A method for establishing a Hamiltonian model of a virtual generator for an inverter

Abstract

The invention discloses a method for establishing a Hamiltonian model of an inverter virtual generator, belonging to the technical field of generator modeling and control. The modeling method is to establish corresponding differential equations and energy functions for a stator unit, an excitation unit and a rotor unit of the virtual generator respectively, wherein the methods for establishing the energy functions of the three units are different, the energy function of the stator unit is obtained through the electric energy and magnetic energy of the winding; the energy function of the excitation unit is obtained through RC circuit simulation; the rotor energy function is the rotor rotational kinetic energy, the energy function of the virtual generator is obtained by superimposing the energy functions of the above units, and on this basis, the Hamiltonian model of the virtual generator is obtained through mathematical transformation and derivation; the inverter modeling method provided by the invention provides a basis for studying the operation and stable control of various networks including a battery+inverter power supply branch.

Description

Technical Field

[0001] The invention belongs to the technical field of generator modeling and control, and in particular to a method for establishing a Hamiltonian model of an inverter virtual generator. Background Art

[0002] The function of the inverter is to convert DC to AC and supply it to the AC system or AC users. At the same time, it can also convert AC to DC and supply it to the DC system or users. For example, in a microgrid, it is connected to an energy storage battery and converts the DC power of the energy storage battery into AC power to supply the AC bus. At this time, the inverter works in the inverter state, which is equivalent to a generator; at the same time, it can also convert the power of the AC system into DC to charge the battery and work in the rectification state. The inverter can also be used to connect AC and DC systems to perform power conversion between the two systems. At present, with the increasing scale of new energy development, the inverter is an indispensable and important device in the multi-energy complementary system including wind, light, battery energy storage, etc. In the network containing the inverter, its design, operation and stability control research all need to involve the model problem of the inverter. In the modeling method of the inverter, the relationship between input and output is usually given directly. This model is relatively simple, and the control variables involved are mainly control signal pulses, and the internal variables cannot be displayed. The new research regards the inverter as a virtual generator and establishes its mathematical model from the perspective of the generator. The model can reflect the variables inside the inverter. Summary of the invention

[0003] The present invention provides a Hamiltonian modeling method for a virtual generator of an inverter, derives a Hamiltonian model in a standard form, and provides a modeling basis for further utilizing a structure and a damping matrix to operate and control the inverter.

[0004] Since the inverter converts the DC of the energy storage battery connected to it into AC to supply the load, from the perspective of the load, the inverter side can be regarded as a generator that provides AC power, that is, as a virtual generator. The modeling of the inverter can be converted into the modeling of the virtual generator. The present invention proposes a method for Hamiltonian modeling of an inverter, which is essentially to perform Hamiltonian modeling on an equivalent virtual generator. The modeling method is to establish corresponding differential equations and energy functions for the stator unit, excitation unit, and rotor unit of the virtual generator respectively, wherein the methods for establishing the energy functions of the three units are different. The energy function of the stator unit is obtained through the electric energy and magnetic energy of the winding; the energy function of the excitation unit is obtained through RC circuit simulation; the rotor energy function is the rotor rotational kinetic energy, and the energy function of the virtual generator is obtained by superimposing the energy functions of the above units, and the Hamiltonian model of the virtual generator is obtained through mathematical transformation and derivation. The specific modeling method is as follows:

[0005] (i) Establish the virtual generator stator unit differential equation through the electrical energy and magnetic energy of the winding

[0006] The bridge arm branch of the virtual generator is used as the three-phase stator winding of the generator, and the resistance of each phase winding is set to R and the inductance is set to L. X , the capacitance is C, the stator three-phase current is i a 、i b 、i c , denoted as I abc ; The internal potential of the three phases of the stator is e a 、e b 、e c , denoted as E abc ; The three-phase terminal voltage of the generator is u a 、u b 、u c , denoted as U abc ; According to electromechanical coupling dynamics, let the charge on the three-phase capacitor be e a-q 、e b-q 、e c-q , which is analogous to generalized displacement, then the generalized velocity is I abc , potential E abc As an external force, the magnetic energy of the virtual generator system is W m =L X (I a 2 +I b 2 +I c 2 ) / 2, the electric field energy is W e =(e a-q 2 +e b-q 2 +e c-q 2 ) / (2C), the dissipated energy is F d =R(I a 2 +I b 2 +I c 2 ) / 2, the corresponding stator unit Lagrangian function is magnetic energy minus electric energy, that is, L1 = W m -W e , the Lagrange equation is:

