Power conversion system

Abstract

The present invention provides a power conversion system that enables highly efficient power transmission over a wide voltage range, while simultaneously achieving both stable power control and responsiveness. [Solution] The control device 106a controls the phase of the drive pulse edge to control the period during which both the primary and secondary AC voltages of the isolation transformer 102 are at zero voltage, or controls the phase of the drive pulse edge to control the period δ during which the primary and secondary AC voltages of the isolation transformer 102 are at opposite polarity, according to the magnitude of the control variable D. At that time, the power or current transmitted through the isolation DC / DC converter changes linearly with respect to the input control variable over the entire range including the control range of the discontinuous current mode and the control range of the continuous current mode. Input control variables A transformation is applied to generate control variables.

Description

[Technical Field]

[0001] This invention relates to a power conversion system utilizing an isolated DC / DC converter. [Background technology]

[0002] Figure 7 is a circuit diagram showing an example configuration of a power conversion system 100 using an isolated DC / DC converter 110. The isolated DC / DC converter 110 has an isolation transformer 102 in which the primary and secondary windings are electrically isolated. A series inductor 104a is connected to the primary winding of the isolation transformer 102. This series inductor 104a is either the leakage inductance of the primary winding of the isolation transformer 102 or an external inductance added to this leakage inductance. Note that if only the leakage inductance is used for power transmission, the external inductance is not necessary. A similar series inductor 104b is connected to the secondary winding of the isolation transformer 102.

[0003] The first bridge circuit 111 is a circuit that supplies a primary AC voltage v1 to the primary winding of the isolation transformer 102. This first bridge circuit 111 is a full bridge circuit in which switching elements 101a and 101b connected in series and switching elements 101c and 101d connected in series are connected in parallel. In this example, each of the switching elements 101a to 101d consists of a MOSFET (Metal Oxide Semiconductor Field Effect Transistor) and a diode connected in antiparallel to it. A capacitor 103a is connected in parallel to the first bridge circuit 111. A primary DC voltage E1 is then supplied to the first bridge circuit 111. In this first bridge circuit 111, the primary AC voltage v1 to the isolation transformer 102 is output from between the intermediate node between switching elements 101a and 101b and the intermediate node between switching elements 101c and 101d.

[0004] The second bridge circuit 112 is a circuit that supplies a secondary AC voltage v2 to the secondary winding of the isolation transformer 102. This second bridge circuit 112 is, like the first bridge circuit 111, a bridge circuit in which switching elements 101e and 101f connected in series and switching elements 101g and 101h connected in series are connected in parallel. A capacitor 103b is connected in parallel to the second bridge circuit 112. And a secondary DC voltage E2 is applied to the second bridge circuit 112. In this second bridge circuit 112, a secondary AC voltage v2 for the isolation transformer 102 is output from between the intermediate node between the switching elements 101e and 101f and the intermediate node between the switching elements 101g and 101h.

[0005] The DC voltage detection unit 107a is a circuit that detects the primary DC voltage E1 applied to the first bridge circuit 111. Also, the DC voltage detection unit 107b is a circuit that detects the secondary DC voltage E2 applied to the second bridge circuit 112.

[0006] The control device 106 is a device that generates drive pulses Ga to Gd for driving the switching elements 101a to 101d of the first bridge circuit 111 and drive pulses Ge to Gh for driving the switching elements 101e to 101h of the second bridge circuit 112.

[0007] The drive circuit unit 105a drives the switching elements 101a to 101d with the drive pulses Ga to Gd generated by the control device 106, and the drive circuit unit 105b drives the switching elements 101e to 101h with the drive pulses Ge to Gh generated by the control device 106.

[0008] Based on the primary DC voltage E1 detected by the DC voltage detection unit 107a and the secondary DC voltage E2 detected by the DC voltage detection unit 107b, the control device 106 controls the phase of the edges of the drive pulses Ga to Gh for driving the switching elements 101a to 101h, and controls the power transmission of the isolation DC / DC converter 110.

[0009] Hereinafter, referring to the waveform diagram of FIG. 8, an operation example of the power conversion system 100 will be described. In the power conversion system 100, the first bridge circuit 111 and the second bridge circuit 112 output a primary-side AC voltage v1 and a secondary-side AC voltage v2 having the same period (wavelength). In the following description, the terms phase angle or phase difference are used, which means the relative lengths of various periods expressed with 2π for one period (one wavelength) of the primary-side AC voltage v1 and the secondary-side AC voltage v2. Also, in the following description, the secondary-side DC voltage E2 and the secondary-side AC voltage v2 mean the voltage values converted to the primary side. That is, when the number of turns of the primary-side winding of the isolation transformer 102 is n1 and the number of turns of the secondary-side winding is n2, the voltage value obtained by multiplying the actual secondary-side DC voltage by the coefficient n1 / n2 (the voltage value converted to the primary side) is the secondary-side DC voltage E2. The same applies to the secondary-side AC voltage v2. Further, in the following description, the low-voltage side and the high-voltage side mean the side where low voltage is generated and the side where high voltage is generated among the primary side and the secondary side of the isolation DC / DC converter 110. For example, if there is a relationship of E1 < E2 between the primary-side DC voltage E1 and the secondary-side DC voltage E2 converted to the primary side, the primary side is the low-voltage side and the secondary side is the high-voltage side, and if there is a relationship of E1 > E2, the primary side is the high-voltage side and the secondary side is the low-voltage side.

[0010] In the operation example of FIG. 8, there is a relationship of E1 < E2 between the primary-side DC voltage E1 and the secondary-side DC voltage E2. Therefore, the primary side is the low-voltage side and the secondary side is the high-voltage side. In this operation example, the control device 106 causes the first bridge circuit 111 to output a primary-side AC voltage v1 of a rectangular wave having an amplitude of ±E1 and a duty ratio of 50%, and causes the second bridge circuit 112 to output a secondary-side AC voltage v2 of a rectangular wave having an amplitude of ±E2, a duty ratio of 50%, and delayed by a phase angle δ with respect to the primary-side AC voltage v1. Here, the duty ratio may be slightly shifted from 50%. When the phase of the secondary-side AC voltage v2 is delayed with respect to the primary-side AC voltage v1 in this way, in the isolation DC / DC converter 110, power transmission from the primary side to the secondary side is performed. Hereinafter, the operation of this power transmission will be described.

