JP4242825B2 - Motor model calculation method, motor simulation method, motor simulation apparatus, and motor model calculation program - Google Patents

Description

  The present invention relates to an improvement of a motor model calculation method, a motor simulation method, a motor simulation apparatus, and a motor model calculation program, which are effective for simulation of a control system using an AC motor, for example.

In various tasks such as development, debugging, adaptation, and verification of control algorithms for motor devices using AC motors, motors and inverters are used by using a motor model as a virtual motor and an inverter model as a virtual inverter that drives the motor model. The behavior is simulated in real time. The motor model and the inverter model used for this real-time simulation are defined using equations as described in Patent Document 1 below, for example. The equations include, for example, a method for defining the relationship between voltage and current using a stationary coordinate system and a method for defining using a rotating coordinate system (so-called dq axis).
JP 2004-236392 A

  However, when simulating an AC motor or an inverter using an equation using a stationary coordinate system, the calculation becomes very complicated and difficult to perform a high-precision real-time simulation in a short step period.

  For this reason, conventionally, simulation of an AC motor or an inverter is usually performed using an equation that uses a rotating coordinate system that is relatively easy to calculate compared to a stationary coordinate system, but the rotating coordinate system is used. Since the coordinate axis conversion process is necessary, there is a problem that the calculation accuracy is lowered. Moreover, even in the arithmetic processing of equations using a rotating coordinate system, it is not easy to execute motor simulation at high speed with limited calculation resources because of the necessity of coordinate axis conversion processing.

  The present invention has been made in view of the above problems, and provides a motor model calculation method, a motor simulation method, a motor simulation apparatus, and a motor model calculation program capable of high-speed and high-precision real-time simulation while saving computer resources. Its purpose is to do.

  Note that the motor model calculation method and simulation method of the present invention are substantially expressed in the form of calculation resource calculation processing technology, that is, in the form of a computer program. Realized. Accordingly, since the program for executing the method of the present invention includes the method of the present invention in a state where it can be executed very easily, the distribution of such a program corresponds to the implementation of the method of the present invention or the act of promoting the method. Note that it is included in the method of the present invention.

The calculation method of the motor model of the first invention is:
Defined by an equation on a stationary coordinate system showing the state of an AC motor having a rotor that generates a field flux ψr and a stator around which each phase armature winding is wound. A motor model calculation method using a motor model including i and each phase armature voltage U as a variable,
A motor model is constructed by converting an inverse matrix of the inductance matrix L (θ), which is a predetermined function having the rotation angle θ as a variable, into a matrix λ (θ), which is a function having the rotation angle θ as a variable,
This matrix λ (θ) is calculated to calculate the value of the inverse matrix of the inductance matrix L (θ), and the value of this inverse matrix is substituted into the equation forming the motor model to obtain the value of the desired variable ,
The inductance matrix L (θ) is an inductance matrix of each phase armature winding indicating the relationship between the current magnetic flux ψs that is the armature winding linkage magnetic flux by each phase armature current i and each phase armature current i. And
The inverse matrix of the inductance matrix L (theta) is, d-axis inductance Ld of the AC motor, q-axis inductance Lq of the AC motor, is calculated by the matrix calculating λ a (theta) based on the leakage inductance Ll Rukoto It is characterized by.

That is, the motor model calculation method according to the present invention can simply represent the motor model because the part relating to the armature inductance of the equation forming the motor model is defined using the inverse matrix of the inductance matrix L (θ). Since the inverse matrix is converted to the matrix λ (θ) and then the calculation is performed, the calculation process can be greatly simplified. As a result, the motor model can be used even in a limited calculation time like a high-speed real-time simulation. It is possible to calculate with high accuracy.
In addition, since the inductance matrix L (θ) and its inverse matrix and the matrix λ (θ) equal to this inverse matrix can be simply configured, high-speed calculation of the inverse matrix of the inductance matrix L (θ) is possible. Become.
Further, the inverse matrix λ (θ) is calculated based on the d-axis inductance Ld of the AC motor, the q-axis inductance Lq of the AC motor, and the leakage inductance Ll. That is, since each term of the matrix λ (θ) is defined as a function of the d-axis inductance Ld of the AC motor, the q-axis inductance Lq of the AC motor, and the leakage inductance Ll, a matrix equal to the inverse matrix of the inductance matrix L (θ) Arithmetic processing of each term of λ (θ) is facilitated. Therefore, the calculation of the matrix λ (θ) can be performed at high speed and high accuracy.

In preferred embodiment 1 , when the armature resistance of each phase is Rs, each phase armature current is i, and each phase armature voltage is U, the inductance matrix L (θ) and its inverse matrix are used to define the phase. Since the equation shown in the following Equation 13 is used as the motor model, a high-speed and high-precision motor model can be calculated.

好適態様２において、前記方程式（すなわちモータモデル）として、少なくとも電流磁束ψｓ、電機子抵抗Ｒｓ、インダクタンス行列Ｌ（θ）の逆行列、各相電機子電圧Ｕ及び界磁束ψｒの間の数量関係を示す第１の方程式と、少なくとも各相電機子電流ｉ、電流磁束ψｓ及びインダクタンス行列Ｌ（θ）の逆行列の間の数量関係を示す第２の方程式とを用いるので、モータモデルをインダクタンス行列Ｌ（θ）を用いずに定義することができる。その結果として、インダクタンス行列Ｌ（θ）に関する演算を省略することができるので、一層の高速高精度の演算が可能となる。

In the preferred embodiment 2 , as the equation (that is, the motor model), at least the current flux ψs, the armature resistance Rs, the inverse matrix of the inductance matrix L (θ), each phase armature voltage U, and the field flux ψr Since the first equation shown and the second equation showing the quantitative relationship among at least each phase armature current i, current magnetic flux ψs and the inverse matrix of the inductance matrix L (θ) are used, the motor model is represented by the inductance matrix L It can be defined without using (θ). As a result, since the calculation related to the inductance matrix L (θ) can be omitted, it is possible to perform calculation with higher speed and higher accuracy.

