SISO model establishment method suitable for multi-machine interaction characteristic analysis

Abstract

The invention discloses an SISO model establishment method suitable for multi-machine interaction characteristic analysis. The SISO model establishment method comprises the steps of establishing an SISO model of a single grid-following type converter connected to a power grid; establishing an SISO model for accessing a single network-forming converter to a power grid; and step 3, coupling the obtained single-machine SISO model to the same steady-state coordinate system through matrix transformation, and further establishing a dynamic interaction model of a parallel-connection network-following type converter and a network-constructing type converter, namely obtaining the SISO model suitable for multi-machine interaction characteristic analysis. According to the constructed model, power grid frequency disturbance serves as an input variable, the frequency response dynamic state of the converters is completely described, the problem that a multi-input-multi-output system is difficult to analyze is solved, the two converters connected in parallel are finally converted into two mutually-acting SISO systems, a synchronization link only appears once in an open-loop transfer function of the system, and the synchronization efficiency is greatly improved. And loop shaping of the phase-locked loop and the power synchronization loop is facilitated.

Description

Technical Field

[0001] The present invention belongs to the field of control interaction model construction of hybrid systems, and more specifically, relates to a SISO (Single-Int Single-Output) model establishment method suitable for multi-machine interaction characteristic analysis. Background Art

[0002] With the development of new energy, DC transmission, energy storage and other technologies, large-scale power electronic equipment is connected to the power grid and profoundly changes the dynamic characteristics of modern power systems, among which the problems of reduced grid strength and reduced inertia are particularly prominent. The load influence, harmonic pollution, reactive power demand, current saturation and other factors of power electronic equipment themselves will lead to problems such as grid voltage drop and frequency deviation, which will weaken the strength of the grid; at the same time, the large-scale centralized access of new energy on the power generation side, the intensive DC transmission and feed-in on the transmission side, the distributed generation, microgrid and DC distribution network feed-in on the distribution side, and the access of a large number of power electronic loads on the power consumption side have all led to a reduction in system inertia, and the problem of frequency stability has become increasingly prominent.

[0003] In response to the above problems, energy storage systems have been widely used in inertial response, frequency modulation, voltage control, etc. By improving the power outer loop, the grid-following energy storage system working in the active-reactive control mode can achieve the regulation effect on the power grid. However, the energy storage system synchronized by the phase-locked loop does not have the active support capability and cannot autonomously control the frequency and voltage of the power grid. With the increase in the penetration rate of new energy, it is no longer sufficient to provide the system stability required by the power grid. On the other hand, in the event of a fault, the grid frequency drops at a large initial frequency change rate, and the grid-following energy storage shows the defect of insufficient inertial support capability in response time.

[0004] In the context of high penetration of grid-connected new energy, in order to provide the stability required by the power system, a feasible approach is to configure the grid-connected converter as a grid-connected converter with voltage source characteristics to achieve active support for the power grid. The grid-connected converter has the ability to form an autonomous network, the power loop outputs voltage instructions, and can self-synchronize the phase. Since 2016, many foreign institutions and organizations have issued guidance documents, proposing that the converter should have the ability to form a network, and put forward multiple requirements such as frequency and voltage control, weak network operation, and fault ride-through.

[0005] Due to different synchronization modes, the dynamic behaviors of grid-forming and grid-following converters are very different: the stability margin of the grid-following converter based on phase-locked loop synchronization gradually decreases with the decrease of the short-circuit ratio of the power grid, so there is an instability problem under weak power grid; however, as the strength of the power grid decreases, the degree of interaction between the grid-forming converter based on power synchronization and the AC power grid decreases, showing better stability. Therefore, the equipment with different synchronization modes has different applicability to the strength of the power grid, and the synchronization stability problem of the hybrid system composed of grid-following and grid-forming equipment needs further study. The existing models established for the hybrid system are all high-order, strongly coupled multi-input and multi-output models, which treat the entire system as a "black box" and the various links inside it are not divided. Therefore, it is not conducive to extracting a single feature for theoretical analysis, and the interaction characteristics between the two converters are still unclear. Summary of the invention

[0006] The present invention proposes a SISO model establishment method suitable for multi-machine interaction characteristic analysis. The grid frequency disturbance is used as the input variable to fully describe the frequency response dynamics of the converter. The model solves the problem of difficulty in analyzing the MIMO system. The two parallel converters are finally converted into two interacting SISO systems, and the synchronization link only appears once in the open-loop transfer function of the system, which is helpful for loop shaping of the PLL and power synchronization loop.

[0007] To achieve the above object, the present invention provides a SISO model establishment method suitable for multi-machine interaction characteristic analysis, comprising the following steps:

[0008] Step 1: Establish a SISO model of a single grid-following converter connected to the grid;

[0009] Step 2: Establish a SISO model of a single grid-forming converter connected to the grid;

[0010] Step 3. Following the derivation process of the single-machine SISO model obtained in step 1 and step 2, the single-machine SISO model obtained in step 1 and step 2 is coupled to the same steady-state coordinate system through matrix transformation, and then a dynamic interaction model of the parallel grid-following converter and the grid-forming converter is established, that is, a SISO model suitable for multi-machine interaction characteristic analysis with grid frequency disturbance as input is obtained.

[0011] Furthermore, step 1 establishes a SISO model of a single grid-following converter connected to the grid, specifically including:

[0012] Construct the circuit structure and control block diagram of a single grid-following converter connected to the AC grid through an LCL filter;

[0013] According to the circuit structure and control block diagram of a single grid-following converter connected to the grid, write the PLL dynamic equation, grid dynamic equation and current controller dynamic equation;

[0014] By combining the PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation, with the grid frequency disturbance as input and the frequency measured by the PLL as output, a SISO model of a single grid-following converter connected to the grid is obtained.