[0011] In the isolated DC / DC converter 110, the voltage difference between the primary AC voltage v1 and the secondary AC voltage v2 is equal to the leakage inductance l of the isolation transformer 102 and the external inductance L. aux The inductance L = l + L is formed by this. aux A current i is applied to the primary winding of the isolation transformer 104, satisfying equation (1.1). In addition, a current corresponding to this current i (the same current as current i if the turns ratio of the primary and secondary sides of the isolation transformer 102 is 1) flows through the secondary winding of the isolation transformer 104. di / dt=(v1(t)-v2(t)) / L ……(1.1)

[0012] In this example of operation, the primary AC voltage v1 and the secondary AC voltage V2 are of opposite polarity during the period from the rising edge of the primary AC voltage v1 to the phase angle δ and from the falling edge of the primary AC voltage v1 to the phase angle δ. Therefore, during this period, a larger voltage difference is applied to the inductance L than during other periods, and the time gradient of the current i becomes larger, as shown in Figure 8.

[0013] Therefore, the power P transmitted from the primary side to the secondary side increases depending on the phase difference δ between the primary AC voltage v1 and the secondary AC voltage v2. Specifically, if the fundamental wave angular frequencies of the primary AC voltage v1 and the secondary AC voltage v2 are ω, the power P transmitted from the primary side to the secondary side is given by the following equation (1.2). P =(E1E2 / (ωL))δ(1-(δ / π)) ……(1.2)

[0014] Therefore, the control device 106 controls the transmission power P between the primary and secondary sides by controlling the phase of the edges of the drive pulses Ga to Gh for driving the switching elements 101a to 101h, thereby controlling the period (phase angle δ) during which the primary AC voltage v1 and secondary AC voltage v2 of the isolation transformer 102 are of opposite polarity.

[0015] By the way, in this example of operation, if the phase difference δ between the primary AC voltage v1 and the secondary AC voltage v2 is increased in order to increase the transmitted power P, there is a problem that the peak value of the current i flowing through the isolation transformer 104 becomes excessive. One way to solve this problem is through continuous current mode phase control. This is a phase control that reduces the peak value of the current i by performing pulse width modulation on one of the primary AC voltage v1 or the secondary AC voltage v2.

[0016] Figure 9 is a waveform diagram showing an example of the operation of phase control in continuous current mode. In this example, the secondary AC voltage v2 on the high-voltage side maintains a voltage with opposite polarity to the primary AC voltage v1 for a period of phase angle δ from the rising edge of the primary AC voltage v1 on the low-voltage side, then maintains a zero voltage for a period of phase angle φ, and then rises to a voltage with the same polarity as the primary AC voltage v1. In other words, in phase control in continuous current mode, the pulse width of the secondary AC voltage v2 on the high-voltage side, which is generated with a phase angle δ delay, is shortened by the phase angle φ (to zero voltage).

[0017] In this way, the current i flowing through the isolation transformer 104 changes with a large time gradient for a period of phase angle δ, and then changes with a smaller time gradient than the previous period for a period of phase angle φ, reaching a peak value, thus avoiding an excessive peak value.

[0018] In this example of operation shown in Figure 9, the control device 106 controls the transmission power P between the primary and secondary sides by controlling the period (phase angle δ) during which the AC voltages on the primary and secondary sides of the isolation transformer 102 are of opposite polarity. This transmission power P is given by the following equation. P =(E1E2 / (ωL))((π-φ)(2δ+φ)-2δ 2 ) / (2π) ...(1.3)

[0019] The phase control of the continuous current mode described above has a problem. Specifically, a reverse power is generated that is transmitted in the opposite direction to the transmission direction determined by the phase relationship between the primary AC voltage v1 and the secondary AC voltage v2, resulting in the generation of reactive power.

[0020] For example, in the operation example shown in Figure 9, the phase of the secondary AC voltage v2 lags behind the primary AC voltage v1, and the power transmission direction is from the primary to the secondary. However, in continuous current mode phase control, the polarity of the current i flowing through the isolation transformer 104 reverses within a period of phase angle δ starting from the rising edge (or falling edge) of the primary AC voltage v1. Within this period of phase angle δ, for the period after the timing of the polarity reversal of the current i, the reverse power P is transmitted in the direction from the secondary to the primary, which is the opposite direction of the transmission direction determined by the phase relationship between the primary AC voltage v1 and the secondary AC voltage v2. b This occurs. This reverse power P b This refers to the power P transmitted from the primary side to the secondary side before the timing of the polarity reversal of the current i within a period of phase angle δ. f It cancels out.

[0021] Thus, in phase control of continuous current mode, the reverse power P is transmitted in the opposite direction to the original transmission direction. b This occurs, resulting in a decrease in transmission efficiency. This problem is particularly pronounced when the DC voltage difference between the primary and secondary sides is large or when the load is light, and it causes increased conduction losses (deterioration of power transmission efficiency).

[0022] One way to solve the problem of phase control in continuous current mode is to use phase control in discontinuous current mode. This avoids the generation of reverse power by creating a period in which both the primary AC voltage v1 and the secondary AC voltage v2 are at zero voltage.

[0023] Figure 10 is a waveform diagram showing an example of the operation of phase control in discontinuous current mode. In this example, both the primary AC voltage v1 and the secondary AC voltage v2 simultaneously change from a voltage of the first polarity (positive polarity in this example) to zero voltage. After that, both maintain zero voltage for a period of phase angle γ, and then the primary AC voltage v1 on the low-voltage side changes to a voltage of the second polarity (negative polarity in this example), which is opposite to the first polarity. Subsequently, the secondary AC voltage v2 on the high-voltage side changes to a voltage of the second polarity with a phase angle of φ-δ lag. After that, the primary AC voltage v1 and the secondary AC voltage v2 change from a voltage of the second polarity to a voltage of the first polarity, drawing waveforms similar to those described above.

[0024] In this example of operation, the current i flowing through the isolation transformer 102 increases during a phase angle φ-γ period when the primary AC voltage v1 is a voltage of the first or second polarity and the secondary AC voltage v2 is a zero voltage. Subsequently, the current i flowing through the isolation transformer 102 decreases to zero during a period when both the primary AC voltage v1 and the secondary AC voltage v2 are voltages of the same polarity, and this operation is repeated.

[0025] Then, during the period of phase angle γ after the current i flowing through the isolation transformer 102 decreases to zero, both the primary AC voltage v1 and the secondary AC voltage v2 become zero voltages, the change in the current i flowing through the isolation transformer 102 stops, and polarity reversal does not occur. Therefore, no reverse power is generated.

