Direct current microgrid high frequency oscillation stability risk assessment method

Abstract

The application discloses a DC microgrid high-frequency oscillation stability risk assessment method. The DC microgrid comprises a balancing unit, a constant power load and a DC line. The balancing unit comprises a distributed power supply and a power electronic device adopting a DC voltage control strategy, and is used for maintaining the stability of a common DC bus voltage and power balance. The constant power load comprises a distributed power supply and a power electronic device with constant power operation characteristics. The DC microgrid high-frequency oscillation stability risk assessment method comprises data-driven modeling, frequency identification, model reconstruction and risk assessment.

Description

Technical Field

[0001] This invention belongs to the field of DC microgrid stability analysis and evaluation, and particularly relates to a method for assessing the stability risk of high-frequency oscillations in DC microgrids. Background Technology

[0002] Because they can flexibly accommodate new energy sources such as photovoltaics and wind power, and provide efficient and reliable power supply for the increasing number of DC loads such as electric vehicles and LED lighting, DC microgrids based on advanced power electronics technology will inevitably become an important component of new power distribution systems. [1] .

[0003] With the increasing penetration of new energy sources and the growing proportion of power electronic equipment, the high-frequency oscillation stability problem of DC microgrids based on flexible DC technology is becoming increasingly prominent, and in severe cases, it may threaten the stable and reliable operation of the system. [2 [3] The University of Sydney observed high-frequency oscillations of around 450 Hz in a DC microgrid experiment. [4] Tianjin University observed a high-frequency oscillation phenomenon of around 300Hz in its multi-source DC microgrid experimental platform. [5] Therefore, conducting research on high-frequency oscillation stability risk assessment of DC microgrids has significant theoretical and practical value for guiding the optimization design of controller parameters and improving the high-frequency stability of DC microgrids.

[0004] To evaluate the high-frequency oscillation stability of DC microgrids, stability assessment methods based on detailed impedance or state-space models are usually adopted. Reference [6] evaluated the impact of constant power loads on the high-frequency stability of DC microgrids based on detailed impedance models. It found that the increase in the number of constant power load aggregations led to the enhanced impedance multiplication effect in the frequency domain, reduced the system stability margin, and the Nyquist curve would include the (-1,0) point, resulting in high-frequency oscillation instability of the system. Reference [7] analyzed the Nyquist curve based on the impedance model and found that the interaction of source and load impedances near the LC resonant frequency band under grid-connected mode may lead to system instability, and the increase in CPL penetration level will significantly reduce the high-frequency stability margin of the system. Reference [8] evaluated the impact of dynamic interaction between various types of distributed power sources, loads and lines on the high-frequency oscillation stability of DC microgrids based on the impedance model. Through impedance frequency characteristic analysis, it was found that there are two crossover points in the mid-to-high frequency band. The mid-frequency crossover point is mainly affected by the dynamic interaction of the control loop, while the high-frequency crossover point is mainly affected by the line impedance. Moreover, the impact of constant power loads on system stability is different in different frequency bands. In addition, references [9,10] established a detailed state-space model of a multi-source DC microgrid and evaluated the impact of the droop coefficient on the high-frequency stability of the system through eigenvalue analysis. They found that increasing the droop coefficient would cause the high-frequency mode eigenvalues ​​of the system to shift to the right half-plane, increasing the risk of high-frequency oscillation instability. Reference

[11] found, through participation factor analysis based on the state-space model, that the high-frequency oscillation problem is caused by the dynamic interaction between the power control loop and the AC grid. Furthermore, as the proportional coefficient of the power control loop increases, the eigenvalues ​​of the dominant high-frequency mode of the system will move from the left half-plane to the right half-plane, and the system will face the risk of high-frequency oscillation instability. Due to their high model order, the detailed impedance or state-space models mentioned above are difficult to evaluate the high-frequency stability of the system clearly and intuitively from a mechanistic perspective.

[0005] In the inventor's previous patent

[12] , a method for analyzing the high-frequency oscillation stability of DC microgrids was proposed. The key point was to analyze the high-frequency oscillation stability mechanism of DC microgrids through the established reduced-order equivalent circuit model. However, the proposed method relies on obtaining detailed information of all devices and components in the system in advance, and assumes that the dominant high-frequency mode of the system is known. Due to the large number of devices and their different characteristics in DC microgrids, or to protect trade secrets and user information, there are often "black box" devices with unknown information. The inventor's aforementioned patent method is difficult to apply to the risk assessment of high-frequency oscillation stability of DC microgrids containing "black box" devices.

