Small-signal model-based capacity ratio optimization analysis method for network-following hybrid system

Abstract

The invention belongs to the field of power supply and dispatching, and provides a method for optimizing and analyzing the capacity ratio of a follow-up network hybrid system based on a small signal model, which comprehensively considers the voltage and frequency stability of the system so as to determine the optimal capacity ratio of the follow-up network hybrid energy storage system in different power grid scenes. The method comprises the following steps of: firstly, establishing a full-order state space small signal model of a network-following hybrid grid-connected system according to different expressions of a network-following converter control loop; then, a characteristic value analysis method and a participation factor analysis method are utilized to analyze the lowest network construction permeability of the basic requirement for maintaining the system stability under different power grid strengths, and it is revealed that dominant control links influencing the system stability under different working conditions and parameters are different.

Description

A Capacity Ratio Optimization Analysis Method for Hybrid Systems Based on Small Signal Model Technical Field

[0001] This invention belongs to the field of power supply and dispatch, specifically involving a capacity allocation optimization analysis method for hybrid interconnected power grid systems based on a small-signal model. Background Technology

[0002] Grid-connected and grid-connected converters exhibit different performance characteristics in terms of system stability. Grid-connected converters have current source characteristics, tracking the grid phase and outputting power. In weak grid conditions, they may experience instability due to interactions between loops or with the grid. Grid-connected converters, on the other hand, act as voltage sources, enhancing grid strength and actively supporting voltage. However, when a grid-connected converter is connected in parallel with a strong grid, it is equivalent to two voltage sources connected through a small tie impedance, making it prone to instability. Furthermore, the power frequency response transfer function of the grid-connected converter, especially under weak grid conditions, exhibits weak or even negative virtual inertia and damping, which can increase the rate of frequency change and induce oscillations. In contrast, grid-connected converters provide frequency support and regulation by simulating the behavior of a synchronous machine, which is beneficial for the safety and stability of the system frequency.

[0003] Regarding the configuration of grid-connected / integrated energy storage, some existing technologies estimate the grid-connected / integrated energy storage ratio under weak grid conditions based on the multi-infeed generalized short-circuit ratio for static voltage stability. Other existing technologies, considering both voltage stability and frequency security, present capacity configuration schemes based on the economics of grid-connected / integrated energy storage, demonstrating the impact of grid-connected / integrated energy storage capacity ratio on system safety and stability, but without considering small-disturbance stability at frequency. To balance voltage and frequency small-disturbance stability and more accurately analyze the system's oscillation mechanism and its impact on the configuration ratio, some existing technologies analyze the small-signal stability at frequency in multi-VSG parallel scenarios using the eigenvalue method. Furthermore, some existing technologies study the small-disturbance stability of grid-connected / integrated hybrid systems in islanded scenarios using the state-space method, but do not consider the impact of grid strength variations on the configuration ratio stability boundary in grid-connected scenarios. Additionally, differences in grid-connected / integrated control loops can also cause variations in capacity configuration. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a capacity allocation optimization analysis method for hybrid systems with integrated grids based on a small-signal model, thereby resolving issues in the prior art. The technical solution adopted by this invention is as follows: a capacity allocation optimization analysis method for hybrid systems with integrated grids based on a small-signal model, comprising: Step 1, constructing a hybrid single-feed system with integrated grid and integrated grid types, including integrated grid converters and grid-connected converters, each converter being connected to a common grid connection point via corresponding filter lines and transmission lines, and then connected to the AC power grid; Step 2, constructing a small-signal model, including the small-signal model of the integrated grid converter, the small-signal model of the integrated grid converter, the small-signal model of the filter lines, and the small-signal model of the AC power grid; integrating these to obtain the small-signal model of the hybrid system with integrated grids; Step 3, stability analysis of the hybrid system with integrated grids under different capacity allocation ratios.

[0005] Furthermore, in step 2, when constructing the small-signal model of the filter circuit, it includes: modeling the filters and connecting lines of the grid-type converter and the interconnected grid-type converter. The filter circuit equation is: Linearizing the filter circuit equations yields the small-signal model of the filter circuit: ; where u di and i di Let u represent the d-axis components of the output voltage and current of converter i, respectively. qi and i qi Let u represent the q-axis components of the output voltage and current of converter i, respectively. Ldi i Ldi It is divided into the d-axis components of its port voltage and current, u Lqi i Lqi It is divided into the d-axis components of its port voltage and current, ω i Its angular frequency, u bdi Let u be the d-axis component of the voltage at PCC in the local coordinate system of converter i; bqi Let L be the q-axis component of the voltage at PCC in the local coordinate system of converter i. fi and C fi For its filter inductor and filter capacitor, R fi For its LC filter, L ci and R ci The equivalent line inductance and equivalent line resistance at its connection to PCC; A Fi C FuLi C Fubi and C Fwi This is the corresponding coefficient matrix; the symbol △ represents the small signal component of the corresponding variable.