[0026] In this example of operation, the power P transmitted from the primary side to the secondary side depends on the peak value of the current i flowing through the isolation transformer 102. The peak value of the current i depends on the length of the phase angle φ-γ period. Therefore, the control device 106 controls the period of phase angle γ during which both the AC voltages on the primary and secondary sides of the isolation transformer 102 are at zero voltage, and also controls the phase angles φ and γ to control the transmitted power P between the primary and secondary sides. This transmitted power P is given by the following equation. P =(E1E2 / (ωL))(A(1-A)(π-γ) 2 ) / (2π) ...(1.4) In equation (1.4), A is given by the following equation. A = Low-voltage DC voltage / High-voltage DC voltage < 1 ……(1.5)

[0027] The continuous current mode phase control described above can transmit a certain level of power over a wide voltage range, but it can generate reverse power, which reduces the power transmission efficiency. On the other hand, while discontinuous current mode phase control can avoid the generation of reverse power, it has the problem of being difficult to transmit a certain level of power over a wide voltage range, including when the voltage difference between the primary and secondary sides is small.

[0028] Therefore, Patent Document 1 discloses a power conversion system that controls the phase of a discontinuous current mode, which controls the period during which both the AC voltages on the primary and secondary sides of an isolation transformer are at zero voltage by controlling the phase of the edge of the drive pulse, or controls the phase of a continuous current mode, which controls the period during which the AC voltages on the primary and secondary sides of an isolation transformer are at opposite polarities by controlling the phase of the edge of the drive pulse, according to the magnitude of the control variable. [Prior art documents] [Patent Documents]

[0029] [Patent Document 1] Japanese Patent Publication No. 2024-82491 [Overview of the Initiative] [Problems that the invention aims to solve]

[0030] According to the power conversion system disclosed in Patent Document 1, phase control in discontinuous current mode or phase control in continuous current mode is performed depending on the magnitude of the control variable, making it possible to transmit power with high efficiency over a wide voltage range. However, the power conversion system disclosed in Patent Document 1 has the following problems.

[0031] Figure 11 illustrates the power transmission characteristics in a power conversion system disclosed in Patent Document 1. In Figure 11, the horizontal axis represents the control variable D, and the vertical axis represents the transmitted power P of the power conversion system. In this example of operation, in the range 0 ≤ D ≤ π (a), phase control of the discontinuous current mode is performed according to the control variable D. In the range π ≤ D ≤ 3π / 2 (c), phase control of the continuous current mode is performed according to the control variable D.

[0032] As illustrated in Figure 11, in the range (a) where phase control of the discontinuous current mode is performed, the change in the transmitted power P with respect to the control variable D is gradual. Therefore, in this range (a), if the control gain of the transmitted power P is low, the response tracking performance deteriorates. On the other hand, in the range (c) where phase control of the continuous current mode is performed, the change in the transmitted power P with respect to the control variable D is steep. Therefore, in this range (c), if the control gain of the transmitted power P is set high, the stability deteriorates. Thus, the power conversion system of Patent Document 1 has the problem that stability deteriorates when the control gain is set high to match range (a), and response tracking performance deteriorates when the control gain is set low to match range (c), making it difficult to achieve both stability and response tracking performance.

[0033] This invention has been made in view of the circumstances described above, and aims to provide a power conversion system that can transmit power with high efficiency over a wide voltage range, and that can achieve both stable control of transmitted power and responsiveness. [Means for solving the problem]

[0034] A power conversion system according to one aspect of this invention comprises an isolation transformer, an isolation DC / DC converter having a first bridge circuit and a second bridge circuit connected to the primary and secondary sides of the isolation transformer, respectively, and each including at least one switching element, a DC voltage detection unit that detects both the primary DC voltage supplied to the first bridge circuit and the secondary DC voltage supplied to the second bridge circuit, a control device that generates drive pulses for each of the switching elements of the first bridge circuit and the second bridge circuit based on the primary DC voltage and secondary DC voltage detected by the DC voltage detection unit and a control variable, and a drive circuit unit that drives the switching elements of the first bridge circuit and the second bridge circuit based on the drive pulses, and the control The device controls the phase of the edges of the drive pulse to perform discontinuous current mode phase control, which controls the period during which both the primary and secondary AC voltages of the isolation transformer are at zero voltage, or continuous current mode phase control, which controls the period during which the primary and secondary AC voltages of the isolation transformer are at opposite polarities, according to the magnitude of the control variable. At that time, the device generates the control variable by converting the input control information so that the power or current transmitted through the isolation DC / DC converter changes linearly with respect to the input control variable over the entire range including the range of the control variable in which the discontinuous current mode phase control is performed and the range of the control variable in which the continuous current mode phase control is performed.

[0035] In a preferred embodiment, the control device generates the control variables by transforming the input control information using the inverse function of a function that relates the control variables to the power or current transmitted through the isolated DC / DC converter.

[0036] In another preferred embodiment, the control device generates a first control variable by transforming the input control information using the inverse function of the function relating the control variable to the power or current in the discontinuous current mode, and generates a second control variable by transforming the input control information using the inverse function of the function relating the control variable to the power or current in the continuous current mode, and if the first control variable falls within the range of control variables for which phase control of the discontinuous current mode should be performed, the control device performs phase control of the discontinuous current mode based on the first control variable, and if the second control variable falls within the range of control variables for which phase control of the continuous current mode should be performed, the control device performs phase control of the continuous current mode based on the second control variable. [Effects of the Invention]

[0037] According to one aspect of this invention, a power conversion system is configured such that the control device performs phase control in discontinuous current mode or continuous current mode according to the magnitude of the control variable, thereby enabling highly efficient power transmission between the primary and secondary sides of an isolated DC / DC converter over a wide voltage range. Furthermore, this power conversion system generates control variables by converting the input control information so that the power or current transmitted through the isolated DC / DC converter changes linearly with respect to the input control variable across the entire range, including the range of control variables in which phase control is performed in discontinuous current mode and the range of control variables in which phase control is performed in continuous current mode. This allows for both stability of power transmission control and responsiveness. [Brief explanation of the drawing]