[0006] To evaluate the stability of such systems containing "black box" equipment, a data-driven approach can be used. Reference

[13] proposes an online identification method for small disturbance stability characteristic parameters based on subspace optimal mode decomposition under random data-driven approach, and evaluates the small disturbance stability of the system by using the identified oscillation frequency and damping ratio information. Reference

[14] proposes a data-driven method for evaluating the subsynchronous oscillation stability of wind farms connected to the DC grid, and analyzes the system stability by analyzing the influence of wind speed / current fluctuation clusters on the amplitude of the subsynchronous component. However, the above data-driven stability evaluation methods can only provide numerical results characterizing the system stability, and can only passively observe the system stability change law through numerical results. They cannot evaluate the system stability from the mechanism level, and it is difficult to quantify the degree of influence of local equipment on the system stability.

[0007] The problem this patent aims to solve is how to combine reduced-order modeling with data-driven approaches to autonomously identify the dominant high-frequency points of a DC microgrid and achieve integrated closed-loop high-frequency stability risk assessment of a DC microgrid containing "black box" equipment, encompassing "data-driven modeling, frequency adaptive identification, reduced-order circuit model reconstruction, stability risk assessment, and parameter optimization design."

[0008] References

[0009] [1] Dong Xuzhu, Hua Zhuhu, Shang Lei, et al. Morphological characteristics and technological prospects of new power distribution systems [J]. High Voltage Engineering, 2021, 47(09):3021-3035.

[0010] [2] Peng Ke, Chen Jiajia, Xu Bingyin, et al. Stability and key control issues of flexible DC distribution system [J]. Automation of Electric Power Systems, 2019, 43(23):90-98, 115.

[0011] [3] Li Pengfei, Li Xialin, Wang Chengshan, et al. A review of stability analysis models and mechanisms of medium and low voltage flexible DC distribution systems [J]. Electric Power Automation Equipment, 2021, 41(05):3-21.

[0012] [4]Wu M, Lu D DA Novel Stabilization Method of LC Input Filter WithConstant Power Loads Without Load Performance Compromise in DC Microgrids[J]. IEEE Transactions on Industrial Electronics, 2015, 62(7): 4552-4562.

[0013] [5] Guo Li, Feng Yibin, Li Xialin, et al. Stability analysis and damping control method of DC microgrid [J]. Proceedings of the CSEE, 2016, 36(04): 927-936.

[0014] [6] Zheng Kaiyuan, Du Wenjuan, Wang Haifeng. Impedance analysis of the influence of aggregated constant power load on the stability of DC microgrid [J]. Power System Technology, 2021, 45(01):134-148.

[0015] [7]Mohamad AMI,Mohamed YA I.Impedance-Based Analysis andStabilization of Active DC Distribution Systems With Positive FeedbackIslanding Detection Schemes[J].IEEE Transactions on Power Electronics, 2018,33(11):9902-9922.

[0016] [8] Rashidirad N, Hamzeh M, Sheshyekani K, et al. High-FrequencyOscillations and Their Leading Causes in DC Microgrids[J]. IEEE Transactionson Energy Conversion, 2017, 32(4): 1479-1491.

[0017] [9]Guo L, Zhang S, Li

[0018]

[10] Li

[0019]

[11] Amin M, Molinas M.Small-Signal Stability Assessment of PowerElectronics Based Power Systems:A Discussion of Impedance-and Eigenvalue-Based Methods[J].IEEE Transactions on Industry Applications, 2017,53(5):5014-5030.

[0020]

[12] Li Xialin, Li Pengfei, Guo Li, et al. Stability Analysis Method for High-Frequency Oscillations in DC Microgrids [P]. China: ZL202011455000.2, May 17, 2022.

[0021]

[13] Zhou Shuyu, Cai Guowei, Yang Deyou, et al. Online evaluation method for small-disturbance stability of power system driven by random data [J]. Automation of Electric Power Systems, 2022, 46(1):94-100.

[0022]

[14] Xu Xinyu, Bian Xiaoyan, Zhang Qian, et al. Analysis of influencing factors of subsynchronous oscillation of doubly fed wind farm connected to grid via VSC-HVDC based on data-driven method [J]. Power System Protection and Control, 2021, 49(21):80-87. Summary of the Invention

[0023] This invention proposes a method for assessing the high-frequency oscillation stability risk of a DC microgrid. Utilizing electrical information measured at equipment ports, a data-driven detailed impedance model of the DC microgrid is established based on optimization theory. Combining frequency sweeping with a reduced-order equivalent circuit model, the high-frequency oscillation frequency of the DC microgrid is estimated using frequency matching principles. Using the obtained high-frequency oscillation frequency estimate, a reduced-order equivalent circuit model of the DC microgrid is reconstructed. The high-frequency oscillation stability risk of the system is assessed from the perspective of the equivalent circuit. Furthermore, the impact of sub-modules on the high-frequency stability of the system is quantified by physical parameters such as the equivalent resistance and equivalent inductance of sub-modules such as balancing units and constant power loads. This guides the optimization design of system controller parameters, thereby improving the high-frequency stability of the DC microgrid. The technical solution of this invention is as follows:

[0024] A method for assessing the high-frequency oscillation stability risk of a DC microgrid, wherein the DC microgrid includes a balancing unit, a constant power load, and a DC line. The balancing unit includes distributed power sources and power electronic devices employing a DC voltage control strategy to maintain the voltage stability and power balance of the common DC bus. The constant power load includes distributed power sources and power electronic devices with constant power operation characteristics. The method is characterized by comprising data-driven modeling, frequency identification, model reconstruction, and risk assessment.

