Large signal stability analysis method for complex micro-grid

Abstract

The invention discloses a large signal stability analysis method for a complex micro-grid. The method comprises the following specific steps: establishing a nonlinear state space model of each component of the micro-grid, forming a system-level nonlinear model of the alternating current micro-grid by using the model of each component, performing piecewise linearization on the original nonlinear model by using a Takagi-Sugeno (TS) multiple modeling method, and constructing a linear matrix inequality group. Secondly, solving a linear matrix inequality group, constructing an energy function of the micro-grid, and mapping the energy function to a two-dimensional plane to obtain an analytic expression of an attraction domain; and finally, the influence mechanism of the system parameters on the stability of the large signal is obtained by adjusting the system parameters and solving the attraction domain under each working condition. The method can be used for analyzing the stability of the actual complex micro-grid, and theoretical guidance is provided for planning and parameter design of the micro-grid.

Description

Technical Field

[0001] The present invention belongs to the field of AC microgrid control technology, and specifically relates to a large signal stability analysis method for a complex microgrid. Background Art

[0002] Replacing traditional thermal power generation with renewable energy can reduce carbon emissions and reduce the consumption of fossil energy. Microgrids are an effective way to develop and utilize renewable energy. Microgrids usually complete power conversion through inverters. At present, the control strategies of inverters are mainly divided into two categories: grid-following control and grid-forming control. Among them, the grid-forming inverter behaves as a voltage source, providing voltage and frequency support for the off-grid microgrid. The grid-following inverter behaves as a current source, and its front-stage converter usually adopts maximum power point tracking (MPPT) control, which can achieve efficient utilization of renewable energy. The combination of grid-following (GFL) and grid-forming (GFM) inverters can achieve efficient utilization of energy while maintaining the stability of the microgrid voltage and frequency. In addition, microgrids also contain complex nonlinear loads. The nonlinear and multi-time scale coupling characteristics of these power electronic devices bring great challenges to the stability analysis of microgrids.

[0003] Chinese invention CN112993969B proposes a large signal stability analysis method based on mixed potential theory, which provides a theoretical basis for system design. However, this method is designed for DC microgrids, while the dynamic process of AC microgrids is relatively more complex. Actual microgrids usually contain multiple types of inverters and complex loads. The present invention proposes a large signal stability analysis method for an actual microgrid model that includes a grid-following inverter, a grid-building inverter and multiple types of loads. The multiple types of loads include constant impedance load (CIL), constant current load (CCL), constant power load (CPL), collectively referred to as ZIP load. Summary of the invention

[0004] The purpose of the present invention is to provide a large signal stability analysis method for a complex AC microgrid composed of multiple inverters and nonlinear loads, so as to solve the problem that the range of reliable linearization near the steady-state operating point is difficult to quantify when using a stability analysis method based on small signals.

[0005] The technical solution of the present invention is: a large signal stability analysis method based on piecewise linearization. It is characterized by comprising the following steps:

[0006] Step 1: Establish the large signal average model of the grid-building converter and the grid-following inverter in the dq coordinate system and write it in the form of state space expression. When modeling, it is necessary to consider the power loop, voltage loop and other controllers at all levels.

[0007] Step 2: Establish a nonlinear state space model of constant power load and a node tie line dynamic model. Then, based on the ZIP load and the output characteristics of multiple types of converters, the node voltage equations of the AC microgrid are established.

[0008] Step 3: Based on the state space model of each subsystem, a system-level nonlinear model of the complex microgrid is established.

[0009] Step 4: Use the Takagi-Sugeno (TS) multiple modeling method to process the nonlinear model of the microgrid. Then construct and solve the linear matrix inequality (LMI) to obtain the energy function and transient stability boundary.

[0010] Step 1 is implemented as follows:

[0011] Microgrids have the ability to operate independently off-grid and need to be supported by an opposing voltage source for voltage and frequency. Therefore, grid-forming converters are essential for microgrids. First, the state space model of the grid-forming converter is established.

[0012] According to the main circuit differential equation of the inverter and the droop controller, the voltage and current dual closed-loop control system establishes the large signal state space model of the grid-connected inverter as follows:

[0013]

[0014] Among them, x invi is the state vector of the i-th grid-connected inverter in the microgrid. is the control matrix. com is the reference angular frequency of the common coordinate system, v bdqi is the voltage vector of the ith node.

[0015] Similarly, the state space model of the grid-following inverter is established based on the main circuit average model and the voltage and current dual closed-loop control system as follows:

[0016]

[0017] Among them, x GFL =[u dc3 ,m1,m2,m3,i fd3 ,i fq3 ,u od3 ,u oq3 ,i od3 ,ioq3 ] T is the state vector of the grid-following inverter, and m1, m2, and m3 are the intermediate variables introduced by integral control in the voltage and current double closed-loop control system. bDQ2 is the voltage vector of the second node in the common coordinate system.