[0038] [Figure 1] This is a circuit diagram showing the configuration of a power conversion system, which is one embodiment of this invention. [Figure 2] This waveform diagram shows an example of the operation of phase control in discontinuous current mode performed in the power conversion system. [Figure 3] This waveform diagram shows an example of the operation of phase control in continuous current mode performed in the power conversion system. [Figure 4] This waveform diagram shows an example of the overall operation of the power conversion system. [Figure 5] This diagram illustrates the current transmission characteristics in the power conversion system. [Figure 6] This is a diagram showing the configuration of the control device for the power conversion system. [Figure 7] This is a circuit diagram showing an example configuration of a power conversion system. [Figure 8] This waveform diagram shows the basic operating waveforms of the power conversion system. [Figure 9] This waveform diagram shows an example of the operation of phase control in continuous current mode in the power conversion system. [Figure 10] This waveform diagram shows an example of the operation of phase control in discontinuous current mode in the power conversion system. [Figure 11] This figure illustrates the power transmission characteristics in the power conversion system disclosed in Patent Document 1. [Modes for carrying out the invention]

[0039] The embodiments of this invention will now be described with reference to the drawings. Figure 1 is a circuit diagram showing the configuration of a power conversion system 100a, which is one embodiment of this invention. In this power conversion system 100a, the control device 106 in the conventional power conversion system (Figure 7) is replaced by a control device 106a.

[0040] Elements other than the control device 106a in the power conversion system 100a are the same as those in the conventional power conversion system (Fig. 7). That is, the isolated DC / DC converter 110 includes an isolation transformer 102, a first bridge circuit 111 and a second bridge circuit 112 that are connected to the primary side and the secondary side of the isolation transformer 102 respectively and each include at least one switching element. The DC voltage detection unit 107a detects the primary side DC voltage E1 applied to the first bridge circuit 111, and the DC voltage detection unit 107b detects the secondary side DC voltage E2 applied to the second bridge circuit 112. The drive circuit unit 105a drives the switching elements 101a - 101d of the first bridge circuit 111 based on the drive pulses Ga - Gd generated by the control device 106a, and the drive circuit unit 105b drives the switching elements 101e - 101h of the second bridge circuit 112 based on the drive pulses Ge - Gh generated by the control device 106a.

[0041] The control device 106a has a conversion unit 121. This conversion unit 121 is a means for generating a control variable D by performing a conversion on the input control variable I DC The input control variable I DC is, for example, a command value related to the power or current to be transmitted by the isolated DC / DC converter 110.

[0042] In a preferred embodiment, the input control variable I DC is given from a higher-level device that controls the power conversion system 100a to the control device 106a. In another preferred embodiment, based on the operating status of the isolated DC / DC converter 110 and the load status, the control device 106a determines the input control variable I DC

[0043] The control device 106a generates drive pulses Ga - Gh for driving each of the switching elements of the first bridge circuit 111 and the second bridge circuit 112 based on the control variable D generated from this input control variable I DC and the primary side DC voltage E1 and the secondary side DC voltage E2 detected by the DC voltage detection units 107a and 107b.

[0044] ​ As described above, while phase control in continuous current mode can transmit a certain level of power over a wide voltage range, it suffers from the problem of reduced power transmission efficiency due to the generation of reverse power. On the other hand, while phase control in discontinuous current mode can avoid the generation of reverse power, it has the problem of difficulty in transmitting a certain level of power over a wide voltage range, including cases where the voltage difference between the primary and secondary sides is small. Therefore, if only one of the two—continuous current mode phase control or discontinuous current mode phase control—is performed, it is difficult to transmit power efficiently over a wide voltage range. Thus, in this embodiment, both continuous current mode phase control and discontinuous current mode phase control are performed by the control device 106a.

[0045] Furthermore, as described above, in continuous current mode phase control, the phase angle δ of the phase lag between the primary AC voltage v1 and the secondary AC voltage v2, and the phase angle φ of the period during which the high-voltage AC voltage maintains zero voltage are the targets of manipulation. On the other hand, in discontinuous current mode phase control, there is no phase lag (phase angle δ) between the primary AC voltage v1 and the secondary AC voltage v2, and the phase angle γ of the period during which both the low-voltage and high-voltage AC voltages maintain zero voltage, and the phase angle φ of the period during which the high-voltage AC voltage maintains zero voltage are the targets of manipulation. Moreover, in this case, since one of the phase angles γ or φ depends on the other, the actual target of manipulation is only one of the phase angles γ or φ. Therefore, in this embodiment, a single control variable D is associated with the target of manipulation for discontinuous current mode phase control, and the same control variable D is also associated with the target of manipulation for continuous current mode phase control, so that either discontinuous current mode phase control or continuous current mode phase control is performed according to the magnitude of the control variable D.

[0046] Specifically, in this embodiment, the control device 106a controls the transmission of power P between the primary and secondary sides of the isolated DC / DC converter 110 by controlling the phase of the edges of the drive pulses Ga to Gh, thereby controlling the period during which both the primary AC voltage v1 and the secondary AC voltage v2 are at zero voltage, or by controlling the phase of the edges of the drive pulses Ga to Gh, thereby controlling the period during which the primary AC voltage v1 and the secondary AC voltage v2 are at opposite polarities, according to the magnitude of the control variable D.

[0047] The control variable D can take values ​​between 0 and 3π / 2. When the control variable D is greater than or equal to 0 and less than or equal to π, the control device 106a performs phase control in discontinuous current mode. When the control variable D is greater than or equal to π and less than or equal to 3π / 2, the control device 106a performs phase control in continuous current mode.

[0048] In this embodiment, the transmission power P between the primary and secondary sides increases as the control variable D increases, but the relationship between the control variable D and the transmission power P is illustrated in Figure 11 above. That is, in the range where phase control of the discontinuous current mode is performed (a), the change in transmission power P with respect to the control variable D is gradual, but in the range where phase control of the continuous current mode is performed (c), the change in transmission power P with respect to the control variable D is steep. For this reason, when the control variable D is given to the control device 106a to perform phase control, it is difficult to achieve both stability in transmission power control and responsiveness.

[0049] Therefore, in this embodiment, the conversion unit 121 controls the power or current transmitted through the isolated DC / DC converter 110 over the entire range including the range of control variable D for discontinuous current mode phase control and the range of control variable D for continuous current mode phase control, and the input control variable I DC The input control variable IDC is transformed to generate the control variable D so that it changes linearly with respect to the input variable. Details of the transformation unit 121 will be described later.

