CN111709202B - Two-stage DC-DC converter small signal harmonic equivalent circuit modeling method based on harmonic steady state value - Google Patents
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Abstract
The invention discloses a two-stage DC-DC converter small-signal harmonic equivalent circuit modeling method based on harmonic steady state values, which comprises the steps of determining duty ratios according to voltage requirements of front and rear stages of a DC/DC converter to form a harmonic state space model under the steady state condition; obtaining harmonic steady state values of all state variables by the harmonic state space model; adding small disturbance to each input variable in the harmonic state space model to form a harmonic small signal model; generating a plurality of harmonic equivalent circuits containing controlled sources based on the harmonic small signal model and harmonic steady state values of all state variables; and forming a two-stage DC/DC converter small-signal harmonic equivalent circuit based on the equivalent controlled source relation of the harmonic equivalent circuits containing the controlled sources. According to the invention, an equivalent circuit construction method is provided according to a DC-DC converter harmonic model, and finally a harmonic equivalent circuit of the DC-DC converter is obtained, so that the organic combination of a mathematical principle and circuit characteristics is realized.
Description
Technical Field
The invention belongs to the field of power electronics modeling, and particularly relates to a two-stage DC-DC converter harmonic equivalent circuit modeling method based on a harmonic state space.
Background
At present, for modeling of the converter, a state space averaging method based on linear time variation is widely used, but the accuracy is low, and the actual dynamic process of the high-frequency converter cannot be reflected well. In recent years, a harmonic state space-based modeling method is applied to modeling of power electronic variable devices, which analyzes harmonic coupling characteristics and harmonic stability by adding additional harmonic impedance. However, the harmonic state space modeling method is mainly used for modeling single power electronic equipment at present, and when facing a system with multiple converters, a state equation in a pure mathematical form is too abstract, and a circuit characteristic method deeper than general numerical simulation is urgently needed to be combined with harmonic state space mathematical description.
Disclosure of Invention
Aiming at the problems, the invention firstly provides an equivalent circuit construction method according to a DC-DC converter harmonic model, and finally obtains a harmonic equivalent circuit of the DC-DC converter, thereby realizing the organic combination of mathematical principles and circuit characteristics.
In order to achieve the technical purpose and achieve the technical effect, the invention is realized by the following technical scheme:
a two-stage DC-DC converter small signal harmonic equivalent circuit modeling method based on harmonic steady state values comprises the following steps:
determining a duty ratio according to the voltage requirements of the front stage and the rear stage of the DC/DC converter, and forming a harmonic state space model under the steady state condition;
obtaining harmonic steady state values of all state variables by the harmonic state space model;
adding small disturbance to each input variable in the harmonic state space model to form a harmonic small signal model;
generating a plurality of harmonic equivalent circuits containing controlled sources based on the harmonic small signal model and harmonic steady state values of all state variables;
and forming a two-stage DC/DC converter small-signal harmonic equivalent circuit based on the equivalent controlled source relation of the harmonic equivalent circuits containing the controlled sources, and completing modeling of the two-stage DC/DC converter harmonic equivalent circuit.
Optionally, the harmonic state space model is specifically:
wherein s is a complex number and represents the dynamic behavior of the state variable in the frequency domain; o is 2h+1 order zero matrix, I is 2h+1 order identity matrix, and h is truncated harmonic frequency; c (C) 1 Is the front-stage capacitance parameter L of a two-stage DC-DC converter 1 Is the front-stage inductance parameter, C of the two-stage DC-DC converter 2 Is the post-stage capacitance parameter L of the two-stage DC-DC converter 2 The inductor is a rear-stage inductance parameter of the two-stage DC-DC converter, and R is a load parameter of the two-stage DC-DC converter; Λ=diag (-j 2 pi hf) 0 ,…-j2πf 0 ,0,j2πf 0 ,…-j2πhf 0 ) Displaying the harmonic information of the state variables; d (D) 1 And D 2 For 2h+1 th order from d 1 (t) and d 2 (t) expanded double toeplitz matrix, I L1 、U C1 、I L2 、U C2 V (V) 1 A vector representing the frequency domain magnitudes of each of the positive and negative subharmonics.