[0015] Furthermore, the PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation are listed according to the control block diagram of a single grid-following converter, specifically including:

[0016] The output frequency dynamics of the converter is determined by the PLL, and the PLL dynamic equation is expressed as:

[0017]

[0018] Among them, PI PLL (s) = k ppll +k ipll / s is the transfer function of the phase-locked loop PI controller, Δθ and Δω are the phase angle and angular frequency disturbances of the rotating coordinate system respectively; in steady state, v d The direction of the voltage coincides with the d-axis of the system coordinate system. At this time, the phase angle difference between the voltage at the PCC point and the grid voltage is δ. When a small disturbance occurs in the system, v q ≠0, the dynamic process of PLL will cause the system frequency to deviate from the steady-state value. Its action law is described by the PLL dynamic equation. Since the input of PLL is the voltage at the PCC point, at v gdq When it is constant, it is related to the output current of the converter, so the frequency dynamic characteristics of the system are coupled with the voltage and current;

[0019] The output port of the converter is connected to the power grid, the voltage and current satisfy the constraints, and the dynamic equation of the power grid is:

[0020]

[0021] Where Z g is the grid impedance matrix, V gdq is the grid voltage steady-state matrix, I dq is the converter output current steady-state matrix, L g , R g , ω are the grid inductance, resistance and angular frequency respectively, Δθ is the phase angle of the rotating coordinate system, Δθ g is the disturbance of the grid voltage phase, V gd and V gq is the steady-state value of the grid voltage, I d and I q is the steady-state value of the converter output current;

[0022] The modulation voltage of the GFL converter is determined by the current control loop, which is formulated in the dq axis of the GFL converter as:

[0023]

[0024] Among them, PI cl (s) = k pc +k ic / s is the transfer function of the current PI controller. Rearrange the above formula and let i dqref =0, eliminating the intermediate variable The dynamic equation of the current controller is obtained as follows:

[0025]

[0026] Furthermore, by combining the PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation, the grid frequency disturbance is used as input, and the frequency measured by the PLL is used as output, the SISO model of a single grid-following converter connected to the grid is obtained as follows:

[0027]

[0028] Among them G pll (s) = [0PI PLL (s)].

[0029] Furthermore, step 2 establishes a SISO model for a single grid-forming converter connected to the grid, specifically including:

[0030] Construct the circuit structure and control block diagram of a single grid-type converter connected to the grid through an LC filter;

[0031] According to the control block diagram inside the single grid-forming converter and its circuit structure connected to the grid, write the power synchronization control equation, grid dynamic equation and the admittance model of the single grid-forming converter in its own controller coordinate system;

[0032] By combining the power synchronization control equation, the grid dynamic equation and the admittance model of a single grid-forming converter in its own controller coordinate system, the SISO model of a single grid-forming converter connected to the grid is obtained.

[0033] Furthermore, the power synchronization control equation and the voltage and current control loop equation are listed according to the control block diagram inside the single grid-forming converter, and the admittance model of the grid-forming converter in its own controller coordinate system is obtained according to the circuit structure of the single grid-forming converter connected to the power grid, which specifically includes:

[0034] The output frequency of the grid-type converter is dynamically determined by the PSC, and the power synchronization control equation is expressed as:

[0035]

[0036] Where Δp=p ref -p is the disturbance of the converter output power, J and D p are the inertia coefficient and damping coefficient respectively;

[0037] The AC line is merged into the output impedance of the GFM. The port constraints are the same as when a single GFL is connected to the grid. The modulation voltage of the converter is determined by the voltage and current control loop. The voltage and current control loop equation is formulated as:

[0038]

[0039] Among them, PI vl (s), PI cl (s) are the transfer functions of the voltage and current PI controllers respectively. Rearrange the above formula and let v dqref = 0, eliminate the intermediate variables, and obtain the admittance model of the networked converter in its own controller coordinate system:

[0040]

[0041] Furthermore, by combining the power synchronization control equation, the grid dynamic equation and the admittance model of the grid-forming converter in its own controller coordinate system, the SISO model of a single grid-forming converter connected to the grid is obtained as follows:

[0042]

[0043] in:

[0044]

[0045] Furthermore, the step 3 of establishing a dynamic interaction model of the parallel grid-following converter and the grid-building converter specifically includes:

[0046] Build a generalized structure of a single GFL connected in parallel with a GFM and connected to the grid;

[0047] According to the generalized structure of a single GFL connected in parallel with the GFM and connected to the grid, the circuit equation of the system and the impedance equation of the converter are written in the GFM steady-state coordinate system by using matrix transformation. The first characterization equation group reflecting the transmission of the disturbance of the power grid and the power angle of the two converters to the voltage at the PCC point is obtained by combining the circuit equation and the impedance equation of the converter.

[0048] The second characterization equation group is written to reflect that the voltage disturbance and current disturbance of the two converters enter the synchronization link and affect the power angle of the converter, and the first characterization equation and the second characterization equation are combined to obtain a SISO model suitable for multi-machine interaction characteristics with grid frequency disturbance as input.

