Method and system for calculating model parameters for a coil to be modelled

Abstract

Method for calculating model parameters for a coil (L), comprising of: incorporating the coil into a converter (1) with a switching element (2); connecting a resistive load (9); applying an input voltage (U.sub.in); controlling the switching element in order to obtain a periodically varying voltage across the coil; measuring at least a first and second quantity representative of respectively the voltage (U.sub.L) across and the current (i.sub.L) through the coil; determining at least one voltage value and at least one current value on the basis of the measured first and second quantity; calculating a loss resistance and/or a loss power of the coil on the basis of the at least one voltage value and the at least one current value.

Claims

1. A method for measuring at least one coil and calculating model parameters for the at least one coil to be modelled, the method comprising the following steps of: incorporating the at least one coil to be modelled into a DC to DC converter with at least a first switching element, which converter has input terminals and output terminals; connecting an adjustable resistive load between the output terminals of the DC to DC converter; applying an input voltage at the input terminals of the converter; controlling the first switching element in accordance with a frequency and duty cycle to obtain a voltage varying periodically in time across a coil of the at least one coil to be modelled, which voltage depends for at least a part of a period on the input voltage; wherein there is an output voltage across the adjustable resistive load, and the coil is incorporated such that for a part of the period the voltage across the coil is substantially equal to the difference between the input voltage and the output voltage; adjusting the adjustable resistive load to operate the DC to DC converter in a continuous current mode; measuring at least a first quantity representative of the voltage across the coil at successive points in time in at least said part of a period; measuring at least a second quantity representative of the current through the coil at successive points in time in at least said part of a period; determining at least one voltage value for the voltage across the coil on the basis of the measured first quantity; determining at least one current value for the current through the coil on the basis of the measured second quantity; calculating at least one of a loss resistance or a loss power of the coil on the basis of the at least one voltage value and the at least one current value; determining on the basis of the measured second quantity at least one first and second current value for the current through the coil at respectively a first and second point in time of the successive points in time in said part of the period; and calculating an inductance of the coil on the basis of said at least one voltage value, said at least one of the loss resistance or the loss power, and said at least one first and second current value; and repeating the above stated steps for a different frequency so as to determine a frequency dependent inductance of the coil.

2. The method of claim 1, wherein the loss power is calculated as an average of the product of the voltage across the coil and the current through the coil, based on the measurements of the first and second quantities at the successive points in time.

3. The method of claim 1, wherein the loss resistance is calculated as the quotient of the loss power and the square of an effective current through the coil, which effective current is calculated on the basis of the measurements of the second quantity.

4. The method of claim 3, wherein the loss resistance is calculated as the quotient of the loss power and the square of an effective current through the coil, which effective current is calculated on the basis of the at least one first and second current value.

5. The method of claim 1, wherein the inductance is calculated as $L=\frac{R_{\mathrm{LS}}.Math.t_{\mathrm{on}}}{\ln \left[\frac{I_{\min }.Math.R_{\mathrm{LS}}-U_{\mathrm{Lg}1}}{I_{\max }.Math.R_{\mathrm{LS}}-U_{\mathrm{Lg}1}}\right]}$ wherein I.sub.min corresponds to the first current value measured at the first point in time t=0 and I.sub.max corresponds to the second current value measured at the second point in time t=t.sub.on; U.sub.Lg1 corresponds to the average of the at least one voltage value; and R.sub.LS is the loss resistance.

6. The method of claim 1, wherein the voltage value is calculated as an average making use of the measurements of the first quantity.

7. The method of claim 1, wherein said part of the period is a part in which the coil is charged, wherein said part has a duration t.sub.on.

8. The method of claim 7, wherein the voltage value is calculated as $U_{Lg1}=\frac{1}{t_{on}}{}_0^{t_{on}}{u}_L\left(t\right)dt$ wherein u.sub.L(t) is the voltage across the coil at point in time t and u.sub.L(t) is determined on the basis of the measurements of the first quantity.

9. The method of claim 1, wherein the DC to DC converter further comprises a second switching element, for instance a diode.

10. The method of claim 9, wherein the second switching element comprises a transistor.

11. The method of claim 9, wherein the second switching element is connected to a first terminal of the at least one coil and between the input terminals of the converter when the first switching element is closed.