[0006] Furthermore, in step 2, the small-signal model of the grid converter includes the small-signal model of the phase-locked loop (PLL) and the small-signal model of the PQ dual closed-loop control. Specifically, for the small-signal model of the PLL, its state equation is: ; where k pllp With k plli These are the PI parameters of the phase-locked loop (PLL); δ1 represents the phase angle difference between the output voltages of the grid-connected converter and the grid-connected converter, and xpll is an intermediate variable in the PLL integrator; A pllp A plli The corresponding coefficient matrix; for the small-signal model of PQ dual closed-loop control, the construction process includes: calculating the output power P1 and Q1 of the grid converter, and obtaining the power small-signal model after linearization: ;in , To determine the steady-state dq-axis components of the output current of the grid-connected converter, , To determine the steady-state dq-axis components of the output voltage of the grid-connected converter, we introduce the variable x. pq1 x idq1 Representing the integral outputs of the PI controllers in the power outer loop and current inner loop respectively, we obtain the small-signal model of the PQ outer loop of the grid converter: The expression for the inner current loop of a grid converter is: The output equation of the grid converter is: ;D 1pq D 1i E 1i B C1 E xi E xpq The corresponding coefficient matrix is ​​used; the state variables of the grid-type converter are selected as follows: Based on the PQ outer loop small-signal model, the grid-connected converter's inner current loop, and the grid-connected converter's output equations, the small-signal model for PQ dual closed-loop control is obtained: Among them, A VSC1 B VSC1 C VSC1 B ω This is the corresponding coefficient matrix; The dq axis components are converted to the common DQ coordinate system after the output current of the grid converter is transformed.

[0007] Furthermore, in step 2, when constructing the small-signal model of the AC power grid, the following is included: Constructing the small-signal model of the power grid phase angle is as follows: ;δ g This represents the phase angle difference between the grid voltage and the output voltage of the grid-connected converter; transforming the grid voltage to a common coordinate system, we have: ;where U g0δ is a steady-state quantity of the grid voltage amplitude. g0 This represents the steady-state phase angle difference between the grid voltage and the output voltage of the grid-connected converter. , R represents the steady-state component of the grid voltage along the dq axis in the common DQ coordinate system. g and L g Let be the equivalent inductance and resistance of the power grid; the circuit equation between the common connection point and the AC power grid is: Linearizing the circuit equations yields a small-signal model of the AC power grid: A gi A gu A gub A gw This is the corresponding coefficient matrix.

[0008] Furthermore, in step 2, when constructing the small-signal model of the grid-type converter, droop control with an additional inertial element is added. The mathematical model of the grid-type converter under droop control with an additional inertial element is expressed as follows: ; Where k1 is the frequency-active droop coefficient, k2 is the voltage-reactive droop coefficient, and ω p ω0 is the cutoff frequency of the low-pass filter, U0 is the reference frequency, and P is the reference voltage amplitude. 2ref Q is the active power reference value. 2ref Here, is the reactive power reference value, and s is the complex frequency domain differential operator. Linearizing this mathematical model yields the small-signal model for the droop control of the additional inertial element in a grid-type converter: ; The results of the analysis are as follows: ; A M1 A M2 B C2 The corresponding coefficient matrix is ​​used; the state variables of the network converter are selected as follows: The small-signal model of a grid-type converter is shown below: A VSC2 B VSC2 C VSC2 This is the corresponding coefficient matrix; The dq axis components are converted to the common DQ coordinate system after the output current of the grid converter is transformed.

[0009] Furthermore, in step 2, the small-signal model of the integrated network hybrid system is obtained, including: introducing a virtual ground resistance R. VN At this point, the nodal equations of the common grid connection point are: Linearizing the equation for this node, we get: B VNThe corresponding coefficient matrix is ​​used to obtain the small-signal model of the hybrid grid system: A sys Here is the corresponding coefficient matrix; where the system state variables are: .

[0010] Furthermore, step 3 includes: defining the total capacity of the grid-type converter and the grid-connected converter as S respectively. M and S L The network penetration rate γ is defined as: Among them, S M and S L n represents the total capacity of the grid-connected converter and the grid-linked converter. M and n L The number of grid-connected converters and grid-connected converters are respectively; the grid penetration rate γ is used to reflect the stability of the grid-connected hybrid system. The minimum grid penetration rate under different grid strengths is analyzed using eigenvalue analysis and participation factor analysis.