[0049] Furthermore, the simultaneous circuit equation and the impedance equation of the converter obtain a first set of characterizing equations reflecting the transmission of the disturbance of the power grid and the power angles of the two converters to the voltage at the PCC point;

[0050] The second characterization equation group reflecting the voltage disturbance and current disturbance of the two converters entering the synchronization link to affect the converter power angle is written, and the first characterization equation and the second characterization equation are combined to obtain a SISO model suitable for multi-machine interaction characteristics with grid frequency disturbance as input, which specifically includes:

[0051] The transformation matrix T is used to transform the steady-state coordinate system. The circuit equation of the system and the impedance equation of the converter are expressed as follows:

[0052]

[0053] Among them, the GFL controller coordinate system is referred to as c1 system, the GFM controller coordinate system is referred to as c2 system, Δθ1 and Δθ2 are the disturbances of the PLL and PSC output phase angles respectively, V dq1 and V dq2 It represents the steady-state value of the PCC voltage in the c1 and c2 systems, I dq1 and I dq2 represents the steady-state value of the current of the two converters in their own coordinate system, let θ 12 is the phase angle of the GFL coordinate system leading the GFM coordinate system in the steady state, and the transformation matrix T is expressed as:

[0054]

[0055] Write the corresponding equation in the GFM controller coordinate system to get a dual expression. Ignore θ1, and combine the circuit equation of the system and the impedance equation of the converter to get the first set of equations that reflects the mechanism of the transmission of the disturbance of the power grid and the power angle of the two converters to the voltage at the PCC point:

[0056]

[0057] In two different controller coordinate systems, the voltage and current disturbances enter their respective synchronization links, generate the power angles of the two converters, and form a frequency closed loop. The second characterization equation group of the influence of voltage and current disturbances on the converter power angle is obtained as follows:

[0058]

[0059] Combine the first characterization equation group and the second characterization equation group, and eliminate And order:

[0060]

[0061] The SISO model suitable for multi-machine interaction characteristics with power grid frequency disturbance as input is obtained:

[0062]

[0063] The present invention has the following beneficial effects:

[0064] 1. The present invention uses the grid frequency disturbance as the input variable and can fully describe the frequency response dynamics of the converter. The model solves the problem of difficult analysis of the MIMO system, and finally transforms the two parallel converters into two interacting SISO systems. The synchronization link only appears once in the open-loop transfer function of the system, which is helpful for the loop shaping of the PLL and the power synchronization loop (PSC).

[0065] 2. The invented model is used to analyze the interaction mechanism of the parallel GFL and GFM system, including two aspects of interaction: the supporting effect of GFM access of different capacities and locations on GFL frequency and voltage, and the impact of GFL access on GFM stability. Furthermore, the key controller parameters under different grid strengths are evaluated to make the interaction mechanism of the parallel GFM and GFL system clear, providing reference value for the design of controller parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is the circuit structure and control block diagram of the GFL converter;

[0067] Figure 2 is the converter coordinate system relationship under steady state and small disturbance conditions;

[0068] Figure 3 It is a SISO model of GFL converter based on frequency dynamics;

[0069] Figure 4 It is the circuit structure and control block diagram of GFM converter;

[0070] Figure 5 It is a GFM converter SISO model based on frequency dynamics;

[0071] Figure 6 It is a generalized structure of a single GFL connected in parallel with a GFM and connected to the grid;

[0072] Figure 7 It is a multi-machine interaction model based on frequency dynamics of the present invention;

[0073] Figure 8 It is the comparison and verification result of the model of the present invention and the time domain simulation;

[0074] Fig. 9 is the GFL frequency dynamic model taking into account GFM access;

[0075] Fig.10 is the PLL output characteristics under different power grid strengths, where (a) is the Nyquist criterion of the model, and (b) is the Bode plot of the model;

[0076] Fig.11 It is the comparison of the system dynamic characteristics before and after approximation;

[0077] Fig.12 The figure is the comparison of PLL output characteristics before and after GFM access, where (a) is the frequency domain characteristic and (b) is the time domain characteristic;

[0078] Fig.13 is a comparison of PLL output characteristics after different GFM capacities are connected, where (a) is the Nyquist criterion of the PLL and (b) is the Bode plot of the model;

[0079] Fig.14 It is the PLL output time domain waveform after different GFM capacities are connected;

[0080] Fig.15 are the output characteristics (SCR = 1.5) under different electrical distances and PLL bandwidths, where (a) is under different electrical distances and (b) is under different PLL bandwidths;

[0081] Fig.16 is the output characteristic of PLL at different electrical distances (SCR = 5), where (a) is the Nyquist criterion of PLL, and (b) is the Bode plot of the PLL system;

[0082] Fig.17 is the comparison of PSC output characteristics before and after GFL access, where (a) is the frequency domain characteristics and (b) is the time domain characteristics;

[0083] Fig.18 : are the output characteristic diagrams of PSC under different grid strengths, where (a) is its Nyquist criterion diagram and (b) is the Bode diagram. DETAILED DESCRIPTION

[0084] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0085] The embodiment of the present invention proposes a SISO model establishment method suitable for multi-machine interaction characteristic analysis, which takes the grid frequency disturbance as the input variable to fully describe the frequency response dynamics of the converter. The model solves the problem of difficulty in analyzing the MIMO system. The two parallel converters are finally converted into two interacting SISO systems, and the synchronization link only appears once in the open-loop transfer function of the system, which is helpful for the loop shaping of the PLL and the power synchronization loop (PSC). Using this model, the interaction mechanism of two different types of converters, GFL and GFM, is analyzed, specifically including two aspects of interaction: the supporting effect of GFM access of different capacities and positions on GFL frequency and voltage, and the influence of GFL access on GFM stability. Furthermore, the key controller parameters under different grid strengths are evaluated, and the simulation results prove the effectiveness of the proposed modeling method and analysis.