[0018] Step 2 is implemented as follows:

[0019] The node tie line contains line inductance and parasitic resistance, and its dynamic process is affected by the voltage dynamics of adjacent nodes. The corresponding state space model is as follows:

[0020]

[0021] Among them, i lDQi(i+1) is the value of the current on the tie line between the i-th and i+1-th nodes in the common dq coordinate system.

[0022] The constant power load in the ZIP load is realized by PWM rectifier. To reduce current harmonics, the constant power load is connected to the microgrid through an LC filter, and the corresponding state space equation is as follows:

[0023]

[0024] Among them, x CPLi State vector of the constant power load connected to the ith node. and are the system matrix and the control matrix respectively.

[0025] The output voltage of the grid-connecting inverter remains unchanged, and the node voltage is affected by the load conditions and the output current of the grid-connecting inverter. The constant impedance load and constant current load of the ZIP load are used to construct the node voltage equation:

[0026]

[0027] Among them, v bDQ is the node voltage vector, is the output current vector of the grid-connected inverter, is the output current vector of the grid-following inverter, i lDQ is the current vector of the node connection line, i cplDQ is the input current vector of the constant power load, I CCL is the input current vector of the constant current load.

[0028] In Step 1 and Step 2, the state space model of each subsystem in the complex microgrid including parallel grid inverters, grid-connected inverters and ZIP loads has been constructed. In Step 3, the system-level state space model of the microgrid is constructed in combination with the relationship between the signal flows of each subsystem as follows:

[0029]

[0030] where x mg =[x inv ,i lDQ ,i cplDQ ] is the state vector of the AC microgrid, x inv =[x inv1 ,x inv2 ,···,x invi ] is the state vector of the multi-inverter. A mg (x mg )and are the nonlinear system matrix and input matrix respectively.

[0031] To facilitate analysis, the steady-state operating point of the microgrid is moved to the origin of the coordinate system by constructing a new state vector. Combined with equation (6), the original system model can be transformed into an autonomous model.

[0032] Step 4 is implemented as follows:

[0033] The TS multiple modeling method is used to piecewise linearize the system-level nonlinear model. A linear matrix inequality group is constructed for each linear model. The linear matrix inequality group is solved using an iterative algorithm to further obtain the energy function of the high-dimensional state space. The energy function is then mapped to a specific state variable (x m ,x n ) can obtain the required energy function and basin of attraction (BOA) expression:

[0034]

[0035] Where P is the positive definite matrix obtained by solving LMI, To maintain the energy boundary of transient stability. V m,n is the state variable (x m ,x n ), BOA m,n is (x m ,x n ) domain of attraction on the plane. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1Schematic diagram of a complex microgrid containing multiple types of inverters and complex nonlinear loads;

[0037] Figure 2 For x 11 -x 12 Energy function visualization image on a plane;

[0038] Figure 3 The influence of DC voltage drop on the attraction domain;

[0039] Figure 4 The time domain waveforms of the DC side and AC voltage of the microgrid after the DC voltage drops;

[0040] Figure 5 The influence of the input power change of the grid-following inverter on the attraction domain;

[0041] Figure 6 It is the time domain waveform of the inverter output current after the previous stage input power changes. DETAILED DESCRIPTION

[0042] The following embodiments of the present invention are implemented based on the technical solution and provide detailed implementation methods, but the protection scope of the present invention is not limited to the following embodiments.

[0043] like Figure 1 As shown, the power source in the AC microgrid includes two grid-forming inverters and one grid-following inverter. The two grid-forming inverters are connected in parallel at the PCC, each carrying a group of ZIP loads.

[0044] The grid-following inverter works in the current source mode and does not directly supply power to the load. Instead, it is connected to the AC microgrid through node 2 to inject active or reactive current into the microgrid.

[0045] The power outer loop of the grid-forming inverter adopts droop control, which is responsible for frequency and voltage regulation and is also used to generate voltage reference. The inner loop adopts voltage and current double closed-loop control in the dq synchronous coordinate system to maintain the voltage source characteristics of the grid-forming converter.

[0046] The grid-following inverter keeps synchronous operation with the grid-building inverter through a phase-locked loop, and the front-stage converter adopts MPPT control to achieve efficient use of new energy. The inner loop control system of the inverter adopts a control structure of a DC voltage control loop cascaded with an output current control loop, and the controller also uses a PI regulator in the dq coordinate system.

