Power supply stability analysis of power networks considering load-risk-emergency multi-source data
Data publikacji: 27 lut 2025
Otrzymano: 24 paź 2024
Przyjęty: 23 sty 2025
DOI: https://doi.org/10.2478/amns-2025-0144
Słowa kluczowe
© 2025 Li Junhui et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
The increase in urban and industrial load demand is driven by a combination of factors, including socio-economic development, technological advancements, population growth, and accelerated urbanization. As the demand for urban and industrial loads has been increasing, the power supply capacity of the power system has been expanding. However, this expansion has also revealed many issues, such as system stability. Power supply stability analysis is an important theoretical problem that aims to improve the reliability and quality of power supply, and it serves as the foundation for formulating reasonable and effective power supply schemes and optimizing dispatching operations. Therefore, power supply stability analysis of power systems has very important practical significance [1-6].
The purpose of power supply stability analysis is to systematically study and evaluate various parameters and conditions in the operation of the power system, and to take measures to control these factors in order to improve the stability of the power supply system. Currently, there are many uncertain factors in the power grid, such as power load, voltage fluctuation, generator output, and power system failures.
Study on Power Quality of grid-connected Hybrid Energy Systems by Kumar Sachin et al [7] optimized proportional resonant current controller based on a genetic algorithm is investigated to improve the performance of shunt active power filters. Deepak Sharma and Abdul Hamid Bhat's Performance Evaluation of DSTATCOM for Power Supply and Load Disturbance Based on Clarke Transform Technology [8], Vasyl HUDYM et al [9] improved the accuracy of voltage harmonic coefficient estimation of power supply system.
Traditional analysis methods are based on a single data source, such as state estimation or probabilistic power flow method. Due to the diverse, complex, and stochastic nature of uncertainty factors, analysis methods relying solely on a single data source struggle to comprehensively and accurately capture all critical factors affecting the stability of grid power supply. Additionally, traditional analysis methods typically focus only on the impact of a single data source such as load level or emergency measures on the power supply stability of the power system.In this case, existing studies have proposed a variety of data sources to consider the influence of these factors on the power supply stability of the system. However, these studies often only consider a few typical factors’ impact on the system’s power supply stability. Consequently, this study presents a methodology for assessing the stability of power supply within power networks, integrating load, risk, and emergency multi-source data. By employing iterative control models, the stability of the power supply system is analyzed and evaluated using Fourier analysis on the load side, thereby establishing a framework for more in-depth investigations into the effects of nonlinear loads on system risk and the impact of multiple emergency factors on grid power supply stability.
The power network model is a mathematical model based on load-risk-emergency multiple factors, its main function is to study the interaction between load, risk, and emergency. The model is a nonlinear dynamic system, in which the node voltage analytical model is a mathematical model used to describe the node voltage change[12-14], and the interaction between the node load, risk, and emergency is mainly reflected in the node voltage. The interaction among load, risk, and emergency can be calculated by this model. This paper establishes the power network model as shown in Figure 1.
Relationship diagram of different risk degrees based on harmonic content.
The model uses a directed acyclic graph to describe the power network, which is characterized by the fact that the electrical connection information of nodes does not change with the network topology, so the interaction between node voltage and load, risk, and emergency only needs to be considered in the node voltage analytic model. By constructing the power network model in Figure 1, we can intuitively see how the multi-factors of load-risk-emergency affect the power supply stability of the grid. In Figure 1, the interaction between load, risk, and emergency is represented by a sideline, and the interaction between node voltage, load, and emergency in the node voltage analytic model is represented by a sideline. Nonlinear load model, the nonlinear load will cause harmonics
By analyzing the node voltage analysis model and load, risk, and emergency data, a power supply stability analysis framework based on multi-source data is established. The framework consists of the node voltage analysis model, load, and emergency data
Part composition. The node voltage analysis model is improved to make it more suitable for multi-source data analysis. Figure 1 illustrates the relationship diagram between different risk levels and their harmonic content.