In the preferred embodiment 3 , since the equations shown in the following equations 15 and 16 are used as the motor model, there is no need to calculate the inductance matrix L (θ) or a function using the variable as a variable, and the motor model can be operated at high speed and high accuracy. Can be calculated.

In the preferred embodiment 4 , the reciprocal λd of the d-axis inductance Ld, the reciprocal λq of the q-axis inductance Lq, and the reciprocal λl of the leakage inductance Ll are substituted into the following equations 37 and 38 to calculate the inductance reciprocal functions λas and λa,

演算したインダクタンス逆数関数λａｓ、λａとリーケージインダクタンスＬｌの逆数λｌとを下記の数３９〜数４４に代入して行列λ（θ）の各項λ１１、λ１２、λ１３、λ２１、λ２２、λ２３、λ３１、λ３２、λ３３を演算する。このようにすれば、行列λ（θ）の各項を更に簡単に定義することができるので、行列λ（θ）の各項を一層高速高精度に演算することができる。

The calculated inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll are substituted into the following Equations 39 to 44, and the terms λ11, λ12, λ13, λ21, λ22, λ23, λ31, λ32 and λ33 are calculated. In this way, each term of the matrix λ (θ) can be more easily defined, so that each term of the matrix λ (θ) can be calculated with higher speed and accuracy.

  The motor model calculation method described in each of the above items can have a form of a program executed by a computer. The calculation method of the motor model defined by this program has a feature that enables high-speed and high-precision calculation as described above.

A second invention is a motor that simulates in real time the state of a virtual motor defined by the motor model by periodically executing a calculation step of calculating the state of the motor model using the motor model calculation method. Features a simulation method. According to this motor simulation method, the state calculation of the motor model can be executed with high speed and high accuracy as described above, so that high speed and high accuracy motor simulation is possible.

  In a preferred aspect 1, the characteristic value of the virtual motor, which is composed of the constants of the equation and defined by the motor model, is set to an external command, the state of the motor model which is a variable value of the calculated motor model, It changes according to at least one of the predetermined motor states calculated by the program. In particular, this change is made during the calculation of the motor model of the present invention. The predetermined motor state calculated by another program is, for example, an armature temperature that changes during operation of the virtual motor, that is, during calculation of the motor model, and the characteristic value of the virtual motor is an armature resistance. In this way, a change in armature resistance due to a change in armature temperature during operation of the virtual motor can be given to the motor model being calculated, so that a more accurate calculation of the motor model becomes possible. In addition, for example, by calculating the armature resistance change due to the above armature temperature with an external device and substituting it into the motor model, the armature resistance change due to the temperature during virtual motor operation can be reflected in the motor model being calculated. it can.

According to a third aspect of the present invention, a virtual motor state defined by the motor model is simulated in real time by periodically executing a calculation step of calculating the state of the motor model using the motor model calculation method described above. A motor simulation apparatus characterized by having an arithmetic unit is characterized. According to this motor simulation apparatus, since the state calculation of the motor model can be executed at high speed and high accuracy as described above, high speed and high accuracy motor simulation is possible.

In a preferred aspect 1, it is defined by an equation on a stationary coordinate system indicating a state of an AC motor having a rotor that generates a field flux ψr and a stator around which each phase armature winding is wound, and the equation is Using a stationary coordinate system motor model including at least each phase armature current i and each phase armature voltage U as variables, and substituting numerical values for the predetermined variables of the stationary coordinate system motor model, values of other variables A stationary coordinate system computing unit for computing
Dq rotation coordinate system calculation for performing coordinate system conversion calculation for converting the state of the AC motor consisting of the value of the variable on the stationary coordinate system state calculated by the stationary coordinate system calculation unit into a value on the dq rotation coordinate system A stationary coordinate system calculation unit,
Based on an external motor control command, a calculation step for calculating the state of the stationary coordinate system motor model is periodically executed to simulate the state of the virtual motor corresponding to the stationary coordinate system motor model in real time, and the dq The rotating coordinate system calculation unit converts the current state of the motor and the AC motor into a value on a dq rotating coordinate system and outputs it as display data to the outside in response to a rotating coordinate system display command input from the outside. Yes. In this way, the motor simulation can be executed with high speed and high accuracy by the stationary coordinate system motor model while confirming the external motor state on the dq rotation coordinate system.

The motor model calculation program of the fourth invention is defined by an equation on a stationary coordinate system indicating the state of an AC motor having a rotor that generates a field flux ψr and a stator on which each phase armature winding is wound. The equation is a motor model calculation program for calculating a motor model including at least each phase armature current i and each phase armature voltage U as variables, and is configured by a function having a rotation angle θ as a variable. A matrix λ (θ) that is a function equal to the inverse matrix of the inductance matrix L (θ) indicating the relationship between the current magnetic flux ψs that is the armature winding interlinkage magnetic flux by each phase armature current i and each phase armature current i a step of computing, by substituting the value of the matrix lambda (theta) have a obtaining a desired value of a variable of the equation as the values of the inverse matrix of the inductance matrix L (theta) included in the equation ,
The step of calculating the matrix λ (θ) is characterized in that the matrix λ (θ) is calculated based on the d-axis inductance Ld of the AC motor, the q-axis inductance Lq of the AC motor, and the leakage inductance Ll .
By using this program, the motor model can be calculated at a much higher speed than before as described above.

