High-order resonance network analysis method based on local resonance theory

Abstract

The invention discloses a high-order resonance network analysis method based on a local resonance theory, and aims to solve the problems that a multi-element high-order resonance network is difficult to analyze quickly, the efficiency of establishing a target resonance network is low, a gain curve is difficult to acquire and the like. The high-order resonance network is divided into a single frequency band or a plurality of frequency bands; 2, analyzing local equivalent elements of the basic series / parallel resonance network according to a local resonance theory, and obtaining local resonance equivalent circuits of different frequency bands; and step 3, performing gain analysis on each frequency band according to the drawn equivalent circuit. According to the method, a basic series-parallel resonance network is researched, a corresponding equivalent circuit is obtained for each frequency point, a local resonance theory is summarized, and a more efficient and convenient analysis method is provided for a high-order resonance network based on the resonance theory. The invention belongs to the technical field of resonant converters.

Description

Technical Field

[0001] The invention relates to a high-order resonance network analysis method based on local resonance theory, and belongs to the technical field of resonance converters. Background Art

[0002] With the rapid development of modern industry, high-efficiency and high-power-density power converters are highly anticipated in many fields. In recent years, the gradually mature wide-bandgap semiconductor devices have made it possible to further increase the switching frequency and power density. Therefore, resonant converters suitable for high frequency and with wide-range soft switching performance will be more widely used.

[0003] At present, LLC resonant converter has much higher efficiency than traditional hard-switching circuits due to the ZVS-ON characteristic of the primary switch tube and the ZCS-OFF characteristic of the secondary diode, and it also greatly reduces the switching loss, which provides a possible way to further increase the switching frequency in line with the high-frequency trend of switching power supplies. Correspondingly, in recent years, in order to meet the needs of various applications, many modifications have been made to the LLC resonant cavity and many high-order derivative topologies have been designed. For example, the CL-LLC resonant converter with a notch filter improves the gain characteristics of the LLC high-frequency band, and the CLLLC resonant converter enables the LLC resonant network to have good bidirectional operation characteristics. However, these derivative topologies are all high-order resonant networks, which makes the working principle difficult to analyze. When using the conventional FHA analysis method, a large number of formulas need to be derived. When the order of the resonant network is high, the formula will become very complicated and not conducive to characteristic analysis, and it cannot provide guidance and suggestions for the subsequent improvement of other topologies, and cannot be applied to high-order resonant networks.

[0004] On the other hand, before constructing the resonant network, it is necessary to quickly analyze the selected resonant network. When using the fundamental wave analysis method, the gain change trend can only be determined by drawing a gain curve. When the gain formula cannot be obtained, it is difficult to obtain a gain curve. It is also difficult to analyze the specific working conditions of the circuit from the gain formula alone, and it is impossible to analyze the changes in the electrical parameters of each resonant component caused by frequency change. In response to this problem, many literatures have proposed a variety of high-order resonant converters, but there is still no systematic analysis method for high-order resonant networks. Summary of the invention

[0005] In order to solve the problems that the multivariate high-order resonant network is difficult to analyze quickly, the efficiency of establishing the target resonant network is low, and the gain curve is difficult to obtain, the present invention further proposes a high-order resonant network analysis method based on local resonance theory.

[0006] The technical solution adopted by the present invention to solve the above problems is:

[0007] The present invention provides a method for analyzing a high-order resonant network based on local resonance theory, comprising the following steps:

[0008] Step 1: Divide the high-order resonant network into a single or several frequency bands based on the full resonant frequency point or the special frequency point as the boundary;

[0009] Step 2: Analyze the local equivalent components (partial inductance or partial capacitance) of the basic series / parallel resonant network according to the local resonance theory, and obtain the local resonance equivalent circuits of different frequency bands;

[0010] Step 3: Perform gain analysis on each frequency band based on the drawn equivalent circuit.

