Probability stability analysis method and device for flexible direct current interconnection system

Abstract

The invention relates to a probability stability analysis method and device for a flexible direct current interconnection system, and the method comprises the steps: modeling each part in a low-voltage flexible interconnection system into a port admittance capable of reflecting the internal dynamic and external interaction characteristics, establishing a low-voltage flexible direct-current interconnection system source-load admittance model for the grid-connected inverter and the electric vehicle charging station; substituting the source-load admittance model of the low-voltage flexible direct-current interconnection system into an s-domain node admittance matrix, and obtaining an oscillation mode of the low-voltage flexible interconnection system by solving determinant zero points of the s-domain node admittance matrix; and based on the oscillation mode of the low-voltage flexible interconnection system, determining a relational expression between a moment output by the low-voltage flexible interconnection system and a cumulant by using a point estimation method, and expanding the relational expression by using a series expansion method to obtain a probability density of an oscillation mode real part of the low-voltage flexible interconnection system. According to the invention, the broadband oscillation of the low-voltage flexible direct-current interconnection system can be accurately and comprehensively analyzed.

Description

Technical Field

[0001] The present invention relates to the technical field of low-voltage AC / DC hybrid power distribution, and in particular to a probabilistic stability analysis method and device for a flexible DC interconnection system. Background Art

[0002] The use of flexible DC technology to interconnect and supply multiple substations with complementary temporal and spatial characteristics of loads between low-voltage distribution stations is a new solution to improve the power supply capacity and quality of low-voltage distribution networks.

[0003] In actual operation, the integration of power electronic equipment and new loads introduces operational characteristics of source and load volatility and spatiotemporal randomness, impacting the stable operation of existing distribution networks. Without probabilistic assessment and proactive control of operational scenarios, broadband oscillations can occur, leading to power outages and equipment damage. Therefore, studying the probabilistic stability analysis theory of flexible interconnected devices under multiple random perturbations has become a key technical issue that urgently needs to be overcome to ensure the safe and reliable operation of new power electronic distribution networks. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a probabilistic stability analysis method and device for a flexible DC interconnection system, which can accurately and comprehensively analyze the broadband oscillation of a low-voltage flexible DC interconnection system.

[0005] The technical solution adopted by the present invention to solve the technical problem is to provide a probabilistic stability analysis method for a flexible DC interconnection system, comprising the following steps:

[0006] Each component in the low-voltage flexible interconnection system is modeled as a port admittance that can reflect its internal dynamic and external interactive characteristics. A source-load admittance model of the low-voltage flexible DC interconnection system is established for the grid-connected inverter and electric vehicle charging station.

[0007] Substituting the source-load admittance model of the low-voltage flexible DC interconnection system into the s-domain node admittance matrix, and obtaining the oscillation mode of the low-voltage flexible interconnection system by solving the determinant zero point of the s-domain node admittance matrix;

[0008] Based on the oscillation mode of the low-voltage flexible interconnection system, a point estimation method is used to determine the relationship between the moment and the cumulative output of the low-voltage flexible interconnection system. The relationship is then expanded using a series expansion method to obtain the probability density of the real part of the oscillation mode of the low-voltage flexible interconnection system.

[0009] The source-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system is expressed as: Among them, Y source is the source side admittance of the low voltage flexible DC interconnection system, Y VSCis the DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system, C dc is the parallel filter capacitor on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, Z line is the line impedance on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0010] The DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system is expressed as: Among them, V dc is the steady-state voltage value of the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq Represents the component of the output duty cycle in the dq synchronous rotating coordinate system, Z g is the AC grid impedance, expressed as: Z L is the AC line impedance, expressed as: L g 、R g Represent the grid inductance and resistance respectively, L and R represent the AC line inductance and resistance respectively, ω1 represents the constant speed of the coordinate system, G vi To control the influence of the link on the system admittance, the inverter constant voltage control G vi =H i H v , when the inverter is in constant power control G vi =I,H i is the current PI control loop, H v is the voltage PI control loop, I represents the unit matrix, and G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as: H i is the current PI control loop transfer function, G PLL Represents the phase-locked loop PI control link, I d and I q The steady-state values of the current under the d-axis and q-axis, D d and D q Represents the steady-state value of the duty cycle under the d-axis and q-axis respectively, V d and V q They represent the steady-state values of the voltage on the d-axis and q-axis, respectively, and ω represents the steady-state value of the angular velocity.

[0011] The load-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system is expressed as: load =Y EVCS +sC L , where Y load is the load-side admittance of the low-voltage flexible DC interconnection system, Y EVCSis the admittance of the electric vehicle charging station, C L is the parallel filter capacitor on the DC side of the electric vehicle charging station in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0012] The admittance of the electric vehicle charging station is expressed as: D dc0 Represents the steady-state value of the duty cycle, I L0 Indicates the steady-state value of the inductor current, H idc is the constant current control transfer function, L d is the energy storage inductor of the converter in the electric vehicle charging station, V EVCS0 Indicates the DC input voltage, R d is the low voltage DC circuit damping resistor in the electric vehicle charging station, C d It is the voltage stabilizing capacitor of the converter in the electric vehicle charging station.