12. The method of claim 1, wherein the DC to DC converter is one of the following: a buck converter, boost converter, buck-boost converter, non-inverting buck-boost converter, series or parallel resonant converter, fly-back converter, full or half bridge buck converter.

13. The method of claim 1, wherein the first switching element is connected between an input terminal of the DC to DC converter and the coil.

14. The method of claim 1, wherein an input capacitor is connected between the input terminals of the DC to DC converter and an output capacitor is connected between the output terminals of the DC to DC converter.

15. The method of claim 1, wherein the at least one coil forms part of a transformer with a first coil and a second coil, wherein the measurement of the at least one first quantity comprises of: measuring at least one first quantity representative of the voltage across the first coil; and measuring at least one first quantity representative of the voltage across the second coil; wherein the measurement of at least one second quantity comprises of: measuring at least one second quantity representative of the current through the first coil; and measuring at least one second quantity representative of the current through the second coil; wherein determining of the at least one voltage value comprises of: determining at least one voltage value for the voltage across the first coil on the basis of the measured first quantity; and determining at least one voltage value for the voltage across the second coil on the basis of the measured first quantity; wherein determining of the at least one current value comprises of: determining at least one current value for the current through the first coil on the basis of the measured second quantity; and determining at least one current value for the current through the second coil on the basis of the measured second quantity; wherein calculation of a loss resistance and/or a loss power comprises of: calculating a magnetization inductance and a magnetization loss resistance on the basis of the at least one voltage value for the first and second coil and the at least one current value for the first and second coil; calculating an equivalent leakage inductance and an equivalent loss resistance on the basis of the at least one voltage value for the first and second coil and the at least one current value for the first and second coil.

16. A system for measuring at least one coil and calculating model parameters for the at least one coil to be modelled, the system comprising: a DC to DC converter with at least a first switching element and the at least one coil to be modelled incorporated therein; which converter has input terminals and output terminals; an adjustable resistive load with a resistor between the output terminals of the converter; a voltage source connected for the purpose of providing an input voltage at the input terminals of the converter; a controller configured to control the first switching element according to a plurality of set frequencies and duty cycles in order to obtain a voltage varying periodically in time across the coil of the at least one coil to be modelled, such that voltage depends for at least a part of a period on the input voltage; wherein there is an output voltage across the adjustable resistive load, and the coil is incorporated such that for a part of the period the voltage across the coil is substantially equal to the difference between the input voltage and the output voltage; a voltage measuring apparatus configured to measure at least a first quantity representative of the voltage across the coil at successive points in time in at least said part of a period; a current measuring apparatus configured to measure at least a second quantity representative of the current through the coil at successive points in time in at least said part of a period; a computer configured to i. adjust the adjustable resistive load to operate the DC to DC converter in a continuous current mode; ii. determine a. at least one voltage value for the voltage across the coil on the basis of the measured first quantity, b. at least one current value for the current through the coil on the basis of the measured second quantity; iii. determine, on the basis of the measured second quantity, at least a first and second current value for the current through the coil at respectively a first and a second point in time of the successive points in time in said part of the period; iv. calculate at least one of a loss resistance or a loss power of the coil on the basis of said at least one voltage value and said at least one current value; v. calculate a frequency-dependent inductance of the coil on the basis of said at least one voltage value, said at least one of the loss resistance or the loss power, and said at least one first and second current value; wherein the computer is further configured to repeat the steps i-v for a different frequency.

17. The system of claim 16, wherein the computer means is configured to determine loss power as an average of the product of the voltage across the coil and the current through the coil, based on the measurements of the first and second quantities at the successive points in time.

18. The system of claim 16, further comprising a second switching element, wherein the second switching element comprises a transistor, and wherein the second switching element is connected to a first terminal of the at least one coil and between the input terminals of the converter when the first switching element is closed.

