, it can be used in multilayer neural networks, and such networks can also be trained using the backpropagation method. The sigmoid function is bounded by two horizontal lines, y = 1 and y = 0, which normalize the output value of each neuron. In addition, the sigmoid function has a smooth gradient, which prevents abrupt jumps when calculating output values. As shown in the sigmoid function graph (Figure 2), for values of x in the range from –2 to 2, the output y changes rapidly. This indicates that even a small variation in the value of x within this interval causes a significant change in the corresponding y value. Figure 2. Sigmoid activation function. Another advantage of the sigmoid function is that its output values are limited within a fixed range — specifically, the interval [0,1]. In comparison, a linear function varies within the range of (−∞, +∞). This property of the sigmoid ensures that even for large activation values, the resulting output errors remain bounded and do not grow excessively [7–10]. Below, the problem of comprehensive optimization of the power system state based on an artificial neural network (ANN) model is considered. RESULTS As an object of research, the 14-bus test system developed by the Institute of Electrical and Electronics Engineers (IEEE) was selected (Figure 3). In developing the ANN-based comprehensive optimization model of the power system, the active powers of all buses were taken as input data. Since the load power factors vary depending on the nature of each load, the change in Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 35 active load naturally leads to a corresponding change in reactive load, determined by its power factor. Considering these aspects, during the training of the neural network, the active power of each load Pload,j was used as the input variable. Figure 3. IEEE 14-bus test scheme of the electric power system As output data, the following optimized parameters were considered: PCi - active powers of all generating units involved in the optimization; Qi - reactive powers of the controllable sources; Ui - voltages of the reference buses; КТ - tap ratios of the adjustable transformers. In the comprehensive optimization of the electric power system, the ANN establishes the following connections by taking into account the aforementioned influencing factors: [PCi , Qi , Ui ,КТ ]= f (Pload.j) 14 13 12 11 10 98 7 6 5 4 3 2 1 13,5 +j5,8 [MBA] 14,9 +j5 [MBA] 21,7 +j12,7 [MBA] 94,2 +j19,0 [MBA] 47,8 +j3,9 [MBA] 7,6 +j1,6 [MBA] 11,2 +j7,5 [MBA] 29,5 +j16,6 [MBA] 9 +j5,8 [MBA] 3,5 +j1,8 [MBA] 6,1 +j1,6 [MBA] 232,3 +j165,5 [MBA] 10,29 +j42,5 [Om] 3,7 +j11,3 [Om] 10,84 +j33,1 [Om] 11,06 +j33,5 [Om] 8,95 +j37,7 [Om] 12,77 +j32,6 [Om] 2,55 +j8,02 [Om] 0,02 +j33,05 [Om] 0,02 +j20,9 [Om] 6,06 +j16,1 [Om] 15,65 +j36,6 [Om] 18,09 +j37,9 [Om] 12,62 +j24,8 [Om] 23,44 +j48,88 [Om] 32,58 +j66,3 [Om] 24,04 +j51,1 [Om] K5-6=0,932 K4-9=0,965 0,0 +j106,22 [Om] 0,0 +j39,44 [Om] K4-7=0,978 42,1 +j38,1 [Om] CTK CTK Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 36 In model development, the dataset is divided into three parts: training, validation, and testing. This step is crucial for evaluating the model’s performance and ensuring accurate assessment. Each subset serves a specific purpose and contributes to improving the model’s generalization capability. Training — to allow the model to learn the relationships between input and output data; Validation — to select the model’s hyperparameters; Testing — to evaluate the actual performance of the model. In the present study, the initial dataset was proposed to be split into training, validation, and test sets with the following ratios: 80% training, 10% validation, 10% testing; 70% training, 15% validation, 15% testing; 60% training, 20% validation, 20% testing. Research shows that the efficiency of ANN training depends on the number of samples selected. For instance, considering the total number of initial data, 80% of 400 randomly selected samples (320 samples) are used for training. In this case, the validation and test sets are relatively small, which may lead to overfitting, as the model can memorize the training data excessively. Consequently, validation and test results may not provide a reliable estimate of the model’s performance. If the ratio is 70/15/15, it can be considered a balanced distribution. In such a scenario, there is sufficient data for training, while the validation and test sets are large enough to prevent overfitting. A larger validation set allows for more reliable hyperparameter selection and performance evaluation. When the ratio is 60/20/20, there is less data for training, which may result in insufficient learning. Therefore, in the present study, the 70/15/15 ratio was selected. Figure 4 shows the training results graphically. Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 37 Figure 4. Training results graph The number of neurons in the hidden layers directly affects the model’s performance and how effectively it can learn from different datasets. Choosing the correct number of neurons in each layer is a critical step for the optimal operation of a neural network, as it determines the network’s learning capability, generalization ability, and computational complexity. In this study, the optimal number of neurons was evaluated within the range of 0 to 14. The model’s error is usually assessed using the mean squared error (RMSE), calculated as follows:  =  −= n iii yy n RMSE 1 2 )( 1 (4.5) Figure 5 illustrates the relationship between the number of neurons and the root mean square error (RMSE) in graphical form. As observed from the graph, when each layer contains 4 neurons, the RMSE decreases significantly, indicating that the model learns the errors in the training data more effectively. However, when the number of neurons exceeds 4, the RMSE begins to increase noticeably. This suggests that having too many neurons can lead to overfitting, where the model adapts excessively to the training data, reducing its generalization ability. Consequently, the model may perform poorly on new, unseen data. Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 38 Figure 5. Graph of the change in root mean square error (RMSE) depending on the number of neurons Based on the analysis of Figure 5, selecting 4 neurons in the hidden layer is optimal, as this configuration results in the lowest RMSE. This choice ensures effective training of the model and enables it to learn the patterns within the data efficiently. In this configuration, the network consists of 3 layers: the first, second, and third (output) layers, with each layer containing 4 neurons. Figure 6. Graph of the change in root mean square error (RMSE) depending on the number of epochs Figure 6 shows the change in the root mean square error (RMSE) during the training process depending on the number of epochs. The data were analyzed over an epoch range from 0 to 80. Educational Research in Universal Sciences ISSN: 2181-3515 VOLUME 4 | ISSUE 14 | 2025 https://t.me/Erus_uz Multidisciplinary Scientific Journal November, 2025 39 From the graph, it can be observed that the ANN achieves maximum performance and accuracy at around 50 epochs. At this number of epochs, the neural network reaches a state of saturation, and the 50th epoch is considered a critical point. Based on this, further training in the program is conducted over 50 epochs. Achieving this result helps to enhance the model’s efficiency and accuracy. CONCLUSION The study was conducted based on the selection of a Cascade Forward Neural Network (CFNN) modification. These cascade neural networks can be applied to process any type of input and output data. The considered model is capable of capturing both linear and nonlinear relationships between inputs and outputs. This feature allows for obtaining accurate and reliable results in a short time, even in large-scale power systems with numerous generating units and loads. Proper selection of the hyperparameters of neural network models significantly enhances their overall efficiency and reliability. Optimal hyperparameter tuning is a crucial factor that not only improves the training process but also substantially enhances the general performance and quality of the model. REFERENCES: 1. T. Gayibov, B. Uzakov, A. Shanazarov. Algorithm of power system mode optimization taking into account losses in networks and functional constraints. // AIP Conference Proceedings 2612, 050011 (2023) https://doi.org/10.1063/5.0117667. 2. Braspenning P J, Thuijsman F and Weijter A J M M. 1995. 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