Alternatively, the process may be carried out in a single-stage,
alternatively, the process may be carried out in a single-stage,
alternatively, the process may be carried out in a single-stage,
alternatively, the process may be carried out in a single-stage,I L2 ＝[I L2-h ,…,I L20 ,…,I L2h ] T ；U C1 ＝[U C1-h ,…,U C10 ,…,U C1h ] T ；U C2 ＝[U C2-h ,…,U C20 ,…,U C2h ] T 。
optionally, the calculation formula of the harmonic steady-state value of each state variable is:
wherein O is 2h+1 order zero matrix, I is 2h+1 order identity matrix, and h is truncated harmonic frequency; c (C) 1 Is the front-stage capacitance parameter L of a two-stage DC-DC converter 1 Is the front-stage inductance parameter, C of the two-stage DC-DC converter 2 Is the post-stage capacitance parameter L of the two-stage DC-DC converter 2 The inductor is a rear-stage inductance parameter of the two-stage DC-DC converter, and R is a load parameter of the two-stage DC-DC converter; Λ=diag (-j 2 pi hf) 0 ,…-j2πf 0 ,0,j2πf 0 ,…-j2πhf 0 ) Displaying the harmonic information of the state variables; d (D) 1 And D 2 For 2h+1 th order from d 1 (t) and d 2 (t) expanded double toeplitz matrix, I L1ss 、U C1ss 、I L2ss U and U C2ss Representation I L1 、U C1 、I L2 U and U C2 Is 2h+1 dimension vector form; v (V) 1 A 2h+1-dimensional vector representing the frequency domain magnitudes of the preceding input voltage harmonics.
Optionally, the harmonic small signal model is:
in the formula DeltaV 1 The input voltage disturbance quantity is 2h+1-dimensional vector form; ΔD of 1 、ΔD 2 The duty ratio disturbance quantity is 2h+1-order double-toplitz matrix form; ΔI L1 、ΔU C1 、ΔI L1 、ΔU C2 The disturbance quantity of the four state variables is in the form of 2h+1-dimensional vector.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention is convenient to form a transfer function based on frequency domain harmonic by constructing a small signal harmonic model, and is beneficial to designing a controller based on frequency domain harmonic space so as to explore the influence of system harmonic on the system steady state;
2. the invention realizes mapping of the mathematical model to the circuit model, is beneficial to understanding of the harmonic model, and has reference significance for establishing a harmonic equivalent circuit and analyzing stability of the AC/DC hybrid power distribution network in the background of the multi-transformer.
Drawings
In order that the invention may be more readily understood, a more particular description of the invention will be rendered by reference to specific embodiments that are illustrated in the appended drawings, in which:
FIG. 1 is a topology of a two-stage DC/DC converter;
FIG. 2 is a harmonic equivalent circuit represented by equation 7 (a);
FIG. 3 is a harmonic equivalent circuit represented by equation 7 (b);
fig. 4 is a harmonic equivalent circuit represented by formula 7 (c);
fig. 5 is a harmonic equivalent circuit represented by formula 7 (d);
FIG. 6 is a diagram of the resulting unified two-stage DC/DC converter harmonic equivalent circuit;
FIG. 7 is a flow chart of a method for modeling a harmonic equivalent circuit of a two-stage DC-DC converter based on a harmonic state space according to the present invention;
FIG. 8 is a schematic diagram of a process for processing variables into vector form.
Detailed Description
The present invention will be described in further detail with reference to the following examples in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the invention.
The principle of application of the invention is described in detail below with reference to the accompanying drawings.
The invention discloses a two-stage DC-DC converter harmonic equivalent circuit modeling method based on harmonic state space, which adopts topology of front-stage Buck and rear-stage Boost to equivalent DC/DC converter with Buck and Boost functions in a DC power distribution network, wherein the front-stage parameter is inductance L 1 =1.6 mH, capacitance C 1 =15 μf, input voltage V 1 =80v, switching period function d 1 (t) information is the switching frequency f 1 =8khz, the required voltage on the capacitor is 56V; the latter parameter is inductance L 2 =1.2 mH, capacitance C 2 =20 μf, load R 2 =20Ω, switching period function d 2 (t) information is the switching frequency f 2 =10khz, output load voltage 70V. The modeling method specifically comprises the following steps:
step1: from the preceding capacitor voltage, the duty cycle d is determined 1 =70%; the duty ratio d is obtained by the requirement of the output voltage of the rear stage 2 =20%. At this time, the time domain state space equation of the two-stage DC/DC converter can be obtained as formula (1):
in the formula (1), d 1 (t) is the corresponding d 1 Rectangular wave with frequency of 8kHz, duty ratio of 70% and phase of 0; d, d 2 (t) is the corresponding d 2 Rectangular wave with frequency of 10kHz, duty cycle of 20% and phase of 0. The time-varying state equation can be converted into a steady harmonic state space equation of a frequency domain, which is shown as a formula (2), namely a harmonic state space model under a steady state condition.