The voltage of node i is i= (x,y,z), where x and y represent the load and risk of node i respectively, and z represents the emergency load of node i. In the above model, the load level and risk level of node i are first determined. Since both the load level and the risk level of the node can be regarded as a demarcation point of its risk level, the load level of the node can be regarded as a demarcation point. Secondly, the emergency load level of node i is calculated. The load level is divided into three categories: high, medium, and low, in which the low category contains more loads and the emergency load is larger. Since the network has serious accident probability and accident consequences, it is necessary to evaluate the security of the network according to the possible consequences of the incident. At present, the security assessment methods that are relatively mature at home and abroad include state estimation method, failure mode Impact and hazard analysis (FMECA), fault tree analysis (FTA), Monte Carlo simulation method (MCM), network attack assessment method (NBI) and so on.
The infinite gain of the repetitive control system at the fundamental and harmonic frequencies of the external periodic excitation signal leads to the decrease of the gain at other frequencies and deteriorates the control performance of the system at these frequencies. Therefore, repetitive control can not only suppress aperiodic disturbance but even amplify the effect of aperiodic disturbance on the system. To improve the aperiodic disturbance suppression performance of repetitive control systems, some scholars have proposed methods such as adaptive repetitive control. These methods reduce the sensitivity of disturbance in the system output channel by improving the robustness of the controller itself and are regarded as passive disturbance suppression methods. It is difficult for traditional DOF repetitive control systems to simultaneously track the reference input signal with high precision and keep the output invariance of the controlled object after it is disturbed by uncertainty, so it is often necessary to make a compromise between tracking control and disturbance suppression.
The diagram shows the structure of the inverter-based repetition control system proposed in this paper, where r(t) is the reference input signal, e(t) is the tracking error, c(t) is the output of the improved repetition controller, C(s) is the repetition control feedforward compensator, and yp(t) is the system output. Figure 2 shows the repetitive control design.
Repetitive control design drawing
Consider the feedback control system depicted in Figure 3, with the assumption that both H1 and H2 possess finite-gain stability properties, and examine the feedback control system configuration as presented in Figure 3.
Feedback Control System
It is stated that the gains of the systems H1 and H2 are not greater than a non-negative constant. If a minimum value exists for this non-negative constant, it is defined as the gain of systems H1 and H2. The feedback control system is considered stable if the gain adheres to the condition of being the non-negative constant multiplied by 1.
This paper presents a repetitive control system design method for inverters. By estimating and compensating for the effect of aperiodic disturbance on system output in real-time, the disturbance suppression performance and robustness of the system are improved. High-precision tracking of periodic reference input signals is realized. The basic control system design helps decrease system harmonic content and enhance stability. Here, the layout of the advanced repetitive controller and the principles of composite repetitive control are outlined. Figure. 4 presents the system risk analysis framework focused on nonlinear load conditions.
Block diagram of system risk analysis based on nonlinear load
The higher the bandwidth of the observer, the better the observation capability, but this makes the observer more sensitive to noise. Therefore, a small value should be gradually increased until the observation accuracy meets the requirements. The larger the bandwidth of the controller, the stronger the control effect, the faster the output response of the system, but the more serious the over-harmonic oscillation, and the lower the stability. Therefore, the selection of parameters, on the one hand, can be manually adjusted according to the aforementioned experience, and on the other hand, it can be used to set relevant performance indicators by using optimization algorithms to obtain the optimal parameters.
Using a two-machine setup, the power supply stability analysis technique presented in this study is employed to evaluate the impact of load, risk, and emergency factors on system stability. Included among these, Figure. 5 captures the waveform data collection of the middle-stage waveform on the nonlinear load side before repetitive control intervention. Figure. 6 is Fourier analysis of harmonic content of the midstream waveform of the nonlinear load side before repetitive control is applied; Figure. 7 is waveform data collection of the midstream waveform of the nonlinear load side before repetitive control is applied. Figure. 8 shows the harmonic content of the waveforms in the front section of the nonlinear load side before repeated control is applied.
