Electromagnetic transient modeling and simulation method for internal fault of permanent magnet synchronous generator

Abstract

The invention relates to an electromagnetic transient modeling and simulation method of a permanent magnet synchronous generator, which can reflect various types of internal faults, and the method comprises the following steps: 1, according to different fault types, establishing mathematical models of the permanent magnet synchronous generator in different fault states, and according to the different fault types, establishing a mathematical model of the permanent magnet synchronous generator in the different fault states, according to the different fault types, establishing a mathematical model of the permanent magnet synchronous generator in the different fault states, and according to the mathematical model, establishing a mathematical model of the permanent magnet synchronous generator in the different fault states, and according to the mathematical model, establishing a mathematical model of the permanent magnet synchronous generator in the different fault states, and establishing a mathematical model of the permanent magnet synchronous generator in the different fault states; 2, focusing matrix elements required to be updated according to fault characteristics, and selecting current or flux linkage as a state variable; 3, performing discretization equivalence on the mathematical equation of the permanent magnet synchronous generator by using a backward Euler integral method, integrating two state variables, unifying the model to obtain an equivalent circuit equation, and constructing an equivalent circuit of the permanent magnet synchronous generator; 4, the equivalent circuit of the permanent magnet synchronous generator is connected with an external electrical network, and the equivalent model carries out node admittance matrix iteration solution on the whole circuit based on an EMTDC solver; and updating other concerned electrical information such as the stator current, the rotor current, the electromagnetic torque, the rotating speed, the rotor angle and the like until the simulation is finished.

Description

Technical Field

[0001] The invention belongs to the technical field of power system modeling and simulation, and in particular relates to an electromagnetic transient modeling and simulation method for a permanent magnet synchronous generator that can reflect various types of internal faults. Background Art

[0002] Offshore wind power has the characteristics of high annual utilization hours, no occupation of land resources, abundant resources, and easy local consumption. With the increase of unit complexity and the harsh operating environment, various faults are prone to occur during operation. At present, long-distance and large-capacity offshore wind farms face problems such as difficult fault repair and large losses due to fault downtime. Permanent magnet synchronous generator (PMSG) is the most complex component of offshore direct-drive and semi-direct-drive units. It has advantages such as no excitation winding, high power density, and high efficiency, but its failure rate is higher than other components. Therefore, timely detection of PMSG internal faults and avoiding the deepening of faults are of great significance to improving the long-term stable operation time of wind turbines.

[0003] For the analysis of complex internal fault conditions of PMSG, a large amount of fault data under different fault types is required. However, it is not suitable to obtain fault data through large-scale experiments, especially for long-term loss and degradation types of faults. The experiments are extremely time-consuming and costly. Simulation can effectively reflect the fault characteristics of PMSG and cover a variety of conditions at no cost. Some modeling methods have also been applied to the internal fault modeling of PMSG, but there are problems such as large amount of calculation and low accuracy, and it is difficult to couple with external circuits, and only PMSG faults can be simulated separately. Electromagnetic transient simulation software based on node analysis realizes discrete component modeling through a graphical interface, allowing intuitive component placement and interconnection, which is more convenient for circuit connection. Moreover, the realization of multiple identical components does not rely on listing their state space equations, but through the dragging of visual components, so it is more convenient and suitable for simulation of various scenarios including single wind turbines and complex wind farms. At present, mainstream electromagnetic transient simulation software such as Matlab / Simulink, PSCAD / EMTDC and RTDS all provide PMSG models, but the gray box model of commercial software only gives the most primitive mathematical model, does not consider the internal fault function, and the overall level of refinement is not enough.

