JP5948258B2 - Time-period nonlinear field analysis method and time-period nonlinear field analysis program - Google Patents

Description

  The present invention relates to a time-periodic nonlinear field analysis method and a time-periodic nonlinear field analysis program.

  In fields such as electromagnetic field analysis, a differential equation that handles a transient phenomenon having a time differential term may be transiently analyzed to obtain a solution having a half-periodicity with respect to the time axis. In this case, if the time constant of the time decay term is long, a transient analysis with many time steps is required to obtain the target stationary field. There is a TP-EEC method as a stable numerical solution capable of continuous correction for solving this problem. This method is shown in Non-Patent Document 1 and Non-Patent Document 2, for example.

  The TP-EEC method directly uses the periodicity with respect to time, and the physical quantity to be analyzed cannot be corrected unless a half-cycle transient analysis is performed. Although the correction is completed in about three times, the calculation of about 1.5 cycles is required when the half-cycle boundary condition is satisfied before the correction is completed. Further, it is necessary to solve the matrix equation in one correction calculation, and there is a problem that the calculation cost for correction is relatively high. There is a simple TP-EEC method as a simple method that greatly reduces the calculation cost. However, since the correction capability is weaker than that of the TP-EEC method, there is a problem that the convergence time is relatively long.

  As an improvement of these TP-EEC method and simplified TP-EEC method, there is a multiphase AC TP-EEC method. In the three-phase AC system, this is called the three-phase AC TP-EEC method. Usually, the three-phase alternating current simple TP-EEC method that greatly reduces the calculation cost is often used. This method is shown in Non-Patent Document 3, for example.

"Problems left for effective use of two-dimensional electromagnetic field analysis (Part 3)" Tomasasu Masamasa, Fujita Masashi, Ueda Takashi, IEEJ stationary and rotating machine joint study material, SA-08-62 / RM-08- 69, 2008 "Improvement of convergence of time integration in nonlinear transient electromagnetic field analysis based on time-periodic finite element method and EEC method" Yasuhito Takahashi, Masamasa Tokumasa, Masashi Fujita, Shinji Wakao, Takefumi Iwashita, Masanori Kanazawa, IEEJ Transactions BVol. 129 ( 2009) No.6 pp.791-798 "Problems left for effective use of two-dimensional electromagnetic field analysis (Part 4)" Tomasasu Masamasa, Fujita Masashi, Ueda Takashi, Electrotechnical Institute of Static and Rotating Machine Joint Study Group, SA-09-6 / RM-09- 6, 2009

  In the multiphase AC TP-EEC method in an m-phase AC system (m is a natural number), the physical quantity to be analyzed cannot be corrected unless a transient analysis with a period of 1 / (2m) is performed. Specifically, in the three-phase AC simplified TP-EEC method, the physical quantity to be analyzed cannot be corrected unless a transient analysis of 1/6 period is performed. Although the correction is completed in about three times, the three-phase alternating current simple TP-EEC method requires a transient analysis of about a half cycle when the half cycle boundary condition is satisfied before the correction is completed. In the analysis of a small-scale system, a transient analysis of about a half cycle is not so burdensome, but in the analysis of a large-scale system, even a transient analysis of about a half cycle is a large burden.