[0011] This invention has the following beneficial effects: Based on the differences in the unstable links of grid-connected converters and grid-connected converters, this invention establishes a small-signal dynamic model of the state space of a grid-connected hybrid system, laying a theoretical foundation for subsequent stability analysis; Based on the grid penetration rate, this invention quantitatively reveals the basic law that the minimum grid penetration rate required for the stability of the hybrid system under different power grid scenarios decreases significantly with the increase of power grid intensity, providing a clear stability domain judgment for the capacity configuration of grid-connected converters under different power grid conditions. Attached Figure Description

[0012] Figure 1 shows a hybrid single-feed system with grid-like and grid-connected configurations; Figure 2 shows a schematic diagram of the dq coordinate system for a multi-machine parallel system; Figure 3 shows a schematic diagram of a phase-locked loop controller; Figure 4 shows a schematic diagram of PQ dual closed-loop control; Figure 5 shows a schematic diagram of droop control with an additional inertial element; Figure 6 shows the eigenvalue root locus and participation factor locus when γ changes; In the figures: (a) represents λ 21,22 The eigenvalue trajectory, (b) is λ 21,22 Participating factor trajectory, (c) is λ 15,16 The eigenvalue trajectory, (d) is λ 15,16 Participating factor trajectories; Figure 7 shows the eigenvalue trajectories and participating factor trajectories when SCR changes; In the figure: (a) is λ 15,16 The eigenvalue trajectory, (b) is λ 15,16 Participating factor trajectories; Figure 8 shows the system stability region considering grid penetration and grid strength; Detailed Implementation

[0013] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to Figures 1-8. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0014] This invention comprehensively considers system voltage and frequency stability to determine the optimal capacity ratio of a grid-connected hybrid energy storage system under different grid scenarios. First, based on the different performance of the grid-connected converter control loop, a full-order state-space small-signal model of the grid-connected hybrid system is established. Then, using eigenvalue analysis and participation factor analysis, the minimum grid penetration rate required to maintain basic system stability under different grid intensities is analyzed, revealing that the dominant control links affecting system stability differ under different operating conditions and parameters.

[0015] Specifically, this invention proposes a capacity allocation optimization analysis method for hybrid systems based on a small-signal model, comprising the following steps: Step 1, constructing hybrid single-infeed systems of grid-connected and grid-connected types, including grid-connected converters and grid-connected converters. Each converter is connected to a common grid connection point via corresponding filter lines and transmission lines, and then connected to the AC power grid; consider the hybrid single-infeed system of grid-connected and grid-connected types as shown in Figure 1. Assume there are n in the hybrid system. M Taiwan-type grid converter and n L Since the dynamic interaction of converters within the substation is not considered, the substation can be represented by one equivalent grid-type converter and one equivalent grid-connected converter. The grid-type converter uses droop control with an additional inertial element to provide voltage and frequency support, while the grid-connected converter uses dual closed-loop control (power outer loop, current inner loop) and a phase-locked loop (PLL) for synchronization. The two converters are connected to the common grid connection point (PCC) via LC filters and transmission lines.

[0016] The subscripts i=1 and 2 represent the relevant parameters of the grid-type converter and the network-type converter, respectively, and the subscript dq represents the dq-axis component of the corresponding variable. In Figure 1, u dqi and i dqi The output voltage and current of converter i are respectively, u Ldqi i Ldqi These represent the port voltage and current of converter i, respectively, and u bdq L is the voltage at PCC. fi and C fi These are the filter inductor and filter capacitor of converter i, respectively, R fi L is the equivalent resistance of the LC filter of converter i. ci and R ci These are the equivalent line inductance and equivalent line resistance, R, connected between converter i and PCC, respectively.g and L g This represents the equivalent inductance and resistance of the power grid.

[0017] Step 2, construct small-signal models, including small-signal models of grid-connected converters, grid-connected converters, filter lines, and AC grids; integrate to obtain the small-signal model of the grid-connected hybrid system; Step 2 specifically involves: (2.1) First, perform reference coordinate system and coordinate transformation: the grid-connected converter control system is established in its own phase-locked loop (PLL) coordinate system, the grid-connected converter control system is established in its own constructed coordinate system, and the lines and AC system are established in the corresponding main circuit coordinate system. Therefore, it is necessary to transform the interface variables in the grid-connected hybrid system. In this invention, the rotating coordinate system of the grid-connected converter is selected as the common rotating coordinate system, denoted as the DQ coordinate system. Figure 2 shows the relationship between the dq coordinate system of the grid-connected converter and the grid and the common rotating coordinate system. Among them, d1q1 (denoted as dq) is the grid-connected coordinate system, d2q2 (denoted as DQ) is the grid-connected coordinate system, U g For power grid phasors.

[0018] The phase angle of a grid-type converter satisfies: (1) In the formula, δ2 is the phase angle of the grid converter and ω2 represents the dynamic output angular frequency of the grid converter.

[0019] Linearizing equation (1), we obtain the small-signal state equation for the phase angle δ2 of the grid converter: (2) In the formula, Δx represents the small perturbation of x.

[0020] The phase angle of the grid converter satisfies: (3) In the formula, δ1 represents the phase angle difference between the output voltage of the grid-type converter and the grid-type converter, and ω1 represents the dynamic output frequency of the grid-type converter.