[0086] The method specifically comprises the following steps:

[0087] Step 1: Establish a SISO model of a single GFL (grid-following) converter connected to the grid. Figure 1 is the circuit structure and control block diagram of the three-phase power converter connected to the AC grid through the LCL filter in the dq coordinate system. Let e dq =[e d e q ] T is the output potential vector of the converter bridge arm, and the voltage at PCC point v dq =[v d v q ] T , the output current is i dq =[i d i q ] T , the parameters of the LCL filter are L f1 ,L f2 ,C f , the power grid uses an ideal voltage source in series with an inductor L g To simulate, the grid voltage vector is represented by v gdq =[v gd v gq ] T. The converter uses SRF-PLL to achieve grid synchronization, and the reference value of the current control loop comes from the active and reactive power control loops of the previous stage. Existing studies have shown that the main factor affecting the stability of the GFL converter under weak grid conditions is the coupling between the PLL and the current control loop. The change in PCC voltage is transmitted through the phase-locked loop, which seriously affects the converter current. The self-synchronization loop formed significantly reduces the synchronization stability of the GFL converter. In order to simplify the model, the power control loop, that is, constant current command control, is ignored in the research of this invention; at the same time, since the high-frequency current component flowing through the filter capacitor has little effect on the synchronization stability, the capacitor branch can be disconnected, and the inverter side filter inductor L f1 and the grid-side filter inductor L f2 After merging, use L f express.

[0088] The output frequency of the converter is dynamically determined by the PLL and is expressed as:

[0089]

[0090] Among them, PI PLL (s) = k ppll +k ipll / s is the transfer function of the phase-locked loop PI controller, Δθ and Δω are the phase angle and angular frequency disturbances in the rotating coordinate system, respectively. The superscript 'c' represents the physical quantity in the controller coordinate system, and '~' represents the disturbance. For the sake of simplicity, the '~' symbol will be omitted in the following text, and lowercase letters will all represent disturbances.

[0091] Figure 2 is the phasor diagram of the power converter. In steady state, v d The direction coincides with the d-axis of the system coordinate system ( Figure 2 Medium s axis), at this time, the phase angle difference between the PCC voltage and the grid voltage is δ. When a small disturbance occurs in the system, v q ≠0, the dynamic process of PLL will cause the system frequency to deviate from the steady-state value. Its action law is described by equation (1). Since the input of PLL is the voltage at the PCC point, when v gdq When it is constant, it is related to the output current of the converter, so the frequency dynamic characteristics of the system are coupled with the voltage and current.

[0092] The output port of the converter is connected to the grid, and the voltage and current satisfy the constraints:

[0093]

[0094] Where Z g is the grid impedance matrix, Δθ g is the disturbance of the grid voltage phase, V gd and Vgq is the steady-state value of the grid voltage, I d and I q is the steady-state value of the converter output current.

[0095] The modulation voltage of the converter (i.e., the reference input for generating the PWM signal) is determined by the current control loop, which can be formulated in the dq axis of the converter as:

[0096]

[0097] Among them, PI cl (s) = k pc +k ic / s is the transfer function of the current PI controller. We rearrange equation (3) and let i dqref =0, eliminating the intermediate variable The admittance model of the converter in its own controller coordinate system is obtained:

[0098]

[0099] Equations (1), (2) and (4) describe the PLL dynamics, grid dynamics and current controller dynamics respectively. Combining equations (1), (2) and (4), with the grid frequency disturbance as input and the PLL measured frequency as output, we get the SISO model that integrates the dynamics of the entire system:

[0100]

[0101] Among them G pll (s) = [0PI PLL (s)].

[0102] Figure 3 It describes the above transfer function model. Equation (5) describes how the output frequency of the converter tracks the grid frequency and contributes to the synchronization process under the action of PLL. Compared with the traditional modeling method that focuses on the output voltage and current of the converter, this model examines the output frequency characteristics of the converter. Since there is no need to consider the components of the two shaft systems, this modeling method avoids the complex analysis of the MIMO model. The instability dominated by PLL and PSC in the converter synchronization link is due to the instability of internal states such as the shaft system rotor angle and phase lock angle, which in turn stimulates the instability of the output voltage / current phase, which belongs to the category of synchronization stability. This model fully captures the grid synchronization dynamics of the converter, so it is very suitable for the study of synchronization stability.

[0103] Although the control objectives and synchronization methods are different, the method proposed in the previous section is still applicable to the modeling of GFM type converters.

[0104] Step 2: Establish a SISO model of a single GFM (grid-forming) converter connected to the grid. Figure 4 This is the circuit structure and control block diagram of a single GFM connected to the grid through an LC filter. f and L c The converter uses power synchronization control (PSC) to achieve synchronization with the power grid, and the AC voltage control (AVC) generates the d-axis reference value of the AC voltage, which is sent to the voltage and current double closed-loop controller of the subsequent stage to generate the modulation voltage. The voltage controller controls the voltage v on the capacitor. Cdq . In contrast to GFL, GFM exhibits better stability under weak grid conditions, but under strong grid conditions, due to the enhanced coupling between the PSC loop and the voltage loop, the power angle disturbance of the grid is fed forward through the voltage and current loops, which reduces the synchronous stability of the system. Since the reactive power regulation part has little effect on the synchronous stability of GFM, the AVC loop is omitted in the present invention, constant AC voltage control is adopted, and the capacitor branch is still disconnected, and the model is built in the controller coordinate system of GFM.

[0105] The output frequency of the converter is dynamically determined by the PSC and is expressed as:

[0106]

[0107] Where Δp=p ref -p is the disturbance of the converter output power, J and D p are the inertia coefficient and damping coefficient, respectively. Similar to GFL, when the power of the converter is disturbed, the dynamic process of PSC will cause the system frequency to deviate from the steady-state value, and its action law is described by equation (6).