[0025] Part One, Data-Driven Modeling, uses the following methods:

[0026] Based on the information obtained, all devices in the system are divided into the following three categories: ① Devices with known physical and control structures but some unknown parameters; ② Devices with completely unknown physical and control structures and parameters; ③ Devices with completely known physical and control structures and parameters. For the third category of "white box" devices with completely known information, their equivalent impedance models are directly derived and established. For the first two categories of "black box" devices with partially or completely unknown information, an impedance modeling approach based on optimization theory and data-driven methods is adopted to establish impedance models for balancing units and constant power load devices, respectively, thus obtaining the impedance model of the DC microgrid.

[0027] Part Two, Frequency Identification, the method is as follows:

[0028] 1) Set the high-frequency dominant oscillation frequency ω(k);

[0029] 2) Set the range of the high-frequency dominant oscillation frequency ω(k) and its initial value ω(1), and set the number of iterations k = 1;

[0030] 3) At the set dominant high-frequency oscillation frequency ω(k), the output impedance of the balancing unit is reduced in order, and further combined with the line impedance to obtain the reduced-order equivalent impedance Z of the balancing unit in the form of equivalent resistance and equivalent inductance in series. eq The specific form is as follows:

[0031] Z eq =R eq +sL eq

[0032] In the formula, R eq and L eq Z eq The equivalent resistance and equivalent inductance;

[0033] 4) Obtain the equivalent negative resistance R of the constant power load by measuring the power and DC voltage information of the constant power load on-site. p By combining the equivalent RL circuit model of the balancing unit, the line impedance, and the output capacitor, the reduced-order total impedance Z of the entire DC microgrid system is obtained. total,eq The specific form is as follows:

[0034]

[0035] In the formula, C dc A capacitor is connected in parallel at the common busbar;

[0036] 5) Calculate the reduced-order total impedance Z total,eq The eigenvalues ​​are used to obtain the imaginary part of the high-frequency dominant mode, i.e., the estimated value of the dominant high-frequency oscillation frequency ω. est (k), and calculate the frequency difference Δω(k)=ω(k)-ω est (k);

[0037] 6) If Δω(k) is less than the frequency cutoff error ε, then the frequency estimate ω est If (k) represents the frequency point where the system may have a high-frequency oscillation risk, the iteration terminates and this value is output; otherwise, the value of ω(k+1) is updated to be the current oscillation frequency ω(k) and the frequency increment Δω at a fixed step size. step The sum, plus the iteration count k;

[0038] 7) If ω(k+1) does not exceed the preset range of the high-frequency dominant oscillation frequency ω(k), then return to step 3); if ω(k+1) exceeds the preset range of the high-frequency dominant oscillation frequency ω(k), then reset the high-frequency dominant oscillation frequency ω(k) and return to step 2.

[0039] Part Three, Model Reconstruction, the method is as follows:

[0040] Using the identified dominant high-frequency oscillation frequency estimate ω est (k) The impedance model of the balancing unit is reduced in order to obtain the equivalent RL circuit model of the balancing unit at this frequency. Combined with the equivalent circuit model of the constant power load, the reduced-order equivalent circuit model of the DC microgrid is obtained.

[0041] Part Four, Risk Assessment, the methods are as follows:

[0042] Based on the reduced-order equivalent circuit model of the reconstructed DC microgrid, the high-frequency oscillation stability risk of the system is assessed from the perspective of equivalent circuit. The impact of the sub-modules on the high-frequency stability of the system is quantitatively evaluated by physical parameters such as the equivalent resistance and equivalent inductance of the balancing unit and the constant power load sub-module.

[0043] Furthermore, for the modeling of type ② equipment where the physical and control structures are known, but some parameter information is unknown, the method is as follows:

[0044] Derivation and establishment of the polynomial equivalent impedance model Z for this type of device with unknown parameters T At this time, the DC voltage at the equipment outlet is dynamically expressed as follows:

[0045]

[0046] In the formula, a1, a2, ..., a m and b1, b2, ..., b n These represent parameters whose information is unknown in the device, Δu T and Δi T G1(s) and G2(s) represent the changes in DC voltage and output current at the device port, respectively. G1(s) and G2(s) represent polynomials with constant coefficients. Since the physical and control structure of this "black box" device is known, m and n are both deterministic constant values.