[0021] The phase angle small-signal model of the grid converter is then: (4) When establishing the small-signal model of the hybrid system, the grid-connected converter and the grid-connected converter need to be unified to the common reference DQ coordinate system for analysis. The output current i of the grid-connected converter needs to be... dq1 Transform to the DQ coordinate system using the following method: (5) The small-signal model of the coordinate transformation of the output current of the grid converter is: (6) Among them, Similarly, for the output voltage of a grid-connected converter, its transformation expression is: (7) The small-signal model of the coordinate transformation of the output voltage of the grid converter is: (8) Among them, (2.2) Small-signal model of the filter circuit: The filters and connecting lines of the grid-type converter and the ground-type converter in Figure 1 are modeled respectively. This invention assumes that the controller output reference voltage is the port voltage of the converter. The filter circuit equation is as follows: (9) Where i=1, 2 represent the filter circuit equations of the grid converter in their respective coordinate systems; where: ; ; ; Linearizing equation (9) yields the small-signal models of the converter's filter and circuit: (10) Where, u di and i di Let u represent the d-axis components of the output voltage and current of converter i, respectively. qi and i qi Let u represent the q-axis components of the output voltage and current of converter i, respectively. Ldi i Ldi It is divided into the d-axis components of its port voltage and current, u Lqi i Lqi It is divided into the d-axis components of its port voltage and current, ω i Its angular frequency, u bdi Let u be the d-axis component of the voltage at PCC in the local coordinate system of converter i; bqi Let L be the q-axis component of the voltage at PCC in the local coordinate system of converter i. fi and C fi For its filter inductor and filter capacitor, R fi For its LC filter, L ci and R ci The equivalent line inductance and equivalent line resistance at its connection to PCC; A Fi C FuLi C Fubi and C Fwi This is the corresponding coefficient matrix; the symbol △ represents the small signal component of the corresponding variable.

[0022] (2.3) Small-signal model of grid-connected converter: The small-signal model of grid-connected converter includes the small-signal model of phase-locked loop (PLL) and the small-signal model of PQ dual closed-loop control. The small-signal model of GFL is built below. Since GFL is prone to instability under weak grid conditions, the reason is that its PLL dynamic characteristics are coupled with the grid impedance. At the same time, its current inner loop bandwidth may conflict with the grid impedance. Therefore, it is necessary to analyze the impact of GFL's PLL and current inner loop on stability. The main reason why GFM is prone to instability under strong grid conditions is that its power loop is sensitive to grid changes. It is necessary to focus on analyzing its control loop model. Since this invention does not consider the impact of dynamic interaction between GFM and GFL on stability, the small-signal model of GFM inner loop is not further considered.

[0023] For the small-signal model of the phase-locked loop: In the grid-type converter control system in the dq coordinate system, the phase-locked loop is crucial, tracking the q-axis component of the output voltage to provide the frequency and phase reference values ​​of the control system.

[0024] As shown in Figure 3, the phase of the output point is tracked by a phase-locked loop (PLL) in a grid-type converter. The mathematical model of the PLL can be expressed as: In equation (11), ω0 is the reference angular frequency, k pllp With k plli These are the PI parameters of the phase-locked loop, u q1 This refers to the q-axis component of the voltage tracked by the phase-locked loop.

[0025] For ease of representation, the PI loop of the phase-locked loop can be decomposed and a variable x can be introduced. pll The output of its integral stage is shown in Figure 3, which is: (12) Linearizing equation (12), we have: (13) Combining equations (11) and (13), we have: (14) It can be found that x pll It has the same dimensions as ω1.

[0026] Therefore, the state equation of the phase-locked loop can be written as: (15) Among them, , k pllp With k plli These are the PI parameters of the phase-locked loop (PLL); δ1 represents the phase angle difference between the output voltages of the grid-connected converter and the grid-connected converter, and xpll is an intermediate variable in the PLL integrator; A pllp A plli This is the corresponding coefficient matrix.

[0027] For the small-signal model of PQ dual closed-loop control: as shown in Figure 4, the PQ controller uses the input variable P... ref and Q refAs a power reference, the actual power P1 and Q1 are collected to control the output power of the grid-type converter.

[0028] The output power P1 and Q1 of the grid converter can be determined by the output voltage u. dq1 and output current i dq1 The instantaneous power calculation module yields the following result: (16) The power small-signal model is obtained after linearization: (17) of which , To determine the steady-state dq-axis components of the output current of the grid-connected converter, , To represent the steady-state dq-axis components of the grid-connected converter output voltage; to facilitate the representation of the PI element, a variable x is introduced. pq1 x idq1 Figure 4 shows the outputs of the integral components of the PI controller in the power outer loop and the current inner loop, respectively.

[0029] Furthermore, the small-signal model of the PQ outer loop of the grid-type converter can be obtained: (18) Among them, .