[0047] The main circuit model including the DC side circuit, three-phase inverter bridge, LC filter and feeder is established in the dq coordinate system. The state space model of the grid inverter is further established by combining the droop controller and the voltage and current double closed-loop system:

[0048]

[0049] Among them, ω com is the reference angular frequency of the common coordinate system, v bdqi is the voltage vector of the ith node. invi is the state vector of the i-th grid-connected inverter in the microgrid. is the system matrix, is the control matrix, is the output matrix. In the average model of the grid-connected inverter, the DC side circuit and AC / DC coupling effect will bring nonlinear terms, so the equation shown in formula (8) is a nonlinear state space model.

[0050] Similarly, the state space model of the grid-following inverter is established in the dq coordinate system. The grid-following inverter does not use a power controller, but inverts the power of the previous stage into current and injects it into the microgrid. The DC voltage loop in the inverter control system is used to maintain the DC side voltage constant and provide a reference voltage for the modulation process. The nonlinear state space model is established as follows:

[0051]

[0052] Among them, x GFL =[u dc3 ,m1,m2,m3,i fd3 ,i fq3 ,u od3 ,u oq3 ,i od3 ,i oq3 ] T is the state vector of the grid-following inverter, and m1, m2, and m3 are the intermediate variables introduced by integral control in the voltage and current double closed-loop control system. bDQ2 is the voltage vector of the node connected to the grid-connected inverter in the microgrid.

[0053] The two grid-connected inverters are connected via a node tie line. The tie line includes line inductance and parasitic resistance, and the line current dynamics are affected by the node voltage:

[0054]

[0055] Among them, i lDQi(i+1) is the value of the current on the tie line between the i-th and i+1-th nodes in the common dq coordinate system. Different from the inverter model, the above equation is a linear state space equation.

[0056] Among ZIP loads, constant power loads have strong nonlinear and negative damping characteristics, which have a great impact on the stable operation of the microgrid. Therefore, a separate constant power load model is established as follows:

[0057]

[0058] Among them, x CPLi State vector of the constant power load connected to the ith node. and They are the system matrix and control matrix of constant power load respectively.

[0059] Under the action of the inner loop control system, the output voltage of the grid-connected inverter remains stable. The node voltage dynamics are affected by the load conditions and the output current of the grid-connected inverter. The node voltage equation for building a microgrid is as follows:

[0060]

[0061] Among them, v bDQ is the node voltage vector, is the output current vector of the grid-connected inverter, is the output current vector of the grid-following inverter, i lDQ is the current vector of the node connection line, i cplDQ is the input current vector of the constant power load, I CCL is the input current vector of the constant current load.

[0062] Through the state space model of each link of the microgrid, including the grid inverter, grid inverter, nonlinear load, node tie line, and node voltage equation, the system-level large signal model of the microgrid can be obtained. The autonomous model of the microgrid can be obtained by transforming the steady-state operating point to the coordinate origin through coordinate transformation.

[0063]

[0064] The Takagi Sugeno (TS) multiple modeling method is used to simplify high-order nonlinear models. The original nonlinear model is approximately described by a sufficient number of local linear models, and then the linear matrix inequality (LMI) is constructed and solved through an iterative algorithm to obtain the energy function of the system.

[0065] The microgrid system has multiple state variables, so the energy function obtained is a hypersphere in the high-dimensional state space, which is not convenient for analysis. Therefore, for the state variables of interest, they are mapped to the two-dimensional space, and the corresponding attraction domain can be obtained:

[0066]

[0067] Among them, x m,n =(x m ,x n ) T , P is the positive definite matrix obtained by solving LMI, To maintain the energy boundary of transient stability. Vm,n is the state variable (x m ,x n ), BOA m,n is (x m ,x n ) domain of attraction on the plane.

[0068] Mapping high-dimensional energy function to x 11 -x 12 plane, we can obtain the corresponding energy function and x 11 -x 12 The attraction domain on the plane is obtained, so as to know the influence of the DC side voltage of the grid-forming converter on the large signal stability of the microgrid. 11 -x 12 The energy function and attraction domain expressions on the plane are as follows:

[0069]

[0070] Among them, x 11 ,x 12 is the change in the DC side voltage and current of the grid-connected inverter GFM2. The three-dimensional visualization of the energy function is shown in Figure 2 shown.

[0071] Figure 3 The influence of the DC voltage drop of GFM2 on the attraction domain. When the state variables fall within the attraction domain after a large disturbance, the system can converge to a new steady-state operating point. If the variables fall outside the attraction domain, the system will experience transient instability.

[0072] When the DC voltage drops to 800V, the attraction domain decreases, and the system transient stability margin decreases. When the DC voltage drops further to 600V, the attraction domain further decreases, and the system is more likely to become unstable.