[0007]

[0008] because Expanding the above equation (1) yields:

[0009]

[0010] Using the relationship between capacitor charge and voltage abc-q=CU abc , the charge variable e in the electric field energy abc-q Replaced by voltage U abc , using X ad The base value system is subjected to standard processing and Park transformation and the 0-axis component is ignored. The generalized displacement is taken as the voltage u of the d and q axes. dq =[u d u q ] T , the generalized velocity is taken as the current i of the d and q axes dq =[i d i q ] T , then the Lagrangian function of the virtual generator stator becomes:

[0011]

[0012] Among them, X L and X C is the standard reactance of inductance and capacitance converted to d and q coordinates, i d 、i q is the current component of the stator d and q axes, u d 、u q is the d-axis component of the machine-end voltage and the q-axis component of the machine-end voltage, u t is the terminal voltage, satisfying u t 2 =u d 2 +u q 2 ;

[0013] After multiplying both sides of formula (2) by the Parker transformation matrix and performing scalar processing, the scalar equation under d and q coordinates is obtained:

[0014]

[0015] (ii) Establish virtual generator excitation differential equation through RC circuit simulation

[0016] In a three-phase symmetrical system, the internal potential can be expressed in vector form as The internal potential effective value E is analogous to the excitation voltage of the virtual generator, and the internal potential phase angle is The transfer function of the virtual generator excitation unit can be constructed by referring to the generator excitation system. Its first-order transfer function is as follows (the following uses the standard value system):

[0017]

[0018] Among them, ΔE=E-E0 is the increment of the internal potential E, E0 is the initial value of the internal potential, u ref 、ut are the reference voltage and the terminal voltage, K E is the excitation gain factor, T E is the time constant of the excitation system;

[0019] The controller of the virtual generator excitation unit is constructed using reactive power droop control, and the reactive power droop control law is Q ref -Q=-b Q (u ref -u t ), where reactive b Q is the reactive power droop coefficient. Substituting the reactive power droop control law and the expression of reactive power Q into (5), the differential equation of the excitation system is obtained as follows:

[0020]

[0021] in, Q ref is the reference value of the virtual generator reactive power, Q, u t They are the measured reactive power and terminal voltage of the virtual generator respectively;

[0022] (iii) Establish the virtual generator rotor differential equation

[0023] The inverter is constructed as a virtual generator. The number of magnetic pole pairs is assumed to be 1, and the salient pole effect is ignored. The motion equation of the virtual generator under the standard system is as follows:

[0024]

[0025] Among them, the internal potential Angle is equal to the generator power angle; T B is the inertia time constant T of the virtual generator B =Jω B 2 / P B , J is the moment of inertia; P B is the virtual generator power base value, p m is the virtual generator mechanical power, p e is the electromagnetic power of the virtual generator, D is the damping coefficient, ω, ω ref are the reference values ​​of the virtual generator angular velocity and angular velocity, respectively;

[0026] In the virtual generator, the inverter output mechanical power is controlled by the active power droop control law p ref -p m =-b p (ω ref -ω) is determined, where p ref is the virtual generator active power reference value, b pis the active droop coefficient. The specific calculation method is: Calculate the output mechanical power p according to the change of the virtual generator angular velocity ω m =p ref +b p (ω ref -ω) and substitute it into (7), we get the following formula (8):

[0027] (iv) Establishing a virtual generator Hamiltonian model

[0028] The key to establishing the Hamiltonian model of a virtual generator is to find its Hamiltonian function. The method for establishing the Hamiltonian function in the present invention is: firstly, the Lagrangian functions of the three units of the stator, the excitation and the rotor are established; secondly, the Hamiltonian function of each unit is obtained by defining the generalized momentum; finally, the Hamiltonian function of each part is superimposed to obtain the Hamiltonian function of the virtual generator; on this basis, a unified Hamiltonian model is obtained by conversion and deduction;