19. A method for measuring at least one coil and calculating model parameters for the at least one coil to be modelled, the method comprising the following steps of: incorporating the at least one coil to be modelled into a DC to DC converter with at least a first switching element, which converter has input terminals and output terminals; connecting an adjustable resistive load between the output terminals of the DC to DC converter; applying an input voltage at the input terminals of the converter; controlling the first switching element in accordance with a frequency and duty cycle to obtain a voltage varying periodically in time across a coil of the at least one coil to be modelled, which voltage depends for at least a part of a period on the input voltage; wherein there is an output voltage across the adjustable resistive load, and the coil is incorporated such that for a part of the period the voltage across the coil is substantially equal to the difference between the input voltage and the output voltage; verifying whether the DC to DC converter operates in a discontinuous current mode or in a continuous current mode; if it is determined that the DC to DC converter operates in a discontinuous current mode modifying the resistive load and repeating the step of verifying; and if it is determined that the DC to DC converter operates in a continuous current mode performing the steps of: measuring at least a first quantity representative of the voltage across the coil at successive points in time in at least said part of a period; measuring at least a second quantity representative of the current through the coil at successive points in time in at least said part of a period; determining at least one voltage value for the voltage across the coil on the basis of the measured first quantity; determining at least one current value for the current through the coil on the basis of the measured second quantity; calculating at least one of a loss resistance or a loss power of the coil on the basis of the at least one voltage value and the at least one current value; determining on the basis of the measured second quantity at least one first and second current value for the current through the coil at respectively a first and second point in time of the successive points in time in said part of the period; calculating an inductance of the coil on the basis of said at least one voltage value, said at least one of the loss resistance or the loss power, and said at least one first and second current value; and repeating the above stated steps for at least one of a different input voltage, a different frequency, or a different duty cycle.

Description

(1) The invention will be further elucidated on the basis of a number of non-limitative exemplary embodiments of the method and the system according to the invention with reference to the accompanying drawings, in which:

(2) FIG. 1 is a schematic view of an embodiment of a system according to the invention;

(3) FIG. 2 is a flow diagram illustrating the measuring steps of an embodiment of the method according to the invention;

(4) FIG. 3 shows a first embodiment of a measurement setup according to the invention;

(5) FIG. 4 is a graph illustrating schematically the voltage measured across the coil and the current measured through the coil in the embodiment of FIG. 3;

(6) FIG. 5 illustrates a second embodiment of a measurement setup according to the invention;

(7) FIG. 6 illustrates a third embodiment of a measurement setup according to the invention;

(8) FIG. 7 illustrates a fourth embodiment of a measurement setup according to the invention;

(9) FIG. 8 illustrates a fifth embodiment of a measurement setup according to the invention;

(10) FIG. 9 illustrates a sixth embodiment of a measurement setup according to the invention;

(11) FIG. 10 illustrates a seventh embodiment of a measurement setup according to the invention; and

(12) FIGS. 11A and 11B illustrate a model for respectively a coil and a transformer.

(13) A first embodiment of a system and method according to the invention will now be illustrated with reference to FIGS. 1 and 2. The system comprises a DC to DC converter 1 with a first switching element 2. The coil 3 to be modelled is incorporated into the DC to DC converter 1. Converter 1 has input terminals 4a, 4b and output terminals 5a, 5b. Connected between output terminals 5a, 5b is a resistive load 6 with an adjustable resistor R.sub.L. Further provided is an adjustable voltage source 7 for the purpose of providing an input voltage U.sub.in at input terminals 4a, 4b of the converter. Control means (not shown) are further provided for the purpose of providing a signal for controlling the first switching element 2 at a frequency f.sub.SW, and a duty cycle . Measuring means 8 are further provided for measuring the voltage across the coil and the current through the coil. These measuring means are preferably adapted to measure the voltage across the coil u.sub.L and the current through the coil i.sub.L at successive points in time which cover a number of periods T=1/f.sub.SW. Note that it is possible that measuring means 8 do not measure u.sub.L and i.sub.L directly, but measure other quantities representative of respectively u.sub.L and i.sub.L. Further provided is a computer means 9 for calculating the loss power P.sub.loss, the loss resistance R.sub.LS and the inductance L of the coil.

(14) Following assembly of the measurement setup of FIG. 1, the limits must be determined for the input parameters U.sub.in, f.sub.SW, and R.sub.L in order to define the measurement range, see step 20 of FIG. 2. In a subsequent step 21 a value is set for U.sub.in, f.sub.SW and on the basis of the defined measurement range, and the resistance R.sub.L of the load is set in a second step 22. Verification then takes place of whether the converter circuit is operating in a Discontinuous Current Mode (DCM) or in a Continuous Current Mode (CCM). In the embodiment illustrated in FIG. 2 measurements are performed only in the CCM mode. If it is determined that the circuit is in a DCM mode, the input parameters are modified in steps 21 and/or 22. Note however that it is also possible to apply the method according to the invention when the converter is in a DCM mode.