  In a preferred aspect 1, the step of calculating the matrix λ (θ) includes the following equation: Substituting into Equation 38, the reciprocal inductance functions λas and λa are calculated,

演算したインダクタンス逆数関数λａｓ、λａとリーケージインダクタンスＬｌの逆数λｌとを下記の数３９〜数４４に代入して行列λ（θ）の各項λ１１、λ１２、λ１３、λ２１、λ２２、λ２３、λ３１、λ３２、λ３３を演算するステップであることを特徴とするモータモデル演算プログラム。

The calculated inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll are substituted into the following Equations 39 to 44, and the terms λ11, λ12, λ13, λ21, λ22, λ23, λ31, A motor model calculation program characterized by being a step of calculating λ32 and λ33.

このプログラムを用いることにより、既述したように従来より格段に高速にモータモデルを演算することができる。

By using this program, the motor model can be calculated at a much higher speed than before as described above.

  A preferred embodiment of the motor model calculation method of the present invention will be described below. However, the present invention is not limited to the following embodiments, and it is natural that the technical idea of the present invention may be realized by combining known techniques or equivalent techniques. In the following description, a three-phase PM (magnet field) AC motor is used as an example. However, generating a field flux by a magnet is essentially equivalent to generating a field flux by passing a field current through a field coil, so it can be applied to a field coil AC motor. is there. Furthermore, in the induction motor and the reluctance (hysteresis) motor that generate the magnetic field flux generated by the rotor by supplying the alternating current from the stator side to the rotor side, the field flux is defined in the same manner as in the following embodiments. By doing so, the following motor model can be adopted.

(First motor model)
The first motor model (equation indicating the relationship between current and voltage) will be described below. The relationship among the output AC voltage U of each phase of the three-phase AC motor model, each phase armature current i, and the magnetic flux ψ interlinking with each phase armature winding is defined by Equations 1 to 4.

ψは３相電機子巻線鎖交磁束、Ｒｓは電機子巻線抵抗、Ｅは３×３の単位行列であり数５により示される。

ψ is a three-phase armature winding interlinkage magnetic flux, Rs is an armature winding resistance, E is a 3 × 3 unit matrix, and is represented by Equation 5.

ＵｕはＵ相電機子電圧、ＵｖはＶ相電機子電圧、ＵｗはＷ相電機子電圧、ＩｕはＵ相電機子電流、ＩｖはＶ相電機子電流、ＩｗはＷ相電機子電流、ψｕはψのＵ相成分、ψｖはψのＶ相成分、ψｗはψのＷ相成分である。

Uu is a U-phase armature voltage, Uv is a V-phase armature voltage, Uw is a W-phase armature voltage, Iu is a U-phase armature current, Iv is a V-phase armature current, Iw is a W-phase armature current, and ψu is A U-phase component of ψ, ψv is a V-phase component of ψ, and ψw is a W-phase component of ψ.

In the case of the three-phase PM type synchronous motor model, the three-phase armature winding linkage magnetic flux ψ is formed by the three-phase armature winding linkage magnetic flux ψs formed by the three-phase armature winding current i and a permanent magnet. Since this is the sum of the three-phase armature winding interlinkage magnetic flux ψr , Equation 1 can be converted into Equation 6 to Equation 7. Hereinafter, for the sake of simplicity, the three-phase armature winding interlinkage magnetic flux ψs is sometimes referred to as a current magnetic flux, and the three-phase armature winding interlinkage magnetic flux ψr is sometimes referred to as a field magnetic flux. Therefore, Equation 5 can be converted into Equation 6 to Equation 7.

ただし、ψｓｕはψｓのＵ相成分、ψｓｖはψｓのＶ相成分、ψｓｗはψｓのＷ相成分、ψｒｕはψｒのＵ相成分、ψｒｖはψｒのＶ相成分、ψｒｗはψｒのＷ相成分である。ψｒｕ、ψｒｖ、ψｒｗは次の数８〜数１０により定義される。

Where ψsu is the U phase component of ψs, ψsv is the V phase component of ψs, ψsw is the W phase component of ψs, ψru is the U phase component of ψr, ψrv is the V phase component of ψr, and ψrw is the W phase component of ψr. is there. ψru, ψrv, ψrw are defined by the following equations 8 to 10.

ψｍは永久磁石による電機子巻線鎖交磁束の最大値、θは回転子回転角である。３相電機子巻線電流ｉにより形成される３相電機子巻線鎖交磁束ψｓは数１１により定義される。

ψm is the maximum value of the armature winding interlinkage magnetic flux by the permanent magnet, and θ is the rotor rotation angle. The three-phase armature winding linkage magnetic flux ψs formed by the three-phase armature winding current i is defined by Equation 11.

Ｌ（θ）は、電流磁束ψｓと各相電機子電流ｉとの関係を示す行列関数、すなわち３相電機子巻線のインダクタンス行列である。インダクタンス行列Ｌ（θ）は、円筒形ＰＭモータのインダクタンス行列は定数行列となるが、突極型又は逆突極型ＰＭモータの場合、数１２により定義される回転子回転角θの関数となる。以下の実施例では、演算処理が複雑な突極型又は逆突極型ＰＭモータの場合を説明する。

L (θ) is a matrix function indicating the relationship between the current magnetic flux ψs and each phase armature current i, that is, the inductance matrix of the three-phase armature winding. The inductance matrix L (θ) is a constant matrix for the cylindrical PM motor. In the case of a salient pole type or reverse salient pole type PM motor, the inductance matrix L (θ) is a function of the rotor rotation angle θ defined by Equation 12. . In the following embodiment, a case of a salient pole type or reverse salient pole type PM motor having a complicated calculation process will be described.