[0108] The AC line is merged into the output impedance of the GFM. The port constraint remains unchanged as equation (2). The modulation voltage of the converter is determined by the voltage and current control loop and is formulated as follows:

[0109]

[0110] Among them, PI vl (s), PI cl (s) are the transfer functions of the voltage and current PI controllers respectively. After rearranging the equation, let v dqref = 0, eliminate the intermediate variables, and obtain the admittance model of the converter in its own controller coordinate system:

[0111]

[0112] Combining equations (2), (6) and (8) yields the SISO model that integrates the dynamics of the entire system:

[0113]

[0114] in:

[0115]

[0116] Figure 5 It is a GFM converter SISO model based on frequency dynamics. Equation (9) has exactly the same structure as equation (5). The current controller of GFL corresponds to the voltage controller of GFM, and the PLL loop of GFL corresponds to the PSC loop of GFM. The two equations respectively describe the response of a single converter to the grid frequency, and separate the grid dynamics from the dynamics of the synchronization link, which is helpful for loop shaping.

[0117] Step 3: Establish a dynamic interaction model of parallel GFL and GFM converters. Now consider the case where a GFL and GFM are connected to the grid in parallel. Figure 6 It is a generalized grid structure of a single GFL connected in parallel with a GFM. Zc is the impedance of the connection line between the GFM outlet and the PCC. The superscripts c1 and c2 represent the GFL controller coordinate system and the GFM controller coordinate system respectively. The subscript 1 represents the physical quantity of the GFL, and the subscript 2 represents the physical quantity of the GFM.

[0118] Due to the existence of line impedance, the steady-state coordinate systems of the two converters do not overlap. Here, the transformation matrix T is used to transform the steady-state coordinate systems. The circuit equation of the system and the impedance equation of the converter are expressed as:

[0119]

[0120] Among them, Δθ1 and Δθ2 are the disturbances of the PLL and PSC output phase angles respectively, V dq1 and V dq2 It represents the steady-state value of the PCC voltage under the c1 and c2 systems. The same is true for the grid voltage. I dq1 and I dq2 represents the steady-state value of the current of the two converters in their own coordinate system. Let θ 12 is the phase angle of the GFL coordinate system leading the GFM coordinate system in the steady state, and the transformation matrix T is expressed as:

[0121]

[0122] The description of formula (11) is completed in the c2 coordinate system. Similarly, the corresponding equation can be written in the c1 coordinate system to obtain a dual expression. Note that θ 12 Generally it is very small, so it is ignored, and the first characterization equation group is obtained by combining the equations in equation (11):

[0123]

[0124] Equation (13) describes how the disturbances of the power grid and the power angles of the two converters are transmitted to the PCC point voltage. In two different controller coordinate systems, the disturbances of voltage and current enter their respective synchronization links, generate the power angles of the two converters, form a frequency closed loop, and obtain the second characterization equation group of the influence of voltage and current disturbances on the converter power angle:

[0125]

[0126] Simultaneous expression (13), (14), elimination And order:

[0127]

[0128] The SISO model suitable for multi-machine interaction characteristics with power grid frequency disturbance as input is obtained:

[0129]

[0130] Figure 7 It is the transfer function model obtained by the above formula with the grid frequency disturbance as input. In this model, the two converters take the phase Δθ1 and Δθ2 of their respective coordinate systems as outputs, and show different dynamic responses to the grid frequency disturbance, and there is a coupling relationship between them. This model describes its synchronization process very well. Since the voltage and current of the converter are only intermediate variables, from the input and output ports, the model can be described by two SISO transfer functions, thus avoiding the difficulty of analyzing the MIMO system.

[0131] Figure 8 To compare the results of the frequency domain model with the time domain simulation, a step disturbance of 1 rad / s was applied to the grid frequency in Simulink. The step response of the above model was consistent with the results of the electromagnetic transient simulation, verifying the correctness of the modeling.

[0132] In equation (15), the steady-state value of the low-frequency current is of a small magnitude and can be ignored, and it is approximately assumed that V dq =V gdq , combined with equation (4) and equation (8), without considering the line impedance, Y 11 , Y 12 and Y 21 There is an approximate relationship between them:

[0133]

[0134] Where S represents the capacity of the converter.

[0135] Fig. 9is the SISO model of the GFL converter taking into account the GFM access. Based on the previous analysis, the dynamic interaction between GFM and GFL under different grid strengths, electrical distances and capacities is analyzed. In formula (16), Δθ 1- Δθ g , Δθ 2- Δθ g As the principal element, Δθ g Eliminate and get:

[0136]

[0137] Further we get:

[0138]

[0139] Let the transfer function in the above figure be G mf (s). At this point, the GFM branch can be converted into the GFL frequency loop to obtain the GFL converter SISO model taking into account the GFM access. The red part represents the impact of GFM on the GFL frequency dynamics. Its open-loop transfer function is shown in formula (20):

[0140]

[0141] Compared with GFL when connected alone, the interaction between GFM and GFL is reflected in two aspects. One is due to the physical impedance of the access Y IV2 (s), which is related to the circuit parameters of GFM and the parameters of the voltage and current controller, and affects the first term Y in the above formula 11 The value of GFM in parallel is the addition of the admittance of the two. The other part is due to the difference in the synchronization link. The inertia and damping characteristics of GFM are reflected in this item because the converters with the same synchronization mode do not have this item in parallel.

[0142] Now, we will use formula (20) to consider the influence of three parameters: grid strength, GFM capacity and electrical distance on the GFM support characteristics.

[0143] 1) Under different grid strengths

[0144] When the system short circuit ratio SCR varies between 1.4 and 4.4, the frequency of the PLL output after GFL is connected alone and GFL is connected in parallel with 20% capacity GFM is considered. Fig.10 (a) describes the Nyquist diagram of the parallel system, which is used to determine the stability of the system. When the grid strength increases, the Nyquist curve gradually approaches the critical point (-1,0j) and the system begins to become unstable. Fig.10(b) shows the frequency support effect of GFM on GFL under different grid strengths. After GFM is connected, the characteristics of the parallel system in the low frequency band are significantly changed, and the instability problem under weak grid is significantly improved. However, as the grid strength increases further, the system stability margin also decreases, until SCR = 4.4, the phase-frequency characteristic of the system crosses the -180° phase line at around 6Hz and becomes unstable. The oscillation in this frequency band is generated by GFM under strong grid. Therefore, when the grid is strong, the damping coefficient of GFM should be appropriately increased to improve the stability of the parallel system.