[0050] The details of the phase control in this embodiment will be described below. The following describes the case where power is transmitted from the primary side to the secondary side of the isolated DC / DC converter 110. Furthermore, the following describes the case where the primary side is the low-voltage side and the secondary side is the high-voltage side.

[0051] Figure 2 is a waveform diagram showing an example of phase control in discontinuous current mode. In Figure 2, / Gb, / Gd, / Gf, and / Gh represent the level-inverted waveforms of the drive pulses Gb, Gd, Gf, and Gh. The same applies to the other waveform diagrams (Figures 3 and 6). In the example in Figure 2, the control device 106a controls the inflection points Q before and after the peak point P1 (P2) of the current i flowing through the isolation transformer 102. 11 and Q 12 (Q 21 and Q 22 The phase of the drive pulse edge is controlled so that the current values ​​of ) match.

[0052] Specifically, the control device 106a controls the phase of the edges of the drive pulses Ga~Gh such that the sum of the time integral of the first differential voltage (E1-0>0 in the example of Figure 2) during the first period T1 (phase angle φ-γ) when a first differential voltage (E1-0>0 in the example of Figure 2) is generated between the primary AC voltage v1 on the low-voltage side and the secondary AC voltage v2 on the high-voltage side, and the time integral of the second differential voltage (E1-E2<0 in the example of Figure 2) which has the opposite polarity to the first differential voltage (E1-E2<0 in the example of Figure 2) is generated between the primary AC voltage v1 on the low-voltage side and the secondary AC voltage v2 on the high-voltage side, is zero. That is, in the example of Figure 2, the phase of the edges of the drive pulses Ga~Gh is controlled so that the following equation (2.1) is satisfied. E1(φ-γ)+(E1-E2)(π-φ)=0 ……(2.1) Although the primary DC voltage E1 and the secondary DC voltage E2 do technically fluctuate over time, they are treated as constant voltages in equation (2.1) above because their time constants are large.

[0053] With this control, the current i in the isolation transformer 102, which is generated by the voltage difference between the primary AC voltage v1 and the secondary AC voltage v2, becomes zero at the start of the third period T3 (the period with a phase angle γ) when both the primary AC voltage v1 and the secondary AC voltage v2 are at zero voltage, thereby avoiding the generation of reverse power.

[0054] The above describes the phase control of the edges of the drive pulses Ga~Gh during the period before and after the timing of a positive peak point P1 occurring in the current i. The phase control of the edges of the drive pulses Ga~Gh during the period before and after the timing of a negative peak point P2 occurring in the current i is similar.

[0055] One objective of this embodiment is to perform phase control of drive pulses Ga~Gh based on a single control variable D, not only in continuous current mode but also in discontinuous current mode. Therefore, in this embodiment, in discontinuous current mode, the phase angle γ is determined based on the control variable D, and the phase angle φ is made dependent on this phase angle γ. Specifically, this is as follows.

[0056] Solving equation (2.1) for φ yields equation (2.2). φ(γ) =(1-(E1 / E2))π+(E1 / E2)γ =(1-A)π+Aγ ……(2.2) Here, A is as shown in equation (1.5) above.

[0057] Furthermore, the control variable D in the discontinuous current mode is related to the phase angle γ as shown in the following equation. D = π - γ ……(2.3)

[0058] Then, given a control variable D such that 0 ≤ D ≤ π, the control device 106a calculates the phase angle γ from the control variable D according to equation (2.3), and calculates the phase angle φ from the phase angle γ according to equation (2.2).

[0059] The above explanation focused on the change in the differential voltage between the primary AC voltage v1 and the secondary AC voltage v2. However, the explanation can be made by focusing on the changes in the primary AC voltage v1 and the secondary AC voltage v2 individually, as follows.

[0060] In phase control of the discontinuous current mode, the control device 106a sequentially generates a first period T1 in which one of the primary AC voltage v1 or secondary AC voltage v2 of the isolation transformer 102 (specifically the low-voltage side) has a first polarity (positive polarity in the example of Figure 2) and the other (specifically the high-voltage side) has zero voltage; a second period T2 in which both the primary AC voltage v1 and the secondary AC voltage v2 have the first polarity; and a third period T3 in which both the primary AC voltage v1 and the secondary AC voltage v2 have zero voltage, and reduces the third period T3 according to the magnitude of the control variable D (see equation (2.3) above).

[0061] Furthermore, in phase control of the discontinuous current mode, the control device 106a controls the phase of the edges of the drive pulses Ga~Gh such that the sum of the time integral of the difference voltage between the primary AC voltage v1 and the secondary AC voltage v2 in the first period T1 and the time integral of the difference voltage between the primary AC voltage v1 and the secondary AC voltage v2 in the second period T2 is zero (see equation (2.1) above).

[0062] Next, we will explain a specific example of phase control of the edge of the drive pulse in discontinuous current mode. In the following explanation, unless otherwise specified, the phase angle refers to the phase of the rising edge of the drive pulse Ga, / Gb in Figure 2 (phase angle θ). 12 This is the phase angle with (=0) as the reference position (starting point). That is, the phase angle θ 34 These are the phase angle of the rising edge of the drive pulse Gc / Gd relative to the reference position, and the phase angle θ. 56 These are the phase angle of the rising edge of the drive pulse Ge / Gf relative to the reference position, and the phase angle θ. 78 This is the phase angle of the rising edge of the drive pulse Gg / Gh relative to the reference position.

[0063] In the operation example shown in Figure 2, the falling edge of the primary AC voltage v1 towards zero voltage (the start of the third period T3) is generated by the rising edges of the drive pulses Gc and / Gd. The falling edge of the primary AC voltage v1 towards zero voltage has a phase angle of π-γ. Therefore, the phase angle θ of the rising edges of the drive pulses Gc and / Gd is also present. 34 This is calculated by the following equation (2.4). θ 34 =π-γ =π-π+D =D ……(2.4)

[0064] Furthermore, the rising edge of the secondary AC voltage v2 towards zero voltage (the start of the third period T3) is generated by the rising edges of the drive pulses Ge and / Gf. The falling edge of the secondary AC voltage v2 towards zero voltage has a phase angle of -γ. Therefore, the phase angle θ of the rising edges of the drive pulses Ge and / Gf. 56 This is calculated by the following equation (2.5). θ 56 =-γ =D-π ……(2.5)

[0065] Furthermore, the falling edge of the secondary AC voltage v2 from zero voltage (the start of the second period T2) is generated by the rising edges of the drive pulses Gg and / Gh. The falling edge of the secondary AC voltage v2 from zero voltage is generated by the phase angle θ 56 It has +π+φ. Therefore, the phase angle θ of the rising edge of the drive pulses Gg and / Gh. 78 This is calculated by the following equation (2.6). θ 78 =θ56+π+φ =D-π+π+φ =D-π+π+π-AD =π+(1-A)D ……(2.6) The above describes the phase control of the discontinuous current mode in this embodiment.