[0047] Online measurement equipment ports include electrical information such as DC voltage and output current, and are designed for the polynomial equivalent impedance model Z. T Based on optimization theory, the unknown parameters are identified and estimated. The objective function of this optimization problem is:

[0048]

[0049] In the formula, a 1,est a 2,est , ..., a m,est and b 1,est b 2,est , ..., b n,est These represent the estimated values ​​of the unknown parameters in the device, Δu and Δu, respectively. T,i This represents a DC voltage sequence with equal time intervals within a time period T after the disturbance. The DC voltage sequence corresponding to the time period is obtained from the estimation model, where k is the total number of DC voltage measurements within the time period T. The estimation model is shown below:

[0050]

[0051] Based on the above estimation method, the specific numerical information of the unknown parameters in the device is identified, and then the equivalent impedance model of the "black box" device with known parameters is obtained.

[0052] Furthermore, for modeling type ③ equipment whose physical and control structures and parameter information are completely unknown, the method is as follows:

[0053] For a "black box" device whose physical and control structures and parameter information are completely unknown, the equivalent impedance model Z of this "black box" device is... T The order is unknown, meaning the parameters m and n of the numerator and denominator are unknown. In this case, the aforementioned method is still used: online measurement of the DC voltage and current information at the device's ports; the order of its equivalent impedance model is pre-set, i.e., the values ​​of m and n are set; fitting is performed based on optimization theory; and the order of the equivalent impedance model is continuously adjusted according to the fitting results. When the fitting results match the actual dynamics of the "black box" device, the values ​​of m and n are finally determined, and the equivalent impedance model of the "black box" device is obtained. Attached Figure Description

[0054] Figure 1 DC microgrid topology;

[0055] Figure 2 Balanced cell topology and its control strategy;

[0056] Figure 3 Flowchart of a method for assessing the stability risk of high-frequency oscillations in DC microgrids;

[0057] Figure 4 Equivalent model of DC microgrid;

[0058] Figure 5 An experimental platform for DC microgrids based on RT-BOX hardware-in-the-loop;

[0059] Figure 6 Frequency identification process and results using the basic parameters in Table 1;

[0060] Figure 7 Frequency identification process and results when the droop coefficient increases from 0.5 to 1;

[0061] Figure 8 Experimental results when the droop coefficient changes

[0062] Figure 9 Frequency identification process and results when the DC voltage control proportional coefficient is increased from 0.5 to 1;

[0063] Figure 10 Experimental results when the proportional coefficient of DC voltage control changes Detailed Implementation

[0064] This invention proposes a method for assessing the high-frequency oscillation stability risk of a DC microgrid, comprising data-driven modeling, frequency identification, model reconstruction, risk assessment, and parameter optimization. 1) Data-driven modeling: Utilizing electrical information measured at device ports, a detailed impedance model of the DC microgrid is established based on optimization theory; 2) Frequency identification: Combining frequency sweeping with a reduced-order equivalent circuit model, the high-frequency oscillation frequency of the DC microgrid is estimated using frequency matching principles; 3) Model reconstruction: Using the obtained high-frequency oscillation frequency estimate, a reduced-order equivalent circuit model of the DC microgrid is reconstructed; 4) Risk assessment: The high-frequency oscillation risk of the system is assessed from the perspective of the equivalent circuit, and the impact of sub-modules on the system's high-frequency stability is quantified using physical parameters such as equivalent resistance and equivalent inductance corresponding to sub-modules such as balancing units and constant power loads; 5) Parameter optimization: Based on the high-frequency oscillation stability risk assessment results, the controller parameter optimization design is guided to improve the high-frequency stability of the DC microgrid.

[0065] The DC microgrid topology considered in this invention is as follows: Figure 1 As shown, a DC microgrid consists of balancing units, constant power loads, and DC lines. Distributed power sources and power electronic devices employing DC voltage control strategies can be considered as balancing units to maintain the stability of the common DC bus voltage and power balance. Balancing units are connected to the common DC bus via DC lines, while constant power loads are directly connected to the common bus. A balancing unit consists of a DC voltage source and a bidirectional DC-DC converter to achieve stable DC bus voltage control. In real-world scenarios, distributed power sources and power electronic devices with constant power operation characteristics can be considered as constant power loads. o C represents the DC voltage source voltage of the balancing unit. s and i s These represent the parallel capacitor at the outlet of the balancing unit and the output current; R l and L l These are the resistance and inductance of the DC line output from the balancing unit, respectively; u dc and C dc These represent the DC voltage and parallel capacitance of the common bus, respectively; P cpl and i p These represent the output power and current of a constant power load, respectively.

[0066] Balanced cell topology and its control strategy, such as Figure 2 As shown, R o and L o These are the resistance and inductance measured from the DC voltage source of the balancing unit, respectively. o It is the output current of the DC voltage source.

[0067] To maintain stable voltage and power distribution on the common DC bus, the balancing unit control system adopts a droop-based DC voltage control strategy, which includes voltage droop control and a dual-loop DC voltage / current control loop, as follows:

[0068]

[0069] In the formula, i set and u set These are the set values ​​for the output current and voltage of the balancing unit, respectively, k d k represents the droop coefficient. pu and k iu k represents the proportional and integral coefficients of the DC voltage control, respectively. pi and k ii These are the proportional and integral coefficients for the current inner loop control, i oref To represent the inner loop reference value of the current generated by the DC voltage controller, d s This indicates the output duty cycle.

