CN114186400B - Equivalent modeling method of power electronic transformer based on H-bridge constant admittance unit - Google Patents

Abstract

The invention relates to an equivalent modeling method (equivalent modeling method of power electronic transformer(PET)based on H-bridge fixed admittance unit), of a power electronic transformer based on an H-bridge type admittance unit, which mainly aims at cascading H-bridge type PET (CASCADED H-bridge-type PET, CHB-PET) in an input-series-output-parallel (input series output parallel, ISOP) mode. The core technical scheme of the invention is as follows: 1. adopting a transformer port decoupling idea to form a power module accompanying circuit; 2. deducing an H-bridge type constant admittance unit by utilizing short circuit shrinkage to obtain a power module equivalent circuit; 3. forming a CHB-PET dual-port decoupling equivalent model by considering an ISOP type connection mode; 4. and (5) accessing an external circuit to calculate the electric quantity of the port, and inversely solving the internal information of the admittance unit.

Description

Equivalent modeling method of power electronic transformer based on H-bridge constant admittance unit

Technical Field

The invention relates to an equivalent modeling method for a power electronic transformer based on an H-bridge type constant admittance unit, and belongs to the technical field of power system simulation.

Background Art

The electromagnetic transient simulation of power electronic transformer (PET) faces the huge challenge of "high matrix order, small simulation step size, and low simulation efficiency". The existing PET serial equivalent model uses the nested fast simultaneous solution method to reduce the number of system nodes, which has a significant speed-up effect, but there is an uncertainty in admittance. During the elimination process, the matrix inversion needs to be performed at each step to update the admittance value, which will affect the simulation efficiency when the number of modules is large.

Aiming at the problem of low efficiency of electromagnetic transient simulation of power electronic transformer, the present invention proposes a power electronic transformer equivalent modeling method based on H-bridge type constant admittance unit. Taking the 4-node H-bridge circuit commonly seen in PET as a unit, the constant admittance equivalent circuit is derived by using short-circuit contraction, and the PET serial equivalent model is generated by combining according to the connection mode. The model establishment process avoids matrix inversion operation, saves computing resources, and improves the model simulation rate.

Summary of the invention

The present invention provides a method for establishing a CHB-PET electromagnetic transient equivalent model based on an H-bridge type constant admittance unit, and the modeling method comprises the following steps:

Step 1: Equivalently treat the switch group as a binary resistor, discretize the transformer and energy storage element, use the port voltage single-step approximation to decouple the primary and secondary sides of the transformer, and obtain the accompanying circuit of the power module.

Step 2: Divide the power module into dual active bridge (DAB) units 1 and 2 and unit H of the input side H bridge, and use short-circuit contraction to derive their fixed admittance equivalent circuits to form an equivalent model of the power module.

Step 3: Consider connecting the Thevenin circuit on the high-voltage side of the power module in series and the Norton circuit on the low-voltage side in parallel to form a CHB-PET two-port decoupling equivalent model.

Step 4: Substitute the formed equivalent model into the external circuit to solve the port voltage and current, and use the port electrical quantities to inversely solve the power module terminal potential and the internal node voltage of the constant admittance unit.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 CHB-PET power module topology

Figure 2 Power module companion circuit based on H-bridge constant admittance unit (Abstract attached)

Figure 3 Power module equivalent circuit

Figure 4 Final equivalent circuit of power module

Figure 5 ISOP type CHB-PET dual-port decoupling equivalent model

DETAILED DESCRIPTION

The present invention provides a method for equivalent modeling of a power electronic transformer based on an H-bridge type constant admittance unit; the modeling steps of the present invention will be further described in detail below.

Step 1:

The CHB-PET single module topology is shown in Figure 1, where the "switch group" circuit formed by 12 IGBTs and diodes in parallel can be equivalent to a binary resistor "R _ON /R _OFF ", and the value is determined by the switch group conduction signal; the DAB input and output side capacitors C ₁ and C ₂ are discretized into Norton equivalent circuit forms by the trapezoidal integration method.