[0073] Figure 4 The time domain waveforms of the DC side and AC measurement responses of the microgrid after the DC side voltage drops. When the voltage drops to 850V, although the system stability margin decreases, the state variables are still within the attraction domain and converge to a new steady-state operating point after oscillation. However, when the voltage drops further to 770V, the state variables fall outside the attraction domain, the system becomes unstable, and the waveforms of the DC side and AC measurement begin to oscillate and diverge.

[0074] To further explore the impact of the input power of the grid-connected inverter on transient stability, the energy function is mapped to x 38 -x 39 Plane, the obtained energy function and attraction domain expressions are as follows:

[0075]

[0076] Among them, x 38 , x 39 They are the changes in the d-axis component and q-axis component of the voltage at node 2 to ground, respectively.

[0077] Figure 5 When the input power of the front stage of the grid-following inverter changes, the system 38 , x 39 Changes in the attraction domain on the plane. As the input power increases, the attraction domain decreases significantly. For the system to be stable, the voltage at node 2 must be high enough.

[0078] The grid-following inverter is connected to the microgrid through node 2, so the voltage level of node 2 determines the active power limit transmitted by the grid-following inverter. in When it increases, the voltage level at node 2 must remain high enough to maintain power balance with the grid-connected inverter.

[0079] Figure 6 It is the time domain waveform of the output current of the grid-following inverter in the dq coordinate system when the input power of the previous stage changes. in After jumping from 9kW to 10kW, the output current i od3 and i oq3 can converge to a new operating point, because x 38 and x 39 Still in x 38 , x 39 However, in P in After jumping to 12kW, the attraction domain is further reduced, and the voltage at node 2 is no longer in the attraction domain. Therefore, the output current oscillates and diverges.

Claims

1. A system-level large-signal nonlinear state-space model for a complex AC microgrid, characterized by: It includes two grid-building inverters, one grid-following inverter and two groups of ZIP loads. Among them, the ZIP load includes constant impedance load, constant current load and constant power load. The expression of the large signal model of the microgrid in the dq coordinate system is as follows: Among them, x mg is the state variable of the system, the system matrix A mg and control matrix The expression is as follows: Among them, A GFM ,B GFM ,C GFM They are the system matrix, control matrix and output matrix of the grid-connected inverter respectively; A GFL ,B GFL ,C GFL They are the system matrix, control matrix and output matrix of the grid-following inverter respectively; A net ,B net are the system matrix and control matrix of the node connection line respectively; A cpl ,B cpl are the system matrix and control matrix of constant power load respectively; M GFM ,M GFL ,M net ,M cpl They are the coefficient matrices associated with the grid-connecting inverter, grid-following inverter, node connecting line and constant power load in the node voltage equation respectively. is the control matrix of the network transformer in the common coordinate system, I CCL is the input current of the constant current load; Construct new state variables to move the equilibrium point of the system model to the origin of the coordinate system. The expression of the system autonomy model obtained according to the new state variables is: Among them, A cov , x cov are the system matrix and state variables of the autonomous model respectively. is the steady-state value of the original nonlinear system.

2. A method for solving the energy function and attraction domain of a high-dimensional nonlinear system, characterized in that: The following steps are included: The original nonlinear model is approximately equivalent to the superposition of multiple linear models by using the piecewise linearization method. The state matrices of the linear models are A1, A2, …, A k ; Construct a linear matrix inequality group for a set of linear models, solve the linear matrix inequality group, and obtain a high-dimensional energy function: Where P is the positive definite matrix obtained by solving the linear matrix inequality system, x cov is the state variable of the autonomous model; For a specific state variable (x m ,x n ), and mapping it to two-dimensional space, we can obtain the corresponding attraction domain: in, To maintain the energy boundary of transient stability, P m,n is the element with m rows and n columns in the matrix P.

3. A large signal instability mechanism of a complex AC microgrid, characterized by: a. The DC side voltage of the grid inverter plays an obvious supporting role in the stability of large signals. The drop of DC side voltage will reduce the attraction domain and weaken the stability of the system. When the DC voltage drops too deep, the state variables will fall outside the attraction domain, causing the system oscillation to become unstable; b. The input power of the front stage of the grid-connected inverter and the voltage at the grid connection point have a significant impact on the transient stability of the system. If the active power value of the front stage input is increased, the attraction domain of the grid connection point voltage gradually decreases. The voltage level at the grid connection point determines the active power limit transmitted by the grid-connected inverter. When the input power of the front stage increases, in order to maintain the stable operation of the system, the voltage level at the grid connection point must be kept high enough to maintain the power balance of the grid-connected inverter.

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