(1) The invention of claim 1 and claim 3 is a time period nonlinear field analysis method and analysis program for performing a transient analysis including a time derivative term by executing arithmetic processing in a plurality of time steps by an arithmetic device. And the conventional subject mentioned above is solved by performing the following procedures with an arithmetic unit.
In the first procedure, the transient analysis is performed on each of the first physical quantity to the third physical quantity belonging to each phase of the m-phase AC system (m is any natural number of 3 or more). In the second procedure, based on each of the first physical quantity to the third physical quantity obtained by the first procedure, an arbitrary time shorter than 1 / (2 m) times the period of the first physical quantity The time fluctuation amount in the width is calculated as the first time fluctuation amount, the second time fluctuation amount, and the third time fluctuation amount. In the third procedure, at least two of the time fluctuation amounts in the time width in each of the fundamental wave components in the steady state of the first physical quantity to the third physical quantity , and the jth physical quantity (j is 1 to 3). The relational expression established between the fundamental wave component in the steady state and the natural number) is read out.
In the fourth procedure, the at least two time variation amounts selected from the first time variation amount to the third time variation amount obtained in the second procedure are input to the read relational expression. Thus, the “value indicated by the term corresponding to the fundamental wave component in the steady state of the j-th physical quantity” is calculated and replaced with the new value of the j-th physical quantity. In the fifth procedure, k times the difference obtained by subtracting the value of the j-th physical quantity immediately before replacement in the fourth procedure from the value of the j-th physical quantity replaced in the fourth procedure (0 <k ≦ c, where c satisfies 1 <c <2.) is added to the value of the j-th physical quantity immediately before the replacement in the fourth procedure, and the addition result is replaced with the value of the j-th physical quantity. . These first to fifth procedures are executed a plurality of times in each case where j can take.
(2) The inventions of claim 2 and claim 4 are a time-period nonlinear field analysis method and analysis program for performing a transient analysis including a time derivative term by executing arithmetic processing in a plurality of time steps with an arithmetic device. The conventional problems described above are solved by executing the following procedure using the arithmetic device.
In the first procedure, the transient analysis is performed on a physical quantity belonging to an m-phase AC system (m is any natural number). In the second procedure, with respect to the physical quantity obtained by the first procedure, a first time, a second time, which are set at arbitrary time intervals shorter than 1 / (2 m) times the period of the physical quantity, And the value of 3rd time and 4th time (however, the case where 2nd time and 3rd time are the same) set by the time interval same as the said time interval is obtained.
In the third procedure, based on the values obtained at the first to fourth times, a first time fluctuation amount that is a time fluctuation amount of the physical quantity between the first time and the second time, and A second time fluctuation amount that is a time fluctuation amount of the physical quantity between the third time and the fourth time is calculated. In the fourth procedure, the time fluctuation amount between the first time and the second time of the fundamental wave component in the steady state of the physical quantity, the third time and the fourth time of the fundamental wave component of the physical quantity in the steady state. And the relational expression established between the fundamental wave component in the steady state at the fourth time of the physical quantity is read out. In the fifth procedure, “the term corresponding to the fundamental wave component in the steady state at the fourth time of the physical quantity obtained by inputting the first temporal variation amount and the second temporal variation amount into the relational expression is obtained. The “indicated value” is replaced with the value of the new physical quantity at the fourth time. And the said 1st-5th procedure is performed in multiple times.

  Furthermore, the time-periodic nonlinear field analysis program according to the present invention for solving the above-described problems is a computer-readable recording medium in which a series of processes in the time-periodic nonlinear field analysis method is coded and the program is recorded. Features.

  According to the present invention, since the correction can be continuously performed by the transient analysis having a shorter time width than the conventional TP-EEC method or the multiphase AC TP-EEC method, a stable steady field can be obtained at a higher speed.

The figure which shows the example of a basic procedure of the analysis method of this invention. The figure for demonstrating the analysis method of 1st Embodiment. The figure explaining an example of the analysis system which implement | achieves 1st-3rd embodiment with the analysis procedure shown in FIG. The figure which shows the time change of the difference | error with the theoretical solution in the 1st numerical calculation example performed based on the analysis method of 2nd Embodiment. The figure of the synchronous motor connected with the circuit used for the 2nd numerical calculation example performed based on the analysis method of 2nd Embodiment. The U-phase coil current waveform figure in the 2nd numerical calculation example performed based on the analysis method of 2nd Embodiment. The torque waveform figure in the 2nd numerical calculation example performed based on the analysis method of 2nd Embodiment. The figure which shows the tolerance | permissible plus error of the correction | amendment calculated | required using the 2nd numerical calculation example performed based on the analysis method of 2nd Embodiment. The figure which shows the tolerance | permissible plus error of the correction | amendment calculated | required using the 2nd numerical calculation example performed based on the analysis method of 2nd Embodiment. The figure for demonstrating the analysis method of 3rd Embodiment.