[0145] Note that the bandwidth of the PSC is much smaller than that of the PLL. If the line impedance is not considered, there is also σ(Y IV2 )>>σ(Y IV1 )(σ represents the singular value of the matrix) Therefore, G in formula (20) psc (Y 22 +Y 21 ) is much smaller than G pll Y 12 The amplitude of , after neglecting it, is:

[0146]

[0147] Furthermore, in the low frequency band, G pll Y 12 The amplitude is >> 1, ignoring the second term in the denominator; in the high frequency band, G psc Y 11 The amplitude of decays rapidly, and the first term in the numerator is ignored. Therefore, the final open-loop transfer function can be approximately written as:

[0148]

[0149] Among them, ω1 and ω2 are certain segment point frequencies, which are approximately 10 to 20 Hz in this example.

[0150] Fig.11 It is the Bode diagram of the open-loop transfer function before and after approximation. Under weak power grid, equation (22) can describe the frequency characteristics of the system more accurately. From this, we can see that after GFM is connected, the effect of PLL in the low frequency band will be ignored, and it will only work in the high frequency band; the low frequency characteristics of the system will be determined by the PSC loop. Compared with the low frequency characteristics of equation (23) when GFM is connected alone, it is the dominant part of the low frequency band in equation (22).

[0151] G GFM (s) = G psc (EZ g Y IV2 ) -1 V gdq ≈G psc Y 11(twenty three)

[0152] Fig.12 (a) describes in detail the change of GFL output frequency before and after GFM is connected to the weak grid. At this time, the system short-circuit ratio SCR is about 1.5. Before GFM is connected, the phase margin PM of the Bode diagram is ≈ 0. Fig.12 In the time domain waveform (b), a large oscillation appears. When the GFM is connected, the characteristics of the system in the low frequency band are significantly changed. Limited by the bandwidth of the PSC loop, the frequency response speed of the GFL slows down, and the phase in the low frequency band starts to decrease from -90 degrees, thereby retaining a phase margin of about 60 degrees near the crossover frequency. The overshoot in the time domain waveform (d) disappears, and the oscillation is significantly suppressed.

[0153] 2) Different GFM capacities

[0154] Under a certain grid strength, GFM must support GFL and its capacity has a lower limit. Fig.12 As shown in (a), when SCR = 1.4, as the GFM capacity decreases, the Nyquist curve gradually approaches (-1, 0j) and the system stability margin decreases. Fig.12 (b) describes the GFL frequency response Bode diagram as the GFM capacity changes. The GFM has a significant impact on its low frequency band. The access of a larger GFM reduces the system's crossover frequency, slows down the response, and increases the stability margin. At this time, the system's oscillation mode is also below 10Hz, indicating that the oscillation is generated by the GFM loop. Because as the capacity decreases, the grid strength from the GFM perspective gradually increases. Fig.14 The frequency waveform of PLL output after GFM with different capacities is connected is given.

[0155] It can be seen that even a GFM with a capacity of only 0.2 pu can significantly improve the system stability. This is because its voltage source control method makes it have a large small signal admittance in the low frequency band (refer to formula (8)). At the same time, we found that a GFM with too small capacity will affect the entire system due to the instability of its own link. At this time, it is necessary to reduce the bandwidth of the PSC loop to increase the stability margin.

[0156] 3) At different electrical distances

[0157] The electrical distance is reflected in the line impedance connecting the GFM to the PCC point. In order to examine its impact on the stability of the parallel system, two cases, SCR=1.5 and SCR=5, are taken. Fig.15(a) is the Bode plot of the PLL output frequency when the line impedance is changed when SCR=1.5. The results show that when the electrical distance from GFM to GFL is too far, the existence of the line impedance weakens the voltage source characteristics of the GFM, which is insufficient to support the stable operation of the GFL. The change of line impedance is equivalent to changing the small signal admittance of the GFM port, as described in equation (24), and its impact is mainly concentrated in the medium and high frequency bands. Fig.15 (b) shows the output frequency characteristics of PLLs with different bandwidths when the fixed line impedance is 0.3pu. Reducing the bandwidth of the PLL can improve the stability margin of the GFL, and the frequency of oscillation will also decrease. At the same time, since the GFM is closer to the voltage source characteristics in the low frequency band, when the electrical distance between the GFM and the GFL is far, the bandwidth of the PLL should be appropriately reduced to improve stability.

[0158] Fig.16 The figure shows the influence of line impedance on system characteristics under strong grid (SCR=5). The existence of GFM connection line can enhance its own stability. Too small line impedance may cause instability of GFM loop, such as Fig.16 (a). Fig.16 As can be seen in (b), the larger the line impedance, the higher the system stability margin and the slower the system response speed. In order to improve the stability of GFM under strong network conditions, virtual resistance (VR) control is usually introduced to simulate the effect of line resistance.

[0159] Under weak grid conditions, the access of GFM can significantly enhance the synchronous stability of GFL, while under strong grid conditions, it is also necessary to consider how the access of GFL affects the stability of GFM. The original model is dualized, and the impact of GFL on GFM is converted to the GFM branch. The open-loop transfer function with GFM frequency as the output variable is obtained as follows:

[0160]

[0161] By performing similar approximate processing, we obtain the output frequency characteristics of the low-frequency GFM:

[0162]

[0163] The small amount G in the denominator is ignored. psc Y 21 +G pll Y 22 -1 and a small amount of G in the molecule psc Y 11 .