[0013] The electric vehicle charging station power in the S-domain node admittance matrix should be modeled probabilistically.

[0014] When determining the relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system using the point estimation method, the power of the electric vehicle charging station is used as an input sample, and the real part of the oscillation mode of the low-voltage flexible interconnection system is used as an output sample.

[0015] The relationship is expressed as: Among them, m ik is the k-th order moment output by the low voltage flexible interconnection system, γ k It is the cumulative amount corresponding to the k-th order moment output by the low voltage flexible interconnection system.

[0016] When the relational expression is expanded using the series expansion method, the relational expression is expanded using the Cornish-Fisher series expansion method.

[0017] The technical solution adopted by the present invention to solve the technical problem is to provide a probabilistic stability analysis device for a flexible DC interconnection system, comprising:

[0018] Establish a module for modeling each component in the low-voltage flexible interconnection system as a port admittance that can reflect the inherent dynamic and external interactive characteristics, and establish a low-voltage flexible DC interconnection system source-load admittance model for grid-connected inverters and electric vehicle charging stations;

[0019] A solution module is introduced to bring the source-load admittance model of the low-voltage flexible DC interconnection system into the S-domain node admittance matrix, and obtain the oscillation mode of the low-voltage flexible interconnection system by solving the determinant zero point of the S-domain node admittance matrix;

[0020] An estimation and expansion module is configured to determine, based on the oscillation mode of the low-voltage flexible interconnection system, a relationship between a moment and a cumulative amount output by the low-voltage flexible interconnection system using a point estimation method, and expand the relationship using a series expansion method to obtain a probability density of a real part of the oscillation mode of the low-voltage flexible interconnection system.

[0021] The source-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: Among them, Y source is the source side admittance of the low voltage flexible DC interconnection system, Y VSC is the DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system, C dc is the parallel filter capacitor on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, Z line is the line impedance on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0022] The DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system is expressed as: Among them, V dc is the steady-state voltage value of the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq Represents the component of the output duty cycle in the dq synchronous rotating coordinate system, Z g is the AC grid impedance, expressed as: Z L is the AC line impedance, expressed as: L g 、R g Represent the grid inductance and resistance respectively, L and R represent the AC line inductance and resistance respectively, ω1 represents the constant speed of the coordinate system, G vi To control the influence of the link on the system admittance, the inverter constant voltage control G vi =H i H v , when the inverter is in constant power control G vi =I,H i is the current PI control loop, H v is the voltage PI control loop, I represents the unit matrix, and G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as: H i is the current PI control loop transfer function, G PLL Represents the phase-locked loop PI control link, I d and I q The steady-state values of the current under the d-axis and q-axis, D d and D qRepresents the steady-state value of the duty cycle under the d-axis and q-axis respectively, V d and V q They represent the steady-state values of the voltage on the d-axis and q-axis, respectively, and ω represents the steady-state value of the angular velocity.

[0023] The load-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: load =Y EVCS +sC L , where Y load is the load-side admittance of the low-voltage flexible DC interconnection system, Y EVCS is the admittance of the electric vehicle charging station, C L is the parallel filter capacitor on the DC side of the electric vehicle charging station in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0024] The admittance of the electric vehicle charging station is expressed as: D dc0 Represents the steady-state value of the duty cycle, I L0 Indicates the steady-state value of the inductor current, H idc is the constant current control transfer function, L d is the energy storage inductor of the converter in the electric vehicle charging station, V EVCS0 Indicates the DC input voltage, R d is the low voltage DC circuit damping resistor in the electric vehicle charging station, C d It is the voltage stabilizing capacitor of the converter in the electric vehicle charging station.

[0025] The electric vehicle charging station power in the S-domain node admittance matrix should be modeled probabilistically.

[0026] When the estimation expansion module uses the point estimation method to determine the relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system, the power of the electric vehicle charging station is used as an input sample and the real part of the oscillation mode of the low-voltage flexible interconnection system is used as an output sample.

[0027] The relationship is expressed as: Among them, m ik is the k-th order moment output by the low voltage flexible interconnection system, γ k It is the cumulative amount corresponding to the k-th order moment output by the low voltage flexible interconnection system.

[0028] When the estimation expansion module uses the series expansion method to expand the relational expression, the Cornish-Fisher series expansion method is used to expand the relational expression.

[0029] The technical solution adopted by the present invention to solve its technical problem is: providing an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein when the processor executes the computer program, the steps of the probabilistic stability analysis method of the flexible DC interconnection system are implemented.

[0030] The technical solution adopted by the present invention to solve its technical problem is: providing a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the probabilistic stability analysis method of the flexible DC interconnection system are implemented.