The high-frequency isolation transformer in DAB is discretized by trapezoidal integration method, and the electrical coupling between the primary and secondary sides is approximately released by using the single step of port voltage, which is organized into two Norton equivalent circuits, as shown in equation (1). Ignoring the copper loss and iron loss of the transformer, _LA is the auxiliary inductance between the primary and secondary sides of the transformer, _L1 and _L2 are the leakage reactance of the primary and secondary sides of the transformer, _Lm is the transformer excitation reactance, and Δt is the system simulation step.

in

At this time, the transformer is equivalent to two independent Norton circuits, where G _T1 = Y ₁₁ and G _T2 = Y ₂₂ are equivalent admittances and are both constant values, and j _T1-H (t) and j _T2-H (t) are equivalent current sources updated in a single step. j _T1-H (t) and j _T2-H (t) are only related to the port voltage and current values at the previous moment, realizing the decoupling of the primary and secondary sides of the transformer. After the above process, the power module can be equivalent to the accompanying circuit form of Figure 2.

Step 2:

The power module is divided into DAB units 1 and 2 and input side H-bridge unit H. Unit 1 and unit 2 have the same circuit structure, both of which are 4-node H-bridge circuit units. Under non-locking operation conditions, the switch group state of DAB satisfies the complementarity of the same bridge arm, and its working mode can be expressed by the switch function T ₁₁ and T ₁₂ , as shown in formula (2):

Therefore, there are only 4 working modes for units 1 and 2, and their equivalent admittances are also at most 4. Taking unit 1 as an example to derive its definite admittance form, first write the node admittance equation of unit 1 as formula (3), which is recorded as the block matrix form of formula (4):

By using the short-circuit contraction to eliminate the internal nodes of unit 1, the equivalent circuit expression containing only the external terminals _H1 and _H2 is obtained as shown in equation (5):

Among them, Y _1-EX is the external equivalent admittance matrix of unit 1, and J _1-S is the equivalent historical current source. After the external terminal potential is obtained by EMT solution of the external circuit, the internal node voltage can be inversely solved using formula (6).

In order to simplify the calculation results, remember:

In formula (6), Y _1-22 is a 2nd-order symmetric matrix, and its inverse matrix is It can be directly obtained as shown in formula (8):

in

d ₁₁ and d ₁₂ are both constants. Substituting equations (7) and (8) into equation (5), we can obtain Y _1-EX and J _1-S . At this time, unit 1 is short-circuited and shrinks to a 2-node Norton equivalent circuit, where G _eq1 = Y _1-EX (1,1) and J _eq1 = J _1-S (2). Combined with the switch state of the bridge arm, the equivalent circuit parameters of unit 1 can be derived:

According to formula (10), considering all working modes, the equivalent conductance value of unit 1 only contains three certain cases, which is a fixed admittance unit. The derivation process of unit 2 is the same as that of unit 1, so the power module is equivalent to that shown in Figure 3.

At this time, unit H is still a 4-node circuit. In the non-locked state, the H-bridge operation mode of CHB includes two modes: input and bypass, and both satisfy the complementary signal of the same bridge arm switch. It can also be derived as a fixed admittance unit. The derivation process is as follows: write the node admittance equation of unit H and obtain the inverse matrix

in

When the H bridge is put into operation, _TH1 ≠ _TH2 is satisfied. At this time, the equivalent conductance of unit H is the same as that of the first case of unit 1:

G _eqH ＝G _S -G _R d _Z1 -2G _X d _Z2 (13)

J _eqH ＝K _H G _B (d _Z2 -d _Z1 )J _eq1

in

When the H bridge is bypassed, T _H1 = T _H2 , then:

G _eqH =G _S -d _P (17)

J _eqH = 0 (18)

The power module is ultimately equivalent to the two-port decoupling equivalent circuit shown in Figure 4. The equivalent conductances are all constant values, which are selected according to the control signal during simulation; the equivalent historical current source is updated by the energy storage element historical current source in a single step, which is related to the control signal.

Step 3:

Considering the connection mode of the ISOP type power module, the Norton circuit on the high voltage side can be transformed into the Thevenin form, and finally the N equivalent circuits are connected in series on the high voltage side and in parallel on the low voltage side to form the CHB-PET two-port decoupling equivalent model as shown in Figure 4. The equivalent parameter calculation formula is shown in formula (19). Where S represents the series side, P represents the parallel side, N represents the number of modules, and i is the module number.