[0029] (a) Establish the Hamiltonian function of the stator unit

[0030] Define generalized momentum: According to the Hamiltonian principle, the Hamiltonian function of the system is H (1) =p T i dq -L1, where L1 is the Lagrangian function, which has been obtained as shown in formula (3), p = [p d , p q ] T ,i dq =[i d i q ] T , so the stator unit Hamiltonian function H (1) for:

[0031]

[0032] (b) Establish the Hamiltonian function of the excitation unit

[0033] The basic form of the virtual excitation unit is given in the first-order transfer function model in equation (5). It is simulated according to the typical RC circuit. The electric energy on the capacitor of the circuit system can be used as the Hamiltonian function of the system. Therefore, the Hamiltonian function of the excitation system H (2) for:

[0034]

[0035] Where ΔE is the increment of the internal potential E, which is also the voltage across the capacitor in the equivalent circuit; T E is the time constant of the excitation system, which is also the capacitance value of the capacitive element;

[0036] (c) Establish the rotor unit Hamiltonian function

[0037] The energy of the rotor unit is the rotor inertia kinetic energy. Its kinetic energy can be written according to the rotor speed. After being converted into the Hamiltonian function, its form remains unchanged. Therefore, the Hamiltonian function H of the virtual generator rotor is (3) for:

[0038]

[0039] Where T B is the inertia time constant of the virtual generator, ω is the angular velocity of the virtual generator;

[0040] The Hamiltonian function of the virtual generator is equal to the sum of the energies of the stator, rotor and excitation unit, that is, the superposition of equations (9), (10) and (11):

[0041]

[0042] Refer to the expressions of d-axis and q-axis currents in the traditional generator third-order model: Hamiltonian function i d 、i q Implicit power angle According to the rules of partial derivatives of implicit functions, we can get: At the same time, from the Hamiltonian function H in (12), we can obtain: Since the virtual generator adopts d-axis voltage orientation, e d =E,e q =0;u d is the d-axis component of the terminal voltage, u q is the q-axis component of the terminal voltage, and the terminal voltage u t It is expressed as: When the inverter is connected to the bus, t It is represented by the bus voltage, which is the input control term in the Hamiltonian model and is denoted by u tin ;

[0043] The generator stator equation (4) is converted into the corresponding Hamiltonian equation as follows:

[0044]

[0045] The transformation of the rotor Hamiltonian equation is to convert the active power droop control law p ref -p m =-b p (ω ref -ω) into formula (8), and consider The rotor motion equation (8) is transformed into:

[0046]

[0047] The equation (6) of the excitation unit is rearranged as follows:

[0048]

[0049] Select the state variable as Rewrite equations (13), (14), and (15) into a unified form (16) and use matrix transformation to obtain J(x) = [T(x) - T T R(x) = -[T(x) + T T (x)] / 2, from the perspective of the inverter virtual generator principle, the frequency is the input controllable variable, and the input angular velocity of the virtual generator is denoted by ω in ,ω in By approximately replacing ω, the standard form of the inverter generalized Hamiltonian model is obtained as follows:

[0050]

[0051] in:

[0052]

[0053]

[0054]

[0055] Among them, J(x) is the antisymmetric structure matrix, R(x) is the symmetric structure matrix, g(x) is the control input channel matrix, u is the input matrix, and the input of the system includes the input of the virtual generator angular velocity ω in and bus voltage u tin .

[0056] The beneficial effects of the present invention are:

[0057] 1. The conventional inverter model is based on the input and output relationship obtained from its working circuit. The model is simple and its control variable is a trigger pulse, which cannot meet the more precise and complex control of the inverter. The present invention establishes a Hamiltonian model of the inverter through a virtual generator method. The model reflects the relationship between the internal variables and parameters of the inverter. It is a new method for inverter modeling and provides a basis for various controls based on the virtual generator model.

[0058] 2. The present invention provides a new method for modeling virtual generators. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 Inverter structure;

[0060] Figure 2Circuit simulation diagram of the transfer function of the virtual generator excitation unit;

[0061] Figure 3 Simulation structure diagram;

[0062] Figure 4 The change diagram of inverter active pe and reactive Q. DETAILED DESCRIPTION

[0063] In order to further illustrate the content of the present invention, further analysis is performed in conjunction with specific examples.