[0004] Therefore, it is necessary to propose a modeling and simulation method for electromagnetic transient of permanent magnet synchronous generator that can reflect various types of internal faults. The model is based on the detailed mathematical model of permanent magnet synchronous generator under different fault types, and the mathematical equation is discretized by using the backward Euler method. The unified equivalent circuit of permanent magnet synchronous generator is obtained by integrating two state variables, and then the equivalent model of permanent magnet synchronous generator is obtained. The model can simulate winding faults such as winding asymmetric fault, winding single-phase grounding fault, winding short circuit fault, etc., permanent magnet uniform demagnetization, local demagnetization fault and eccentric fault and other types of internal faults, which can accurately reflect the fault characteristics and provide a model basis for the research of PMSG internal fault detection and protection strategy. Summary of the invention

[0005] The present invention provides a method for electromagnetic transient modeling and simulation of a permanent magnet synchronous generator that can reflect various types of internal faults. The modeling method comprises the following steps:

[0006] Step 1: According to different fault types, determine the fault characteristics, and obtain the electromagnetic transient and electromechanical transient mathematical models of the permanent magnet synchronous generator under each fault type, wherein the mathematical model includes the voltage equation, flux equation, and motion equation of the permanent magnet synchronous generator. It is characterized in that the mathematical model determines the electromagnetic transient and electromechanical transient characteristics of the permanent magnet synchronous generator.

[0007] Step 2: Use Parker transformation to convert the voltage equation and flux equation in the abc coordinate system described in step 1 to the dq0 coordinate system. According to the fault characteristics, focus on the changes in the resistance matrix, inductance matrix and permanent magnet flux terms in the voltage equation and flux equation, and select current or flux as the state variable. It is characterized in that: the distribution of winding inductance changes, the inductance matrix in the dq0 coordinate system is not a constant matrix, and if the current is still used as the state variable, there are complex time-varying partial derivatives of the inductance matrix, which are difficult to solve in the modeling process. Therefore, a discretization and decoupling method using flux as the state variable is proposed, which avoids the calculation of partial derivatives to a certain extent.

[0008] Step 3: Use the backward Euler integration method to discretize the current-voltage equation with current as the state variable and the flux-voltage equation with flux as the state variable in the dq0 coordinate system described in step 2 to obtain the relationship between the stator and rotor current and voltage. Combining the two situations, the equations are unified in form, only the elements in the equations are different, written in block matrix form, separating the dq0 and damping equations, and obtaining a unified stator and rotor current expression. In order to facilitate the interface between PMSG and the external electrical network, it is converted to the abc coordinate system.

[0009] At the same time, the motion equation in step 1 is discretized to obtain the speed expression and the rotor angle expression. It is characterized in that: the stator current I abc (t), rotor current Ikdq (t), speed ω r The expressions for (t) and rotor angle θ(t) are as follows:

[0010] I abc (t) = G abc (t)U abc (t)+I abcEQ (t-Δt)

[0011] I kdq (t) = G kdq (t)U abc (t)+I kdqEQ (t-Δt)

[0012]

[0013] θ(t)=θ(t-Δt)+Δtω r (t)

[0014] In the formula, G abc (t) and G kdq (t) are the stator and rotor admittance matrices respectively; I abcEQ (t-Δt) and I kdqEQ (t-Δt) are the column vectors of the historical values ​​of the stator and rotor equivalent current sources respectively; U abc (t) is the stator voltage column vector; J is the angular moment of inertia; K D is the mechanical damping coefficient; T m is the mechanical torque; T e is the electromagnetic torque of the generator.

[0015] Step 4: According to the expression described in step 3, an equivalent model of the permanent magnet synchronous generator under internal fault state can be obtained, including an electromagnetic transient equivalent circuit and an electromechanical transient model. The decoupling equivalent circuit under internal fault state of the permanent magnet synchronous generator is represented by three controlled current sources. It is characterized in that the admittance matrix in the equivalent circuit equation under internal fault state of the permanent magnet synchronous generator is asymmetric and does not satisfy the properties of the node admittance matrix. Therefore, a controlled current source is used to equalize the permanent magnet synchronous generator, and the size of the controlled current source is calculated by the discretized mathematical equation under different fault types, which is related to the fault type.

[0016] Step 5: Put the permanent magnet synchronous generator equivalent circuit obtained in step 4 into the EMTDC solution system to perform iterative solution of the node admittance moment. Update the generator stator and rotor current, electromagnetic torque, rotor speed, rotor angle and other information according to the external terminal voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Schematic diagram of PMSG structure.

[0018] Figure 2 This is a schematic diagram of demagnetization failure.