[0011] Furthermore, in step 2,

[0012]

[0013] In the formula, ω s ,ω r are the power switching frequency and the resonant cavity resonant frequency respectively, L and C are the resonant inductance and resonant capacitance respectively, and L eq , C eq They are the equivalent inductance and equivalent capacitance obtained by equivalent the resonant unit using the local resonant network.

[0014] Furthermore, in step three, a gain analysis is performed on the local equivalent circuit of each frequency band, and a gain curve is obtained by integrating each frequency band.

[0015] Furthermore, the method for obtaining the gain curve is as follows:

[0016] Step 1: Analyze the composition of the gain according to the obtained equivalent circuit, and perform series voltage division analysis on each sub-gain, study the gain characteristics of each key frequency point, and obtain the gain curve of each frequency band;

[0017] Step 2: According to the obtained equivalent circuit, the load is short-circuited and open-circuited to obtain the effect of the load on the gain;

[0018] Step 3: Obtain a gain curve of the entire frequency band based on the gains of each frequency band.

[0019] The beneficial effects of the present invention are:

[0020] 1. The present invention studies the basic series-parallel resonant network, obtains the corresponding equivalent circuit for each frequency point, summarizes the local resonance theory, and based on the resonance theory, provides a more efficient and convenient analysis method for high-order resonant networks.

[0021] 2. The present invention takes the CLLLC resonant converter as an example and applies the local resonance theory to reduce the frequency band of the CLLLC five-element resonant network to a third-order resonant network, which can more clearly show the voltage division change process of each resonant element.

[0022] 3. The local resonance theory proposed in the present invention can be applied not only to CLLLC resonant converters, but also to the analysis of various other high-order resonant networks, helping to quickly build high-order resonant networks with specific functions and quickly analyze the gain curve of unknown high-order resonant networks. There is no need to derive complex formulas, thereby improving work efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the CLLLC resonant converter topology of the present invention;

[0024] Figure 2 It is the CLLLC frequency band reduction equivalent circuit of the local resonance theory of the present invention;

[0025] Figure 3 The gain characteristic of the CLLLC resonant converter based on the local resonance theory of the present invention is [0~ω m ];

[0026] Figure 4 The gain characteristic of the CLLLC resonant converter based on the local resonance theory of the present invention is [ω m ~ω r ];

[0027] Figure 5 The gain characteristic of the CLLLC resonant converter based on the local resonance theory of the present invention is [ω r ~∞];

[0028] Figure 6 is the gain characteristic of the CLLLC resonant converter using the local resonance theory of the present invention;

[0029] Figure 7 This is the gain characteristic of the CLLLC resonant converter using the fundamental wave analysis method of the present invention. DETAILED DESCRIPTION

[0030] Specific implementation method: This implementation method is described in conjunction with the accompanying drawings. This implementation method describes a high-order resonant network analysis method based on local resonance theory, wherein the local resonance theory includes the following contents:

[0031] (1) The basic resonant cavity in the resonant network is composed of two energy storage elements of different properties. It can be a series or parallel resonant network. The two energy storage elements have a resonant peak, and the resonant cavity is fully resonant.

[0032] (2) Under different power supply frequencies, a certain energy storage element in the basic resonant cavity can be divided into two partial elements (partial inductance or partial capacitance) in the form of series or parallel connection, and one of the two partial elements can undergo local full resonance with the other energy storage element, which is referred to as local resonance.

[0033] (3) The remaining partial components that do not participate in the local resonance are the equivalent impedance of the resonant cavity. This partial component can replace the original resonant cavity and other components in the circuit to re-form the circuit. In other words, a resonant element can be split into several partial components, each of which participates in different local resonances.

[0034] (4) When multiple local resonances occur, the components that do not participate in the local resonances can still form a basic resonant cavity and further cause local resonances.