[0070] (1) Risk assessment of high-frequency oscillation stability of DC microgrid

[0071] To effectively assess the high-frequency oscillation stability risk of DC microgrids, a method for assessing the high-frequency oscillation stability risk of DC microgrids is proposed, which includes data-driven modeling, frequency identification, model reconstruction, risk assessment, and parameter optimization. The flowchart of the high-frequency oscillation stability risk assessment method is shown below. Figure 3 As shown, the detailed steps are as follows:

[0072] Step 1: Data-driven modeling. The specific implementation method is as follows:

[0073] Based on the information obtained, all devices in the system can be divided into three categories: ① Devices with known physical and control structures but some unknown parameters; ② Devices with completely unknown physical and control structures and parameters; ③ Devices with completely known physical and control structures and parameters. For the third category of "white-box" devices with completely known information, their equivalent impedance models can be directly derived and established. For the first two categories of "black-box" devices with partially or completely unknown information, a data-driven modeling method can be used. The basic modeling approach for the three types of devices is as follows.

[0074] (1) The physical and control structure and parameter information of the equipment are known. Impedance modeling method can be used to directly obtain... Figure 4 (a) shows the detailed impedance model of the DC microgrid. Where Z... u This represents the detailed equivalent output impedance of the balancing unit. R p The equivalent negative resistance of a constant power load is represented in the following form:

[0075]

[0076] In the formula, U dc This represents the steady-state value of the DC voltage of the common bus.

[0077] (2) The physical and control structure of the equipment is known, but some parameter information is unknown.

[0078] First, a polynomial equivalent impedance model Z for the device, containing unknown parameters, can be derived and established. T At this time, the dynamic DC voltage output of the equipment can be expressed as follows:

[0079]

[0080] In the formula, a1, a2, ..., a m and b1, b2, ..., b n These represent parameters whose information is unknown in the device, Δu T and Δi T G1(s) and G2(s) represent the changes in DC voltage and output current at the device's ports, respectively. G1(s) and G2(s) represent polynomials with constant coefficients. Since the physical and control structure of this "black box" device is known, m and n are both deterministic constant values.

[0081] Secondly, online measurement of electrical information such as DC voltage and output current at the device port is performed on the equivalent impedance model Z in polynomial form shown in equation (3). T Based on optimization theory methods (steepest descent method, Newton's method, etc.), the unknown parameters are identified and estimated. The objective function of this optimization problem is:

[0082]

[0083] In the formula, a 1,est a 2,est , ..., a m,est and b 1,est b 2,est , ..., b n,est These represent the estimated values ​​of the unknown parameters in the device, Δu and Δu, respectively. T,i This represents a DC voltage sequence with equal time intervals within a time period T after the disturbance. The DC voltage sequence corresponding to the time period is obtained from the estimation model, where k is the total number of DC voltage sequences measured within the time period T. The estimation model is shown in equation (5):

[0084]

[0085] Based on the above estimation method, the specific numerical information of the unknown parameters in the device can be identified, and then the equivalent impedance model of the "black box" device with completely known parameters can be obtained.

[0086] (3) The physical and control structure and parameter information of the equipment are completely unknown.

[0087] For a "black box" device whose physical and control structures and parameter information are completely unknown, the equivalent impedance model Z of this "black box" device is... T The order is unknown, that is, the parameters m and n of the numerator and denominator in equation (3) are unknown. At this time, a similar fitting method can still be adopted to measure the DC voltage and current information of the device port online, pre-set the order value of its equivalent impedance model (the values ​​of m and n), perform fitting based on the optimization theory, and continuously adjust the order of the equivalent impedance model (the values ​​of m and n) according to the fitting results. When the fitting results are in good agreement with the actual dynamics of the "black box" device, the values ​​of m and n can be finally determined, and the equivalent impedance model of the "black box" device can be obtained.

[0088] Based on the above data-driven modeling approach, we can finally obtain Figure 4 (a) shows a detailed impedance model of a DC microgrid. However, using Figure 4 (a) Detailed models can only analyze the impact of system physical parameters and control parameters on system stability by passively observing the amplitude and phase characteristics of source-load output / input impedance or the Nyquist curve transformation law. It is difficult to quantitatively assess the degree of high-frequency stability risk of DC microgrids from a mechanistic perspective. Therefore, based on the aforementioned data-driven modeling, we will further identify the dominant high-frequency oscillation frequency of the system to reduce the model order.