[0019] Figure 3 This is a schematic diagram of an eccentric fault.

[0020] Figure 4 This is the PMSG equivalent circuit.

[0021] Figure 5 Schematic diagram of the PMSG modeling process. DETAILED DESCRIPTION

[0022] The present invention provides a method for electromagnetic transient modeling and simulation of a permanent magnet synchronous generator that can reflect various types of internal faults. The modeling steps of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0023] Step 1: PMSG structure diagram as attached Figure 1 As shown. The center axis of the permanent magnet rotor pole is taken as the d-axis, and the q-axis is assumed to lead the d-axis by 90° electrical angle in the direction of rotor rotation. The stator winding adopts a star-grounded connection method, and it is assumed that the direction of the stator current follows the motor convention. The rotor circuit contains two damping windings, which are coaxial with the d-axis and the q-axis respectively.

[0024] According to different fault types, the fault characteristics are determined, and the electromagnetic transient and electromechanical transient mathematical models of the permanent magnet synchronous generator under each fault type are obtained. The mathematical models include the voltage equation, flux equation, and motion equation of the permanent magnet synchronous generator.

[0025] Under normal conditions, the mathematical equations of the generator dq0 rotating coordinate system are shown in equations (1) to (3):

[0026]

[0027]

[0028] In the formula, u d 、u q , u0 is the dq0 axis stator winding voltage; i d 、i q ,i0,i kd 、i kq are the dq0 axis stator winding current and the rotor damping winding current respectively; R s , R kd , R kq are the stator winding resistance, d-axis damping winding resistance, and q-axis damping winding resistance respectively; ψ d , q , ψ0, ψ kd , kq are the dq0-axis stator winding flux and the d-axis q-axis damping winding flux respectively; L d, L q , L0 and L kkd , L kkq are the dq0-axis stator winding inductance and the d-axis and q-axis damping winding inductance respectively; L akd , L akq are the mutual inductance between the stator d-axis and the d-axis damping winding, and the mutual inductance between the stator q-axis and the q-axis damping winding; ψ f is the permanent magnet flux; J is the rotor's moment of inertia; K D is the mechanical damping coefficient; T m is the mechanical torque; T e is the electromagnetic torque; ω r is the rotor electrical angular velocity; θ is the electrical angle of the d-axis leading the magnetic axis of the a-phase winding.

[0029] Asymmetric faults can be compensated by connecting an additional resistor R add Indicates that the asymmetric resistance R add The magnitude of can indicate the degree of asymmetric fault. The voltage equation when an asymmetric fault occurs in the abc coordinate system can be expressed by equation (4), and the flux equation remains unchanged.

[0030]

[0031] For the winding open circuit fault, when an open circuit fault occurs in two phases of the motor, the motor will stop immediately. Therefore, only one-phase open circuit fault is studied. When the fault phase winding is disconnected, the fault phase current is 0 and the three phases of the motor are unbalanced.

[0032] During a single-phase grounding fault of the winding, the fault phase is grounded and the fault current will surge. Assuming that the single-phase short circuit fault occurs in the stator a phase winding, R g is the ground short-circuit resistance, i f is the fault current under single-phase ground short circuit fault; μ represents the fault location, which indicates the fault range is between 0 and 1. f Flow through the short-circuit resistor R g The short-circuit resistance depends on the severity of the fault. g When it is close to 0, the fault evolves into a complete single-phase ground short circuit fault. The voltage equation and flux equation are shown in equations (5) and (6):

[0033]

[0034] There is no excitation winding on the rotor of the permanent magnet synchronous generator, and there is no rotor electrical excitation fault. Therefore, its rotor fault is mainly manifested as irreversible demagnetization fault of the permanent magnet, including uniform demagnetization and local demagnetization.

[0035] For uniform demagnetization fault, the flux parameters are adjusted by introducing a fault factor K. It is equal to the flux ψ after the fault permanent magnet is degraded.f * and the flux linkage ψ of a normal permanent magnet f The ratio of, that is: ψ f * =K*ψ f .