[0035] According to the local resonance theory, the present invention performs equivalent analysis on the high-order resonant network according to the frequency band, and draws out the "frequency-dependent" equivalent circuit. The analysis method steps are as follows:

[0036] Step 1: Divide the high-order resonant network into a single or several frequency bands based on the full resonant frequency point or the special frequency point as the boundary;

[0037] Step 2: Analyze the local equivalent elements (partial inductance or partial capacitance) of the basic series / parallel resonant network according to the local resonance theory, and obtain the local resonance equivalent circuits of different frequency bands.

[0038]

[0039]

[0040] In the formula, ω s ,ω r are the power switching frequency and the resonant cavity resonant frequency respectively, L and C are the resonant inductance and resonant capacitance respectively, and L eq , C eq They are the equivalent inductance and equivalent capacitance obtained by equivalent the resonant unit using the local resonant network.

[0041] Step 3: Perform gain analysis on each frequency band according to the drawn equivalent circuit, and analyze separately according to the gain composition of the high-order resonant network.

[0042] In step 3, the gain curve is obtained by integrating each frequency band. The steps are as follows:

[0043] Step 3.1: Analyze the composition of the gain based on the equivalent circuit obtained, and perform series voltage division analysis on each sub-gain, study the gain characteristics of each key frequency point, and obtain the gain curve of each frequency band;

[0044] Step 3.2: Based on the obtained equivalent circuit, short-circuit and open-circuit the load to obtain the effect of the load on the gain.

[0045] Step 3.3 obtains the gain curve of the entire frequency band based on the gains of each frequency band obtained.

[0046] Example:

[0047] CLLLC resonant converter has been widely used in bidirectional OBC. The present invention uses the proposed local resonance theory to analyze the CLLLC converter with the following parameters. rs , C rs After equivalent conversion to the original side and L rp , C rp are equal, so here they are unified as L r , C r .

[0048] Table 1 CLLLC resonance parameters

[0049]

[0050] Figure 2 This is the schematic diagram of the T-type equivalent circuit of each frequency band of the CLLLC bidirectional resonant converter. e The equivalent resistance of the DC output resistance load after conversion to the primary side, the following three key frequencies are defined:

[0051]

[0052] Where k is the ratio of resonant inductance to excitation inductance. Converting the angular frequency to frequency can yield three frequencies: f r1 =100kHz, f f1 =28.9kHz, f f2 =39.27kHz.

[0053] (1) The switching frequency is 0 ≤ ω s ≤ω m Frequency band

[0054] When 0≤ω s ≤ω r When L r With C r Partial capacitance C r2 Local resonance occurs, and the remaining capacitance C r1 It does not participate in local resonance; since the resonant inductance and resonant capacitance of the primary and secondary sides are the same, the local resonance that occurs is the same, so the circuit can be equivalent to Figure 2 (a) shown.

[0055] Figure 2The circuit shown in (a) is a CLC equivalent circuit consisting of the residual circuit of the local resonant circuit. s ≤ω r For any switching frequency between r The remaining capacitance C r1 Gradually from C r Increases to infinity, there is further local resonance phenomenon for this circuit, which will be analyzed below.

[0056] For the CLC circuit composed of the remaining circuits, L can be calculated separately r With C r Part of the capacitance C involved in local resonance r2 , and the remaining capacitance C that does not participate in the local resonance r1 :

[0057]

[0058] At 0≤ω s ≤ω r Frequency band, as ω s From 0 to ω r , local resonant capacitance C r2 Continuously decreases, gradually decreasing from infinity to C r ; Residual capacitance C r1 Gradually increases from C r Increase to infinity.

[0059] Analyzing its gain, from the perspective of the CLC equivalent circuit, the load R e The voltage is mainly composed of two parts: the secondary residual capacitance C r1 The series voltage divider G1 of the load and the residual capacitance C of the primary side r1 The series voltage divider G2 of the parallel branch. s = 0, the secondary side residual capacitance C r1 The corresponding reactance is infinite, and the excitation inductance L m The corresponding reactance is 0, and the two gains of the load can be calculated as:

[0060]

[0061] Therefore, when ω s =0, the gain is 0. s As the secondary side residual capacitance C r1 It gradually increases while the corresponding reactance gradually decreases, so the series voltage divider G1 gradually increases.