ただし、Ll は各相の電機子巻線のリーケージインダクタンス成分、Ｌａは各相の電機子巻線の直流インダクタンス成分、Ｌａｓは各相の電機子巻線の交流インダクタンス成分である。次に、数１１を数６に代入することにより、数６を下記の数１３に変換することができる。

Here, Ll is a leakage inductance component of the armature winding of each phase, La is a DC inductance component of the armature winding of each phase, and Las is an AC inductance component of the armature winding of each phase. Next, by substituting Equation 11 into Equation 6, Equation 6 can be converted into Equation 13 below.

したがって、数１３は、インダクタンス行列Ｌ（θ）を用いたＰＭモータのモータモデルに相当する方程式となる。この数１３で示されるモータモデルを用いると、３相電機子電流ｉをｄｑ変換することなく直接導出することが可能となる。

Therefore, Equation 13 is an equation corresponding to a motor model of the PM motor using the inductance matrix L (θ). By using the motor model shown by this equation 13, the three-phase armature current i can be directly derived without performing dq conversion.

  That is, when using the motor model represented by Equation 13, the armature winding resistance Rs, the inductance matrix L (θ), the three-phase armature winding interlinkage magnetic flux ψr formed by a permanent magnet, and the inductance matrix L (θ) The relationship between the three-phase armature current i and the three-phase armature voltage U can be defined. Therefore, the motor model can be calculated by using the equation (13) as the motor model. This motor model is suitable for computer processing because the motor model is described relatively easily by using an inductance matrix L (θ) that is a matrix function and an inverse matrix of the inductance matrix L (θ). . It should be noted that by replacing the inverse matrix of the inductance matrix L (θ) with calculation of a matrix λ (θ) described later, the calculation processing time can be further shortened.

(Second motor model)
The second motor model will be described below. As will be described later, this motor model does not use Equation 13 described above, but instead uses an equation that describes the relationship between the output AC voltage U of each phase and the armature current i of each phase using the current magnetic flux ψs. Defined. For example, in the calculation of the motor model, the three-phase current i can be obtained by using the previously calculated three-phase armature winding linkage magnetic flux ψs. When Expression 11 is transformed, Expression 14 is obtained.

数１４を数６に代入すると、数１５、数１６が得られる。数１６は数１４に等しい。

By substituting Equation 14 into Equation 6, Equations 15 and 16 are obtained. Equation 16 is equal to Equation 14.

数１５を用いると、数１３すなわち第１モータモデルで必要であったｄＬ（θ）／ｄｔを導出するための複雑な演算を省略できることがわかる。つまり、あらかじめ演算した３相電機子巻線鎖交磁束ψｓを用いることによりインダクタンス行列Ｌ（θ）の微分処理を省略することができる。

Using Equation 15, it can be seen that the complicated calculation for deriving dL (θ) / dt required in Equation 13, that is, the first motor model can be omitted. That is, the differentiation process of the inductance matrix L (θ) can be omitted by using the previously calculated three-phase armature winding linkage magnetic flux ψs.

  That is, in this motor model shown in Equations 15 and 16, the armature resistance Rs, the inverse matrix of the inductance matrix L (θ), the three-phase armature voltage (also referred to as each phase armature voltage) U, and the magnet magnetic flux ψr are respectively represented. The current magnetic flux ψs is calculated by calculating and substituting into Equation 15, and further, the inverse matrix of the inductance matrix L (θ) is calculated, and the current magnetic flux ψs and the inverse matrix are substituting into Equation 16 to obtain the three-phase electric machine. It is possible to calculate the child winding current (also referred to as each phase armature current) i. Therefore, the calculation of the second motor model can greatly omit the calculation steps as compared with the calculation of the first motor model described above, so that the calculation time required for each calculation step in the simulation can be shortened. As a result, real-time simulation of a high-speed and high-accuracy motor model can be executed with a small amount of computing resources, and a great practical effect can be generated. Further, in this motor model calculation, the calculation time can be further reduced by replacing the calculation of the inverse matrix of the inductance matrix L (θ) with the calculation of the matrix λ (θ).

(Motor torque calculation formula)
In the motor model calculation, calculation of the motor torque is desired, but the motor torque is a function value of the current, and can be calculated, for example, by calculating Equation 17 for each calculation step of the simulation. Therefore, in the motor model that requires the calculation of the motor torque, the following equation 17 may be added to the motor model. Similarly, power consumption, reactive power, and other electric and physical quantities can be calculated by adding equations defining them to the motor model.

なお、ｐは極数である。

Note that p is the number of poles.

(Calculation method of inverse matrix of inductance matrix L (θ))
In the calculation of the first and second motor models, calculation of the inverse matrix of the inductance matrix L (θ) is required. The inverse matrix of the inductance matrix L (θ) is represented by the symbol of Equation 18.

インダクタンス行列Ｌ（θ）の逆行列、数１２から演算する場合、演算処理が複雑となり、加減乗算にくらべて処理時間が長い除算も必要となるため、演算必要時間の増大によりシミュレーションの高速化高精度化の障害となる。よく知られているように、シミュレーションの演算ステップの時間間隔の延長は演算精度の低下を招く。

When calculating from the inverse matrix of the inductance matrix L (θ), Equation 12, the calculation process is complicated, and division requiring a longer processing time than addition / subtraction multiplication is required. It becomes an obstacle to accuracy. As is well known, extending the time interval of the simulation calculation step causes a reduction in calculation accuracy.

Therefore, in this embodiment, the inverse matrix of the inductance matrix L (θ) is calculated by the following calculation method. The inductance matrix L (θ) expressed by Expression 12 is rewritten into the form of the arithmetic sum of the matrix functions L1, L2, and L3 expressed by Expression 19 to Expression 22. The matrix function L1 can be defined by Equation 20, the matrix function L2 can be defined by Equation 21, and the matrix function L3 can be defined by Equation 22.