[0164] Comparing equation (25) with the first equation in equation (22), it can be seen that the two have almost the same characteristics in the low frequency band, which further explains the frequency support effect of GFM access on the entire system.

[0165] Fig.17 The change of GFM output frequency before and after GFL is input under strong power grid is described. At this time, the system short-circuit ratio SCR is about 5. Fig.17 (a) shows that the access of GFL has almost no effect on the response speed of GFM (fast response in parallel with slow response results in an overall slow response), but it will reduce the phase of GFM in the low-frequency band and reduce its stability margin. Fig.17 (b) In the time domain, it is shown that the access of GFL will enhance the oscillation of GFM under strong network. Therefore, the access of GFL will actually reduce the stability of GFM.

[0166] Fig.18 The output frequency characteristics of PSC under different grid strengths were investigated. Since the frequency characteristics of the system did not change much before and after the GFL was connected, it was unstable under strong grid conditions, just like a single GFM. Fig.10 and Fig.18 The critical stable grid strength is consistent with that of the grid, and an oscillation frequency of about 6 Hz appears when SCR=4.4.

[0167] In summary, the present invention provides a SISO model suitable for the analysis of multi-machine interaction characteristics. This model aims at the problem of MIMO system analysis, and finally transforms two parallel converters into two interacting SISO systems. The synchronization link only appears once in the open-loop transfer function of the system, which is helpful for the loop shaping of PLL and power synchronization loop (PSC). Using this model, the interaction mechanism of two different types of converters, GFL and GFM, is analyzed, specifically including two aspects of interaction: the supporting effect of GFM access with different capacities and positions on GFL frequency and voltage, and the influence of GFL access on GFM stability. Furthermore, the key controller parameters under different grid strengths are evaluated.

[0168] Compared with the traditional model, the present invention can better reveal the internal mechanism and solve the problem of difficult analysis of MIMO system. The model is used to analyze the frequency support characteristics of GFL under different grid strengths, different GFM capacities and different electrical distances, as well as the impact of GFL access on GFM stability. The conclusions are as follows:

[0169] 1. When the electrical distance between GFM and GFL is close, the instability problem of GFL under weak grid is significantly improved. However, when the grid is too strong or the GFM capacity is too small, GFM itself will cause system instability. At this time, it is necessary to increase the damping coefficient of GFM to improve its stability.

[0170] 2. When the electrical distance is too far, the GFM cannot effectively support the frequency and voltage of the GFL, and the GFL generates oscillations under a weak power grid. At this time, it is necessary to increase the bandwidth of the GFM voltage loop and enhance its voltage source characteristics, or appropriately reduce the bandwidth of the PLL and weaken its coupling with the current loop.

[0171] 3. The access of GFL will enhance the coupling of the internal loop of GFM and destroy the stability. Therefore, a certain stability margin needs to be reserved when designing GFM parameters.

[0172] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0173] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A SISO model building method suitable for multi-machine interaction characteristic analysis, characterized in that: The steps include: Step 1: Establish a SISO model of a single grid-following converter connected to the grid; Step 2: Establish a SISO model of a single grid-forming converter connected to the grid; Step 3. Following the derivation process of the single-machine SISO model obtained in step 1 and step 2, the single-machine SISO model obtained in step 1 and step 2 is coupled to the same steady-state coordinate system through matrix transformation, and then a dynamic interaction model of the parallel grid-following converter and the grid-forming converter is established, that is, a SISO model suitable for multi-machine interaction characteristic analysis with grid frequency disturbance as input is obtained.

2. The SISO model establishment method suitable for multi-machine interaction characteristic analysis according to claim 1, characterized in that: Step 1: Establish a SISO model for a single grid-following converter connected to the grid, including: Construct the circuit structure and control block diagram of a single grid-following converter connected to the AC grid through an LCL filter; According to the circuit structure and control block diagram of a single grid-following converter connected to the grid, write the PLL dynamic equation, grid dynamic equation and current controller dynamic equation; By combining the PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation, with the grid frequency disturbance as input and the frequency measured by the PLL as output, a SISO model of a single grid-following converter connected to the grid is obtained.

3. The SISO model establishment method for connecting a single grid-following converter to a grid as claimed in claim 2, characterized in that: The PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation are listed according to the control block diagram of a single grid-following converter, specifically including: The output frequency dynamics of the converter is determined by the PLL, and the PLL dynamic equation is expressed as: Among them, PI PLL (s) = k ppll +k ipll / s is the transfer function of the phase-locked loop PI controller, Δθ and Δω are the phase angle and angular frequency disturbances of the rotating coordinate system respectively; in steady state, v d The direction of the voltage coincides with the d-axis of the system coordinate system. At this time, the phase angle difference between the voltage at the PCC point and the grid voltage is δ. When a small disturbance occurs in the system, v q ≠0, the dynamic process of PLL will cause the system frequency to deviate from the steady-state value. Its action law is described by the PLL dynamic equation. Since the input of PLL is the voltage at the PCC point, at v gdq When it is constant, it is related to the output current of the converter, so the frequency dynamic characteristics of the system are coupled with the voltage and current; The output port of the converter is connected to the power grid, the voltage and current satisfy the constraints, and the dynamic equation of the power grid is: Where Z g is the grid impedance matrix, V gdq is the grid voltage steady-state matrix, I dq is the converter output current steady-state matrix, L g , R g , ω are the grid inductance, resistance and angular frequency respectively, Δθ is the phase angle of the rotating coordinate system, Δθ g is the disturbance of the grid voltage phase, V gd and V gq is the steady-state value of the grid voltage, I d and I q is the steady-state value of the converter output current; The modulation voltage of the GFL converter is determined by the current control loop, which is formulated in the dq axis of the GFL converter as: Among them, PI cl (s) = k pc +k ic / s is the transfer function of the current PI controller. Rearrange the above formula and let i dqref =0, eliminating the intermediate variable The dynamic equation of the current controller is obtained as follows:

4. The SISO model establishment method suitable for multi-machine interaction characteristic analysis as claimed in claim 3, characterized in that: By combining the PLL dynamic equation, the grid dynamic equation and the current controller dynamic equation, the grid frequency disturbance is used as input, and the frequency measured by the PLL is used as output, the SISO model of a single grid-following converter connected to the grid is obtained as follows: Among them G pll (s) = [0PI PLL (s)].