[0062]

[0063] In addition, according to the parallel characteristics, the impedance of the parallel circuit is less than the impedance value of any parallel branch. It can be seen from the parallel branch curve that when ω s When it gradually increases from 0, the impedance of the parallel circuit is approximately equal to the impedance of the excitation inductance branch in the low frequency band.

[0064]

[0065] The residual capacitance C r1 The corresponding reactance also gradually increases and decreases, so the series voltage divider G2 gradually increases, and the total gain increases:

[0066]

[0067] When the load R e When it is equal to 0, the impedance of the parallel branch becomes:

[0068] Z1(ω s )=jω s L m P1 / jω s C r1 (12)

[0069] For the series voltage divider G2, when the switching frequency increases from 0 to ω f1 hour,

[0070]

[0071] Therefore, the load R e When it is equal to 0, in [0~ω f1 ] frequency band, the series voltage dividers G1 and G2 are gradually increased.

[0072] When the load R e When it is equal to infinity, the impedance of the parallel branch becomes:

[0073] Z1(ω s )=jω s L m (14)

[0074] For the series voltage divider G2, when the switching frequency increases from 0 to ω f2 hour,

[0075]

[0076] Therefore, the load R e When it is equal to 0, in [0~ω f2 ] frequency band, the series voltage dividers G1 and G2 are gradually increased.

[0077] In summary, when the load R eIn the process of increasing from 0 to infinity, the series voltage divider G2 has a maximum gain frequency point ω f1 ≤ω m ≤ω f2 Therefore, we can simply draw the change process of the series voltage divider G1 and G2 with frequency as shown in Figure 3 shown.

[0078] The DC gain of CLLLC resonant converter is in [0~ω m ] The frequency band is increasing, but when the load R e When the series voltage divider G1 is small, the gain is small, so the gain change trend is: CLLLC five-element resonant network in [0~ω m ]With the load R e As the value of is increasing, the maximum gain peak value is increasing.

[0079] (2) The switching frequency is ω m ≤ω s ≤ω r Frequency band

[0080] When the switching frequency reaches the maximum gain frequency point ω m When the series voltage divider G2 reaches its maximum value, m ~ω r ] frequency band series voltage divider G2 will gradually decrease. As the frequency continues to increase, the resonant inductor L r The local resonant network composed of the resonant capacitor, the capacitor C participating in the local resonance r2 As the frequency decreases, the remaining resonant capacitance C r1 As the frequency gradually increases, when the switching frequency increases to ω r When the resonant capacitor C r Fully participate in the resonance, so CLLLC in ω r The local resonance equivalent circuit at is Figure 2 (b) as shown.

[0081] For all loads R e For example, the series voltage divider G2 will eventually be at the resonant frequency ω r Gathered at 1,

[0082]

[0083] Correspondingly, for the series voltage divider G1, due to the residual resonant capacitance C on the secondary side r1 becomes infinite, that is, the corresponding reactance is reduced to 0, and at this time the secondary branch only has load R e ,but:

[0084]

[0085] Therefore, we can draw [ω m ,ω r ] The gain curve of the frequency band is as follows Figure 4 shown.

[0086] (3) The switching frequency is ω r ≤ω s Frequency band

[0087] When the switching frequency is higher than the resonant frequency ω r When the resonant inductor L r With the resonant capacitor C r The local resonant cavity formed has a resonant capacitor C at any frequency point in this frequency band. r and resonant inductor L r The partial inductance L r2 Local resonance occurs, and the residual inductance L r1 The energy storage element that does not participate in the local resonance constitutes the LLL resonant converter. In this structure, since the circuit as a whole is inductive, there will be no local resonance phenomenon. The circuit becomes a simple series-parallel voltage divider. Figure 2 (c) It is easier to perform gain analysis.