[0031] Beneficial effects

[0032] Due to the adoption of the above-mentioned technical solution, the present invention has the following advantages and positive effects compared with the prior art: The present invention proposes a probabilistic small-signal stability analysis method, which combines the point estimation method based on the s-domain node admittance matrix to obtain the probability information of the system, and uses the Cornish-Fisher extension method to accurately fit the probability function. This method achieves higher prediction accuracy with a smaller amount of calculation, is easy to implement and has strong practicality, and provides a new idea for the stability analysis of interconnected devices in uncertain environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 4 is a flow chart of a probabilistic stability analysis method for a flexible DC interconnection system according to a first embodiment of the present invention;

[0034] Figure 2 Schematic diagram of the basic structure and control links of the VSC in the low-voltage flexible interconnection system in the first embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of the basic structure and control links of an electric vehicle charging station in a low-voltage flexible interconnection system in the first embodiment of the present invention;

[0036] Figure 4 Schematic diagram of the basic structure of the three-substation low-voltage flexible DC interconnection system in the first embodiment of the present invention;

[0037] Figure 5 It is the VSC DC side admittance analytical curve and sweep frequency curve;

[0038] Figure 6 It is the DC side admittance analytical curve and frequency sweep curve of the electric vehicle charging station;

[0039] Figure 7 It is Matlab / Simulink simulation and Fourier analysis diagram;

[0040] Figure 83 is a comparison diagram of the real part probability density functions of the oscillation modes obtained by the method of the first embodiment of the present invention and the Monte Carlo method. DETAILED DESCRIPTION

[0041] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall equally within the scope limited by the appended claims of the application.

[0042] The first embodiment of the present invention relates to a probabilistic stability analysis method for a flexible DC interconnection system, such as Figure 1 As shown, the following steps are included:

[0043] Step 1: Model each component in the low-voltage flexible interconnection system as a port admittance that can reflect the internal dynamic and external interactive characteristics, and establish a low-voltage flexible DC interconnection system source-load admittance model for the grid-connected inverter and electric vehicle charging station.

[0044] Figure 2 The basic structure and control link of the grid-connected inverter (VSC) in the low-voltage flexible interconnection system are shown. The VSC connects the AC grid and the DC distribution station. The AC line impedance between the AC port of the VSC and the common coupling point (PCC) in the system is Z L , the AC grid impedance is Z g , v dc is the VSC DC side voltage, i dc is the VSC DC side current, e abc is the VSC AC side output voltage, i abc is the VSC AC side output current, v abc is the voltage at the common coupling point; in the modeling process, s is used to represent the Laplace operator, capital letters are used to represent the steady-state values of the corresponding state variables, subscript abc represents the variables in the three-phase stationary coordinate system, and subscript dq represents the variables in the two-phase rotating coordinate system.

[0045] The VSC is synchronized with the grid through a phase-locked loop. PLL is the open-loop transfer function of the phase-locked loop. VSC adopts dual closed-loop control, with the outer loop being the DC voltage control loop, including the DC voltage PI control link H v , control the active current given value i dref The inner loop is the current control loop, which includes the PI control link H for active and reactive currents. i , current decoupling link and AC voltage feedforward link. Phase-locked loop open-loop transfer function H PLL , DC voltage PI control link H v, active and reactive current PI control link H i , and the phase-locked loop control link G PLL The expressions are:

[0046]

[0047] Where K PLLp is the phase-locked loop proportional coefficient, K PLLi is the phase-locked loop integral coefficient, K vp is the voltage control proportional coefficient, K vi is the voltage control integral coefficient, K ip is the current control proportional coefficient, K ii is the current control integral coefficient, V d Indicates the voltage value under the d-axis.

[0048] If the VSC loss is negligible, the power on the VSC AC side is equal to the power on the DC side, that is:

[0049]

[0050] Among them, p dc is the VSC DC side power, e dq is the VSC AC side output voltage, i dq is the VSC AC side output current.

[0051] The relationship between the VSC AC side output voltage, output current, AC line impedance, and grid impedance is:

[0052] e dq =(Z g +Z L )i dq +v gdq (6)

[0053] Where, v gdq Indicates the VSC AC side output voltage; Z g is the AC grid impedance, expressed as:

[0054]

[0055] Where, L g 、R g They represent the grid inductance and resistance under weak grid conditions, and ω1 represents the constant speed of the coordinate system. L is the AC line impedance, expressed as:

[0056]

[0057] Where L and R represent the inductance and resistance of the AC line, respectively.

[0058] Taking a small signal on the AC side, we get:

[0059] Δe dq =(Z g +Z L )Δi dq (9)

[0060] Where Δe dq is the small output voltage signal of the VSC AC side, Δi dq It is the small output current signal of the VSC AC side.

[0061] The small signal relationship between DC power and voltage is:

[0062]

[0063] Where Δp dc is the VSC DC side power small signal, V dc is the steady-state voltage value of the DC side of the grid-connected inverter, I dq I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq It represents the component of the output duty cycle in the dq synchronous rotating coordinate system, H i is the current PI control loop, Δv dc is the small signal of the VSC DC side voltage.