S in the formula (2) is a complex number and represents the dynamic behavior of the state variable in the frequency domain; o is 2h+1 order zero matrix, I is 2h+1 order identity matrix, and h is truncated harmonic frequency; c (C) 1 For the topological pre-stage capacitance parameter of FIG. 1, L 1 For the topological pre-stage inductance parameter of FIG. 1, C 2 For the topological back-end capacitance parameter of FIG. 1, L 2 For the topological post-stage inductance parameter of fig. 1, R is the load (resistance) parameter of the topology of fig. 1; Λ=diag (-j 2 pi hf) 0 ,…-j2πf 0 ,0,j2πf 0 ,…-j2πhf 0 ) The state variable harmonic information is displayed. D (D) 1 And D 2 For 2h+1 th order from d 1 (t) and d 2 (t) expanded double toeplitz matrix as formula (3), I L1 、U C1 、I L2 、U C2 V (V) 1 The form of equation (4) represents a vector of frequency domain magnitudes of the positive and negative harmonics.
I L1 ＝[I L1-h ,…,I L10 ,…,I L1h ] T ；I L2 ＝[I L2-h ,…,I L20 ,…,I L2h ] T
U C1 ＝[U C1-h ,…,U C10 ,…,U C1h ] T ；U C2 ＝[U C2-h ,…,U C20 ,…,U C2h ] T (4)
Step2: and obtaining a harmonic equivalent circuit and harmonic steady state values of all variables by using a harmonic state space model under the steady state condition in Step1, namely enabling the left side of the equal sign of the formula (2) to be zero, and obtaining the steady state values of the state variables as shown in the formula (5).
Step3: adding each input variable of the harmonic state space model under steady state condition in Step1 into small disturbance, and inputting voltage V 1 And front-rear stage duty ratio d 1 、d 2 In the vicinity of the steady-state operating point, i.e. in equation (2), let V 1 ＝V 1ss +ΔV 1 ，D 1 ＝D 1ss +ΔD 1 ，D 2 ＝D 2ss +ΔD 2 Thereby causing small disturbances of the state variables in the two-stage DC/DC converter circuit, i.e L1 ＝I L1ss +ΔI L1 ,U C1 ＝U C1ss +ΔU C1 ,I L2 ＝I L1ss +ΔI L1 ,U C2 ＝U C2ss +ΔU C2 . Then the formula (2) is transformed into the formula (6), wherein Λ is a block diagonal matrix formed by n diagonal matrixes Λ, and n is the number of independent state variables or energy storage elements in the topology; h is the number of truncated harmonics in modeling, and the larger the number is, the more harmonic information is contained; f (f) 0 For harmonic fundamental frequencies, a divisor of the switching frequency is generally selected to include harmonic information of the switching frequency.
s(X ss +ΔX)＝(A ss +ΔA-Λ)(X ss +ΔX)+(B ss +ΔB)(V ss +ΔV)＝(A ss -Λ)X ss +B ss V ss +(A ss -Λ)ΔX+ΔAX ss +B ss ΔV+ΔBV ss (6)
B ss ＝[D 1ss /L 1 O O O] T ΔB＝[ΔD 1 /L 1 O O O] T
Λ＝diag(Λ) n Λ＝diag(-j2πhf 0 ,…,-j2πf 0 ,0,j2πf 0 ,…,j2πhf 0 )
Four independent small signal harmonic expressions are available at this time:
in order to form the state equation in the conventional form, the variables need to be processed into vector form, so for ΔD in equation (7) 1 、ΔD 2 、V 1ss 、I L2ss 、U C2ss Performing transformation in the form of FIG. 8 to extract ΔD 1 、ΔD 2 Transforming it from a bipolartz matrix form into column vectors, V 1ss 、I L2ss 、U C2ss The vector form is transformed into a double toeplitz matrix, and the transformation is followed by: ΔD of 1 V 1ss ＝V′ 1ss ΔD′ 1 ，ΔD 2 U C2ss ＝U′ C2ss ΔD′ 2 ，ΔD 2 I L2ss ＝I′ L2ss ΔD′ 2 The three formulas are established, and the harmonic small signal equation of the two-stage DC/DC converter is in the form of formula (8).
Step4: various equivalent circuits are drawn according to the harmonic small signal model in Step3 and the harmonic steady state value of the variable, such as fig. 2, fig. 3, fig. 4 and fig. 5.