[0030] The expression for the inner current loop of a grid converter is: (19) Among them, k pp This is the proportional coefficient of the power outer loop.

[0031] The output equation of the grid converter is: (20) Among them, K cp and k ci These are the PI parameters for the inner current loop. D 1pq D 1i E 1i B C1 E xi E xpq The corresponding coefficient matrix is ​​used; the state variables of the grid-type converter are selected as follows: The small-signal model of the grid converter is shown below: (21) Among them, Among them, A VSC1 B VSC1 C VSC1 B ω This is the corresponding coefficient matrix; The dq axis components are converted to the common DQ coordinate system after the output current of the grid converter is transformed.

[0032] (2.4) Small-signal model of grid-type converter with droop control and additional inertial element: According to the control block diagram shown in Figure 5, the mathematical model of the grid-type converter with droop control and additional inertial element can be expressed as: (twenty two) (23) Where k1 is the frequency-active droop coefficient, k2 is the voltage-reactive droop coefficient, and ω p ω0 is the cutoff frequency of the low-pass filter, U0 is the reference frequency, and P is the reference voltage amplitude. 2ref Q is the active power reference value. 2ref Here, s is the reactive power reference value, and s is the complex frequency domain differential operator. In the dq coordinate system of the grid converter itself, equations (22) and (23) are linearized respectively to obtain the small-signal model of the droop control of the grid converter with added inertial element, as shown in the following equation.

[0033] (twenty four) (25) Further refinement yields the small-signal model of the grid-type converter with droop control and additional inertial elements, whose standard form is as follows: (26) (27) Among them, ; A M1 A M2 B C2 The corresponding coefficient matrix is ​​used; the state variables of the network converter are selected as follows: The small-signal model of a grid-type converter is shown below: (28)A VSC2 B VSC2 C VSC2 This is the corresponding coefficient matrix; The dq axis components of the grid-connected converter output current after conversion to the common DQ coordinate system; (2.5) Small-signal model of AC power grid: Under the condition of small disturbance, the amplitude U of the grid voltage is considered to be g and frequency ω g This is a constant value. The small-signal model of the power grid phase angle can then be obtained: (29)δ g This represents the phase angle difference between the grid voltage and the output voltage of the grid-connected converter; transforming the grid voltage to a common coordinate system, we have: (30) Where U g0 δ is a steady-state quantity of the grid voltage amplitude. g0 This represents the steady-state phase angle difference between the grid voltage and the output voltage of the grid-connected converter. , R represents the steady-state component of the grid voltage along the dq axis in the common DQ coordinate system. g and Lg Let be the equivalent inductance and resistance of the power grid; referring to Figure 1, the circuit equation between the PCC and the AC power grid is as follows: (31) Linearizing equation (31) yields the small-signal model of the power grid line under the DQ axis, i.e., the small-signal model of the AC power grid: (32) Among them, A gi A gu A gub A gw This is the corresponding coefficient matrix.

[0034] (2.6) Small-signal modeling of the grid-connected hybrid system: Based on the small-signal models of grid-connected and grid-connected converter systems, transmission line small-signal models, and AC grid small-signal models derived above, the small-signal model of the grid-connected hybrid system can be obtained by integration. Therefore, in order to eliminate the node voltage Δu at the grid connection point in equations (21), (28), and (32) bDQ Introducing virtual ground resistance R VN If R VN If it is large enough, R can be ignored. VN The impact on the system can be assessed, and the above-mentioned models can be unified. The nodal equations at point PCC after introducing the virtual ground resistance are shown below.

[0035] (33) Linearizing equation (33), we have: (34) Among them, B VN The corresponding coefficient matrix is ​​given; thus, the small-signal model of the hybrid network system can be obtained: (35) Among them, ; A sys Here is the corresponding coefficient matrix; where the system state variables are: .

[0036] Step 3, Stability Analysis of Hybrid Systems with Different Capacity Ratios; To analyze the stability of hybrid systems with different capacity ratios of converters in the grid, and to provide reference values ​​for the optimal ratio of the hybrid system with different grid intensities, the following analysis is made. To simplify the analysis, the following assumptions are made: 1. The capacity of all individual converters is the base capacity S. b .

[0037] 2. The differences between filter and line parameters are not considered, that is, the filter and line parameters of all single-unit systems are consistent.

[0038] 3. The circuit and filter parameters of the converter unit, as well as the control parameters, already meet the stability requirements of the unit.

[0039] Based on the above assumptions, the differences in the main circuit parameters within the two-machine aggregation model of the hybrid grid system in Figure 1 are only related to their capacity differences. The system capacity baseline value S selected in this invention... b and voltage base value U b The values ​​are 0.5MW and 380V respectively, with a frequency base value f. b The frequency is 50Hz, and the total system capacity is [value missing]. The basic system control parameters and line parameters are shown in Table 1.