[0064] The DC side admittance of the VSC in the low voltage flexible DC interconnection system can be expressed as:

[0065]

[0066] Where G vi To control the influence of the link on the system admittance, the inverter constant voltage control G vi =H i H v , when the inverter is in constant power control G vi =I,H v is the voltage PI control loop, I represents the unit matrix, and G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as:

[0067]

[0068] Figure 2 The basic structure and control links of the electric vehicle charging station in the low-voltage flexible interconnection system are demonstrated. The charging voltage of the electric vehicle charging station is obtained from the DC bus by the DC / DC inverter. The topology structure is equivalent to the step-down DC / DC converter circuit. The power flow is transmitted from the low-voltage DC port to the high-voltage DC port. Figure 2The basic structure and control links of electric vehicle charging station are shown. d is the low voltage DC circuit damping resistance, L d is the energy storage inductor of the converter, C d is the voltage stabilizing capacitor of the converter, V o is the voltage across the capacitor, V i is the converter input voltage, V EVCS is the DC bus voltage, I EVCS is the DC bus current, I L is the inductor current of the bidirectional DC / DC converter, I o is the low voltage DC output current, I c is the capacitor branch current, I Lref is the inductor current reference value, H idc is the constant current control transfer function, D dc is the constant current control output duty cycle.

[0069] The small signal expression for an electric vehicle charging station is as follows:

[0070] D dc0 ΔV EVCS0 +ΔD dc ·V EVCS0 -ΔV o =sL d ΔI L (13)

[0071] sC d ΔV o =ΔI L -ΔI o (14)

[0072] Among them, D dc0 Represents the steady-state value of the duty cycle, ΔV EVCS0 Indicates the DC input voltage small signal, ΔD dc It is a small signal with constant current control output duty cycle, V EVCS0 Indicates the DC input voltage, ΔV o is the small voltage signal across the capacitor, ΔI L It is the small signal of the inductor current of the bidirectional DC / DC converter.

[0073] The control link of the electric vehicle charging station can be expressed as:

[0074] ΔD dc =-H idc ΔI L (15)

[0075] After eliminating the energy storage inductor current, the electric vehicle charging station admittance is as follows:

[0076]

[0077] Figure 3 The topology of the three-station low-voltage flexible DC interconnection system is shown. The three distribution substations are connected to the DC bus through VSC1, VSC2 and VSC3. The VSC DC port is connected to the DC bus through capacitor C dc Parallel filtering, Z line is the DC line impedance between the VSC DC port and the DC bus; the DC port of the electric vehicle charging station is connected to the capacitor C L Parallel filtering. Z dcline = is the DC line impedance between distribution substations. VSC1 is connected to the master station and uses a constant DC voltage control strategy to provide voltage support. VSC2 and VSC3 are connected to the slave stations and use a constant power control strategy to present a constant power load characteristic.

[0078] The admittance model of the source side of the distribution area of each station (i.e., the source side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system) is as follows:

[0079]

[0080] The load-side admittance model of each station's distribution area (i.e., the load-side admittance model in the source-load admittance model of the LV HVDC flexible interconnection system) is as follows:

[0081] Y load =Y EVCS +sC L (18)

[0082] Step 2: Substitute the source-load admittance model of the low-voltage flexible DC interconnection system into the S-domain node admittance matrix, and obtain the oscillation mode of the low-voltage flexible interconnection system by solving the determinant zero point of the S-domain node admittance matrix.

[0083] Figure 4 The low-voltage flexible DC interconnected system in the paper contains three substations. Facing the stability problem of multi-node and multi-machine systems, the S-domain node admittance matrix method can reflect the admittance information of each part of the system with the overall topological structure and characterize the physical meaning of the system.

[0084] Considering uncertainty, the EV charging station power in the node admittance matrix should be modeled probabilistically. The probability of EV charging power is primarily influenced by random factors such as EV owners' travel behavior and traffic conditions. This randomness in EV charging station load can generally be described using a normal distribution. Each EV charging station has a maximum charging capacity, and daily operation also consumes a certain amount of power. Therefore, a truncated normal distribution is developed based on the normal distribution, which is more adaptable to bounded data.

[0085]

[0086] Where Φ(P,μ,σ) is the cumulative distribution function (CDF) of the normal distribution, φ(P,μ,σ) is the probability density function (PDF) of the normal distribution, and P max and P min are the upper and lower cutoff limits, respectively.

[0087] There is a correlation between the charging power of each electric vehicle charging station, and its covariance is as follows:

[0088]

[0089] Among them, P EVi represents the charging power of the electric vehicle charging station in the i-th area, Cov(P EVi, P EVj ) indicates P EVi and P EVj The correlation between E[P EVi ] indicates P EVi The mathematical expectation of .

[0090] The covariance matrix of the electric vehicle charging stations in the Santai District low-voltage flexible DC interconnection system is as follows:

[0091]

[0092] Substituting the source-side admittance model and the load-side admittance model into the s-domain node admittance matrix, the node admittance matrix of the low-voltage flexible DC interconnection system including the electric vehicle charging station is obtained:

[0093]

[0094] By solving the determinant zeros of the node admittance matrix, the oscillation mode of the system can be obtained:

[0095]

[0096] Among them, s k is the kth pair of oscillation modes; f k is the frequency of the kth pair of oscillation modes, σ k is the damping of the kth pair of oscillation modes.