The outline of the procedure of the analysis method according to the present invention will be described with reference to FIG.
FIG. 1 shows an analysis procedure for transiently analyzing a differential equation that handles a transient phenomenon having a time differential term and obtaining a solution having a half-periodicity with respect to the time axis. This analysis procedure will be described. In step 10, an input data file composed of discretized data (mesh data) 11 for numerically solving the differential equation and control data 12 for controlling the analysis process is read by the computer. In step 21, a transient analysis is executed by an analysis execution module that discretizes the differential equation based on these input data. In step 22, the analysis result of the physical quantity to be analyzed is stored for each time step. Next, in step 23, a time fluctuation amount in an arbitrary time width (time interval) shorter than 1 / (2m) period is calculated based on the stored analysis result, and in step 24, this time fluctuation amount is used. To correct (replace) the target physical quantity.
If it is determined in step 26 that the above-described series of correction procedures 25 has been executed a predetermined number of times, the process proceeds to step 27. In step 27, normal transient analysis is performed to obtain a steady field of one cycle. In step 31, the obtained analysis result is stored in the storage device, and in step 32, the analysis result is displayed on the monitor. Even if the steady state is reached, a series of correction procedures 25 may be performed continuously.

――― First embodiment ―――
As a first embodiment, an example of correction of a target physical quantity using a time variation amount in the procedure 24 of FIG. 1 will be shown.

In order to simplify the explanation, the univariate field z (t) will be described. Let us consider a case where the stationary field is semi-periodic, that is, when the period is T and the condition of z (t + T / 2) = − z (t) is satisfied. Here, for convenience of explanation, the target field is displayed in a complex number. As shown in FIG. 2, consider the complex space thought based on the alternating field z _1, consider the AC field z ₂ and z ₃ another two the alternating field z _1. Here, only the fundamental wave is considered. Here, it is assumed that the magnitude of each AC field is normalized to 1, and z ₂ and z ₃ have a phase delay of φ ₁ and φ _{2 with} respect to z ₁ , respectively. Taking the AC field z ₁ as a reference,

と表すことができる。１／（２ｍ）周期よりも短い任意の時間幅（基本波換算で電気角θ）経過後のｚ_１、ｚ_２、ｚ_３の時間変動量をそれぞれ△ｚ_１、△ｚ_２、△ｚ_３とおくと、以下の式（２）となる。

ここにｊは純虚数である。ここで、１／（２ｍ）周期よりも短い任意の時間幅経過後のｚ_１をｚ_１ ^ｎｅｗとおき、ｚ_１ ^ｎｅｗと△ｚ_１、△ｚ_２、△ｚ_３の関係式を

It can be expressed as. 1 / (2m) Optional short duration than the period _z 1 after a lapse of (electrical angle θ at the fundamental _{terms), z 2,} z ₃ time variation amount each _{△ z 1, △ z 2,} △ z 3 Then, the following equation (2) is obtained.

Here, j is a pure imaginary number. Here, 1 / (2m) to _{z 1} after an arbitrary time width elapses shorter than the period _z ^{1 new new} _Distant, ^{z 1 new new} and △ _{z 1,} △ _{z 2,} the △ _{z 3} the relation

By substituting z ₁ ^new = e ^jθ on the left side, substituting Equation (2) on the right side, and comparing the real and imaginary parts of both sides, the constants β and γ are expressed as α. (4) and (5).

_Thus, ^{z 1 new new} and _{△ z 1, △ z 2,} △ relation of _{z 3} and becomes the following equation (6).

This relational expression is a relational expression that the steady-state fundamental wave satisfies. In the first embodiment, this equation is used as a correction equation. Similarly, with respect to a large number of correction target groups z _j (j = 1, 2,..., M) that form the same AC field, by selecting an arbitrary AC field different from the self, Can be corrected.

  Furthermore, a further correction (hereinafter referred to as “relaxation correction”) as shown in the following expression (7) can be applied to the correction value shown in the expression (6).

Here, z ₁ ^{new on} the right side is a value obtained by Equation (6), and z ₁ ^оld is a value before correction at the same time as z ₁ ^new . Here, the relaxation correction means that in this example, the value z ₁ ^оld itself before correction is partially ^changed as shown in the expression (7) without being completely replaced with the value obtained in the expression (6). It means the correction used for. Here, Equation (7) can be rewritten as follows.