(15) Following the measurement of u.sub.L and i.sub.L in step 24, the input parameters are modified in steps 21 and/or 22. The skilled person will appreciate that it is possible to proceed in many different ways here, and can for instance first vary the input voltage U.sub.in, while the other input parameters f.sub.SW, and R.sub.L are kept constant, after which f.sub.SW and/or can be varied and finally R.sub.L. Other sequences can of course also be envisaged.

(16) According to a first variant as illustrated in FIG. 3, the DC to DC converter is a buck converter. The first switching element 102 is connected between an input terminal 104a and a first terminal of coil 103. Coil 103 is connected in series to the first switching element 102. The other terminal of coil 103 is connected via current measuring means 108b to an output terminal 105a. A second switching element in the form of a Schottky diode 110 is further connected between the one terminal of coil 103 and input terminal 104b. Voltage measuring means 108a are also provided for measuring the voltage u.sub.L across the coil. An input capacitor C.sub.dec is connected between the input terminals 104a, 104b. An output capacitor C.sub.out is connected between output terminals 105a, 105b. In addition to the measuring means for i.sub.L and u.sub.L, additional measuring means 111, 112, 113 can be provided for the purpose of measuring respectively the output voltage u.sub.out, the output current i.sub.out, the input current I.sub.in and the input voltage U.sub.in in order to verify the other measurements.

(17) FIG. 4 illustrates schematically typical measurement results for i.sub.L and u.sub.L as a function of time. This schematic graph shows a linear current progression, while the skilled person will appreciate that this progression is typically exponential. The voltage progression is further shown schematically as a block wave, and the skilled person will appreciate that the voltage across the coil is not wholly constant during charging (t.sub.on) and discharging (t.sub.off) of the coil. The current i.sub.L through the coil varies between a minimum value I.sub.min and a maximum value I.sub.max. During charging the voltage across the coil u.sub.L is equal to U.sub.inU.sub.out, and during discharge u.sub.L is equal to u.sub.outu.sub.d, wherein u.sub.d is the voltage across the diode.

(18) For the embodiment of FIG. 3 the loss power can be calculated on the basis of the following formula:

(19) $P_{\mathrm{loss}}=\frac{1}{T}.Math.{}_0^T{i}_L\left(t\right).Math.u_L\left(t\right)\mathrm{dt}$
wherein T is the period, i.sub.L(t) is the current through the coil at point in time t and u.sub.L(t) is the voltage across the coil at point in time t.

(20) According to another possibility, the loss power can be calculated with the following approximate formula:

(21) $P_{\mathrm{loss}}=\frac{I_{\max }+I_{\min }}{2}.Math.\frac{1}{T}\left[U_{\mathrm{Lg}1}.Math.t_{\mathrm{on}}+U_{\mathrm{Lg}2}.Math.t_{\mathrm{off}}\right]$
wherein U.sub.Lg1 is the average of the voltage across the coil between the first point in time t=0 and the second point in time t=t.sub.on, U.sub.Lg2 is the average of the voltage across the coil between the second point in time t=t.sub.on and the end of a period t=T, and t.sub.off=Tt.sub.on.

(22) The loss resistance can then be calculated as:

(23) 0$R_{\mathrm{LS}}=\frac{P_{\mathrm{loss}}}{I_{L_{\mathrm{eff}}}^2}$
wherein I.sub.Leff is the effective current. I.sub.Leff can be calculated in this formula as the RMS value of the current through the coil on the basis of the following formula:

(24) $I_{L_{\mathrm{eff}}}=\sqrt{\frac{1}{T}{}_0^T{\left(i_L\left(t\right)\right)}^2\mathrm{dt}}$
or the effective current can be calculated on the basis of the approximate formula:

(25) $I_{L_{\mathrm{eff}}}=\left(\frac{I_{\max }+I_{\min }}{2}.Math.\sqrt{1+\frac{1}{12}.Math.{\left(\frac{I_{\max }-I_{\min }}{\frac{I_{\max }+I_{\min }}{2}}\right)}^2}\right)$