[0097] The inverse matrix of the node admittance matrix describes the relationship between the node injection current vector and the node voltage vector. By solving the zero point of the node admittance matrix, the oscillation mode of the system can be obtained. When the real part of the zero point obtained is negative, the system is considered stable. This is because the negative real part indicates that the oscillation mode of the system is decaying, that is, the system recovers to the equilibrium state from a small disturbance. When each σ kWhen it is negative, the system is stable. If the system topology and control mode change, the node admittance matrix will update the admittance equation inside the matrix, which has stronger versatility.

[0098] Step 3: Based on the oscillation mode of the low-voltage flexible interconnection system, a point estimation method is used to determine a relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system, and the series expansion method is used to expand the relationship to obtain the probability density of the real part of the oscillation mode of the low-voltage flexible interconnection system.

[0099] Based on the relationship between the EV charging station's power input and the system's oscillatory mode output, obtained from the s-domain node admittance matrix in the previous step, the point estimation method is then used. Based on the first 2m-1 order central moments of the n input variables, m discrete states of each input random variable can be independently derived. This constructs the discrete states of the m × n input random variables. Based on this, the discrete states of the corresponding output random variables are derived. In this way, the first 2m-1 order central moments of the input random variables are approximated.

[0100] In this embodiment, the input sample points are the n-dimensional power vectors P1, P2, ..., P of the electric vehicle charging station. N , where P=[P1,P2,…,P N ] T , the corresponding output samples are the real parts of the key oscillation modes σ1, σ2, ..., σ N The expectation of the output random variable E(σ) is obtained by sample approximation. The expectation of each order of each input random variable μ i and central moment m ik It can be expressed as follows.

[0101]

[0102] After repeating the calculation 2n+1 times, E(σ) can be estimated:

[0103]

[0104] in,

[0105]

[0106] Where, σ μj is the output of the system in the jth state, j = 1, 2…m; σ μ is the output of the system at μ; x ij For each input random variable, there are m discrete state values; p ij is the weight of the concentration point.

[0107] After determining the moment of the system output, the kth order moment m ik With its cumulative amount γk There are the following relationships:

[0108]

[0109] Use the Cornish-Fisher expansion to approximate and obtain the characteristics of the output random variable distribution function. The Cornish-Fisher series expansion method is expressed as follows:

[0110]

[0111] σ(θ)=(y cdf (θ) -1 (31)

[0112] Where σ is the quantile of θ; Φ is the cumulative distribution function of the normal distribution. The adjusted quantile takes into account the effects of skewness and kurtosis. The quantile is the cumulative distribution function y cdf The inverse function of is used to derive the cumulative distribution function through the adjusted quantiles. The probability density function is the derivative of the cumulative distribution function. Taking the derivative of the cumulative distribution function gives the probability density of the real part of the system's oscillation mode.

[0113] The correctness of this implementation is demonstrated below:

[0114] A small perturbation signal is injected into the device under test (DUT) and the voltage and current perturbation components at the DUT port are collected to calculate the precise admittance characteristics of the DUT port. Without injecting a small perturbation signal, the system establishes a steady-state operating point. A wide-band small perturbation signal is then injected into the DUT's DC port and the system is allowed to operate for a period of time. During the injection period, the voltage and current signals at the DUT's DC port are measured, and Fourier analysis and ratio calculation are performed to determine the wide-band DC-side admittance of the DUT's DC port.

[0115] The oscillation waveform of the unstable system is analyzed using the Fourier decomposition method and compared with the oscillation frequency calculated using the S-domain node admittance matrix model. The time domain signal to be analyzed is acquired in Matlab / Simulink, and the signal is ensured to meet the requirements for spectrum analysis.

[0116] The probability density function of the real part of the oscillation mode is fitted by the Cornish-Fisher series expansion method in this embodiment. Since the real part of the oscillation mode is in the negative part, it is a stable region. The probability density function of the negative range is integrated to obtain the stability probability of the system:

[0117]

[0118] The real part of the oscillation mode is in the positive part, which is the unstable region. Integrating the probability density function of the positive interval gives the instability probability of the system:

[0119]

[0120] This embodiment adopts the Monte Carlo method with large-scale samples as a benchmark, defines the probability distribution of input parameters in the Monte Carlo method, generates random samples, performs deterministic calculations on each sample using the s-domain node admittance matrix, and statistically outputs the distribution characteristics of the oscillation mode results.

[0121] The system stability distribution characteristics obtained by the Monte Carlo method are compared with the probability density function obtained by the Cornish-Fisher series expansion method, and the root mean square error (RMSE) is used to obtain a reference for the accuracy of the fitting.

[0122]

[0123] If RMSE PDF <∈ p ,∈ p If it is equal to 0.5, the Cornish-Fisher method is considered to be valid within the engineering error range.

[0124] In order to verify the correctness of the power oscillation suppression strategy proposed in this embodiment, a flexible interconnection device simulation platform was built in the MATLAB / Simulink environment, and the accuracy of the system in probabilistic stability modeling was compared.