次に、行列関数Ｌｃ（θ）を新設し、この行列関数Ｌｃ（θ）を数２３〜数２５により定義する。

Next, a matrix function Lc (θ) is newly established, and this matrix function Lc (θ) is defined by Equations 23 to 25.

数２３の各項を計算すると、数２６〜数２８が得られる。

When each term of Expression 23 is calculated, Expressions 26 to 28 are obtained.

数２６〜数２８によりそれぞれ定義される各項の和に等しい行列関数Ｌｃ（θ）を整理すると、この行列関数Ｌｃ（θ）は数２９となる。

By arranging the matrix function Lc (θ) that is equal to the sum of the terms defined by Expressions 26 to 28, the matrix function Lc (θ) is expressed by Expression 29.

ただし、Ｌｄは電機子巻線のｄ軸インダクタンスであり、数３０で定義される。Ｌｑは電機子巻線のｑ軸インダクタンスであり、数３１で定義される。

Here, Ld is the d-axis inductance of the armature winding and is defined by Equation 30. Lq is the q-axis inductance of the armature winding and is defined by Equation 31.

数２９に示される行列関数Ｌｃ（θ）の逆行列は次の数３２の形となる。

The inverse matrix of the matrix function Lc (θ) shown in Expression 29 has the form of the following Expression 32.

ただし、λｄ＝１／Ｌｄ、λｑ＝１／Ｌｑ、λｌ＝１／Ｌｌである。すなわち、行列関数Ｌｃ（θ）の０でない各項は、電機子巻線のｄ軸インダクタンスＬｄの逆数λｄ、電機子巻線のｑ軸インダクタンスＬｑの逆数λｑ、リーケージインダクタンスＬｌの逆数λｌとなる。

However, λd = 1 / Ld, λq = 1 / Lq, and λl = 1 / Ll. That is, each non-zero term of the matrix function Lc (θ) is an inverse λd of the d-axis inductance Ld of the armature winding, an inverse λq of the q-axis inductance Lq of the armature winding, and an inverse λl of the leakage inductance Ll.

  Next, when the inverse matrix of the inductance matrix L (θ) is obtained from Equation 23, the following Equation 33 is obtained.

ここで、変換行列Ｃは絶対変換行列であるので、次の数３４、数３５が成立する。

Here, since the transformation matrix C is an absolute transformation matrix, the following equations 34 and 35 hold.

従って、インダクタンス行列Ｌ（θ）の逆行列は対称行列であることがわかる。次に、３つの変数λ（θ）、λａｓ、λａを数３６〜数３８により新たに定義する。数３６は、インダクタンス行列Ｌ（θ）の逆行列に等しい行列λ（θ）である。

Therefore, it can be seen that the inverse matrix of the inductance matrix L (θ) is a symmetric matrix. Next, three variables λ (θ), λas, and λa are newly defined by Equations 36 to 38. Equation 36 is a matrix λ (θ) equal to the inverse matrix of the inductance matrix L (θ).

数３６〜数３８により定義される変数λ（θ）、λａｓ、λａを用いて数３５を整理すると、数３６の行列関数λ（θ）の各項が次の数３９〜数４７が得られる。

By rearranging the equation 35 using the variables λ (θ), λas, and λa defined by the equations 36 to 38, the following equations 39 to 47 are obtained for each term of the matrix function λ (θ) of the equation 36. .

結局、数３７〜数３８で算出したλａｓ、λａを用いて数３９〜数４７を演算すること計算された行列関数λ（θ）を演算するだけで、インダクタンス行列Ｌ（θ）の逆行列を演算することができることがわかる。つまり、上記した演算手順に従えば、このインダクタンス行列Ｌ（θ）の逆行列の演算方式は、インダクタンス行列Ｌ（θ）の逆行列を行列λ（θ）の演算に置換して行うことができるため、インダクタンス行列Ｌ（θ）の逆行列を従来より格段に簡単に演算することが可能となったわけである。

Eventually, the inverse matrix of the inductance matrix L (θ) can be obtained simply by calculating the calculated matrix function λ (θ) by calculating Mathematical Formula 39 to Mathematical Formula 47 using λas and λa calculated in Formulas 37 to 38. It turns out that it can calculate. That is, according to the calculation procedure described above, the calculation method of the inverse matrix of the inductance matrix L (θ) can be performed by replacing the inverse matrix of the inductance matrix L (θ) with the calculation of the matrix λ (θ). Therefore, the inverse matrix of the inductance matrix L (θ) can be calculated much more easily than in the past.

  In a comparative example actually performed on the same apparatus, it was proved that the time required for the calculation of the inverse matrix of the inductance matrix L (θ) according to this embodiment can be surprisingly shortened to about 1/7 that of the conventional one. It was done.

(Dq rotating coordinate system calculation unit)
Next, equations that substantially constitute a dq rotating coordinate system calculation unit for performing coordinate system conversion that is optionally used in this embodiment will be described below. However, in the following, i is a three-phase armature current displayed in a stationary coordinate system, U is a three-phase armature voltage displayed in a stationary coordinate system, Id is a d-axis armature current, Iq is a q-axis armature current, and Io is zero. Phase current, Ud is a d-axis armature voltage, Uq is a q-axis armature voltage, and Uo is a zero-phase armature voltage. Equation 50 represents the d-axis reference armature current phase angle, and Equation 51 represents the d-axis reference armature voltage phase angle.

つまり、この実施例ではもともと静止座標系上の三相電機子電流ｉ及び三相電機子電圧Ｕが演算済みであるので回転座標系のモータモデルを演算することなく単なる座標系演算処理のみでｄｑ回転座標系上の現在のモータ状態を表示することができる。

That is, in this embodiment, since the three-phase armature current i and the three-phase armature voltage U on the stationary coordinate system have already been calculated, the dq is simply calculated by the coordinate system calculation process without calculating the motor model of the rotating coordinate system. The current motor status on the rotating coordinate system can be displayed.