[0089] Step 2: Frequency Identification. The specific implementation method is as follows:

[0090] 1) Set the initial value ω(1) of the dominant high-frequency oscillation frequency ω(k) and its range of variation, and set the number of iterations k = 1;

[0091] 2) At the set dominant high-frequency oscillation frequency ω(k), the detailed output impedance Z of the balancing unit is adjusted. ui To reduce the order, substitute s = jω(k) into the equivalent impedance Z of the balancing element. u The equivalent impedance Z is obtained. u The frequency domain form of jω(k) = s is then taken back and combined with the line impedance to obtain the reduced-order equivalent impedance Z in the series form of the balanced unit RL. eq The specific form is as follows;

[0092] Z eq =R eq +sL eq (6)

[0093] In the formula, R eq and L eq Z eq The equivalent resistance and equivalent inductance.

[0094] 3) The equivalent negative resistance of the constant power load is obtained by measuring the power and DC voltage information of the constant power load on-site. Combined with the equivalent RL circuit model of the balancing unit, the line impedance, and the output capacitor, the reduced-order total impedance Z of the entire DC microgrid system is obtained. total,eq The specific form is as follows:

[0095]

[0096] 4) Calculate the reduced-order total impedance Z total,eq The eigenvalues ​​are used to obtain the estimated value ω of the imaginary part (i.e., the high-frequency oscillation frequency) of the high-frequency dominant mode. est (k), and calculate the frequency difference Δω(k)=ω(k)-ω est (k);

[0097] 5) If Δω(k) is less than the frequency cutoff error ε, then the frequency estimate ω est (k) represents the frequency point where the system may have a high-frequency oscillation risk, and this value is output; otherwise, the value of ω(k+1) is updated to be the current oscillation frequency ω(k) and the frequency increment Δω at a fixed step size. step The sum is incremented by 1 for each iteration.

[0098] 6) If ω(k+1) does not exceed the preset range, return to step 2), reset the initial frequency value and range, and continue with the subsequent steps; if ω(k+1) exceeds the preset range, return to step 1), reset the initial frequency value and range, and continue with the subsequent steps.

[0099] Step 3: Model Reconstruction. Drawing on the modeling method of the inventor's previous patent

[12] , the dominant high-frequency oscillation frequency estimate ω obtained from the identification is used. est (k) At the estimated dominant high-frequency oscillation frequency, the impedance model of the balancing unit is reduced in order through frequency domain transformation, preserving the frequency characteristics near the dominant high-frequency mode of the balancing unit. This yields the equivalent RL circuit model of the balancing unit at the dominant high-frequency oscillation frequency, and, combined with the equivalent circuit model of the constant power load, the reduced-order equivalent circuit model of the entire system is obtained, as follows: Figure 4 As shown in (b).

[0100] Step 4: Risk Assessment. Based on the reduced-order equivalent circuit model of the system obtained from the reconstruction, the risk of high-frequency oscillation of the system can be assessed from the perspective of the equivalent circuit. The impact of sub-modules on the high-frequency stability of the system can be quantitatively analyzed by using physical parameters such as the equivalent resistance and equivalent inductance of sub-modules such as balancing units and constant power loads.

[0101] Furthermore, according to the equivalent total parallel impedance Z total,eq Furthermore, the pole expression of a DC microgrid can be obtained as follows:

[0102]

[0103] For a DC microgrid to be stable, the real part of the poles must be less than 0. Therefore, the following criterion must be satisfied:

[0104]

[0105] In the formula, θ1 and θ2 are two criterion factors for stability. When both θ1 and θ2 are greater than 0, the DC microgrid is stable. Therefore, θ1 and θ2 can be used to assess the stability risk of high-frequency oscillations in the system.

[0106] Step 5: Parameter Optimization. Based on the high-frequency oscillation stability risk assessment results, guide the design of controller parameters for optimization, thereby improving the high-frequency stability of the DC microgrid.

[0107] (2) Analysis and Verification

[0108] To verify the effectiveness of the proposed high-frequency oscillation stability risk assessment method for DC microgrids, a system was built as follows: Figure 5 The experimental platform for DC microgrids based on RT-BOX hardware-in-the-loop is shown below. The detailed system topology is as follows: Figure 1 As shown in Table 1, the basic parameters are as follows. Verification and analysis will then be conducted under different operating conditions.

[0109] Table 1 Basic Parameters of DC Microgrids

[0110]

[0111] 1) Effect of droop coefficient

[0112] To verify the effectiveness of the proposed risk assessment method when the droop coefficient changes, the proposed method was applied to evaluate and analyze the following operating conditions. Case 1: Using the basic system parameters shown in Table 1; Case 2: Droop coefficient k d Increase from 0.5 to 1. Fixed step size frequency increment Δω step The frequency is set to 50 rad / s, and the frequency cutoff error ε is set to 50 rad / s. The frequency identification process and results under the two operating conditions are as follows: Figure 6 and Figure 7 As shown. By Figure 6 As can be seen, using the basic parameters in Table 1, after 16 iterations, the frequency deviation is less than the set frequency cutoff error ε, and the frequency estimate eventually converges to 2180 rad / s. Similarly, from... Figure 7 We can obtain the droop coefficient k. d When the value is increased to 1, after 14 iterations, the frequency deviation is less than the set frequency cutoff error ε, and the frequency estimate finally converges to 2234 rad / s. As can be seen above, the proposed method can effectively identify the frequency estimation results under different operating conditions after multiple iterations.