[0125] Table 1 Parameters of low voltage flexible DC interconnection system

[0126]

[0127]

[0128] The operating conditions are as follows: the expected charging power of the electric vehicle charging station at node 1 is 150kW, with a standard deviation of 30kW. The expected charging power of the electric vehicle charging station at node 2 is 250kW, with a standard deviation of 60kW. The expected charging power of the electric vehicle charging station at node 3 is 200kW, with a standard deviation of 50kW.

[0129] The sweep frequency verification results of the VSC DC side and the electric vehicle charging station DC side are as follows: Figure 5 and Figure 6 As shown in the figure, the analytical curve and the frequency sweep curve are consistent, proving the accuracy of the admittance model.

[0130] The oscillation waveform of the system after instability was analyzed using Fourier analysis, and it was found that the oscillation frequency in the Matlab / Simulink time domain simulation was 202Hz. Figure 7 The DC bus voltage oscillation waveform and the results of Fourier analysis of the oscillation model for substation 1 are shown. This is consistent with the oscillation frequency calculated by the S-domain node admittance matrix model, proving the accuracy of the S-domain node admittance matrix model.

[0131] Depend on Figure 8 A comparison of the real part probability density functions of the oscillation modes obtained by the method proposed in this embodiment and the Monte Carlo method shows that the Monte Carlo method uses 5000 samples and Cornish-Fisher expansions from the second to the fourth order to compare with the Monte Carlo method, and the probability density function curves are basically consistent.

[0132] The root mean square errors calculated by the method proposed in this embodiment and the Monte Carlo method are shown in Table 2. All root mean square errors are less than 0.5, which proves that the method proposed in this embodiment has good performance.

[0133] Table 2 Root mean square error of the proposed method

[0134] 2nd-order Cornish-Fisher 3rd-order Cornish-Fisher 4th-order Cornish-Fisher Root mean square error (RMSE) 0.1812 0.1721 0.1715

[0135] It is not difficult to find that this embodiment proposes a probabilistic small-signal stability analysis method, which combines the point estimation method based on the s-domain node admittance matrix to obtain the probability information of the system, and uses the Cornish-Fisher extension method to accurately fit the probability function. This method achieves higher prediction accuracy with a smaller amount of calculation, is easy to implement and has strong practicality, and provides a new idea for the stability analysis of interconnected devices in uncertain environments.

[0136] A second embodiment of the present invention relates to a probabilistic stability analysis device for a flexible DC interconnection system, comprising:

[0137] Establish a module for modeling each component in the low-voltage flexible interconnection system as a port admittance that can reflect the inherent dynamic and external interactive characteristics, and establish a low-voltage flexible DC interconnection system source-load admittance model for grid-connected inverters and electric vehicle charging stations;

[0138] A solution module is introduced to bring the source-load admittance model of the low-voltage flexible DC interconnection system into the S-domain node admittance matrix, and obtain the oscillation mode of the low-voltage flexible interconnection system by solving the determinant zero point of the S-domain node admittance matrix;

[0139] An estimation and expansion module is configured to determine, based on the oscillation mode of the low-voltage flexible interconnection system, a relationship between a moment and a cumulative amount output by the low-voltage flexible interconnection system using a point estimation method, and expand the relationship using a series expansion method to obtain a probability density of a real part of the oscillation mode of the low-voltage flexible interconnection system.

[0140] The source-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: Among them, Y source is the source side admittance of the low voltage flexible DC interconnection system, Y VSC is the DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system, C dc is the parallel filter capacitor on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, Z line is the line impedance on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0141] The DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system is expressed as: Among them, V dc is the steady-state voltage value of the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq Represents the component of the output duty cycle in the dq synchronous rotating coordinate system, Z g is the AC grid impedance, expressed as: Z L is the AC line impedance, expressed as: L g 、R g Represent the grid inductance and resistance respectively, L and R represent the AC line inductance and resistance respectively, ω1 represents the constant speed of the coordinate system, H i is the current PI control loop, H v is the voltage PI control loop, G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as: H i is the current PI control loop transfer function, G PLL Represents the phase-locked loop PI control link, I d and I q The steady-state values of the current under the d-axis and q-axis, D d and D q Represents the steady-state value of the duty cycle under the d-axis and q-axis respectively, V d and V q They represent the steady-state values of the voltage on the d-axis and q-axis, respectively, and ω represents the steady-state value of the angular velocity.

[0142] The load-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: load =Y EVCS +sC L , where Y load is the load-side admittance of the low-voltage flexible DC interconnection system, Y EVCS is the admittance of the electric vehicle charging station, CL is the parallel filter capacitor on the DC side of the electric vehicle charging station in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

[0143] The admittance of the electric vehicle charging station is expressed as: D dc0 Represents the steady-state value of the duty cycle, I L0 Indicates the steady-state value of the inductor current, H idc is the constant current control transfer function, L d is the energy storage inductor of the converter in the electric vehicle charging station, V EVCS0 Indicates the DC input voltage, R d is the low voltage DC circuit damping resistor in the electric vehicle charging station, C d It is the voltage stabilizing capacitor of the converter in the electric vehicle charging station.