[0066] Figure 3 is a waveform diagram showing an example of phase control in the continuous current mode in this embodiment. In this embodiment, not only in the discontinuous current mode but also in the continuous current mode, the inflection points Q before and after the peak point P1 (P2) of the current i flowing through the isolation transformer 102 are shown. 11 and Q 12 (Q 21 and Q 22 The phase of the drive pulse edge is controlled so that the current values ​​of ) match.

[0067] Specifically, the control device 106a controls the phase of the drive pulse edge so that the sum of the time integral of the first differential voltage (E1-0>0 in the example of Figure 3) generated between the primary AC voltage v1 and the secondary AC voltage v2 of the isolation transformer 102 during the fifth period T5 (phase angle φ) and the time integral of the second differential voltage (E1-E2<0 in the example of Figure 2) generated between the primary AC voltage v1 and the secondary AC voltage v2 of the isolation transformer 102 during the sixth period T6 (phase angle π-δ-φ) is zero. That is, in the example of Figure 3, the phase of the drive pulse edge Ga~Gh is controlled so that the following equation (3.1) is satisfied. E1φ+(E1-E2)(π-δ-φ)=0 ……(3.1)

[0068] The above describes the phase control of the edges of the drive pulses during the period before and after the timing of a positive peak point P1 occurring in the current i. Similarly, the phase control of the edges of the drive pulses Ga~Gh during the period before and after the timing of a negative peak point P2 occurring in the current i is the same.

[0069] As already explained, this embodiment controls the phase of the drive pulses Ga~Gh based on a single control variable D in both discontinuous current mode and continuous current mode. Therefore, in this embodiment, in continuous current mode, the phase angle δ is determined based on the control variable D, and the phase angle φ is made dependent on this phase angle δ. Specifically, it is as follows.

[0070] Solving equation (3.1) for φ yields equation (3.2). φ(δ) =(1-(E1 / E2))(π-δ) =(1-A)(π-δ) ……(3.2)

[0071] Furthermore, in continuous current mode, the control variable D is related to the phase angle δ by the following equation. D = δ + π ……(3.3)

[0072] In this embodiment, when a control variable D such that π≦D≦3π / 2 is given, the control device 106a calculates the phase angle δ from the control variable D according to equation (3.3) and calculates the phase angle φ from the phase angle δ according to equation (3.2).

[0073] By performing this type of control, the continuity of the waveform change of the current i flowing through the isolation transformer 102 during mode transitions between discontinuous current mode and continuous current mode is ensured.

[0074] The above explanation focused on the change in the differential voltage between the primary AC voltage v1 and the secondary AC voltage v2. However, the explanation can be made by focusing on the changes in the primary AC voltage v1 and the secondary AC voltage v2 individually, as follows.

[0075] In the phase control of the continuous current mode, the control device 106a sequentially generates a fourth period T4 (phase angle δ) in which the primary AC voltage v1 and secondary AC voltage v2 of the isolation transformer 102 are of opposite polarity, a fifth period T5 (phase angle φ) in which one of the primary AC voltage v1 or secondary AC voltage v2 (specifically the low-voltage side) is of first polarity and the other (specifically the high-voltage side) is at zero voltage, and a sixth period T6 (phase angle π-δ-φ) in which both the primary AC voltage v1 and secondary AC voltage v2 are of first polarity, and increases the fourth period T4 in accordance with the magnitude of the control variable D.

[0076] Furthermore, in the phase control of the continuous current mode, the control device 106a controls the phase of the edges of the drive pulses so that the sum of the time integral of the difference voltage between the primary AC voltage v1 and the secondary AC voltage v2 in the fifth period T5 and the time integral of the difference voltage between the primary AC voltage v1 and the secondary AC voltage v2 in the sixth period T6 is zero (see equation (3.1)).

[0077] Next, a specific example of phase control of the edges of the drive pulses Ga~Gh in continuous current mode will be explained. In the operation example in Figure 3, the polarity reversal of the primary AC voltage v1 (the start of the fourth period T4) is caused by the rising edges of the drive pulses Gc and / Gd. The polarity reversal of the primary AC voltage v1 has a phase angle π. Therefore, the phase angle θ of the rising edges of the drive pulses Gc and / Gd 34 This is calculated by the following equation (3.4). θ 34 =π ……(3.4)

[0078] Furthermore, the rise of the secondary AC voltage v2 to zero voltage (the start of the fifth period T5) is generated by the rising edges of the drive pulses Ge and Gf. The rising edge of the secondary AC voltage v2 to zero voltage has a phase angle δ. Therefore, the phase angle θ of the rising edges of the drive pulses Ge and Gf. 56 This is calculated by the following equation (3.5). θ 56 =δ =D-π ……(3.5)

[0079] Furthermore, the falling edge of the secondary AC voltage v2 from zero voltage (the start of the sixth period T6) occurs at the rising edge of the drive pulses Gg and / Gh. The falling edge of the secondary AC voltage v2 from zero voltage occurs at the phase angle θ 56 It has +π+φ. Therefore, the phase angle θ of the rising edge of the drive pulses Gg and / Gh. 78 This is calculated by the following equation (3.6). θ 78 =θ 56+π+φ =D-π+π+φ =D+φ =D+(1-A)(2π-D) =AD+2π(1-A) =(D-2π)A ……(3.6) The above describes the phase control of the continuous current mode in this embodiment.

[0080] Figure 4 is a waveform diagram showing an example of the overall operation of the power conversion system 100a. Referring to Figure 4 and Figure 11 above, the operation of this embodiment can be summarized as follows.

[0081] In this embodiment, when the control variable D is within the range of 0 ≤ D ≤ π, phase control in discontinuous current mode is performed. In this discontinuous current mode, there is no period (phase angle δ) during which the primary AC voltage v1 and the secondary AC voltage v2 are of opposite polarity. Furthermore, in discontinuous current mode, as the control variable D increases, the period during which both the low-voltage and high-voltage AC voltages maintain zero voltage (phase angle γ = π - D) decreases, and the period during which the high-voltage AC voltage maintains zero voltage (phase angle φ = π - AD) decreases.