[0036] For a local demagnetization fault, a part of a permanent magnet is demagnetized. The fault is not symmetrical. The schematic diagram of local demagnetization is shown in the attached figure. Figure 2 As shown, on the basis of introducing the fault proportional coefficient to adjust the magnitude of the flux amplitude, the demagnetization deviation angle γ is introduced. The flux equation under the permanent magnet demagnetization fault is shown in formula (7). When the demagnetization is uniform, the demagnetization deviation angle γ = 0:

[0037]

[0038] Eccentricity refers to the inconsistency of the air gap distance between the stator and the rotor. The air gap eccentricity model is shown in the attached figure. Figure 3 As shown, by setting the eccentricity ρ m , a motor model capable of simulating rotor eccentricity faults under different eccentricity degrees was established. m With the eccentricity direction γ m The change of eccentricity type needs to be calculated in advance. The rotor eccentricity changes the air gap distribution, which directly affects the inductance of the permanent magnet synchronous generator. The stator inductance parameters change, including the self-inductance part, the mutual inductance part and the additional items caused by eccentricity.

[0039]

[0040] In the formula, O s is the center of the stator, O r is the rotor center, ρ s is the static eccentricity, ρ d is the dynamic eccentricity, and γ0 is the initial eccentricity angle.

[0041] Step 2: Use Parker transformation to convert the voltage equation and flux equation in the abc coordinate system described in step 1 to the dq0 coordinate system. According to the fault characteristics, focus on the changes in the resistance matrix, inductance matrix and permanent magnet flux terms in the voltage equation and flux equation.

[0042] For the mathematical equations in the dq0 rotating coordinate system, the Parker transformation is applied to derive and define the matrix P T for:

[0043]

[0044] The stator and rotor voltage equations in the dq0 coordinate system are as follows:

[0045]

[0046] In the formula, R dq0,kdkq =P T R abc,kdkq P T -1

[0047]

[0048] The stator and rotor flux equations in the dq0 coordinate system are as follows:

[0049]

[0050] Where, L dq0,kdkq =P T L abc,kdkq P T -1 ; p is the permanent magnet flux column vector.

[0051] Further, current or flux linkage is selected as the state variable according to the fault type:

[0052] Under the electrical winding fault type, the matrix R abc,kdkq No longer symmetrical, that is, the corresponding R in the dq0 coordinate system dq0,kdkq Change; Under permanent magnet fault, the permanent magnet flux term ψ p change; only the resistance matrix or the permanent magnet flux term changes, the inductance matrix is ​​a constant matrix, and the current is discretized as the state variable.

[0053]

[0054] Under fault types such as eccentric fault and winding single-phase grounding fault, the winding inductance distribution changes, and the inductance matrix L abc,kdkq Change, that is, L in the magnetic flux equation in the dq0 coordinate system dq0,kdkq It is no longer a constant matrix. If the current is still used as the state variable, there will be complex time-varying partial derivatives of the inductance matrix, which are difficult to solve in the modeling process. Therefore, a discretization and decoupling method using magnetic flux as the state variable is proposed, which avoids the calculation of partial derivatives to a certain extent.

[0055]

[0056] Step 3: Use the backward Euler integration method to discretize the current-voltage equation with current as the state variable and the flux-voltage equation with flux as the state variable in the dq0 coordinate system described in step 2 to obtain the relationship between the stator and rotor currents and voltages.

[0057] Taking current as the state variable and asymmetric fault as an example:

[0058] After eliminating the flux, the stator and rotor current-voltage equations are as follows:

[0059]

[0060] The d- and q-axis coupling part ω in the PMSG equation r (t), ψ(t) is approximately equal to ω r (t-Δt), ψ(t-Δt), and we can get:

[0061]

[0062] In the formula

[0063] Taking the magnetic flux as the state variable, take the eccentricity fault as an example:

[0064] Under eccentricity fault, both the self-inductance and mutual inductance of the stator inductance matrix have additional terms caused by eccentricity, namely, L abc =A0*L0+ΔL abc , where L0 is the stator inductance matrix in the abc three-phase coordinate system under normal conditions, A0 is the eccentricity additional coefficient, and if there is no eccentricity, the additional coefficient A0 = 1.