[0088] For the inductor L involved in local resonance r2 and the residual inductance L r1 The solution is as follows:

[0089]

[0090] When the switching frequency ω s =ω r At this time, the resonant inductor L r Fully participate in the resonance with the capacitor C r In the full resonance, the inductor L participating in the local resonance r2 Equal to the resonant inductance L r , accordingly, the residual inductance L that does not participate in the local resonance r1 =0. As the switching frequency increases, the inductor L r2 Continuously decreases and eventually decreases to 0; the residual inductance L r1 It keeps increasing, and eventually increases to infinity.

[0091] The series voltage divider G1 gradually decreases:

[0092]

[0093] The series voltage divider G2 depends on the rate of increase of the total impedance of the circuit and the rate of increase of the impedance of the parallel circuit:

[0094] Z2(ω s )=jωs L m P(jω s L r1 +R e ) (twenty one)

[0095] Since the impedance of the two parallel branches increases with frequency, the total impedance Z2 of the parallel branches also increases, and the series voltage divider G2 is:

[0096]

[0097] Since the impedance of the residual resonant inductance on the primary side increases much faster with frequency than the impedance of the parallel branch, the series voltage divider G2 also shows a decreasing trend. Therefore, [ω r ~∞] band gain curve is as follows Figure 5 shown.

[0098] In summary, the approximate gain characteristic curve of the CLLLC five-element resonant converter can be drawn without using formula derivation as follows: Figure 6 shown.

[0099] At the same time, the voltage gain analysis of the CLLLC resonant converter is also performed through the "fundamental wave analysis method", and the gain curve is drawn using relevant software. Figure 7 As shown in the figure, by comparing the curve trends, it is found that the gain curve obtained by using the local resonance theory is basically consistent with the gain curve obtained by using the "fundamental wave analysis method", and the key frequencies are completely consistent, which realizes the rapid analysis of the gain curve of the unknown high-order resonant network.

[0100] The above is only a preferred embodiment of the present invention and does not limit the present invention in any form. Although the present invention has been disclosed as a preferred embodiment as above, it is not used to limit the present invention. Any technician familiar with this profession can make some changes or modify the technical contents disclosed above into equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement made to the above embodiments without departing from the content of the technical solution of the present invention, based on the technical essence of the present invention, within the spirit and principles of the present invention, still fall within the protection scope of the technical solution of the present invention.

Claims

1. A high-order resonant network analysis method based on local resonance theory, characterized in that: The method comprises the following steps: Step 1: Divide the high-order resonant network into a single or several frequency bands based on the full resonant frequency point or the special frequency point as the boundary; Step 2: Analyze the local equivalent components of the basic series / parallel resonant network according to the local resonance theory, and obtain the local resonance equivalent circuits of different frequency bands; Step 3: Perform gain analysis on each frequency band based on the drawn equivalent circuit.

2. The high-order resonant network analysis method based on local resonance theory according to claim 1 is characterized in that: In step 2, Parallel resonant network equivalent Series resonant network equivalent In the formula, ω s is the power switching frequency; ω r is the resonant frequency of the resonant cavity; L is the resonant inductance; C is the resonant capacitance; L eq and C eq They are the equivalent inductance and equivalent capacitance obtained by equivalent the resonant unit using the local resonant network.

3. The high-order resonant network analysis method based on local resonance theory according to claim 1 is characterized in that: In step 3, gain analysis is performed on the local equivalent circuit of each frequency band, and gain curves are obtained by integrating each frequency band.

4. The high-order resonant network analysis method based on local resonance theory according to claim 3 is characterized in that: The method to obtain the gain curve is as follows: Step 3.1, analyze the composition of the gain according to the obtained equivalent circuit, and perform series voltage division analysis on each sub-gain, study the gain characteristics of each key frequency point, and obtain the gain curve of each frequency band; Step 3.2, according to the obtained equivalent circuit, conduct short-circuit and open-circuit studies on the load to obtain the effect of the load on the gain; Step 3.3: Obtain the gain curve of the entire frequency band based on the gains of each frequency band.

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