Z ₁ ^new −z ₁ ^оld in the right parenthesis corresponds to the correction amount according to the equation (6). If a negative error of the correction amount is set to −ε (0 <ε ≦ 1), f = 1−ε and 0 Since <f <1, it means that the absolute value of the minus error of the correction amount is allowable in the range of 0% to 100%. However, the plus error of the correction amount will be described later. Although not described in detail in the following embodiments, all may be corrected by this relaxation correction. In that case, z ₁ ^{new on} the right side is a value obtained using a relational expression that is satisfied by the steady-state fundamental wave shown in the embodiment.

  In addition, after performing correction once or a plurality of times with a time width shorter than 1 / (2 m) period, it is possible to switch to a simple correction TP-EEC method or a multiphase alternating current simple TP-EEC method which is a conventional correction method. Is possible. This switching is also possible in the second embodiment, the modified example of the second embodiment, and the third embodiment.

  An example of an analysis system that implements the first embodiment of the present invention is shown in FIG. This analysis system includes a computer 1, a display device 2, a storage medium 3, and an input device 4. In FIG. 3, the storage medium 3 is taken out of the computer 1 to clearly show it, but it may be installed inside the computer 1. It is assumed that the computer 1 stores a program based on at least one of the above-described embodiments. The input device 4 is, for example, a keyboard or a mouse, and has an arbitrary time width shorter than the 1 / (2 m) period for obtaining the above-described time fluctuation amount, or an electrical angular width corresponding thereto, or a time step number corresponding thereto. Depending on circumstances, it is used for inputting input data necessary for analysis, such as mesh data in the analysis space, other analysis condition data, to the computer 1, designating reading / writing of a data file storing the input data, execution of calculation, and the like. After the input data is input, the computer 1 executes arithmetic processing such as reading of the input data and magnetic field calculation according to the stored program. The calculation result is displayed on the display device 2 and stored in the storage medium 3 as a data file. A part of the obtained calculation result may be displayed or stored. Since the analysis is performed while ticking the time step, the calculation proceeds while reusing the data stored in the storage medium 3.

  The analysis system can realize a second embodiment and a third embodiment, which will be described later, as in the first embodiment. Therefore, in the description part of 2nd Embodiment and 3rd Embodiment, description of the said analysis system is only kept simple.

According to the first embodiment, the user can arbitrarily select a time width for calculating the amount of time variation. Further, it is possible to repeatedly correct. Therefore, if the allowable minimum time step width is set, the correction can be made every time step and the steady field can be reached at high speed.
On the other hand, in the m-phase AC system, in the conventional multiphase AC TP-EEC method, correction is performed using a transient analysis result for a period of 1 / (2 m). Although the correction can be repeated, it can only be corrected every 1 / (2 m) period.
Usually, since the time step width for analysis is set to be smaller than 1 / (2 m) period, the first embodiment of the present invention reaches the steady field at a higher speed than the above-described conventional technique. It can be seen that it is possible.

――― Second embodiment ―――
As a special case of the first embodiment, consider a three-phase AC system. In this case, when an AC field _{z 1} and U-phase, respectively alternating field _{z 2} and _{z 3} are V-phase, the W phase. Since φ ₁ = 2π / 3 and φ ₂ = 4π / 3, equation (6) becomes the following equation (9).

Since z ₁ , z ₂ , and z _{3 form} a three-phase alternating current circulation system, when formula (9) is rewritten into correction formulas for all z ₁ , z ₂ , and z ₃ , α is changed to α ₁ again,

It becomes. Considering the equivalence of the three phases, the arbitrary parameters α ₁ , α ₂ , and α ₃ may be set to the same value α. in this case,

Therefore, when α = 1/3 is set, the sum of the physical quantities of the three-phase alternating current system is 0, which is effective in always performing balanced analysis. For example, in the case of a three-phase alternating current, an analysis that guarantees that the sum of the three-phase alternating currents is always zero becomes possible. However, when current leakage at a neutral point where the three-phase alternating currents merge is considered, α ≠ 1/3. In this case, for example, α = 0 or α = 1/2 may be set.

  Here, if the time width for calculating the amount of time variation is set to θ = π / 3 corresponding to 1/6 period, equations (10), (11), and (12) are expressed by the following equation (14): ), (15), and (16), resulting in the formula of the three-phase alternating current simple TP-EEC method that is often used conventionally.