[0064] The main circuit of the inverter unit of the inverter of the present invention is as follows Figure 1 As shown, the DC side is the DC voltage U at the battery outlet de , S1-S6 are power switch devices that make up the three-phase bridge inverter circuit, the inverter outlet is the AC side, L L , C L As the filter element; Figure 1 From the AC port, the inverter converts DC power into AC power. The DC power comes from the battery, which can be regarded as an equivalent generator. After the inverter is replaced by a virtual generator, the present invention needs to establish the differential equations of the stator, excitation, and rotor units of the virtual generator respectively, and then further establish the Hamiltonian model of the virtual generator.

[0065] Example 1

[0066] A method for establishing a Hamiltonian model of an inverter virtual generator, respectively establishing corresponding differential equations and energy functions for the stator unit, excitation unit, and rotor unit of the virtual generator, wherein the energy function of the stator unit is obtained through the electric energy and magnetic energy of the winding, the energy function of the excitation unit is obtained through RC circuit simulation, and the rotor energy function is the rotor rotation kinetic energy. The energy functions of the above units are superimposed to obtain the energy function of the virtual generator, and on this basis, the Hamiltonian model of the inverter virtual generator is obtained through mathematical transformation and derivation, which specifically includes the following steps:

[0067] Step 1: Establish the Lagrangian function and differential equation of the virtual generator stator through the electrical energy and magnetic energy of the winding

[0068] Figure 1 The middle bridge arm branch is used as the three-phase stator winding of the generator, and the resistance of each phase winding is set to R and the inductance is L. X , the capacitance is C, the stator three-phase current is i a 、i b 、i c , denoted as I abc ; The internal potential of the three phases of the stator is e a 、e b 、e c , denoted as Eabc ; The three-phase terminal voltage of the generator is u a u b u c , denoted as U abc ; According to electromechanical coupling dynamics, let the charge on the three-phase capacitor be e a-q 、e b-q 、e c-q , which is analogous to generalized displacement, then the generalized velocity is I abc , potential E abc As an external force, Figure 1 The magnetic field energy of the virtual generator system is the energy storage W of the inductor element. m =L X (I a 2 +I b 2 +I c 2 ) / 2, the electric field energy is the energy storage W of the capacitor element e =(e a-q 2 +e b-q 2 +e c-q 2 ) / (2C), the dissipated energy is the energy dissipated on the resistor element F d =R(I a 2 +I b 2 +I c 2 ) / 2, the corresponding stator unit Lagrangian function is magnetic energy minus electric energy, that is, L1 = W m -W e , L1 satisfies the Lagrange equation:

[0069]

[0070] because Expanding the above equation (1) yields:

[0071]

[0072] Using the relationship between capacitor charge and voltage abc-q =CU abc , the charge variable e in the electric field energy abc-q Replaced by voltage U abc , using X ad The base value system is subjected to standard processing and Park transformation and the 0-axis component is ignored. The generalized displacement is taken as the voltage u of the d and q axes of the machine terminal voltage. dq =[u d u q ]T , the generalized velocity is taken as the current i of the d and q axes dq =[i d i q ] T , then the Lagrangian function of the virtual generator stator becomes:

[0073]

[0074] Among them, X L and X C is the standard reactance of inductance and capacitance converted to d and q coordinates, i d 、i q is the current component of the stator d and q axes, u d 、u q is the d-axis component of the machine-end voltage and the q-axis component of the machine-end voltage, u t is the terminal voltage, satisfying u t 2 =u d 2 +u q 2 ;

[0075] The differential equation of the stator unit needs to be converted to the generator d and q axis coordinates. The conversion method is similar to that of the synchronous generator, that is, the Parker transformation. After multiplying both sides of equation (2) by the Parker transformation matrix and performing scalar processing, the scalar equation under d and q coordinates is obtained:

[0076]

[0077] Formula (4) is the differential equation of the stator unit, which will be used in the subsequent establishment of the Hamiltonian equation;

[0078] Step 2: Establish virtual generator excitation differential equation through RC circuit simulation

[0079] In a three-phase symmetrical system, the internal potential can be expressed in vector form as The internal potential effective value E is analogous to the excitation voltage of the virtual generator, and the internal potential phase angle is The transfer function of the virtual generator excitation unit can be constructed by referring to the generator excitation system. Its first-order transfer function is as follows (the following uses the standard value system):

[0080]