Step 4:

Substitute the formed equivalent model into the external circuit to obtain the port voltage and current V _S , I _S , V _P , and I _P , and define the 2nd and 4th terminals of the module as virtual ground nodes. At this time, the potentials of the 1st and 3rd terminals are the potential differences of the ports on both sides. Taking the power module i in Figure 4 as an example, its terminal potentials are _vi1 , _vi2 , _vi3 , and _vi4 , respectively, and the calculation formula is as follows:

After obtaining the terminal potential, for the high-voltage side, the internal node voltage of unit H is inverted from _vi1 and _vi2 , and after obtaining the port voltage of unit 1, the inverted unit 1 is continued; for the low-voltage side, the node voltage of unit 2 is directly inverted from _vi3 and _vi4 .

For the inverse solution of the internal node voltage of the constant admittance unit, taking unit 1 as an example, combined with the control method and the derivation process of the constant admittance unit, equation (6) can be derived as follows:

in

At this time, the inverse solution process of the internal voltage is only reflected by a coefficient matrix, and the values of each element of the matrix are as follows:

Combined with the working state of unit 1, the coefficient matrix contains only four cases, which can be pre-calculated and stored, and its values are as follows:

in

Among them, c ₁ ~ c ₅ are all fixed values, and their values are shown in Table 1:

Table 1 Unit 1 coefficient matrix value table

Similarly, the inverse expressions of unit H and unit 2 can be obtained, as shown in Table 2. The coefficient matrices A _2×3 and B _2×3 are also constant matrices that vary with the switching function.

Table 2 Inverse solution expression of constant admittance unit

After the voltage of each node is obtained by inverse solution, the energy storage historical current source is updated and ready to enter the next step of long model solution.

Finally, it should be noted that the described embodiments are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

Claims (2)

1. The equivalent modeling method of the power electronic transformer based on the H-bridge type constant admittance unit is characterized in that a constant admittance model of a common H-bridge type circuit in PET is deduced by taking the common H-bridge type circuit as a unit, a PET high-speed electromagnetic transient simulation model is formed according to a connection mode, and the simulation rate of the model is obviously improved on the premise of ensuring high precision, and the method comprises the following steps:

Step 1: discretizing the transformer and the energy storage element, utilizing a single step of port voltage to approximately decouple the primary side and the secondary side of the transformer to obtain a power module accompanying circuit,

Step 2: dividing the power module into units H of double active bridge units 1 and 2 and an input side H bridge, respectively deducing the constant admittance equivalent model thereof to form a power module equivalent model,

Step 3: considering the connection mode of the high-voltage side series connection and the low-voltage side parallel connection of the power module, a CHB-PET dual-port decoupling equivalent model is formed,

Step 4: substituting the formed equivalent model into an external circuit to solve the port voltage and current quantity, reversely solving the terminal potential of the power module and the voltage of the internal node of the admittance determining unit,

The high-frequency isolation transformer in DAB adopts a trapezoidal integral method for discretization, utilizes a single-step length of a port voltage to approximately remove the electric coupling of the primary side and the secondary side, and is arranged into two Norton equivalent circuits, as shown in a formula (1), the copper loss and the iron loss of the transformer are ignored, L _A is auxiliary inductance between the primary side and the secondary side of the transformer, L ₁、L₂ is leakage reactance of the primary side and the secondary side of the transformer respectively, L _m is excitation reactance of the transformer, delta t is a system simulation step length,

At this time, the transformer is equivalent to two independent Norton circuits, wherein G _T1＝Y₁₁、G_T2＝Y₂₂ is equivalent admittance and is constant, j _T1-H(t)、j_T2-H (t) is an equivalent current source updated in a single step length, j _T1-H(t)、j_T2-H (t) is only related to the current value of the port voltage at the last moment, decoupling of the primary side and the secondary side of the transformer is realized, through the above process, the power module can be equivalent to an accompanying circuit form,

The power module is divided into units 1 and 2 of DAB and a unit H of an input side H bridge, the unit 1 and the unit 2 have the same circuit structure and are all 4-node H bridge type circuit units, under the non-locking operation condition, the switch group state of DAB meets the complementation of a bridge arm, the working mode of the switch group is represented by a switch function T ₁₁、T₁₂, and the switch group is represented by the following formula (2):

Therefore, the operation modes of the units 1 and 2 are only 4, the equivalent admittances thereof are at most 4, and in the process of deriving the constant admittance form of the unit 1, the node admittance equation of the unit 1 is firstly written as formula (3), and is recorded as a block matrix form of formula (4):