In the three-phase alternating current simple TP-EEC method, α ₁ = α ₂ = α ₃ = 1/2 is often used normally.
Here, as a first numerical analysis example, consider a stationary field problem formed by the following simultaneous differential equations of a three-phase AC system.

The theoretical steady solution of this equation is the following equation (18). _{Further, a n, φ n, g} n in the formula (18), respectively represented by the following formula (19).

FIG. 4 shows the calculation result when only the fundamental wave n = 1 exists in the source term on the right side. FIG. 4 shows the time change of the error Δ from the steady theoretical solution. In addition to the results without correction, FIG. 4 shows three conventional methods that are capable of continuous correction: simple TP-EEC method, TP-EEC method, three-phase alternating current simple TP-EEC method, and the present invention. The case where correction is applied is shown. Arbitrary parameters α ₁ , α ₂ and α ₃ are set to α ₁ = α ₂ = α ₃ = 1/2 in the three-phase AC simplified TP-EEC method, and α ₁ = α ₂ = α ₃ = 0 in the present invention. did. The correction according to the present invention shows five cases of θ = 1.875 deg, 3.75 deg, 7.5 deg, 15 deg, 30 deg, and the correction processing becomes more frequent as θ is smaller, so that it can converge to a steady field in a short time.

  As shown in these figures, the case where the correction according to the present invention is performed converges to the steady solution at the highest speed.

  Next, as a second numerical analysis example, an example of circuit magnetic field coupling analysis of a synchronous motor by the finite element method is shown. FIG. 5 shows the mesh division of the synchronous motor 100 using permanent magnets used for the verification of the present invention, and the power supply circuit 200 connected to the synchronous motor 100. The synchronous motor 100 includes a stator 101 and a rotor 102, and FIG. 5 shows a mesh division diagram of a half part of the whole due to rotational symmetry. In the stator 101, a field coil 103 for generating a rotating magnetic field is wound around a magnetic pole, and in the rotor 102, a permanent magnet 104 for forming a stator side magnetic pole is embedded. A three-phase AC power supply 201 of the power supply circuit 200 is connected to each UVW phase field coil 103 via a resistor R and an external inductance L.

  In the case of a synchronous motor, the magnetic field generated in the stator 101 is an AC field whose direction reverses positive and negative, and the half-cycle boundary condition is satisfied. On the other hand, since the rotor 102 has a DC component of the magnetic field generated by the permanent magnet 104, the half-cycle boundary condition is not satisfied. In general, since the magnetic field fluctuation of the rotor 102 is very small, in order to obtain a steady magnetic field in the rotating machine at high speed, in a transient analysis for calculating the time evolution, only a half cycle of an unknown variable having a time differential term of the stator 102 is used. Apply corrections corresponding to the boundary conditions.

As specific numerical values used in the analysis, the synchronous motor 100 was calculated to have an axial length of 55 mm, a magnet magnetization of 1.315 T, and a rotation speed of 3000 min ⁻¹ using a time step width divided by 180 periods. Calculation results when a sinusoidal voltage having an effective voltage of 200 V is applied to the voltage source 201 are shown in FIGS. FIG. 6 shows the time change of the U-phase coil current waveform, and FIG. 7 shows the torque waveform. FIGS. 6 and 7 show the cases where there is no correction, the correction results by the conventional simple TP-EEC method and the three-phase alternating current simple TP-EEC method, and equations (10) and (11) in the second embodiment. The calculation results when using (12) are shown. Incidentally, any parameter alpha _1, alpha _2, alpha _3, the three-phase AC simple TP-EEC method _{α 1 = α 2 = α 3} = 1/2, in the second embodiment α ₁ = α ₂ = α ₃ = 0 was set. In the second embodiment, even if α ₁ , α ₂ , and α ₃ are set to 1/2 or 1/3, the result hardly changes. The simple TP-EEC method is correction every 1/2 cycle, and the three-phase alternating current simple TP-EEC method is limited to correction every 1/6 cycle, whereas the present invention is more than 1/6 cycle. Correction can be performed at a short arbitrary time interval, and in the second embodiment, step-by-step continuous correction is performed every hour. This corresponds to θ = 2 deg (= 360 deg / 180) in equations (10), (11), and (12). As shown in FIGS. 6 and 7, in the second embodiment, a steady field is obtained at a higher speed than the conventional simple TP-EEC method and the three-phase alternating current simple TP-EEC method. Recognize. A similar correction effect can be obtained with a synchronous generator.