[0082] In this discontinuous current mode, no reverse power is generated, and the power P transmitted between the primary and secondary sides is given by the following equation. P =((E1E2) / (ωL))A(1-A)D 2 / (2π) ……(4.1) In this discontinuous current mode, no reverse power is generated, allowing for power transmission with minimal losses when the DC voltage difference between the primary and secondary sides is small or under light load conditions.

[0083] In this embodiment, when the control variable D is within the range of π ≤ D ≤ 3π / 2, phase control in continuous current mode is performed. In this continuous current mode, there is no period (phase angle γ) during which both the primary AC voltage v1 and the secondary AC voltage v2 are at zero voltage. In continuous current mode, as the control variable D increases, the period during which the primary AC voltage v1 and the secondary AC voltage v2 are at opposite polarities (phase angle δ = D - π) increases, and the period during which the high-voltage AC voltage remains at zero voltage (phase angle φ = (1 - A)(2π - D)) decreases.

[0084] In this continuous current mode, power is transmitted by utilizing the period during which the primary AC voltage v1 and the secondary AC voltage v2 are of opposite polarity, and the power P transmitted between the primary and secondary sides is given by the following equation. P =((E1E2) / (ωL))(a(A)D 2 +b(A)D+c(A)) / (2π) ... (4.2) Here, a(A), b(A), and c(A) are as follows: a(A) = -(1 + A 2 ) ……(4.3) b(A) = (4A 2 -A+3)π ……(4.4) c(A) = -2(2A) 2 -A+1)π 2 ... (4.5) In this continuous current mode, a certain level of power can be transmitted over a wide voltage range. Furthermore, in continuous current mode, power can be transmitted with high efficiency even under heavy loads.

[0085] As shown in Figure 11, when the control variable D is varied from 0 to 3π / 2, the power P transmitted from the primary side to the secondary side changes continuously. Also, when the control variable D is π (see Figure 11(b)), the operating mode of this embodiment is the mode boundary between the discontinuous current mode and the continuous current mode. At this mode boundary, the phase angles δ, φ, and γ calculated assuming the discontinuous current mode coincide with the phase angles δ, φ, and γ calculated assuming the continuous current mode. Therefore, the change in the current waveform of the isolation transformer is continuous during the transition between the discontinuous current mode and the continuous current mode.

[0086] As described above, according to this embodiment, since phase control in discontinuous current mode or phase control in continuous current mode is performed by the magnitude of a single control variable D, power transmission between the primary and secondary sides can be performed with high efficiency over a wide voltage range.

[0087] Furthermore, according to this embodiment, since both phase control for discontinuous current mode and phase control for continuous current mode are performed by a single control variable D, the control is simple and stable.

[0088] Incidentally, the relationship between the control variable D and the transmitted power P of the isolated DC / DC converter 110 is illustrated in Figure 11 above. In the range where phase control in discontinuous current mode is performed (a), the change in transmitted power P with respect to the control variable D is gradual, but in the range where phase control in continuous current mode is performed (c), the change in transmitted power P with respect to the control variable D is steep. For this reason, when the control variable D is given to the control device 106a to perform phase control, it is difficult to achieve both stability in controlling the transmitted power P and responsiveness. Therefore, in this embodiment, as illustrated in Figure 5, the conversion unit 121 receives the power P or current I (current I in Figure 5) transmitted through the isolated DC / DC converter 110 over the entire range as input to the control variable I. DC The input control information I changes linearly with respect to DCThe control variable D is generated by applying a transformation. Here, "full range" means the entire range including the range of control variables in which phase control is performed in discontinuous current mode (a) and the range of control variables in which phase control is performed in continuous current mode (c).

[0089] Figure 6 is a block diagram showing the configuration of the control device 106a in this embodiment. As shown in Figure 6, the control device 106a is provided with a conversion unit 121 in front of the phase angle calculation unit 122 and the signal generation unit 123.

[0090] Here, the phase angle calculation unit 122 calculates the phase angle θ based on the control variable D and the ratio A of the low-voltage DC voltage to the high-voltage DC voltage. 12 , θ 34 , θ 56 and θ 78 This is a means for calculating the phase. The signal generation unit 123 is a means for generating drive pulses Ga~Gh with controlled phase based on the phase angle calculated by the phase angle calculation unit 122.

[0091] The conversion unit 121 uses the inverse function of the function that relates the control variable D to the power or current transmitted through the isolated DC / DC converter 110 to input control information I DC This is a means of generating a control variable D by applying a transformation.

[0092] In Figure 6, the conversion unit 121 includes a first conversion unit 121a, a second conversion unit 121b, and a switching unit 121c.

[0093] The first conversion unit 121a converts the input control information I by the inverse function of the function that relates the control variable D to the power or current (current in this example) transmitted in discontinuous current mode. DC This is a means of generating the first control variable D1 by applying a transformation to it.

[0094] The above equation (4.1) relates the control variable D to the power P transmitted in the discontinuous current mode. Dividing both the left and right sides of equation (4.1) by the voltage E1 yields the following equation (4.1a). I =(E2 / (ωL))A(1-A)D 2 / (2π) ……(4.1a)

[0095] Equation (4.1a) shows a function relating the control variable D to the current I transmitted in discontinuous current mode. The inverse function of equation (4.1a) is given by the following equation. D =√((ωL / E2)(2π / (A(1-A))I) ……(4.1b)

[0096] The first conversion unit 121a substitutes the given ratio A into equation (4.1b) and sets the input control variable I as the current I. DC By substituting this value, the control variable D is calculated and output as the first control variable D1.

[0097] The second conversion unit 121b converts the input control information I by the inverse function of the function that relates the control variable D to the power or current (current in this example) transmitted in continuous current mode. DC This is a means of generating a second control variable D2 by applying a transformation to it.