[0144] The electric vehicle charging station power in the S-domain node admittance matrix should be modeled probabilistically.

[0145] When the estimation expansion module uses the point estimation method to determine the relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system, the power of the electric vehicle charging station is used as an input sample and the real part of the oscillation mode of the low-voltage flexible interconnection system is used as an output sample.

[0146] The relationship is expressed as: Among them, m ik is the k-th order moment output by the low voltage flexible interconnection system, γ k It is the cumulative amount corresponding to the k-th order moment output by the low voltage flexible interconnection system.

[0147] When the estimation expansion module uses the series expansion method to expand the relational expression, the Cornish-Fisher series expansion method is used to expand the relational expression.

[0148] A third embodiment of the present invention relates to an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the probabilistic stability analysis method for a flexible DC interconnection system of the first embodiment are implemented.

[0149] A fourth embodiment of the present invention relates to a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the steps of the probabilistic stability analysis method of the flexible DC interconnection system of the first embodiment are implemented.

[0150] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage and optical storage, etc.) that contain computer-usable program code.

[0151] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0152] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction method, which is implemented in the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0154] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A probabilistic stability analysis method for a flexible DC interconnection system, characterized in that: include: Each component in the low-voltage flexible interconnected system is modeled as a port admittance that can reflect its internal dynamic and external interactive characteristics. A source-load admittance model of the low-voltage flexible direct current interconnected system is established for the grid-connected inverter and the electric vehicle charging station. The source-load admittance model of the low-voltage flexible direct current interconnected system is introduced into the s-domain node admittance matrix, and the oscillation mode of the low-voltage flexible interconnected system is obtained by solving the determinant zeros of the s-domain node admittance matrix. Based on the oscillation mode of the low-voltage flexible interconnection system, a point estimation method is used to determine the relationship between the moment and the cumulative amount of the oscillation mode of the low-voltage flexible interconnection system. The relationship is then expanded using the series expansion method to obtain the probability density of the real part of the oscillation mode of the low-voltage flexible interconnection system.

2. The probabilistic stability analysis method of the flexible DC interconnection system according to claim 1 is characterized in that: The source-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system is expressed as: Among them, Y source is the source side admittance of the low voltage flexible DC interconnection system, Y VSC is the DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system, C dc is the parallel filter capacitor on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, Z line is the line impedance on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

3. The probabilistic stability analysis method of the flexible DC interconnection system according to claim 2, characterized in that: The DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system is expressed as: Among them, V dc is the steady-state voltage value of the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq Represents the component of the output duty cycle in the dq synchronous rotating coordinate system, Z g is the AC grid impedance, expressed as: Z L is the AC line impedance, expressed as: L g 、R g Represent the grid inductance and resistance respectively, L and R represent the AC line inductance and resistance respectively, ω1 represents the constant speed of the coordinate system, G vi To control the influence of the link on the system admittance, the inverter constant voltage control G vi =H i H v , when the inverter is in constant power control G vi =I,H i is the current PI control loop, H v is the voltage PI control loop, I represents the unit matrix, and G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as: H i is the current PI control loop transfer function, G PLL Indicates the phase-locked loop PI control link, I d and I q The steady-state values of the current under the d-axis and q-axis, D d and D q Represents the steady-state value of the duty cycle under the d-axis and q-axis respectively, V d and V q They represent the steady-state values of the voltage on the d-axis and q-axis, respectively, and ω represents the steady-state value of the angular velocity.

4. The probabilistic stability analysis method of a flexible DC interconnection system according to claim 1, characterized in that: The load-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system is expressed as: load =Y EVCS +sC L , where Y load is the load-side admittance of the low-voltage flexible DC interconnection system, Y EVCS is the admittance of the electric vehicle charging station, C L is the parallel filter capacitor on the DC side of the electric vehicle charging station in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

5. The probabilistic stability analysis method of the flexible DC interconnection system according to claim 4, characterized in that: The admittance of the electric vehicle charging station is expressed as: D dc0 Represents the steady-state value of the duty cycle, I L0 Indicates the steady-state value of the inductor current, H idc is the constant current control transfer function, L d is the energy storage inductor of the converter in the electric vehicle charging station, V EVCS0 Indicates the DC input voltage, R d is the low voltage DC circuit damping resistor in the electric vehicle charging station, C d It is the voltage stabilizing capacitor of the converter in the electric vehicle charging station.

6. The probabilistic stability analysis method of the flexible DC interconnection system according to claim 1, characterized in that: The electric vehicle charging station power in the S-domain node admittance matrix should be modeled probabilistically.

7. The probabilistic stability analysis method of a flexible DC interconnection system according to claim 1, characterized in that: When determining the relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system using the point estimation method, the power of the electric vehicle charging station is used as an input sample, and the real part of the oscillation mode of the low-voltage flexible interconnection system is used as an output sample.