(Three-phase inverter model)
Next, circuit equations that can be used as a three-phase inverter model will be described below. A circuit diagram of this three-phase inverter is shown in FIG. Since the configuration of the three-phase inverter shown in FIG. T1 to T6 are switching elements constituting a three-phase inverter and are not limited to IGBTs. PWMu is a PWM control signal (also referred to as a PWM input signal) applied to the switching element T1 of the U-phase upper arm, PWMv is a PWM control signal applied to the switching element T2 of the V-phase upper arm, and PWMw is the W-phase upper arm. It is a PWM control signal applied to the switching element T3. If the dead time is ignored, a PWM control signal, which is a pulse signal opposite to the PWM control signal applied to the upper-arm switching element in the same phase, is applied to the lower-arm switching element of each phase half bridge. The line voltages Uuv, Uvw, Uwu and the phase voltages Uu, Uv, Uw have a relation of Expression 54, and the PWM control signal of each phase and the line voltage have a relation of Expression 55.

数５４、５５から次の数５６が得られる。Ｅｄは３相インバータに給電するバッテリ電圧である。したがって、数５６は３相インバータクモデルであり、この回路方程式を用いて３相インバータのリアルタイムシミュレーシヨンが可能となる。

From the formulas 54 and 55, the following formula 56 is obtained. Ed is a battery voltage that supplies power to the three-phase inverter. Therefore, Equation 56 is a three-phase inverter model, and real-time simulation of the three-phase inverter can be performed using this circuit equation.

この３相インバータのモデルは、ＰＷＭ制御信号と各相電機子電圧Ｕとの関係を行列関数を用いて定義するため、行列演算プロセッサを用いるなどして演算を高速処理することができるうえ、記述した静止座標系モータモデルの入力パラメータとしての各相電機子電圧Ｕを高速に出力することができるため、第１モータモデルや第２モータモデルのリアルタイムシミュレーションに用いると非常に好都合となる。

In this three-phase inverter model, the relationship between the PWM control signal and each phase armature voltage U is defined using a matrix function, so that the computation can be performed at high speed by using a matrix arithmetic processor, etc. Since each phase armature voltage U as an input parameter of the stationary coordinate system motor model can be output at high speed, it is very convenient when used for real-time simulation of the first motor model and the second motor model.

(PWM control signal correction)
A case where each step of the simulation of the AC motor control algorithm is calculated at regular intervals using the above-described three-phase inverter model and three-phase AC motor model will be considered with reference to the time chart of FIG.

In FIG. 2, tn is the data read time of step n, tn + 1 is the data read time of step n + 1 , tn + 2 is the data read time of step n + 2, tn + 3 is the data read time of step n + 3, and the PWM control signals are temporally adjacent. Assume that a step change occurs at a time point tx between two time points t1 and tn + 1. However, since the step change of the PWM control signal is not read for calculation unless the time point n + 1 is reached, the step of this PWM control signal is performed from the time point tx when the PWM control signal changes to the time point tn + 1 immediately after the change. The change is not reflected in the simulation, resulting in a decrease in simulation accuracy. A similar problem occurs when the PWM control signal changes step at time ty between time tn + 2 and time tn + 3.

  Therefore, in this embodiment, when the PWM control signal changes stepwise between the current data read time tm and the previous data read time tm−1, the average value is used as the value of the current PWM control signal. The current PWM control signal may be used when the PWM control signal coincides between the data read time tm and the previous data read time tm−1 immediately before. This average value is (Ts−Tc) / Ts when the PWM control signal changes from 0 to 1, and becomes Tc / Ts when the PWM control signal changes from 1 to 0. Ts is the step interval, and Tc is the time from the previous data reading time tm-1 to the time tc when the PWM control signal counted changes stepwise. The correction of the PWM control signal can be performed by processing the flowchart shown in FIG.

  Considering further, if the step interval Ts is constant, the average value of the PWM control signal is immediately determined if the time Tc from the previous data reading time tm-1 to the time tc when the PWM control signal counted from the step change is known. In addition, it is possible to determine whether the PWM control signal has undergone a step change at the time tc when the PWM control signal has undergone a step change. Therefore, independent of the main routine for performing the step processing for simulation, if the step change determination of the PWM control signal and the processing for counting the time Tc are performed at shorter step intervals, the next data of this time As soon as the read time is reached, the average value of the PWM control signal can be read as the PWM control signal, and the time extension of the step processing can be prevented.

(Construction of HILS system)
FIG. 4 shows a HILS (hardware in the loop simulation) system of the motor control system using the motor model and the invar model described above. Reference numeral 100 denotes a host PC, and 101 denotes target PCs composed of one or more computers. Reference numeral 102 denotes a motor controller (actual machine) for motor control, but it may be a computer that implements a virtual motor controller program that performs a simulation operation equivalent to the motor controller.

  The target PCs 101 stores the above-described motor model corresponding to one or more three-phase PM type AC motors and a three-phase inverter that drives the motors, and programs that form the inverter models, and calculates these programs. This simulates the state of the AC motor and inverter modeled.

  The motor controller 102 includes a computer device that stores a motor control program for executing a predetermined motor control algorithm, or a hardware device having a function equivalent thereto. The motor controller 102 reads a motor state and an inverter state from the target PCs 101 at a predetermined cycle, executes the motor control algorithm based on the read state, and transmits a command to the motor and inverter obtained as a result to the target PCs 101 at a predetermined cycle. . Thereby, these three sets of AC motors and inverters simulated by the target PCs 101 are controlled according to the motor control algorithm of the motor controller 102.