  Here, as described above, there is no problem with the minus error of correction, but a plus error will be described. Consider that the correction is made according to the following equation, taking into account the positive error.

In the synchronous motor analysis shown in the second embodiment, as a result of calculation for θ = 2 deg, 6 deg, 10 deg, 14 deg, and 20 deg, allowable plus errors that can exhibit a normal correction effect are shown in FIGS. 8 and 9. . Here, FIG. 8 shows the result when α ₁ = α ₂ = α ₃ = 0 as a representative example of α ₁ = α ₂ = α ₃ ≠ 1/3, and FIG. This is a result in the case of α ₁ = α ₂ = α ₃ = _1/3 corresponding to the case where the leakage current is 0 and the sum of the three-phase alternating currents is 0. When α ₁ = α ₂ = α ₃ ≠ 1/3, the plus error may be suppressed to + 3% or less from the result of FIG. When α ₁ = α ₂ = α ₃ = 1/3, the plus error may be suppressed to (85−3.4θ (deg))% or less from the result of FIG. If it writes with a formula, it will become the following formulas (21).

  Similarly to the first embodiment, the second embodiment can also be realized by the analysis system shown in FIG.

  According to the second embodiment, there is an effect that the convergence speed to the stationary field can be significantly increased by a simple correction calculation in the circuit coupled magnetic field analysis of the rotating machine. The comparison with the prior art is the same as in the first embodiment.

――― Modification of the second embodiment ―――
As a modification of the second embodiment, the correction using Expression (7) or (8) and the correction using Expression (20) can be summarized as the following Expression (22).

Here, with respect to the lower limit of c in equation (22), c> 1 from equation (20). Regarding the upper limit of c, when α ₁ = α ₂ = α ₃ ≠ 1/3, c ≦ 1.03 from the result of FIG. When α ₁ = α ₂ = α ₃ = 1/3, c ≦ {1 + 0.01 × (85−3.4θ (deg))} from the result of FIG. In either case, the upper limit of c is less than 2.

――― Third embodiment ―――
As a third embodiment, another embodiment of the correction of the target physical quantity using the time variation in the procedure 24 of FIG. 1 will be described.

Again, for simplicity of explanation, the one-variable field z (t) will be described. Consider a case where the stationary field satisfies the half-periodicity as in the first embodiment. Again, for convenience of explanation, the target field is displayed in a complex number. As shown in FIG. 10, consider the complex space thought based on the alternating field z _1, considered by focusing only on the fundamental wave. It is assumed that the alternating field z ₁ changes with time to z ₁ ′, z ₂ , and z ₂ ′ with time. Here, the _{z 1 z 1} 'the variation of the △ _{z 1} and then, from _{z 2 z 2'} the amount of variation of the △ _{z 2} to. Assuming a situation where the AC field z (t) has already reached a steady state, z ₂ ′ is expressed using Δz ₁ and Δz ₂ . Since this is a conditional expression that the stationary field should satisfy, it is a concept that a transient field that does not reach the steady state gradually converges to the steady field by using this as a correction expression. When the magnitude of the steady AC field z ₁ is normalized to ₁ , z ₁ , z ₁ ′, z ₂ , z ₂ ′ can be expressed by the following formula (23) from FIG.

At this time, Δz ₁ and Δz ₂ are represented by the following equations (24) and (25), respectively.

Therefore, when the constants a and b are obtained by comparing the real part and the imaginary part of both sides with z ₂ as the following expression (26), the following expression (27) is obtained.

Equation (26) believe _{z 2} '→ _{z 2} ^new correcting equation, replacing the left side in the _{z 2} ^{new new,} equation (26) is given by the following expression (28).

  Here, when φ = θ is set, Expression (27) becomes the following Expression (29).

Thus, z ₂ ^new can be expressed by the following equation (30).