[0081] Among them, ΔE=E-E0 is the increment of the internal potential E, E0 is the initial value of the internal potential, u ref 、u t are the reference voltage and the terminal voltage, K E is the excitation gain factor, T Eis the time constant of the excitation system;

[0082] The controller of the virtual generator excitation unit is constructed using reactive power droop control, and the reactive power droop control law is Q ref -Q=-b Q (u ref -u t ), where reactive b Q is the reactive power droop coefficient. Substituting the reactive power droop control law and the expression of reactive power Q into (5), the differential equation of the excitation system is obtained as follows:

[0083]

[0084] in, Q ref is the reference value of the virtual generator reactive power, Q, u t They are the measured reactive power and terminal voltage of the virtual generator respectively;

[0085] Step 3: Establish virtual generator rotor differential equation

[0086] The inverter is constructed as a virtual generator. Assuming that its pole pair number is 1 and ignoring the salient pole effect, the generator motion equation is as follows (using the standard system):

[0087]

[0088] Among them, the internal potential Angle is also the generator power angle; T B is the inertia time constant T of the virtual generator B =Jω B 2 / P B , J is the moment of inertia; P B is the virtual generator power base value, p m is the virtual generator mechanical power, p e is the electromagnetic power of the virtual generator, D is the damping coefficient, ω, ω ref are the reference values ​​of the virtual generator angular velocity and angular velocity, respectively;

[0089] In the virtual generator, the inverter output mechanical power is controlled by the active power droop control law p ref -p m =-b p (ω ref -ω) is determined, where p ref is the virtual generator active power reference value, b p is the active droop coefficient. The specific calculation method is: Calculate the output mechanical power p according to the change of the virtual generator angular velocity ω m =p ref +bp (ω ref -ω) and substitute it into (7), we get the following equation (8):

[0090]

[0091] Note: From the principle of inverter virtual generator, frequency is the input controllable variable, denoted as ω in , the last term in formula (8) is represented by ω in Approximately replacing ω, this transformation can keep equation (8) in the form of an affine nonlinear equation;

[0092] Step 4: Establish a virtual generator Hamiltonian model

[0093] The key to establishing the Hamiltonian model of a virtual generator is to find its Hamiltonian function. The method for establishing the Hamiltonian function in the present invention is: firstly, the Lagrangian functions of the three units of the stator, the excitation and the rotor are established; secondly, the Hamiltonian function of each unit is obtained by defining the generalized momentum; finally, the Hamiltonian function of each part is superimposed to obtain the Hamiltonian function of the virtual generator; on this basis, a unified Hamiltonian model is obtained by conversion and deduction;

[0094] (a) Establish the Hamiltonian function of the stator unit

[0095] Define generalized momentum: According to the Hamiltonian principle, the Hamiltonian function of the system is H (1) =p T i dq -L1, where L1 is the Lagrangian function of the stator unit, which has been obtained as shown in formula (3), p = [p d , p q ] T ,i dq =[i d i q ] T , so the stator unit Hamiltonian function H (1) for:

[0096]

[0097] (b) Establish the Hamiltonian function of the excitation unit

[0098] The basic form of the virtual excitation unit is given in equation (5) as a first-order transfer function model. The transfer function can be a typical transfer function proposed in the literature "A method for establishing the energy function of the generator excitation controller (ZL201510509673.4)". Figure 2 The RC circuit is used to simulate the electric energy on the capacitor of the circuit system, which can be used as the Hamiltonian function of the system. Therefore, the Hamiltonian function of the excitation system is (2) for:

[0099]

[0100] Among them, ΔE is the increment of the internal potential E, which is also the voltage T across the capacitor in the equivalent circuit. E is the time constant of the excitation system, which is also the capacitance value of the capacitive element;

[0101] (c) Establish the rotor unit Hamiltonian function

[0102] The energy of the rotor unit is the rotor inertia kinetic energy. Its kinetic energy can be written according to the rotor speed. After being converted into the Hamiltonian function, its form remains unchanged. Therefore, the Hamiltonian function H of the virtual generator rotor is (3) for:

[0103]

[0104] Where T B is the inertia time constant of the virtual generator, ω is the angular velocity of the virtual generator;

[0105] The Hamiltonian function of the virtual generator is equal to the sum of the energies of the stator, rotor and excitation unit, that is, the superposition of equations (9), (10) and (11):