5. The SISO model establishment method suitable for multi-machine interaction characteristic analysis according to claim 1, characterized in that: Step 2: Establish a SISO model for a single grid-connected converter connected to the grid, including: Construct the circuit structure and control block diagram of a single grid-type converter connected to the grid through an LC filter; According to the control block diagram inside the single grid-forming converter and its circuit structure connected to the grid, write the power synchronization control equation, grid dynamic equation and the admittance model of the single grid-forming converter in its own controller coordinate system; By combining the power synchronization control equation, the grid dynamic equation and the admittance model of a single grid-forming converter in its own controller coordinate system, the SISO model of a single grid-forming converter connected to the grid is obtained.

6. The SISO model establishment method suitable for multi-machine interaction characteristic analysis according to claim 5, characterized in that: The power synchronization control equation and the voltage and current control loop equation are listed according to the control block diagram inside the single grid-forming converter, and the admittance model of the grid-forming converter in its own controller coordinate system is obtained according to the circuit structure of the single grid-forming converter connected to the power grid, which specifically includes: The output frequency of the grid-type converter is dynamically determined by the PSC, and the power synchronization control equation is expressed as: Where Δp=p ref -p is the disturbance of the converter output power, J and D p are the inertia coefficient and damping coefficient respectively; The AC line is merged into the output impedance of the GFM. The port constraints are the same as when a single GFL is connected to the grid. The modulation voltage of the converter is determined by the voltage and current control loop. The voltage and current control loop equation is formulated as: Among them, PI vl (s), PI cl (s) are the transfer functions of the voltage and current PI controllers respectively. Rearrange the above formula and let v dqref = 0, eliminate the intermediate variables, and obtain the admittance model of the networked converter in its own controller coordinate system:

7. The SISO model establishment method suitable for multi-machine interaction characteristic analysis according to claim 6, characterized in that: By combining the power synchronization control equation, the grid dynamic equation and the admittance model of the grid-forming converter in its own controller coordinate system, the SISO model of a single grid-forming converter connected to the grid is obtained as follows: in:

8. The SISO model establishment method suitable for multi-machine interaction characteristic analysis according to claim 1, characterized in that: Step 3 establishes a dynamic interaction model of the parallel grid-following converter and the grid-building converter, which specifically includes: Build a generalized structure of a single GFL connected in parallel with a GFM and connected to the grid; According to the generalized structure of a single GFL connected in parallel with the GFM and connected to the grid, the circuit equation of the system and the impedance equation of the converter are written in the GFM steady-state coordinate system by using matrix transformation. The first characterization equation group reflecting the transmission of the disturbance of the power grid and the power angle of the two converters to the voltage at the PCC point is obtained by combining the circuit equation and the impedance equation of the converter. The second characterization equation group is written to reflect that the voltage disturbance and current disturbance of the two converters enter the synchronization link and affect the power angle of the converter, and the first characterization equation and the second characterization equation are combined to obtain a SISO model suitable for multi-machine interaction characteristics with grid frequency disturbance as input.

9. The specific implementation steps of the dynamic interactive system model of the parallel grid-following converter and the grid-building converter as claimed in claim 8 are characterized in that: The simultaneous circuit equation and the impedance equation of the converter obtain a first characterization equation group reflecting the transmission of the disturbance of the power grid and the power angle of the two converters to the voltage at the PCC point; The second characterization equation group reflecting the voltage disturbance and current disturbance of the two converters entering the synchronization link to affect the converter power angle is written, and the first characterization equation and the second characterization equation are combined to obtain a SISO model suitable for multi-machine interaction characteristics with grid frequency disturbance as input, which specifically includes: The transformation matrix T is used to transform the steady-state coordinate system. The circuit equation of the system and the impedance equation of the converter are expressed as follows: Among them, the GFL controller coordinate system is referred to as c1 system, the GFM controller coordinate system is referred to as c2 system, Δθ1 and Δθ2 are the disturbances of the PLL and PSC output phase angles respectively, V dq1 and V dq2 It represents the steady-state value of the PCC voltage in the c1 and c2 systems, I dq1 and I dq2 represents the steady-state value of the current of the two converters in their own coordinate system, let θ 12 is the phase angle of the GFL coordinate system leading the GFM coordinate system in the steady state, and the transformation matrix T is expressed as: Write the corresponding equation in the GFM controller coordinate system to get a dual expression. Ignore θ1, and combine the circuit equation of the system and the impedance equation of the converter to get the first set of equations that reflects the mechanism of the transmission of the disturbance of the power grid and the power angle of the two converters to the voltage at the PCC point: In two different controller coordinate systems, the voltage and current disturbances enter their respective synchronization links, generate the power angles of the two converters, and form a frequency closed loop. The second characterization equation group of the influence of voltage and current disturbances on the converter power angle is obtained as follows: Combine the first characterization equation group and the second characterization equation group, and eliminate And order: The SISO model suitable for multi-machine interaction characteristics with power grid frequency disturbance as input is obtained:

Images