Fig. 2 is a schematic diagram of an equivalent controlled voltage source DeltaU C1 Equivalent voltage source D 1ss ΔV 1 、ΔD 1 V 1ss Equivalent inductance L with harmonic wave 1 I composition, deltaU C1 、D 1ss ΔV 1 And V is equal to 1ss ΔD 1 Are all 2h+1-dimensional vectors, the form is as shown in formula (4), and the vector contains + -h harmonic information and 0 direct current component, delta U C1 The control amount is DeltaU C1 The control coefficient is a unit matrix I; l (L) 1 I is 2h+1 order matrix form. The current in the loop is ΔI L1 The form is shown as a formula (4); the voltage on the inductor is L 1 I(sI+Λ)ΔI L1 。
Fig. 3 is a schematic diagram of an equivalent controlled current source Δi L1 Equivalent controlled current source ΔI L2 Harmonic equivalent capacitance C 1 I composition. ΔI L1 、ΔI L2 Is 2h+1 dimension vector, the form is as formula (4), C 1 I is 2h+1 order matrix form, and the voltage at two ends of the equivalent capacitor is delta U C1 Is 2h+1 dimension vector; ΔI L1 The control amount is delta I L1 Control coefficient I, deltaI L2 The same situation applies; the equivalent harmonic current flowing through the capacitor is C 1 I(sI+Λ)ΔU C1 。
Fig. 4 is a schematic diagram of an equivalent controlled voltage source DeltaU C1 Equivalent controlled voltage source (I-D 2ss )ΔU C2 Equivalent voltage source delta D 2 U C2ss Harmonic equivalent inductance L 2 I composition. DeltaU C1 、ΔU C2 、ΔI L2 Is 2h+1 dimension vector, the form is as formula (4), L 2 I is 2h+1 order matrix form; deltaU C1 The control amount is DeltaU C1 Control coefficient I, (I-D) 2ss )ΔU C2 The control amount is DeltaU C2 Control coefficient I-D 2ss The method comprises the steps of carrying out a first treatment on the surface of the The voltage at two ends of the equivalent inductance is L 2 I(sI+Λ)ΔI L2 Is 2h+1-dimensional vector.
Fig. 5 is a schematic diagram of an equivalent controlled current source (I-D 2ss )ΔI L2 Equivalent current source DeltaD 2 I L2ss Harmonic equivalent capacitance C 2 I. Harmonic equivalent capacitance RI. ΔI L2 Is 2h+1 dimension vector, the form is as formula (4), C 2 I and RI are 2h+1 order matrix form, and the voltage at two ends of the equivalent capacitor is DeltaU C2 Is 2h+1 dimension vector; (I-D) 2ss )ΔI L2 The control amount is delta I L2 Control coefficient I-D 2ss The method comprises the steps of carrying out a first treatment on the surface of the The equivalent harmonic current flowing through the capacitor is C 2 I(sI+Λ)ΔU C2 。
The values of the equivalent harmonic inductance LI, the equivalent harmonic capacitance CI and the equivalent harmonic resistance RI are in a diagonal array form in a formula (9), and represent that the equivalent harmonic inductance LI, the equivalent harmonic capacitance CI and the equivalent harmonic resistance RI have dynamic effects on all times of harmonic waves; the differential relationship of inductor current and capacitor voltage in the original time domain is expressed in the harmonic frequency domain as LI (si+Λ) Δi L And CI (sI+Λ) ΔU C . Wherein LI (sI+Λ) ΔI L Represents the harmonic voltage across the equivalent harmonic inductance, CI (sI+Λ) ΔU C Representing the harmonic current through the equivalent harmonic inductance.
LI＝diag(L) 2h+1 CI＝diag(C) 2h+1 RI＝diag(R) 2h+1 (9)
Step5: the controlled sources in fig. 2, 3, 4 and 5 are equivalent to a harmonic equivalent circuit coupled by a transformer according to the characteristics of an ideal transformer, as shown in fig. 6, and are composed of a harmonic equivalent inductance L 1 I and L 1 I. Harmonic equivalent capacitance C 2 I and C 1 I. Harmonic equivalent resistor RI and harmonic equivalent power supply D 1ss ΔU C 、ΔD 1 V 1ss 、ΔD 2 U C2ss And delta D 2 I L2ss A harmonic equivalent transformer composition, wherein the harmonic equivalent transformer transformation ratio is I-D 2ss : I. the equivalent controlled sources whose controlled coefficients are the identity matrix I in fig. 2-5 are directly interconnected in the circuit of fig. 6.
Further, KCL and KVL are written into the harmonic equivalent circuit column, the formula (8) can be reversely deduced, the correctness of the harmonic equivalent circuit is verified, and the construction of the harmonic equivalent circuit model of the two-stage DC/DC converter is completed.