8. The probabilistic stability analysis method of the flexible DC interconnection system according to claim 7, characterized in that: The relationship is expressed as: Among them, m ik is the k-th order moment output by the low voltage flexible interconnection system, γ k It is the cumulative amount corresponding to the k-th order moment output by the low voltage flexible interconnection system.

9. The probabilistic stability analysis method of a flexible DC interconnection system according to claim 1, characterized in that: When the relational expression is expanded using the series expansion method, the relational expression is expanded using the Cornish-Fisher series expansion method.

10. A probabilistic stability analysis device for a flexible DC interconnection system, characterized in that: include: Establish a module for modeling each component in the low-voltage flexible interconnection system as a port admittance that can reflect the inherent dynamic and external interactive characteristics, and establish a low-voltage flexible DC interconnection system source-load admittance model for grid-connected inverters and electric vehicle charging stations; A solution module is introduced to bring the source-load admittance model of the low-voltage flexible DC interconnection system into the S-domain node admittance matrix, and obtain the oscillation mode of the low-voltage flexible interconnection system by solving the determinant zero point of the S-domain node admittance matrix; An estimation and expansion module is configured to determine, based on the oscillation mode of the low-voltage flexible interconnection system, a relationship between a moment and a cumulative amount output by the low-voltage flexible interconnection system using a point estimation method, and expand the relationship using a series expansion method to obtain a probability density of a real part of the oscillation mode of the low-voltage flexible interconnection system.

11. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 10, characterized in that: The source-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: Among them, Y source is the source side admittance of the low voltage flexible DC interconnection system, Y VSC is the DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system, C dc is the parallel filter capacitor on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, Z line is the line impedance on the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

12. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 11, characterized in that: The DC side admittance of the grid-connected inverter in the low-voltage flexible DC interconnection system is expressed as: Among them, V dc is the steady-state voltage value of the DC side of the grid-connected inverter in the low-voltage flexible DC interconnection system, I dq It represents the AC side output current in the dq synchronous rotating coordinate system, D dq Represents the component of the output duty cycle in the dq synchronous rotating coordinate system, Z g is the AC grid impedance, expressed as: Z L is the AC line impedance, expressed as: L g 、R g Represent the grid inductance and resistance respectively, L and R represent the AC line inductance and resistance respectively, ω1 represents the constant speed of the coordinate system, G vi To control the influence of the link on the system admittance, the inverter constant voltage control G vi =H i H v , when the inverter is in constant power control G vi =I,H i is the current PI control loop, H v is the voltage PI control loop, I represents the unit matrix, and G represents the effect of the phase-locked loop and current control on the system admittance, which is expressed as: H i is the current PI control loop transfer function, G PLL Indicates the phase-locked loop PI control link, I d and I q The steady-state values of the current under the d-axis and q-axis, D d and D q Represents the steady-state value of the duty cycle under the d-axis and q-axis respectively, V d and V q They represent the steady-state values of the voltage on the d-axis and q-axis, respectively, and ω represents the steady-state value of the angular velocity.

13. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 10, characterized in that: The load-side admittance model in the source-load admittance model of the low-voltage flexible DC interconnection system established by the establishment module is expressed as: load =Y EVCS +sC L , where Y load is the load-side admittance of the low-voltage flexible DC interconnection system, Y EVCS is the admittance of the electric vehicle charging station, C L is the parallel filter capacitor on the DC side of the electric vehicle charging station in the low-voltage flexible DC interconnection system, and s is the Laplace operator.

14. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 13, characterized in that: The admittance of the electric vehicle charging station is expressed as: D dc0 Represents the steady-state value of the duty cycle, I L0 Indicates the steady-state value of the inductor current, H idc is the constant current control transfer function, L d is the energy storage inductor of the converter in the electric vehicle charging station, V EVCS0 Indicates the DC input voltage, R d is the low voltage DC circuit damping resistor in the electric vehicle charging station, C d It is the voltage stabilizing capacitor of the converter in the electric vehicle charging station.

15. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 10, characterized in that: The electric vehicle charging station power in the S-domain node admittance matrix should be modeled probabilistically.

16. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 10, characterized in that: When the estimation expansion module uses the point estimation method to determine the relationship between the moment and the cumulative amount output by the low-voltage flexible interconnection system, the power of the electric vehicle charging station is used as an input sample and the real part of the oscillation mode of the low-voltage flexible interconnection system is used as an output sample.

17. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 16, characterized in that: The relationship is expressed as: Among them, m ik is the k-th order moment output by the low voltage flexible interconnection system, γ k It is the cumulative amount corresponding to the k-th order moment output by the low voltage flexible interconnection system.

18. The probabilistic stability analysis device for a flexible DC interconnection system according to claim 10, characterized in that: When the estimation expansion module uses the series expansion method to expand the relational expression, the Cornish-Fisher series expansion method is used to expand the relational expression.

19. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the probabilistic stability analysis method for a flexible DC interconnection system according to any one of claims 1 to 9 are implemented.

20. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the probabilistic stability analysis method for a flexible DC interconnection system according to any one of claims 1 to 9 are implemented.

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