[0113] Using the estimated high-frequency oscillation values ​​of the system obtained by the above parameter identification, the reduced-order equivalent circuit model of the DC microgrid under different operating conditions is reconstructed, and then the corresponding equivalent resistance, equivalent inductance, and stability criterion factors θ1 and θ2 parameters are solved, as shown in Table 2.

[0114] Table 2. Calculation results of system stability-related parameters when the droop coefficient changes.

[0115]

[0116] Table 2 and the high-frequency stability criterion for DC microgrids show that when the droop coefficient increases from 0.5 to 1, the equivalent resistance in the equivalent circuit model of the balancing unit decreases from 0.018Ω to -0.0124Ω, and the stability criterion factor θ1 changes from positive to negative, causing high-frequency oscillations in the DC microgrid. Therefore, increasing the droop coefficient enhances the equivalent negative resistance characteristic of the balancing unit, leading to high-frequency oscillations in the system. Thus, reducing the droop coefficient weakens the equivalent negative resistance characteristic of the balancing unit, thereby enhancing the high-frequency stability of the entire system.

[0117] To further verify the effectiveness of the high-frequency oscillation risk assessment method when the droop coefficient changes, in situations such as... Figure 5 The experimental verification was carried out using the RT-BOX hardware-in-the-loop DC microgrid experimental platform shown.

[0118] With droop coefficients of 0.5 and 1 respectively, and a sudden increase in constant power load at time t, the dynamic experimental results of the DC bus voltage are as follows: Figure 8 As shown in (a) and (b), the droop coefficient k d When k = 0.5, the DC bus voltage quickly recovers to stability after a brief fluctuation following a load disturbance. This is achieved when the droop coefficient k... d When =1, the DC bus voltage oscillates at high frequency after being disturbed. The experimental results are basically consistent with the theoretical analysis results above, which verifies the effectiveness of the proposed risk assessment method.

[0119] It is evident that the proposed risk assessment method can effectively assess the risk of high-frequency oscillation in the system from the perspective of equivalent circuits, identify the high-frequency oscillation frequency, and quantitatively analyze the impact of system parameters on high-frequency oscillation stability through the equivalent resistance and equivalent inductance of the proposed reduced-order model. This, in turn, guides the optimization of controller parameters and improves the high-frequency stability of DC microgrids.

[0120] 2) Influence of DC voltage control proportional coefficient

[0121] To verify the effectiveness of the proposed risk assessment method when the DC voltage control proportional coefficient changes, the method was applied to evaluate and analyze the following operating conditions. Case 1: Using the system basic parameters shown in Table 1; Case 3: DC voltage control proportional coefficient kpu Increase from 0.5 to 1. Fixed step size frequency increment Δω step Set to 50 rad / s, and the frequency cutoff error ε is set to 50 rad / s. Case 3: DC voltage control proportional coefficient k pu The frequency identification process and results when the value is increased from 0.5 to 1 are as follows: Figure 9 As shown. See the results for Case 1. Figure 6 .Depend on Figure 9 It can be seen that the DC voltage control proportional coefficient k pu When the value is increased to 1, after 15 iterations, the frequency deviation is less than the set frequency cutoff error ε, and the frequency estimate finally converges to 2247 rad / s rad / s.

[0122] Using the estimated high-frequency oscillation values ​​of the system obtained by the above parameter identification, the reduced-order equivalent circuit model of the DC microgrid under different operating conditions is reconstructed, and then the corresponding equivalent resistance, equivalent inductance, and stability criterion factors θ1 and θ2 parameters are solved, as shown in Table 3.

[0123] Table 3. Calculation results of system stability-related parameters when the DC voltage control proportional coefficient changes.

[0124]

[0125] As shown in Table 3, when the DC voltage control proportional coefficient increases from 0.5 to 1, the equivalent resistance in the equivalent circuit model of the balancing unit decreases from 0.018Ω to -0.0008Ω, the stability criterion factor θ1 changes from positive to negative, and the DC microgrid experiences high-frequency oscillations. Therefore, increasing the DC voltage control proportional coefficient enhances the equivalent negative resistance characteristic of the balancing unit, causing high-frequency oscillations in the system. Thus, reducing the DC voltage control proportional coefficient can weaken the equivalent negative resistance characteristic of the balancing unit, thereby enhancing the high-frequency stability of the entire system.