[0040] Table 1: System Control Basic Parameters and Circuit Parameters

[0041] Define the total capacity of the grid-type converter and the grid-connected converter as S respectively. M and S L Then the network penetration rate γ is defined as follows: (36) Wherein, S M and S L n represents the total capacity of the grid-connected converter and the grid-linked converter. M and n L This refers to the number of grid-connected converters and integrated grid-connected converters respectively. Taking the filter inductance parameters as an example, the line parameters of the integrated grid-connected converter have the following proportional relationship: (37) As can be seen from the above equation, under the aforementioned assumptions, the system state matrix A sys In the correlation coefficient matrix of the grid-connected converter, the difference between the line and control parameters is only related to the grid penetration rate γ of the hybrid system. Therefore, under the premise of single-unit stability, the stability of the hybrid system is only related to the grid penetration rate γ. The grid penetration rate γ is used to reflect the stability of the grid-connected hybrid system. Using the eigenvalue analysis method and the participation factor analysis method, the minimum grid penetration rate under different grid intensities is analyzed. Specifically: (3.1) Eigenvalue distribution of the hybrid system connected to the AC grid: In order to analyze the stability law of the system when the grid-connected converter is connected to the grid of different intensities with different grid penetration rates γ, based on the small signal model of the grid-connected hybrid system derived above, according to the system matrix A obtained by equation (35) sys Based on the system parameters in Table 1, the characteristic root distribution table of the system when the grid short-circuit ratio SCR=2 and the grid penetration rate γ=31% can be obtained, as shown in Table 2.

[0042] Table 2: Eigenvalue Distribution Table

[0043] As shown in Table 2, all characteristic roots of the grid-connected system with integrated converters under this operating condition are located in the left half-plane of the coordinate system, indicating that the system is stable under small disturbances. Furthermore, the distribution of all characteristic roots of the system can be divided into high-frequency, mid-frequency, and low-frequency bands. According to the definition of the small-signal model, δ... g δ1 is used to characterize the frequency interaction between the power grid and the converter; δ1 is used to characterize the frequency interaction between the grid converters. pll ω2 is used to characterize the frequency characteristics of each converter. Since this invention uses GFM as a reference, δ2 is always zero.

[0044] Based on the small-signal model of the hybrid grid-connected system derived above, this invention introduces a participation factor variable p to more accurately analyze the relationship between characteristic roots and system state variables under changes in the capacity ratio of grid-connected converters. ki Its expression is as follows.

[0045] (38) In the formula, ψ ik φ ki These are the left and right eigenvectors after system normalization, and the state factor p. ki It can represent the degree to which state variables participate in the eigenvalues.

[0046] Based on the above discussion, assuming the individual converter is stable, the only factors affecting system stability that need to be considered are grid strength and the capacity ratio of the integrated grid converter. Using the characteristic values ​​given in Table 2, we analyze the impact of the integrated grid capacity ratio γ, relevant line parameters of grid strength, and control parameters on the small-disturbance stability of the hybrid system. Due to space limitations, only the characteristic values ​​with a significant impact on system stability are analyzed; characteristic values ​​with smaller changes are not discussed.

[0047] (3.2) Impact of grid penetration rate on system stability: With the grid short-circuit ratio (SCR) fixed at 2, the impact of capacity ratio γ on system stability is analyzed. Assuming that the capacity ratio γ changes from 1% to 95%, the trajectory of the characteristic value and the trajectory of the participating factors with large changes in the system are shown in Figure 6.

[0048] As can be seen from Figure 6(a), a set of conjugate complex eigenvalues ​​λ 21,22 As the ratio γ increases, it gradually approaches the real axis, the system becomes more stable, and the oscillation frequency decreases. Combined with the participation factor trajectory in Figure 6(b), it can be seen that λ 21,22 The dominant state variables are the angular frequency ω2 generated by the grid converter and the phase angle difference δ between the grid voltage and the grid converter. g When the network penetration rate γ ≤ 31%, the eigenvalue λ 21,22 The participation factor gradually increases with increasing power penetration rate, and the increase is quite significant. After the network penetration rate γ exceeds 31%, the eigenvalue λ... 21,22The participation factor does not change much with the change of grid penetration rate, which means that the grid-type converter has provided relatively constant frequency inertia support for the system at this time.