[0098] The above equation (4.2) relates the control variable D to the power P transmitted in the continuous current mode. Dividing both the left and right sides of equation (4.2) by the voltage E1 yields the following equation (4.2a). I =(E2 / (ωL))(a(A)D 2 +b(A)D+c(A)) / (2π) ... (4.2a)

[0099] Equation (4.2a) shows a function relating the control variable D to the current I transmitted in continuous current mode. The inverse function of equation (4.2a) is given by the following equation. D =(-1 / 2)(b(A) / a(A)) ±√((1 / 4)(b(A) 2 / a(A) 2 ) -((c(A) / a(A))-(2π / a(A))(ωL / E2)I)) ...(4.2b)

[0100] The second conversion unit 121b substitutes the given ratio A into equation (4.2b) and sets the input control variable I as the current I. DC By substituting this value, the control variable D is calculated and output as the second control variable D2.

[0101] The switching unit 121c selects the first control variable D1 and supplies it to the phase angle calculation unit 122 if the first control variable D1 falls within the range of the control variable D for which phase control of the discontinuous current mode should be performed, i.e., the range of 0 ≤ D ≤ π. As a result, the phase angle calculation unit 122 performs phase control of the discontinuous current mode based on the first control variable D1.

[0102] Furthermore, if the second control variable D2 falls within the range of the control variable D for which phase control of the continuous current mode should be performed, i.e., the range π ≤ D ≤ 3π / 2, the switching unit 121c selects the second control variable D2 and supplies it to the phase angle calculation unit 122. As a result, the phase angle calculation unit 122 performs phase control of the continuous current mode based on the second control variable D2.

[0103] As described above, in this embodiment, the input control variable I is obtained by the inverse function of the function that relates the control variable D to the transmitted power P or current I. DC Since the control variable D is generated by converting the input, the power P or current I can be changed linearly with respect to the input control variable IDC across the entire range, including the range of control variable D in discontinuous current mode and the range of control variable D in continuous current mode. Therefore, both the stability of the phase control and the responsiveness of the response can be achieved.

[0104] The above describes one embodiment of the present invention, but other embodiments are possible. For example, the following:

[0105] (1) In the above embodiment, Figures 2 and 3 show the relative phase relationship between the primary AC voltage v1 and the secondary AC voltage v2, and an example of the waveform of the drive pulse Ga~Gh to realize such a phase relationship. However, this waveform of the drive pulse Ga~Gh is merely an example, and it is possible to make the relative phase relationship between the primary AC voltage v1 and the secondary AC voltage v2 the same as in Figures 2 and 3 even if the waveform of the drive pulse Ga~Gh is changed. Therefore, the waveform of the drive pulse Ga~Gh can be changed as long as the relative phase relationship between the primary AC voltage v1 and the secondary AC voltage v2 can be made as shown in Figures 2 and 3.

[0106] (2) In the above embodiment, the operation of power transmission from the primary side to the secondary side has been described, but of course, power transmission from the secondary side to the primary side is also possible in the power conversion system 100a. In this case, the isolated DC / DC converter 110 should be controlled so that the phase relationship between the primary side AC voltage v1 and the secondary side AC voltage v2 in the above embodiment is reversed.

[0107] (3) In the above embodiment, the operation when the primary side is the low-voltage side and the secondary side is the high-voltage side has been described, but the operation is the same as in the above embodiment when the primary side is the high-voltage side and the secondary side is the low-voltage side. That is, when the primary side is the high-voltage side and the secondary side is the low-voltage side, in the description of the above embodiment, the high-voltage side should be the primary AC voltage v1 and the low-voltage side should be the secondary AC voltage v2.

[0108] (4) In the above embodiment, the first bridge circuit 111 and the second bridge circuit 112 were made into full bridge circuits, but they may also be made into half bridge circuits.

[0109] (5) In the above embodiment, the input control variable I is obtained by the inverse function of the function that relates the control variable D to the transmitted current I. DC The control variable D was generated by converting it, but the inverse function of the function relating the control variable D to the transmitted power P gives the input control variable I DC You may also convert this to generate the control variable D. [Explanation of Symbols]

[0110] 100, 100a... Power conversion system, 106, 106a... Control device, 110... Isolated DC / DC converter, 102... Isolation transformer, 104... Series inductor, 111... First bridge circuit, 112... Second bridge circuit, 101a~101h... Switching element, 103a, 103b... Capacitor, 105a, 105b... Drive circuit section, 107a, 107b... DC voltage detection section, 121... Conversion section, 121a... First conversion section, 121b... Second conversion section, 121c... Switching section, 122... Phase angle calculation section, 123... Signal generation section.

Claims

1. An isolation DC / DC converter comprising an isolation transformer, and an isolation DC / DC converter comprising a first bridge circuit and a second bridge circuit connected to the primary and secondary sides of the isolation transformer, respectively, each including at least one switching element, A DC voltage detection unit that detects both the primary DC voltage applied to the first bridge circuit and the secondary DC voltage applied to the second bridge circuit, A control device that generates drive pulses for each of the switching elements of the first bridge circuit and the second bridge circuit based on the primary side DC voltage and secondary side DC voltage detected by the DC voltage detection unit and a control variable, The system includes a drive circuit section that drives the switching elements of the first bridge circuit and the second bridge circuit based on the drive pulse, The control device is By controlling the phase of the edge of the drive pulse, a discontinuous current mode phase control is performed to control the period during which both the primary and secondary AC voltages of the isolation transformer are at zero voltage, or Phase control in continuous current mode, which controls the period during which the AC voltages on the primary and secondary sides of the isolation transformer are reversed polarity by controlling the phase of the edge of the drive pulse. This is executed according to the magnitude of the control variable, A power conversion system characterized in that, in the event of such a change, the input control information is transformed to generate the control variables so that the power or current transmitted through the isolated DC / DC converter changes linearly with respect to the input control variables over the entire range, including the range of control variables for which phase control is performed in the discontinuous current mode and the range of control variables for which phase control is performed in the continuous current mode.

2. The power conversion system according to claim 1, wherein the control device generates the control variable by performing a transformation on the input control information using the inverse function of a function that relates the control variable to the power or current transmitted via the isolated DC / DC converter.

3. The power conversion system according to claim 2, wherein the control device generates a first control variable by performing a transformation on the input control information using the inverse function of the function relating the control variable to the power or the current in the discontinuous current mode, and generates a second control variable by performing a transformation on the input control information using the inverse function of the function relating the control variable to the power or the current in the continuous current mode, and if the first control variable falls within the range of control variables for which phase control of the discontinuous current mode should be performed, the phase control of the discontinuous current mode is performed based on the first control variable, and if the second control variable falls within the range of control variables for which phase control of the continuous current mode should be performed, the phase control of the continuous current mode is performed based on the second control variable.

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