[0065]

[0066] Among them, the additional terms of self-inductance and mutual inductance, γ mi / mj and θ mi / mj (i=a,b,c;j=b,c,a) is given by equation (17):

[0067]

[0068] In the formula

[0069] The backward Euler method discretizes to get:

[0070]

[0071] Substitute the flux equation into the voltage equation and replace the d- and q-axis coupling part ω in the PMSG equation. r (t), ψ(t) is approximately equal to ω r (t-Δt), ψ(t-Δt), and we can get:

[0072]

[0073] Combining the two cases, the equations are unified in form, only the elements in the equations are different, and they can be written in block matrix form

[0074]

[0075] Separating dq0 from the damping equation, we get a unified stator and rotor current expression. To facilitate the interface between PMSG and the external electrical network, we convert it to the abc coordinate system to get the stator current I abc (t), rotor current I kdq (t) Expression:

[0076]

[0077] Where:

[0078]

[0079] At the same time, the motion equation in step 1 is discretized to obtain the speed ω r (t) expression and rotor angle θ(t) expression:

[0080]

[0081] In the formula, G abc (t) and G kdq (t) are the stator and rotor admittance matrices respectively; I abcEQ (t-Δt) and I kdqEQ (t-Δt) are the column vectors of the historical values ​​of the stator and rotor equivalent current sources respectively; U abc (t) is the stator voltage column vector; J is the angular moment of inertia; K D is the mechanical damping coefficient; T m is the mechanical torque; T e is the electromagnetic torque of the generator, P(t) -1 is the inverse Parker transform matrix.

[0082] Step 4: According to the expression described in step 3, the equivalent model of the permanent magnet synchronous generator under internal fault conditions can be obtained, including the electromagnetic transient equivalent circuit and the electromechanical transient model. The decoupling equivalent circuit under internal fault conditions of the permanent magnet synchronous generator is represented by three controlled current sources. The admittance matrix in the equivalent circuit equation under internal fault conditions of the permanent magnet synchronous generator is asymmetric and does not satisfy the properties of the node admittance matrix. Therefore, a controlled current source is used to equalize the permanent magnet synchronous generator, and the size of the controlled current source is calculated by the discretized mathematical equation under different fault types, which is related to the fault type. The PMSG equivalent circuit is shown in the attached figure. Figure 4 shown.

[0083] Step 5: Put the equivalent circuit of the permanent magnet synchronous generator obtained in step 4 into the EMTDC solution system. First, calculate the reference value used in the normalization process and store the calculation result in the register to prevent additional calculations for each update. Then determine the fault type. According to different fault types, determine the changes in resistance, inductance, and flux linkage terms, focusing on the block matrices A / B / C / D and J dq0(t-Δt) changes. Secondly, calculate the generator equivalent circuit parameters: that is, the stator winding admittance matrix G abc (t) and the historical current source value I abcEQ (t-Δt); then, the PMSG equivalent circuit is directly connected to the external electrical network to provide an injection current source for the external network. The EMTDC solver iteratively solves the node admittance matrix of the overall circuit of the PMSG equivalent circuit and the external electrical network. Next, according to the external terminal voltage, the generator stator and rotor current, electromagnetic torque, rotor speed, rotor angle and other information are updated. Finally, the updated parameters are stored as the historical values ​​of the next step, and then the next step simulation is entered. The modeling process under PMSG internal fault conditions is shown in the attached figure. Figure 5 shown.