[0126] To further verify the effectiveness of the high-frequency oscillation risk assessment method when the DC voltage control proportional coefficient changes, in the case of... Figure 5 Experimental verification was performed using a hardware-in-the-loop DC microgrid experimental platform based on the RT-BOX shown. The DC voltage control proportional coefficient k was taken respectively. pu Equal to 0.5 and 1, at time t, the constant power load suddenly increases, and the dynamic DC bus voltage is as follows: Figure 10 As shown in (a) and (b), the DC voltage control proportional coefficient k... pu When k = 0.5, the DC bus voltage quickly recovers to stability after a brief fluctuation following a load disturbance. puWhen = 1, the disturbed DC bus voltage oscillates at a high frequency with a period of approximately 2.84 ms (corresponding to an oscillation frequency of approximately 2212 rad / s), which is almost consistent with the theoretical calculation result of 2247 rad / s mentioned above. The experimental results are consistent with the theoretical analysis results mentioned above, verifying the effectiveness of the proposed risk assessment method.

[0127] It is evident that the proposed risk assessment method can effectively assess the risk of high-frequency oscillation in the system from the perspective of equivalent circuits, identify the high-frequency oscillation frequency, and evaluate the influence of system parameters on high-frequency oscillation stability through the equivalent resistance and equivalent inductance of the proposed reduced-order model. This, in turn, guides the optimization of controller parameters and improves the high-frequency stability of DC microgrids.

Claims

1. A method for assessing the high-frequency oscillation stability risk of a DC microgrid, wherein the DC microgrid includes a balancing unit, a constant power load, and a DC line; the balancing unit includes distributed power sources employing a DC voltage control strategy and power electronic devices to maintain the voltage stability and power balance of the common DC bus; the constant power load includes distributed power sources and power electronic devices with constant power operation characteristics; characterized in that... The method for assessing the stability risk of high-frequency oscillations in DC microgrids includes data-driven modeling, frequency identification, model reconstruction, and risk assessment. Part One, Data-Driven Modeling, uses the following methods: Based on the information obtained, all devices in the system are divided into the following three categories: ① Devices with known physical and control structures but some unknown parameters; ② Devices with completely unknown physical and control structures and parameters; ③ Devices with completely known physical and control structures and parameters. For the third category of "white box" devices with completely known information, their equivalent impedance models are directly derived and established. For the first two categories of "black box" devices with partially or completely unknown information, a data-driven modeling approach is adopted to establish impedance models for balancing units and constant power load devices, respectively, to obtain the impedance model of the DC microgrid. Part Two, Frequency Identification, the method is as follows: 1) Set the high-frequency dominant oscillation frequency ω(k); 2) Set the range of the high-frequency dominant oscillation frequency ω(k) and its initial value ω(1), and set the number of iterations k = 1; 3) At the set dominant high-frequency oscillation frequency ω(k), the output impedance of the balancing unit is reduced in order, and further combined with the line impedance to obtain the reduced-order equivalent impedance Z of the balancing unit in the form of equivalent resistance and equivalent inductance in series. eq The specific form is as follows: Z eq =R eq +sL eq In the formula, R eq and L eq Z eq The equivalent resistance and equivalent inductance; 4) Obtain the equivalent negative resistance R of the constant power load by measuring the power and DC voltage information of the constant power load on-site. p By combining the equivalent RL circuit model of the balancing unit, the line impedance, and the output capacitor, the reduced-order total impedance Z of the entire DC microgrid system is obtained. total,eq The specific form is as follows: In the formula, C dc A capacitor is connected in parallel at the common busbar; 5) Calculate the reduced-order total impedance Z total,eq The eigenvalues ​​are used to obtain the imaginary part of the high-frequency dominant mode, i.e., the estimated value of the dominant high-frequency oscillation frequency ω. est (k), and calculate the frequency difference Δω(k)=ω(k)-ω est (k); 6) If Δω(k) is less than the frequency cutoff error ε, then the frequency estimate ω est If (k) represents the frequency point where the system may have a high-frequency oscillation risk, the iteration terminates and this value is output; otherwise, the value of ω(k+1) is updated to be the current oscillation frequency ω(k) and the frequency increment Δω at a fixed step size. step The sum, plus the iteration count k; 7) If ω(k+1) does not exceed the preset range of the high-frequency dominant oscillation frequency ω(k), then return to step 3); if ω(k+1) exceeds the preset range of the high-frequency dominant oscillation frequency ω(k), then reset the high-frequency dominant oscillation frequency ω(k) and return to step 2. Part Three, Model Reconstruction, the method is as follows: Using the identified dominant high-frequency oscillation frequency estimate ω est (k) The impedance model of the balancing unit is reduced in order to obtain the equivalent RL circuit model of the balancing unit at this frequency. Combined with the equivalent circuit model of the constant power load, the reduced-order equivalent circuit model of the DC microgrid is obtained. Part Four, Risk Assessment, the methods are as follows: Based on the reduced-order equivalent circuit model of the reconstructed DC microgrid, the high-frequency oscillation stability risk of the system is assessed from the perspective of equivalent circuit. The impact of the sub-modules on the high-frequency stability of the system is quantitatively evaluated by physical parameters such as the equivalent resistance and equivalent inductance of the balancing unit and the constant power load sub-module.

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