[0049] As can be seen from Figure 6(c), when the network penetration rate is low, the system exhibits a set of unstable eigenvalues ​​λ. 15,16 After the network penetration rate exceeds 31%, the eigenvalues ​​enter the left half-plane, thus stabilizing the system. Combining this with the participation factor trajectory in Figure 6(d), it can be seen that when the network penetration rate is low, λ... 15,16 The dominant state variable is the phase angle difference δ1 between the grid-connected converter and the grid-connected converter, followed by the inner current loop state variable and the outer power loop state variable of the grid-connected converter. As grid penetration increases, the participation factors of δ1 and the state variables in the grid-connected converter control loop gradually decrease, and the grid current state variable begins to dominate. Because the grid-connected converter dominates at low grid penetration rates, under weak grid conditions, the input voltage of the grid-connected converter's phase-locked loop (PLL) and the output current of the converter are tightly coupled through grid impedance, forming an unstable positive feedback loop. This is detrimental to the PLL tracking the phase of the grid-connected inverter, resulting in an unstable system state. However, as grid penetration increases, the system's frequency and voltage support capability strengthens, effectively enhancing system strength. The fluctuations in the voltage tracked by the PLL due to grid impedance decrease, thus stabilizing the system. Since an increase in grid penetration rate also means a decrease in grid connection rate, and grid-connected converters are essentially current source converters, a decrease in grid connection rate essentially means a decrease in the output current of grid-connected converters, and thus the dominant factor of grid current state variables gradually increases.

[0050] (3.3) Impact of grid strength on system stability: The short-circuit ratio (SCR) was increased from 1 to 3.2 to analyze the impact of grid penetration rate on system stability under different grid scenarios. When the grid penetration rate was fixed at 31%, the trajectory of the characteristic value and the trajectory of the participating factors with large changes in the system are shown in Figure 7.

[0051] Figure 7 shows the eigenvalue locus of the system as the SCR increases from 1 to 3.2, and a pair of conjugate eigenvalues ​​λ. 15,16 As grid strength increases, the system shifts to the leftward complex plane, enhancing system stability. That is, when grid strength is weak, a 31% grid penetration rate is insufficient to support system stability; this represents the minimum critical grid penetration rate γ required to support system stability. minThe value decreases as the grid strength increases. Further analysis of the participation factors reveals that δ1 always dominates when the grid penetration rate is low. However, at the boundary point where the system enters the stable interface, the q-axis components of the power loop and the current loop of the grid-connected converter exhibit different trends and a boundary point appears. Before the critical point, as the grid strength increases, the positive feedback effect of the power loop continuously weakens and turns into negative feedback after the critical point, while the current loop does the opposite, thus leading the system into the stable region.

[0052] Figure 8 shows the stability region of the system under small-signal disturbances considering grid penetration rate under different grid strengths. As the grid strength increases, the minimum grid penetration rate required for system stability continuously decreases. A decrease in grid strength increases the instability risk of grid-connected converters. However, grid-connected converters, through their inherent voltage source control mechanism, can actively support the grid connection point voltage and effectively suppress voltage fluctuations. In this case, increasing the grid penetration rate can improve the voltage frequency support capability, making the voltage tracked by the grid-connected converter less prone to instability. Conversely, as the grid strength increases, the grid connection point voltage is less affected by grid impedance, reducing voltage fluctuations tracked by the phase-locked loop of the grid-connected converter. Therefore, a lower grid penetration rate is needed to stabilize the system.

[0053] Based on grid penetration rate, this invention quantitatively reveals the fundamental law that the minimum grid penetration rate required for the stability of hybrid systems under different grid scenarios decreases significantly with the increase of grid intensity. This provides a clear stability domain judgment for the configuration of grid-connected converter capacity under different grid conditions. The capacity matching method proposed in this invention is applicable to power supply in industries such as wind power, solar power, wind power generation, solar power generation, smart grid, AC transmission above 750 kV, large-scale grid security and defense systems, and intelligent dispatching systems.

[0054] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for capacity allocation optimization analysis of hybrid grid systems based on small-signal model, characterized in that, include: Step 1: Construct a hybrid single-feed system with grid connection and grid-connected configuration, including grid-connected converters and grid-connected converters. Each converter is connected to a common grid connection point and then to the AC power grid via corresponding filter lines and transmission lines. Step 2: Construct small-signal models, including small-signal models of grid-connected converters, grid-connected converters, filter lines, and the AC power grid. Integrate these models to obtain the small-signal model of the hybrid system with grid connection and grid connection. Step 3: Perform stability analysis of the hybrid system with grid connection and grid connection under different capacity ratios.

2. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to claim 1, characterized in that, In step 2, constructing the small-signal model of the filter circuit includes: modeling the filters and connecting lines of the grid-type converter and the interconnected grid-type converter. The filter circuit equation is as follows: Linearizing the filter circuit equations yields the small-signal model of the filter circuit: ; where u di and i di Let u represent the d-axis components of the output voltage and current of converter i, respectively. qi and i qi Let u represent the q-axis components of the output voltage and current of converter i, respectively. Ldi i Ldi It is divided into the d-axis components of its port voltage and current, u Lqi i Lqi It is divided into the d-axis components of its port voltage and current, ω i Its angular frequency, u bdi Let u be the d-axis component of the voltage at PCC in the local coordinate system of converter i; bqi Let L be the q-axis component of the voltage at PCC in the local coordinate system of converter i. fi and C fi For its filter inductor and filter capacitor, R fi For its LC filter, L ci and R ci The equivalent line inductance and equivalent line resistance at its connection to PCC; A Fi C FuLi C Fubi and C Fwi This is the corresponding coefficient matrix; the symbol △ represents the small signal component of the corresponding variable.

3. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to claim 1, characterized in that, In step 2, the small-signal model of the grid converter includes the small-signal model of the phase-locked loop (PLL) and the small-signal model of the PQ dual closed-loop control. Specifically, for the small-signal model of the PLL, its state equation is: ; where k pllp With k plli These are the PI parameters of the phase-locked loop (PLL); δ1 represents the phase angle difference between the output voltages of the grid-connected converter and the grid-connected converter, and xpll is an intermediate variable in the PLL integrator; A pllp A plli The corresponding coefficient matrix; for the small-signal model of PQ dual closed-loop control, the construction process includes: calculating the output power P1 and Q1 of the grid converter, and obtaining the power small-signal model after linearization: ;in 、 To determine the steady-state dq-axis components of the output current of the grid-connected converter, 、 To determine the steady-state dq-axis components of the output voltage of the grid-connected converter, we introduce the variable x. pq1 x idq1 Representing the integral outputs of the PI controllers in the power outer loop and current inner loop respectively, we obtain the small-signal model of the PQ outer loop of the grid converter: The expression for the inner current loop of a grid converter is: The output equation of the grid converter is: ;D 1pq D 1i E 1i B C1 E xi E xpq The corresponding coefficient matrix is ​​used; the state variables of the grid-type converter are selected as follows: Based on the PQ outer loop small-signal model, the grid-connected converter's inner current loop, and the grid-connected converter's output equations, the small-signal model for PQ dual closed-loop control is obtained: Among them, A VSC1 B VSC1 C VSC1 B ω This is the corresponding coefficient matrix; The dq axis components are converted to the common DQ coordinate system after the output current of the grid converter is transformed.

4. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to claim 1, characterized in that, Step 2, when constructing the small-signal model of the AC power grid, includes: constructing the small-signal model of the power grid phase angle as follows: ;δ g This represents the phase angle difference between the grid voltage and the output voltage of the grid-connected converter; transforming the grid voltage to a common coordinate system, we have: ;where U g0 δ is a steady-state quantity of the grid voltage amplitude. g0 This represents the steady-state phase angle difference between the grid voltage and the output voltage of the grid-connected converter. 、 R represents the steady-state component of the grid voltage along the dq axis in the common DQ coordinate system. g and L g Let be the equivalent inductance and resistance of the power grid; the circuit equation between the common connection point and the AC power grid is: Linearizing the circuit equations yields a small-signal model of the AC power grid: A gi A gu A gub A gw This is the corresponding coefficient matrix.

5. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to claim 1, characterized in that, In step 2, when constructing the small-signal model of the grid converter, droop control with an additional inertial element is applied. The mathematical model of the grid converter under droop control with an additional inertial element is expressed as follows: ； Where k1 is the frequency-active droop coefficient, k2 is the voltage-reactive droop coefficient, and ω p ω0 is the cutoff frequency of the low-pass filter, U0 is the reference frequency, and P is the reference voltage amplitude. 2ref Q is the active power reference value. 2ref Here, is the reactive power reference value, and s is the complex frequency domain differential operator. Linearizing this mathematical model yields the small-signal model for the droop control of the additional inertial element in a grid-type converter: ； The results of the analysis are as follows: ； A M1 A M2 B C2 The corresponding coefficient matrix is ​​used; the state variables of the grid-type converter are selected as follows: The small-signal model of a grid-type converter is shown below: A VSC2 B VSC2 C VSC2 This is the corresponding coefficient matrix; The dq axis components are converted to the common DQ coordinate system after the output current of the grid converter is transformed.

6. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to any one of claims 1-4, characterized in that, In step 2, the small-signal model of the integrated network hybrid system is obtained, including: introducing a virtual ground resistance R. VN At this point, the nodal equations of the common grid connection point are: Linearizing the equation for this node, we get: B VN The corresponding coefficient matrix is ​​used to obtain the small-signal model of the hybrid grid system: A sys Here is the corresponding coefficient matrix; where the system state variables are: 。 7. The capacity allocation optimization analysis method for hybrid interconnected systems based on a small-signal model according to claim 1, characterized in that, Step 3 includes: defining the total capacity of the grid-type converter and the grid-connected converter as S respectively. M and S L The network penetration rate γ is defined as: Among them, S M and S L n represents the total capacity of the grid-connected converter and the grid-linked converter. M and n L The number of grid-connected converters and grid-connected converters are respectively; the grid penetration rate γ is used to reflect the stability of the grid-connected hybrid system. The minimum grid penetration rate under different grid strengths is analyzed using eigenvalue analysis and participation factor analysis.

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