[0084] Finally, it should be noted that the above description is only a preferred embodiment of the present invention that is easily understood by those skilled in the art, and is not intended to limit the present invention. Any modification, equivalent substitution, and improvement made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for modeling and simulating electromagnetic transients of a permanent magnet synchronous generator that can reflect various types of internal faults. It is characterized by: The present invention determines fault characteristics according to different fault types, and establishes mathematical models of permanent magnet synchronous generators under different fault states such as electrical faults, mechanical faults, and permanent magnet faults; based on the derivation of a detailed mathematical model of the permanent magnet synchronous generator, the mathematical equation is discretized using the backward Euler method, and two state variables are integrated to obtain a unified form equivalent circuit of the permanent magnet synchronous generator. Further, an external electrical network and the equivalent model are solved as a whole by an EMTDC solver, and then based on the information of the external nodes of the generator after the solution, the generator stator and rotor currents, electromagnetic torque, speed, and rotor angle information are updated; the method comprises the following steps: Step 1: According to different fault types, determine the fault characteristics, and obtain the electromagnetic transient and electromechanical transient mathematical models of the permanent magnet synchronous generator under each fault type, wherein the mathematical model includes the voltage equation, flux equation, and motion equation of the permanent magnet synchronous generator. It is characterized in that the mathematical model determines the electromagnetic transient and electromechanical transient characteristics of the permanent magnet synchronous generator. Step 2: Use Parker transformation to convert the voltage equation and flux equation in the abc coordinate system described in step 1 to the dq0 coordinate system. According to the fault characteristics, focus on the changes in the resistance matrix, inductance matrix and permanent magnet flux terms in the voltage equation and flux equation, and select current or flux as the state variable. It is characterized in that: the distribution of winding inductance changes, the inductance matrix in the dq0 coordinate system is not a constant matrix, and if the current is still used as the state variable, there are complex time-varying partial derivatives of the inductance matrix, which are difficult to solve in the modeling process. Therefore, a discretization and decoupling method using flux as the state variable is proposed, which avoids the calculation of partial derivatives to a certain extent. Step 3: Use the backward Euler integration method to discretize the current-voltage equation with current as the state variable and the flux-voltage equation with flux as the state variable in the dq0 coordinate system described in step 2 to obtain the relationship between the stator and rotor current and voltage. Combining the two situations, the equations are unified in form, and only the elements in the equations are different. They are written in block matrix form, and the dq0 and damping equations are separated to obtain a unified stator and rotor current expression. In order to facilitate the interface between PMSG and the external electrical network, it is converted to the abc coordinate system. At the same time, the motion equation in step 1 is discretized to obtain the speed expression and rotor angle expression. It is characterized in that: the stator current I abc (t), rotor current I kdq (t), speed ω r The expressions for (t) and rotor angle θ(t) are as follows: I abc (t)=G abc (t)U abc (t)+I abcEQ (t-Δt) I kdq (t)=G kdq (t)U abc (t)+I kdqEQ (t-Δt) θ(t)=θ(t-Δt)+Δtω r (t) In the formula, G abc (t) and G kdq (t) are the stator and rotor admittance matrices respectively; I abcEQ (t-Δt) and I kdqEQ (t-Δt) are the column vectors of the historical values ​​of the stator and rotor equivalent current sources respectively; U abc (t) is the stator voltage column vector; J is the angular moment of inertia; K D is the mechanical damping coefficient; T m is the mechanical torque; T e is the electromagnetic torque of the generator. Step 4: According to the expression described in step 3, an equivalent model of the permanent magnet synchronous generator under internal fault state can be obtained, including an electromagnetic transient equivalent circuit and an electromechanical transient model. The decoupling equivalent circuit under internal fault state of the permanent magnet synchronous generator is represented by three controlled current sources. It is characterized in that the admittance matrix in the equivalent circuit equation under internal fault state of the permanent magnet synchronous generator is asymmetric and does not satisfy the properties of the node admittance matrix. Therefore, a controlled current source is used to equalize the permanent magnet synchronous generator, and the size of the controlled current source is calculated by the discretized mathematical equation under different fault types, which is related to the fault type. Step 5: Put the permanent magnet synchronous generator equivalent circuit obtained in step 4 into the EMTDC solution system to perform iterative solution of the node admittance moment. Update the generator stator and rotor current, electromagnetic torque, rotor speed, rotor angle and other information according to the external terminal voltage.

2. The method for electromagnetic transient modeling and simulation of a permanent magnet synchronous generator capable of reflecting various types of internal faults according to claim 1 is characterized in that: From step 1 to step 5, the previous step is the basis for the execution of the next step. These five modeling steps are closely linked to each other and executed sequentially, forming an organic and indivisible whole.

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