[0106]

[0107] Refer to the expressions of d-axis and q-axis currents in the third-order model of synchronous generator: Hamiltonian function i d 、i q Implicit active angle According to the rules of partial derivatives of implicit functions, we can get: At the same time, from the Hamiltonian function H in (12), we can also get: Since the virtual generator adopts d-axis voltage orientation, e d =E,e q =0;u d is the d-axis component of the terminal voltage, u q is the q-axis component of the terminal voltage, u d 、u q The terminal voltage u t Expressed as: When the inverter is connected to the bus, t It is represented by the bus voltage, which is the input control term in the Hamiltonian model and is denoted by u tin ;

[0108] Through the above substitution and derivation, the virtual generator stator equation (4) is converted into the following Hamiltonian equation:

[0109]

[0110] The transformation of the rotor Hamiltonian equation is to convert the active power droop control law p ref -p m =-b p (ω ref -ω) into formula (8), and consider The rotor motion equation (8) is transformed into:

[0111]

[0112] The equation (6) of the excitation unit is rearranged as follows:

[0113]

[0114] The above transformation processes are all equivalent transformations based on differential equations, so the corresponding differential equations and Hamiltonian equations are mathematically equivalent;

[0115] Select the state variable as Rewrite equations (13), (14), and (15) into a unified form (16) and use matrix transformation to obtain J(x) = [T(x) - T T R(x) = -[T(x) + T T (x)] / 2, from the principle of the inverter virtual generator, the frequency is the input controllable variable, and the input angular velocity of the virtual generator is denoted by ω in ,ω in By approximately replacing ω, the standard form of the generalized Hamiltonian model is obtained as follows:

[0116]

[0117] in:

[0118]

[0119]

[0120]

[0121]

[0122] J(x) is the antisymmetric structure matrix, R(x) is the symmetric structure matrix, g(x) is the control input channel matrix, u is the input matrix, and the input of the system includes the input of the virtual generator angular velocity ω in and bus voltage u tin .

[0123] Example 2

[0124] To illustrate the application of Example 1, Figure 3 The isolated grid operation structure diagram shown in FIG. 1 shows an inverter using the Hamiltonian model (16) provided by the present invention, and the following is obtained through simulation analysis: Figure 4 As a result, all parameters are converted to the rated power and voltage base value U of the diesel generator. B =380(V) system, the specific analysis is as follows:

[0125] Simulation structure Figure 3 Parameters: (1) Main parameters of diesel generator: rated power 1250kW, rated speed n = 1500r / min, moment of inertia J = 71.822kg.m 2 , equivalent damping coefficient D = 2.1753, diesel generator adopts traditional PID control, its governor PID parameters are: K P =2.0, K I =2.0, K D =0.1, excitation PID parameters: K P =2.0, K I =2.0, K D =0.1; (2) The static load and asynchronous motor parameters are converted into standard values ​​(pu) based on the diesel engine capacity. Each motor has an active power of 0.1 (pu) and a reactive power of 0.047 (pu). The simulation simulates the change of dynamic load by using different numbers of motors; (3) The inverter unit participates in the simulation calculation according to the virtual generator mode, and the stator reactance X L =0.6(pu), the damping coefficient of the inverter unit is D=2, and the active droop coefficient is b p =10, reactive power droop coefficient b Q =-35, excitation system time constant T E =0.2, inverter virtual inertia time constant T B =6.3267, excitation gain coefficient K E =1, pu: standard value.

[0126] Initial operating conditions: the diesel generator has an active power of 0.8 (pu) and a reactive power of 0.6 (pu), and the inverter is in grid-connected standby state, that is, the output active power is 0.0 and the reactive power is 0.0; initially, 7 motors are connected to the bus for operation, absorbing a total of 0.7 (pu) active power and 0.3291 (pu) reactive power, and the remaining active and reactive power are static loads, and the power on the bus is balanced.

[0127] Disturbance condition: At t = 0.5s, a motor is put into operation to simulate the sudden change of nonlinear load. The active power of the motor is 0.1 (pu) and the reactive power is 0.047 (pu). When a motor is put into operation, the transient changes of the active power and reactive power of the inverter are as follows: Figure 4 shown.