  Expressions (28) and (30) are conditional expressions that the fundamental wave component of the stationary field should satisfy. By using this as a correction formula, a transient field that does not reach a steady state can be converged to a steady field at high speed.

  Similar to the first embodiment, the third embodiment can also be realized by the analysis system shown in FIG.

According to the third embodiment, there is an effect that even a single AC field can be corrected at high speed by simple calculation. The user can arbitrarily select a time width for calculating the amount of time variation. Further, it is possible to repeatedly correct. Therefore, if the allowable minimum time step width is set, the correction can be made every time step and the steady field can be reached at high speed.
On the other hand, in the conventional TP-EEC method, correction is performed using a transient analysis result for ½ period. Although the correction can be repeated, it can only be corrected every half cycle. Usually, since the time step width for analysis is set to be smaller than ½ period, the third embodiment of the present invention can reach the stationary field at a higher speed than the above-described conventional technique. It turns out that it is possible.

  Note that the invention described in JP 2012-69024 A (hereinafter referred to as “prior invention”) also has a time width shorter than a 1 / (2 m) period as in the third embodiment of the present invention. It is possible to correct the physical quantity. However, the third embodiment of the present invention can correct with a shorter time width and an arbitrary time width than the prior invention. Further, while the prior invention can be corrected only about three times, the third embodiment of the present invention can be corrected repeatedly any number of times. In the above points, the third embodiment of the present invention is an invention superior to the prior invention.

DESCRIPTION OF SYMBOLS 1 ... Computer, 2 ... Display apparatus, 3 ... Storage medium, 4 ... Input device, 10 ... Input data file, 11 ... Discretization data, 12 ... Control data, 20 ... Analysis process, 21 ... Transient analysis by analysis execution module, 22 ... Analysis result storage, 23 ... Time variation calculation, 24 ... Physical quantity correction, 25 ... Correction process, 26 ... Correction count determination, 27 ... Normal transient analysis, 31 ... Analysis result storage, 32 ... Analysis result monitor display , 100 ... synchronous motor, 101 ... stator,
DESCRIPTION OF SYMBOLS 102 ... Rotor, 103 ... Field coil, 104 ... Permanent magnet, 200 ... External circuit, 201 ... Voltage source

Claims (4)