  The host PC 100 is used to construct these initial types by introducing various constants into the motor model, inverter model, PWM control signal generation algorithm, and the like described above. The initial model constructed on the host PC 100 is then downloaded to the target PCs 101. Further, the host PC 100 outputs various commands to the target PCs 101 during operation of the target PCs 101, and receives and monitors the state of the motor model on the dq rotational coordinate system obtained by coordinate axis conversion by the target PCs 101. Or data transmission for changing a part of the initial model on the target PCs 101. To explain further, the above model that is constructed on the host PC 100 and downloaded to the target PCs 101 is generally called a HILS system. Such a HILS system can be constructed using Matlabs / Simlink from MathWorks, for example.

  In this embodiment, the algorithm that is configured by a program executed on the target PCs 101 and forms the main part of the HILS system is divided into a model calculation unit and a system setting unit, and is preferably downloaded to the target PCs 101. After that, in order to shorten the time required for the calculation step process, it is executed separately by a plurality of computers constituting the target PCs 101.

  The model calculation unit includes a PWM control signal generation algorithm, and calculates a PWM control signal based on the PWM control signal generation algorithm. The model calculation unit includes an algorithm forming an inverter model, and inputs a PWM control signal and a voltage command value to the inverter model to calculate a three-phase input voltage to be output to the motor. The model calculation unit includes an algorithm that constitutes either the first motor model or the second motor model described above, and inputs a three-phase input voltage to the motor model to obtain a three-phase armature current, a rotor angle, and a motor torque. Calculate and output. The model calculation unit includes an algorithm that forms the above-described dq coordinate system calculation unit (coordinate system conversion program), and the dq rotation coordinate system calculation unit is operated periodically or only when an external command is received. Calculate the necessary data on the coordinate system.

The system setting unit has a program that forms a model (algorithm) such as temperature and voltage of each part that is not described except for the motor model and the inverter model. For example, there is a program for calculating the armature temperature according to the current history and calculating the armature resistance Rs based on the armature temperature. This program is periodically calculated in parallel with the calculation of the motor model, that is , the operation of the virtual motor, and the obtained value of the armature resistance Rs is periodically written to the armature resistance Rs in the motor model. Thereby, the motor characteristic value as a constant value of the motor mole can be appropriately changed during the motor model calculation. This change may be made from the outside.

  In this way, a Simulink model is constructed on the host PC 100. Next, this simlink model is executed on the host PC 100 in non-real time to perform basic verification of the simlink model.

  Next, the model calculation unit and the system setting unit constructed as described above are converted into a model description language that can be calculated by the target PCs 101, for example, C language format, and downloaded to the target PCs 101. The target PCs 101 compiles the downloaded program to form an executable file. For the operation system of the target PCs 101, a device suitable for real time, for example, QNX is selected.

  Next, a simulation operation is instructed from the host PC 100 to the target PCs 101, and various variables such as a rotation speed, a rotation direction, a torque, and a voltage are input from the host PC 100 during the execution of the simulation operation. Debug.

  According to the motor control system configured as described above, since the above-described model is used and the PWM control signal is also corrected, high-speed and high-precision simulation can be realized with a small-scale calculation resource.

(Motor model calculation processing)
Calculation steps which are main operations of the model calculation unit configured by a program downloaded to the target PCs 101 will be further described with reference to FIGS. FIG. 5 is a flowchart showing an example of an execution routine of a calculation step performed at a constant cycle by the model calculation unit for calculating the motor model, and FIG. 6 is a flowchart showing the model calculation routine of FIG. . This calculation step is repeated at a predetermined short period (for example, 10 μsec). Further, it is assumed that communication with the system setting unit and the motor controller 102 is executed independently by another program.

  In FIG. 5, it is first determined whether or not a new command such as a model constant change has been input from the system setting unit 201. If it has been input, a model operation to be described later is interrupted and this new command is executed in step S202. . As a result, the inverter model and the motor model can be quickly corrected.

  Thereafter, it is determined whether or not a new command related to the change of the motor state is input from the motor controller 102. If it is input, the model calculation described later is interrupted, and this new command is executed in step S202.

  Next, the previously calculated rotation angle θ and the PWM control signal input from the PWM control signal generation circuit (not shown) are introduced into the routine shown in FIG. 3 to determine the PWM control signal pwm including its amplitude average value (S300). . The routine in step 300 may be executed separately from the model calculation routine S208, and only the routine execution result may be used in this step.

  Next, an inverter model calculation subroutine for performing the above-described inverter model calculation is executed (S302). Since the details of this subroutine are as described above, the description thereof will be omitted.

  Next, steps S304 and S306 for performing motor model calculation are executed. First, in step S304, the value of the matrix λ (θ) is calculated, and then the value of the matrix λ (θ), that is, the value of the inverse matrix of the inductance matrix L (θ) is equivalent to the motor model together with other data values. A desired variable such as each phase armature current i is calculated by substituting into the above-described equation (S306). The calculated value indicating the state of the current motor model is output to the motor controller 102 and the system setting unit in step S210. The system setting unit transmits the current state of the received motor model to the host PC 100 or the motor controller 102 as necessary.

It is a circuit diagram of the three-phase inverter used for the inverter model of this Example. It is a time chart explaining PWM control signal correction of this example. It is a flowchart explaining the PWM control signal correction | amendment of this Example. It is a block diagram which shows the HILS system used in this Example. It is a flowchart which shows an example of the execution routine of the calculation step performed with a fixed period by a model calculating part for the calculation of a motor model. It is a flowchart which shows the model calculation routine of FIG.