(26) The inductance can then be calculated on the basis of the following formula:

(27) $L=\frac{R_{\mathrm{LS}}.Math.t_{\mathrm{on}}}{\ln \left[\frac{I_{\min }.Math.R_{\mathrm{LS}}-U_{\mathrm{Lg}1}}{I_{\max }.Math.R_{\mathrm{LS}}-U_{\mathrm{Lg}1}}\right]}$

(28) Note that for the variant of FIG. 3B the following formulae further apply:
0<t<t.sub.on:u.sub.L(t)=U.sub.inu.sub.out(t)
t.sub.on<t<T:u.sub.L(t)=u.sub.out(t)u.sub.d(t)
wherein u.sub.d(t) is the voltage across the Schottky diode 110. The output voltage u.sub.out(t) could therefore also be measured as approximation for the voltage across the coil. It is generally recommended in practice to measure both u.sub.L(t) and u.sub.out (t).

(29) In the variant illustrated in FIG. 3 the measuring means 108 for measuring the current through the coil are connected in series to the coil. According to another variant, a small resistor could be connected in series to the output capacitor C.sub.out and the current through this resistor could be measured. If the current through the resistor is i.sub.R, then i.sub.L=i.sub.R+i.sub.out. i.sub.R and i.sub.out could therefore also be measured instead of measuring i.sub.L.

(30) FIGS. 5-10 show a number of other possible measurement setups which can be used in an embodiment of the method according to the invention. FIG. 5 illustrates a boost converter, FIG. 6 a buck-boost converter, FIG. 7 a non-inverting buck-boost converter and FIG. 8 a series resonant converter. Since the measurement and calculation principles are similar to those described with reference to FIG. 2, they will not be further elucidated.

(31) Finally, FIGS. 9 and 10 illustrate two further alternative measurement setups which can for instance be used to characterize transformers. FIG. 9 illustrates a fly-back converter and FIG. 10 a full bridge buck converter. In both circuits the voltage U.sub.L1 across the primary winding as well as the voltage U.sub.L2 across the secondary winding are measured. In addition, the current I.sub.L1 through the primary winding and the current I.sub.L2 through the secondary winding are measured. Note that in the circuit of FIG. 10 two identical windings are connected in series. Since these windings are identical, it suffices to measure the current through one of these windings and the voltage across one of these windings. FIG. 11B illustrates a possible model for a transformer in which all losses of the transformer are modelled on the primary side. Note that it is also possible to provide a model in which the losses are modelled on the secondary side. In the illustrated model N1 is the number of windings on the primary side and N2 the number of windings on the secondary side. The model further comprises a magnetization inductance L.sub.M as a result of the finite permeability of the core material of the transformer, a loss resistance R.sub.M as a result of the core, i.e. as a result of the so-called iron losses, an equivalent leakage inductance L.sub.eq as a result of the finite coupling between the primary and the secondary winding, and an equivalent loss resistance R.sub.eq as a result of the serial resistance of the primary and secondary windings. The skilled person will appreciate that the parameters of the model L.sub.M, R.sub.M, L.sub.eq and R.sub.eq can be calculated as a function of the measured voltages and currents U.sub.L1, I.sub.L1, U.sub.L2 and I.sub.L2 on the basis of formulae similar to those as presented above for modelling a single coil. It will once again be possible to use a more precise or an approximate formula.

(32) As example of the method according to the invention a commercial coil was modelled using the method according to the invention. The manufacturer states as model parameters L=150 H, R.sub.LS=68 m at f=0 Hz (DC), I.sub.max=4 A. This coil was then measured using an embodiment of the method according to the invention. The results were as follows: L=144 H, R.sub.LS=320 m, L.sub.Leff=830 mA; at f=10 kHz and =t.sub.on/T=0.5. This demonstrates that the existing models will not produce good results in circuit simulations compared to coils modelled according to an embodiment of the method according to the invention. After all, the coils are never used at 0 Hz (DC) but typically at significantly higher frequencies.

(33) The invention is not limited to the above described exemplary embodiments and the skilled person will appreciate that many changes and modifications can be envisaged within the scope of the invention, which is defined solely by the following claims.