Waveform data acquisition of the mid-section waveform of the nonlinear load side before repeated control is applied
Fourier analysis of the harmonic content of the middle waveform of the nonlinear load side before repeated control is applied
Waveform data acquisition of the mid-section waveform on the nonlinear load side before repeated control is applied
Fourier analysis of the harmonic content of the waveforms in the front section of the nonlinear load side before repeated control is applied
Waveform data of the front and middle waveforms of the nonlinear load side before repetitive control was applied were collected, and welfare analysis was carried out on the collected waveforms. The harmonic content of the middle waveforms of the nonlinear load side before repetitive control was applied reached 29.43%. Figure.8. Fourier analysis of the waveforms in the front section of the nonlinear load side before repeated control is applied shows that the harmonic content reaches 13.83%.
Excessive harmonic content poses a threat to the safe and stable functioning of the power system.
Among them, Figure. 9 is waveform data acquisition of the front-end waveform of the nonlinear load side of the conventional filter; Figure. 10 is Fourier analysis of the harmonic content of the front-end waveform of the nonlinear load side of the conventional filter; Figure 11 is waveform data acquisition of the mid-end waveform of the nonlinear load side of the conventional filter. Figure. 12 shows the Fourier analysis of the harmonic content of the middle waveform on the nonlinear load side with a conventional filter.
Waveform data acquisition of the waveforms in the front-end segment of the nonlinear load side of the conventional filter
Fourier analysis of the harmonic content of the front waveform of the nonlinear load side of the conventional filter
Waveform data acquisition of mid-end waveforms on the nonlinear load side of conventional Filters
Fourier analysis of the harmonic content of the middle waveform on the nonlinear load side of the conventional filter
The waveform data of the nonlinear load side of the conventional filter is collected, and the collected waveform is analyzed by Fourier analysis. The harmonic content of the nonlinear load side waveform of the conventional filter is 29.43%. The Fourier analysis of the waveforms in the front section of the nonlinear load side with conventional filters shows that the harmonic content reaches 29.62%, which is too high. and stable operation of the power system.Thus, conventional filters are not particularly effective in optimizing harmonic content, and they can still compromise the safe and stable operation of the power system.
Among them, Figure. 13 is waveform data collection of the front-end waveform of the nonlinear load side controlled by repetition; Figure. 14 is Fourier analysis of harmonic content of the front-end waveform of the nonlinear load side controlled by repetition; Figure 15 is waveform data collection of the mid-end waveform of the nonlinear load side controlled by repetition. Figure. 16 shows the Fourier analysis of the harmonic content of the middle waveform of the nonlinear load side with repeated control, Figure. 17 shows the nonlinear load side Flux (V.s) based on the current value, and Figure. 18 shows the nonlinear load side Flux (Pu) based on the current value.
Waveform data acquisition of the front-end waveform of the nonlinear load side with repeated control
Fourier analysis of the harmonic content of the front waveform of the nonlinear load side with repetitive control
Waveform data acquisition of the mid-end waveform of the nonlinear load side by applying repetitive control
Fourier analysis of harmonic content of nonlinear load side midsection waveform with repetitive control
Nonlinear load side Flux (V.s) based on the current value
Nonlinear load side Flux (Pu) based on the current value
The waveform data of the front and middle waveforms of the nonlinear load side with repeated control were collected, and the collected waveforms were analyzed by Fourier analysis. The harmonic content of the waveforms in the front waveforms of the nonlinear load side with the conventional filter reached 2.51%, and the harmonic content of the middle waveforms with the conventional filter reached 1.3%. As the harmonic content decreases, it can be clearly seen that repetitive control has a significant effect on optimizing the harmonic content. In addition, the stability of the proposed control strategy was verified by analyzing the magnetic flux (V.s) and magnetic flux (Pu) on the nonlinear load side based on the current value, thereby improving the safe and stable operation of the power system.
This article introduces a design method for repetitive control systems, which is specifically designed to deal with inverter systems with parameter disturbances and external disturbances. On the basis of ensuring system stability, the clever combination of repetitive controllers significantly enhances the anti-interference ability and tracking accuracy of the control system for periodic reference signals. The simulation results further confirm that this method can effectively reduce system harmonics, improve the steady-state performance of the system, and demonstrate excellent robustness. However, this article has only conducted simulation analysis or partial analysis so far. Future research will combine experimental platforms to verify the actual effectiveness and superiority of the control method.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflict of interest.