The foregoing has shown and described the basic principles and main features of the present invention and the advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (5)
1. A two-stage DC-DC converter small signal harmonic equivalent circuit modeling method based on harmonic steady state values is characterized by comprising the following steps:
determining a duty ratio according to the voltage requirements of the front stage and the rear stage of the DC/DC converter, and forming a harmonic state space model under the steady state condition;
obtaining harmonic steady state values of all state variables by the harmonic state space model;
adding small disturbance to each input variable in the harmonic state space model to form a harmonic small signal model;
generating a plurality of harmonic equivalent circuits containing controlled sources based on the harmonic small signal model and harmonic steady state values of all state variables;
forming a two-stage DC/DC converter small-signal harmonic equivalent circuit based on the equivalent controlled source relation of each harmonic equivalent circuit containing a controlled source, and completing modeling of the two-stage DC-DC converter harmonic equivalent circuit;
the harmonic state space model specifically comprises the following steps:
wherein s is a complex number and represents the dynamic behavior of the state variable in the frequency domain; o is 2h+1 order zero matrix, I is 2h+1 order identity matrix, and h is truncated harmonic frequency; c (C) 1 Is the front-stage capacitance parameter L of a two-stage DC-DC converter 1 Is the front-stage inductance parameter, C of the two-stage DC-DC converter 2 Is the post-stage capacitance parameter L of the two-stage DC-DC converter 2 The inductor is a rear-stage inductance parameter of the two-stage DC-DC converter, and R is a load parameter of the two-stage DC-DC converter; Λ=diag (-j 2 pi hf) 0 ,…-j2πf 0 ,0,j2πf 0 ,…-j2πhf 0 ) Displaying the harmonic information of the state variables; d (D) 1 And D 2 For 2h+1 th order from d 1 (t) and d 2 (t) expanded double toeplitz matrix, d 1 (t) is a rectangular wave having a frequency of 8kHz, a duty cycle of 70% and a phase of 0; d, d 2 (t) is a rectangular wave having a frequency of 10kHz, a duty cycle of 20% and a phase of 0, I L1 、U C1 、I L2 、U C2 V (V) 1 A vector representing the frequency domain magnitudes of each of the positive and negative subharmonics;
the calculation formula of the harmonic steady state value of each state variable is as follows:
wherein O is 2h+1 order zero matrix, I is 2h+1 order identity matrix, and h is truncated harmonic frequency; c (C) 1 Is the front-stage capacitance parameter L of a two-stage DC-DC converter 1 Is the front-stage inductance parameter, C of the two-stage DC-DC converter 2 Is the post-stage capacitance parameter L of the two-stage DC-DC converter 2 The inductor is a rear-stage inductance parameter of the two-stage DC-DC converter, and R is a load parameter of the two-stage DC-DC converter; Λ=diag (-j 2 pi hf) 0 ,…-j2πf 0 ,0,j2πf 0 ,…-j2πhf 0 ) Displaying the harmonic information of the state variables; d (D) 1 And D 2 For 2h+1 th order from d 1 (t) and d 2 (t) expanded double toeplitz matrix, I L1ss 、U C1ss 、I L2ss U and U C2ss Representation I L1 、U C1 、I L2 U and U C2 Is 2h+1 dimension vector form; v (V) 1 A 2h+1-dimensional vector representing the frequency domain amplitude of the preceding input voltage harmonic;
the harmonic small signal model is as follows:
in the formula DeltaV 1 The input voltage disturbance quantity is 2h+1-dimensional vector form; ΔD of 1 、ΔD 2 The duty ratio disturbance quantity is 2h+1-order double-toplitz matrix form; ΔI L1 、ΔU C1 、ΔI L1 、ΔU C2 The disturbance quantity of the four state variables is in the form of 2h+1-dimensional vector.
2. The two-stage DC-DC converter small signal harmonic equivalent circuit modeling method based on harmonic steady state values according to claim 1, wherein the method comprises the following steps:
3. the method for modeling a small-signal harmonic equivalent circuit of a two-stage DC-DC converter based on harmonic steady-state values according to claim 1, wherein,
4. the method for modeling a small-signal harmonic equivalent circuit of a two-stage DC-DC converter based on harmonic steady-state values according to claim 1, wherein,
5. the two-stage DC-DC converter small signal harmonic equivalent circuit modeling method based on harmonic steady state values as defined in claim 1, wherein I L1 ＝[I L1-h ,…,I L10 ,…,I L1h ] T ；I L2 ＝[I L2-h ,…,I L20 ,…,I L2h ] T ；U C1 ＝[U C1-h ,…,U C10 ,…,U C1h ] T ；U C2 ＝[U C2-h ,…,U C20 ,…,U C2h ] T 。
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