In the time period nonlinear field analysis method for performing transient analysis including time derivative terms by executing arithmetic processing in multiple time steps with an arithmetic device,
The arithmetic unit is
a first step of performing the transient analysis on each of a first physical quantity to a third physical quantity belonging to each phase of an m-phase AC system (m is any natural number of 3 or more);
Based on each of the first physical quantity to the third physical quantity obtained in the first step, the time fluctuation amount in an arbitrary time width shorter than 1 / (2 m) times the period of the first physical quantity is obtained. A second step of calculating as a first time variation, a second time variation, and a third time variation;
At least two of the temporal fluctuation amounts in the time width in each of the fundamental wave components in the steady state of the first physical quantity to the third physical quantity , and the jth physical quantity (j is any natural number from 1 to 3). A third step of reading a relational expression established between the fundamental wave component in the steady state of
By inputting the at least two time fluctuation amounts selected from the first time fluctuation amount to the third time fluctuation amount obtained in the second step into the read relational expression, a fourth step of calculating a value indicated by a term corresponding to a fundamental wave component in a steady state of the j physical quantity and replacing it with a new value of the j th physical quantity;
K times the difference obtained by subtracting the value of the j-th physical quantity just before replacement in the fourth step from the value of the j-th physical quantity replaced in the fourth step (0 <k ≦ c, where c 1 <c <2 is satisfied), and the fifth step of adding the value of the j-th physical quantity immediately before replacement in the fourth step and replacing the addition result with the value of the j-th physical amount, Run,
Further, in each of the cases that j can take, the first to fifth steps are executed a plurality of times. In the time period nonlinear field analysis method for performing transient analysis including time derivative terms by performing arithmetic processing in multiple time steps with an arithmetic device,
The arithmetic unit is
a first step of performing the transient analysis on a physical quantity belonging to an m-phase AC system (m is any natural number);
For the physical quantity obtained by the first step, the first time, the second time, and the time interval set at arbitrary time intervals shorter than 1 / (2m) times the period of the physical quantity A second step of obtaining values of a third time and a fourth time (including the case where the second time and the third time are the same) set at the same time interval;
Based on the values obtained at the first to fourth times, the first time fluctuation amount that is the time fluctuation amount of the physical quantity between the first time and the second time, and the third time and the fourth time. A third step of calculating a second time fluctuation amount that is a time fluctuation amount of the physical quantity during time;
Time fluctuation amount between the first time and the second time of the fundamental wave component in the steady state of the physical quantity, Time fluctuation amount between the third time and the fourth time of the fundamental wave component of the physical quantity in the steady state And a fourth step of reading a relational expression established between fundamental wave components in the steady state at the fourth time of the physical quantity;
The “value indicated by the term corresponding to the fundamental wave component in the steady state at the fourth time of the physical quantity” obtained by inputting the first time fluctuation amount and the second time fluctuation amount into the relational expression is newly added. A fifth step of replacing the physical quantity with a value at a fourth time,
A method for analyzing a time-periodic nonlinear field, wherein the first to fifth steps are executed a plurality of times. In an analysis program for executing on a computer a time period nonlinear field analysis method for performing transient analysis including time derivative terms by executing arithmetic processing in a plurality of time steps with an arithmetic device,
The analysis program is
a first command for performing the transient analysis on each of the first physical quantity to the third physical quantity belonging to each phase of an m-phase AC system (m is any natural number of 3 or more);
Shorter than 1 / (2m) times the period of the first physical quantity based on each of the first to third physical quantities obtained from the result of the transient analysis executed by the first instruction. A second instruction for calculating a time variation amount in an arbitrary time width as a first time variation amount, a second time variation amount, and a third time variation amount;
At least two of the temporal fluctuation amounts in the time width in each of the fundamental wave components in the steady state of the first physical quantity to the third physical quantity , and the jth physical quantity (j is any natural number from 1 to 3). A third instruction for reading a relational expression established between the fundamental wave component in the steady state and
By inputting the at least two time variation amounts selected from the first time variation amount to the third time variation amount obtained by the second command into the read relational expression, a fourth command for calculating a value indicated by a term corresponding to a fundamental wave component in a steady state of j physical quantity and replacing it with a new value of the j th physical quantity;
K times the difference obtained by subtracting the value of the j-th physical quantity immediately before replacement by the fourth instruction from the value of the j-th physical quantity replaced by the fourth instruction (0 <k ≦ c, where c 1 <c <2 is satisfied), the value of the j-th physical quantity immediately before being replaced by the fourth instruction is added to the fifth instruction for replacing the addition result with the value of the j-th physical quantity. When,
A time-period nonlinear field analysis program having a sixth instruction for executing the first to fifth instructions a plurality of times in each case that j can take. In an analysis program for executing a time period nonlinear field analysis method by a computer that performs a transient analysis including a time differential term by performing arithmetic processing in a plurality of time steps with an arithmetic device,
The analysis program is
a first command for performing the transient analysis on a physical quantity belonging to an m-phase AC system (m is any natural number);
For the physical quantity obtained by the first command, the first time, the second time, and the time interval set at arbitrary time intervals shorter than 1 / (2m) times the period of the physical quantity A second command for obtaining values of the third time and the fourth time (including the case where the second time and the third time are the same) set at the same time interval;
Based on the values obtained at the first to fourth times, the first time fluctuation amount that is the time fluctuation amount of the physical quantity between the first time and the second time, and the third time and the fourth time. A third instruction for calculating a second time fluctuation amount that is a time fluctuation amount of the physical quantity during time;
Time fluctuation amount between the first time and the second time of the fundamental wave component in the steady state of the physical quantity, Time fluctuation amount between the third time and the fourth time of the fundamental wave component of the physical quantity in the steady state And a fourth command for reading a relational expression established between fundamental wave components in the steady state at the fourth time of the physical quantity;
The “value indicated by the term corresponding to the fundamental wave component in the steady state at the fourth time of the physical quantity” obtained by inputting the first time fluctuation amount and the second time fluctuation amount into the relational expression is newly added. A fifth instruction for replacing the physical quantity with a value at a fourth time;
A time period nonlinear field analysis program having a sixth instruction for executing the first to fifth instructions a plurality of times.

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