Explanation of symbols

100 host PC
101 Target PCs
102 Motor controller

Claims (11)

Defined by an equation on a stationary coordinate system showing the state of an AC motor having a rotor that generates a field flux ψr and a stator around which each phase armature winding is wound. A motor model calculation method using a motor model including i and each phase armature voltage U as a variable,
A motor model is constructed by converting an inverse matrix of the inductance matrix L (θ), which is a predetermined function having the rotation angle θ as a variable, into a matrix λ (θ), which is a function having the rotation angle θ as a variable,
This matrix λ (θ) is calculated to calculate the value of the inverse matrix of the inductance matrix L (θ), and the value of this inverse matrix is substituted into the equation forming the motor model to obtain the value of the desired variable,
The inductance matrix L (θ) is an inductance matrix of each phase armature winding indicating the relationship between the current magnetic flux ψs that is the armature winding linkage magnetic flux by each phase armature current i and each phase armature current i. And
The inverse matrix of the inductance matrix L (theta) is, d-axis inductance Ld of the AC motor, q-axis inductance Lq of the AC motor, is calculated by the matrix calculating λ a (theta) based on the leakage inductance Ll Rukoto Motor model calculation method characterized by the above. The motor model calculation method according to claim 1 ,
When the armature resistance of each phase is Rs, each phase armature current is i, and each phase armature voltage is U, the motor model defined using the inductance matrix L (θ) and its inverse matrix is as follows. A method for calculating a motor model, characterized by using an equation expressed by the following equation (13).

The motor model calculation method according to claim 1 ,
As the equation
A first equation showing a quantitative relationship among at least current flux ψs, armature resistance Rs, inverse matrix of inductance matrix L (θ), each phase armature voltage U and field flux ψr;
A second equation showing a quantitative relationship between at least each phase armature current i, current flux ψs and the inverse matrix of the inductance matrix L (θ);
A method for calculating a motor model, wherein The motor model calculation method according to claim 3 ,
An equation represented by the following equations (15) and (16) is used as the motor model.

The motor model calculation method according to claim 1,
Substituting the reciprocal λd of the d-axis inductance Ld, the reciprocal λq of the q-axis inductance Lq, and the reciprocal λl of the leakage inductance Ll into the following equations 37 and 38, the inductance reciprocal functions λas and λa are calculated.

The calculated inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll are substituted into the following formulas 39 to 44, and the terms λ11, λ12, λ13, λ21, λ22, λ23, λ31, A motor model calculation method, wherein λ32 and λ33 are calculated.

  The state of the virtual motor defined by the motor model is simulated in real time by periodically executing a calculation step of calculating the state of the motor model using the motor model calculation method according to claim 1. A characteristic motor simulation method. The motor simulation method according to claim 6 ,
The characteristic value of the virtual motor that is composed of the constants of the equation and is defined by the motor model, at least one of an external command, the state of the motor model, and a predetermined motor state calculated by another program The motor simulation method characterized by changing according to. By periodically executing a computing step of computing the state of the motor model using the calculation method of the motor model according to any one of claims 1 to 7, real-time the status of the virtual motor defined by the motor model A motor simulation device characterized by comprising an arithmetic device for simulation. The motor simulation apparatus according to claim 8, wherein
Defined by an equation on a stationary coordinate system showing the state of an AC motor having a rotor that generates a field flux ψr and a stator around which each phase armature winding is wound. a stationary coordinate system using a stationary coordinate system motor model including i and each phase armature voltage U as a variable, and substituting a numerical value for a predetermined variable of the stationary coordinate system motor model to calculate the value of the other variable An arithmetic unit;
Dq rotational coordinate system computing unit for performing coordinate system conversion computation for transforming the state of the AC motor consisting of the value of the variable on the stationary coordinate system computed by the stationary coordinate system computing unit into a value on the dq rotational coordinate system When,
With
The stationary coordinate system computing unit is
Based on an external motor control command, a calculation step for calculating the state of the stationary coordinate system motor model is periodically executed to simulate the state of the virtual motor corresponding to the stationary coordinate system motor model in real time,
The dq rotation coordinate system calculation unit is
A motor simulation apparatus, wherein a current state of the AC motor is converted into a value on a dq rotational coordinate system and output to the outside as display data in accordance with a rotational coordinate system display command inputted from outside. Defined by an equation on a stationary coordinate system showing the state of an AC motor having a rotor that generates a field flux ψr and a stator around which each phase armature winding is wound. A motor model calculation program for calculating a motor model including i and each phase armature voltage U as a variable,
An inductance matrix L (θ) that is constituted by a function having the rotation angle θ as a variable and indicates a relationship between the current magnetic flux ψs that is an armature winding linkage magnetic flux by each phase armature current i and each phase armature current i. ) Calculating a matrix λ (θ) that is a function equal to the inverse matrix of
Substituting the value of the matrix λ (θ) as the value of the inverse matrix of the inductance matrix L (θ) included in the equation to obtain the value of a desired variable of the equation;
I have a,
The step of calculating the matrix λ (θ) includes:
A motor model calculation program for calculating the matrix λ (θ) based on a d-axis inductance Ld of the AC motor, a q-axis inductance Lq of the AC motor, and a leakage inductance Ll . The motor model calculation program according to claim 10 ,
The step of calculating the matrix λ (θ) includes:
Substituting the reciprocal λd of the d-axis inductance Ld of the AC motor, the reciprocal λq of the q-axis inductance Lq, and the reciprocal λl of the leakage inductance Ll into the following equations 37 and 38, the inductance reciprocal functions λas and λa are calculated

The calculated inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll are substituted into the following formulas 39 to 44, and the terms λ11, λ12, λ13, λ21, λ22, λ23, λ31, A motor model calculation program characterized by being a step of calculating λ32 and λ33.

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