Using the internal node of the short-circuit shrinkage cancellation unit 1, an equivalent circuit expression including only the external terminal H ₁、H₂ is obtained as shown in expression (5):

Wherein Y _1-EX is the external equivalent admittance matrix of the unit 1, J _1-S is the equivalent history current source, after the external terminal potential is obtained by the external circuit EMT solution, the internal node voltage can be reversely solved by using the formula (6),

To simplify the calculation result, note:

Y _1-22 in the formula (6) is a 2-order symmetric matrix, the inverse matrix thereof Can be directly obtained as shown in the formula (8):

d ₁₁、d₁₂ is a constant, substituting the formula (7) and the formula (8) into the formula (5) can obtain Y _1-EX and J _1-S,, and the unit 1 is short-circuited and contracted into a 2-node Norton equivalent circuit, wherein G _eq1＝Y_1-EX(1,1),J_eq1＝J_1-S (2) is combined with the bridge arm switch state, and the equivalent circuit parameters of the unit 1 can be deduced:

From equation (10), considering all modes of operation, the equivalent conductance value of cell 1 contains only three determined cases, the admittance is determined, the derivation process of cell 2 is the same as cell 1,

At this time, the unit H is still a 4-node circuit, and in the non-locking state, the H-bridge operation mode of the CHB comprises two modes of input and bypass, and the two modes are all complementary with the switching signals of the bridge arm, and the unit H can also be deduced into a constant admittance unit, wherein the deduction process is as follows, the node admittance equation of the unit H is written, and the inverse matrix is obtained

When the H bridge is thrown, T _H1≠T_H2 is satisfied, at which time the equivalent conductance of cell H is the same as in the first case of cell 1:

G_eqH＝G_S-G_Rd_Z1-2G_Xd_Z2 (13)

J_eqH＝K_HG_B(d_Z2-d_Z1)J_eq1

Wherein the method comprises the steps of When the H bridge bypasses, T _H1＝T_H2 is satisfied, at this time:

G_eqH＝G_S-d_P (17)

J_eqH＝0 (18)

The power module is finally equivalent to a dual-port decoupling equivalent circuit, wherein the equivalent conductivities are constant values, and the equivalent conductivities are selected according to control signals during simulation; the equivalent history current source is updated by a single step length of the history current source of the energy storage element, and is related to the control signal,

Considering the ISOP type connection mode of the power module, the Norton circuit at the high voltage side can be converted into the Thevenin form, finally N equivalent circuits are connected in a mode of connecting the high voltage side in series and the low voltage side in parallel to form a CHB-PET dual-port decoupling equivalent model, the equivalent parameter calculation formula is shown as a formula (19), wherein S represents the serial side, P represents the parallel side, N represents the number of modules, i is the module number,

Substituting the formed equivalent model into an external circuit to obtain the port voltage and current quantity V _S、I_S、V_P、I_P, forcing the terminals 2 and 4 of the definition module to be virtual ground nodes, wherein the potentials of the terminals 1 and 3 are the potential differences of the ports on two sides, and the terminal potentials of the power module i are V _i1、v_i2、v_i3、v_i4 respectively, and the calculation formula is as follows:

After the terminal potential is obtained, v _i1、v_i2 is used for reversely solving the voltage of the internal node of the unit H on the high-voltage side, and the port voltage of the unit 1 is obtained and then the unit 1 is continuously reversely solved; for the low voltage side, the cell 2 node voltage is directly inverted by v _i3、v_i4,

For the inverse solution of the internal node voltage of the admittance cell, in cell 1, the control scheme and the admittance cell derivation process are combined to derive equation (6) as follows:

at this time, the inverse solution process of the internal voltage is only embodied by a coefficient matrix, and the values of each element of the matrix are as follows:

in combination with the working state of the unit 1, the coefficient matrix only contains four cases, and can be pre-calculated and stored, and the values are as follows:

wherein c ₁～c₅ is a constant value.

2. The method for equivalent modeling of a power electronic transformer based on an H-bridge constant admittance unit according to claim 1, characterized in that the former step is the basis of the execution of the latter step, and the 4 modeling steps are executed in a sequential order, in a form of an organic, indivisible whole.