[0128] Result analysis: The addition of a new motor is equivalent to a sudden change in load. Due to the lag in the regulation of the diesel generator set, the inverter can quickly make up for the active and reactive power shortages on the bus. After the diesel generator set tracks the load and increases its output, the active and reactive power output of the inverter gradually decreases and finally reaches zero, entering the standby state to prepare for the next time. Figure 4 The simulation reflects the above analysis results. The inverter output is zero 0.5 seconds ago. After the motor is put into operation 0.5 seconds later, the active power output of the inverter increases rapidly to 0.1 (pu), and then the oscillation decreases and finally becomes zero, turning into standby state to prepare for the next time. The compensation of reactive power is the same as that of active power.

[0129] The simulation results show the correctness of the inverter model.

Claims

1. A method for establishing a Hamiltonian model of an inverter virtual generator. It is characterized in that Corresponding differential equations and energy functions are established for the stator unit, excitation unit, and rotor unit of the virtual generator respectively. The energy function of the stator unit is obtained through the electric energy and magnetic energy of the winding, the energy function of the excitation unit is obtained through RC circuit simulation, and the rotor energy function is the rotor rotation kinetic energy. The energy functions of the above units are superimposed to obtain the energy function of the virtual generator. On this basis, the inverter virtual generator Hamiltonian model is obtained through mathematical transformation and derivation, which specifically includes the following steps: (i) Establish the virtual generator stator unit differential equation through the electrical energy and magnetic energy of the winding The bridge arm branch of the virtual generator is used as the three-phase stator winding of the generator, and the resistance of each phase winding is set to R and the inductance is set to L. X , the capacitance is C, the stator three-phase current is i a 、i b 、i c , denoted as I abc ; The internal potential of the three phases of the stator is e a 、e b 、e c , denoted as E abc ; The three-phase terminal voltage of the generator is u a 、u b 、u c , denoted as U abc ; According to electromechanical coupling dynamics, let the charge on the three-phase capacitor be e a-q 、e b-q 、e c-q , which is analogous to generalized displacement, then the generalized velocity is I abc , potential E abc As an external force, the magnetic energy of the virtual generator system is W m =L X (I a 2 +I b 2 +I c 2 ) / 2, the electric field energy is W e =(e a-q 2 +e b-q 2 +e c-q 2 ) / (2C), the dissipated energy is F d =R(I a 2 +I b 2 +I c 2 ) / 2, the corresponding stator unit Lagrangian function is magnetic energy minus electric energy, that is, L 1 =W m -W e , the Lagrange equation is: because Expanding the above equation (1) yields: Using the relationship between capacitor charge and voltage abc-q =CU abc , the charge variable e in the electric field energy abc-q Replaced by voltage U abc , using X ad The base value system is subjected to standard processing and Park transformation and the 0-axis component is ignored. The generalized displacement is taken as the voltage u of the d and q axes. dq =[u d u q ] T , the generalized velocity is taken as the current i of the d and q axes dq =[i d i q ] T , then the Lagrangian function of the virtual generator stator becomes: Among them, X L and X C is the standard reactance of inductance and capacitance converted to d and q coordinates, i d 、i q is the current component of the stator d and q axes, u d 、u q is the d-axis component of the machine-end voltage and the q-axis component of the machine-end voltage, u t is the terminal voltage, satisfying u t 2 =u d 2 +u q 2 ; After multiplying both sides of formula (2) by the Parker transformation matrix and performing scalar processing, the scalar equation under d and q coordinates is obtained: (ii) Establish virtual generator excitation differential equation through RC circuit simulation In a three-phase symmetrical system, the internal potential is expressed in vector form as The internal potential effective value E is analogous to the excitation voltage of the virtual generator, and the internal potential phase angle is The transfer function of the virtual generator excitation unit is constructed with reference to the generator excitation system, and the per-unit value system is adopted. The first-order transfer function is as follows: Where, ΔE=EE 0 is the increment of the internal potential E, E 0 is the initial value of the internal potential, u ref 、u t are the reference voltage and the terminal voltage, K E is the excitation gain factor, T E is the time constant of the excitation system; The controller of the virtual generator excitation unit is constructed using reactive power droop control, and the reactive power droop control law is Q ref -Q=-b Q (u ref -u t ), where reactive b Q is the reactive power droop coefficient. Substituting the reactive power droop control law and the expression of reactive power Q into (5), the differential equation of the excitation system is obtained as follows: in, Q ref is the reference value of the virtual generator reactive power, Q, u t They are the measured reactive power and terminal voltage of the virtual generator respectively; (iii) Establish the virtual generator rotor differential equation The inverter is constructed as a virtual generator. The number of magnetic pole pairs is assumed to be 1, and the salient pole effect is ignored. The motion equation of the virtual generator under the standard system is as follows: Among them, the internal potential phase angle Angle is equal to the generator power angle; T B is the inertia time constant T of the virtual generator B =Jω B 2 / P B , J is the moment of inertia; P B is the virtual generator power base value, p m is the virtual generator mechanical power, p e is the electromagnetic power of the virtual generator, D is the damping coefficient, ω, ω ref are the reference values ​​of the virtual generator angular velocity and angular velocity, respectively; In the virtual generator, the inverter output mechanical power is controlled by the active power droop control law p ref -p m =-b p (ω ref -ω) is determined, where p ref is the virtual generator active reference value, b p is the active droop coefficient. The specific calculation method is: Calculate the output mechanical power p according to the change of the virtual generator angular velocity ω m =p ref +b p (ω ref -ω) and substitute it into (7), we get the following equation (8): (iv) Establishing a virtual generator Hamiltonian model (a) Establish the Hamiltonian function of the stator unit Define generalized momentum: According to the Hamiltonian principle, the Hamiltonian function of the system is H (1) =p T i dq -L 1 , where L 1 is the Lagrangian function, and it has been found that p = [p d , p q ] T ,i dq =[i d i q ] T , so the stator unit Hamiltonian function H (1) for: (b) Establish the Hamiltonian function of the excitation unit The basic form of the virtual excitation unit is given in the first-order transfer function model in equation (5). It is simulated according to the typical RC circuit. The electric energy on the capacitor of the circuit system is used as the Hamiltonian function of the system. Therefore, the Hamiltonian function of the excitation system H (2) for: Among them, ΔE is the increment of the internal potential E, which is also the voltage across the capacitor in the equivalent circuit, T E is the capacitance value of the capacitor element; (c) Establish the rotor unit Hamiltonian function The energy of the rotor unit is the rotor inertia kinetic energy. Its kinetic energy is written according to the rotor speed. After being converted into the Hamiltonian function, its form remains unchanged. Therefore, the Hamiltonian function H of the virtual generator rotor is (3) for: Where T B is the inertia time constant of the virtual generator, ω is the angular velocity of the virtual generator; The Hamiltonian function of the virtual generator is equal to the sum of the energies of the stator, rotor and excitation unit, that is, the superposition of equations (9), (10) and (11): Refer to the expressions of d-axis and q-axis currents in the traditional generator third-order model: Hamiltonian function i d 、i q Implicit power angle According to the rules of partial derivatives of implicit functions, we can get: At the same time, from the Hamiltonian function H in (12), we can obtain: Since the virtual generator adopts d-axis voltage orientation, e d =E,e q =0;u d is the d-axis component of the terminal voltage, u q is the q-axis component of the terminal voltage, and the terminal voltage u t It is expressed as: When the inverter is connected to the bus, t It is represented by the bus voltage, which is the input control term in the Hamiltonian model and is denoted by u tin ; The generator stator equation (4) is converted into the corresponding Hamiltonian equation as follows: The transformation of the rotor Hamiltonian equation is to convert the active power droop control law p ref -p m =-b p (ω ref -ω) into formula (8), and consider The rotor motion equation (8) is transformed into: The equation (6) of the excitation unit is rearranged as follows: Select the state variable as Rewrite equations (13), (14), and (15) into a unified form (16) and use matrix transformation to obtain J(x) = [T(x) - T T R(x) = -[T(x) + T T (x)] / 2, from the principle of the inverter virtual generator, the frequency is the input controllable variable, and the input angular velocity of the virtual generator is denoted by ω in ,ω in By approximately replacing ω, the standard form of the inverter generalized Hamiltonian model is obtained as follows (16): in: J(x) is the antisymmetric structure matrix, R(x) is the symmetric structure matrix, g(x) is the control input channel matrix, u is the input matrix, and the input of the system includes the input of the virtual generator angular velocity ω in and bus voltage u tin .

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