CN113158614A - Stability analysis method for electromagnetic transient simulation algorithm of double-source bridge converter - Google Patents

Abstract

The invention relates to a stability analysis method (A stability analysis method of the electromagnetic transient simulation algorithm of the dual-active-bridge converter) of an electromagnetic transient simulation algorithm. The core technical scheme of the invention is as follows: 1. by simplifying a Dual Active Bridge (DAB) converter, an equivalent circuit suitable for stability analysis is established, and a state equation of the simplified circuit is written in parallel; 2. the Lyapunov method is used for proving the stability of a physical system formed by the DAB converter; 3. a stability analysis method of a discrete system when the DAB converter is processed by adopting an electromagnetic transient simulation algorithm is provided.

Description

Stability analysis method for electromagnetic transient simulation algorithm of double-source bridge converter

Technical Field

The invention relates to a stability analysis method for an electromagnetic transient simulation algorithm of a double-active-bridge converter, belonging to the technical field of power system simulation.

Background

Because of the typical characteristics of "high frequency", "isolated" and "multi-module", the electromagnetic transient simulation speed of a Power Electronic Transformer (PET) based on detailed devices is very slow and cannot meet the requirements, so many electromagnetic transient simulation algorithms for PET are proposed at home and abroad. However, when different electromagnetic transient simulation algorithms are used for discretization of PET, the numerical integration stability may limit the value of the simulation step length, and even cause instability of simulation, so that it is necessary to research a stability analysis method of the electromagnetic transient simulation algorithm.

The invention provides a stability analysis method of an electromagnetic transient simulation algorithm, aiming at a double-active-bridge converter widely adopted in a PET structure. The stability analysis method provided by the method proves the stability of a physical system through a Lyapunov method on the basis of the establishment of a simplified circuit of the DAB converter and the solution of a state equation, and provides a discrete system stability analysis method of different DAB converter electromagnetic transient simulation algorithms.

Disclosure of Invention

The invention provides an electromagnetic transient equivalent modeling method of a double-active-bridge converter, which comprises the following steps:

step 1: analyzing the operation principle of the DAB converter, combining the control modes of the input side and the output side, carrying out equivalence on the input and the output ports, and establishing a simplified circuit of the DAB converter. And selecting the capacitor voltage and the transformer current as state variables, and solving a state equation of the DAB converter through a kirchhoff voltage-current law.

Step 2: by selecting a special positive definite matrix P, the fact that a quadratic function meeting the Lyapunov condition can be found for a physical system formed by the DAB converter is proved, and the stability of the continuous physical system is further proved.

And step 3: and aiming at the DAB converter electromagnetic transient simulation algorithm, a stability analysis method of the discrete system is provided.

Drawings

Fig. 1 is a DAB unit topology diagram.

Fig. 2 is a simplified circuit diagram of a DAB unit (abstract figure).

Detailed Description

The invention provides an electromagnetic transient equivalent modeling method of a double-active-bridge converter; the modeling steps of the present invention will be described in further detail below.

Step 1: DAB Unit topology is shown in FIG. 1, where L_TIs an auxiliary inductor.

The DAB unit is first simplified as follows: (1) the ports on two sides of the DAB unit adopt constant voltage control (such as constant direct current voltage control of MMC and PWM control of CHB), and the capacitance value of the capacitor is larger, so that an external circuit at two ends can be equivalent to a Thevenin equivalent circuit with small resistance (the voltage fluctuation is smaller); (2) and (4) considering the interpolation function of the IGBT switch group on the H bridge as a binary resistance model. The simplified circuit for building a DAB unit is shown in figure 2.

Using binary resistor R for switch group₁～R₈It shows that to avoid straight-through with the bridge arm, it should satisfy:

for the transformer column KVL:

therefore, the voltage-current relationship of the transformer is:

namely, it is

Wherein:

taking the left half side circuit of the DAB unit as an example, based on kirchhoff's law, the following can be obtained:

obtaining by solution:

therefore, the expressions of the obtained primary voltage of the transformer and the input side capacitance voltage of the DAB unit are as follows:

similarly, the right half-side circuit can be solved, and then the DAB converter state equation is established as follows:

is marked as

Wherein

Step 2: as known from the Lyapunov direct method,

stable, equivalent to the presence of all symmetric matrices P: p is positively defined, and A^TP + P · a negative definite, where the characteristic root real parts of matrix a are all less than 0, and are represented by the formula E ═ x^TThe quadratic function determined by P.x is called the quadratic Lyapunov function.

Taking E (t) as the energy storage function of the whole system, for the capacitance:

for the transformers shown in equations (2) to (4),

therefore, take the symmetric matrix P as:

it is clear that P is positive, as determined by Hillwitter (Sylvester) criterion. For DAB converters, the equation of state determined in step 1 indicates that A^TP + P.A satisfies:

thus, A^TSince P + P · a is negative, the Lyapunov condition is satisfied at this time, and the physical system constituted by the DAB converter is stable.

And step 3: for discrete systems, the Lyapunov stable conditions of the DAB unit translate to: a symmetric positive definite matrix P exists such that:

G^T·P·G-P＜0 (14)

for different electromagnetic transient simulation algorithms, discretizing the DAB unit circuit shown in the step 1, and writing a state variable iterative expression containing single-step gain G in a column mode:

x(t)＝G·x(t-Δt) (15)

substituting the expression (15) into the expression (14), solving a simulation step value range which enables the expression (14) to be established, and determining the stability of the discrete system.

An existing ISOP type DAB converter electromagnetic transient equivalent modeling method [ see literature: in the great morning auspicious, the Dingjiang river Duckweed in the construction, Zhao Cheng Yong, input series output parallel DAB converter equivalent modeling method [ J/OL ] China Motor engineering newspaper 1-11] is taken as an example, and the specific steps of discrete system stability analysis are given in the patent.

In the method, the capacitor of the DAB converter is dispersed by adopting a trapezoidal integration method, and the method is a dispersion integration method which is stable for any simulation step length; however, the transformer is discrete by adopting a decoupling integral method, and has stability problem.

For the differential equation of the transformer shown in the formulas (3) and (4), the integral decoupling method expression of the transformer is as follows:

note the book

The combined formulae (9) and (16) give:

therefore:

wherein the stability of the continuous system is known

In order to determine the matrix negatively,

is a positive definite matrix, therefore, there must be Δ t_max> 0, such that when Δ t < Δ t_maxThe time equation (14) holds, and the discrete system is stable.

Finally, it should be noted that: the described embodiments are only some embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.

Claims (2)

1. A stability analysis method for an electromagnetic transient simulation algorithm of a double-active-bridge converter is disclosed. The method is characterized in that simplified circuit construction and state equation analysis are carried out on a Double Active Bridge (DAB) converter, the stability of a physical system formed by the DAB converter is proved, and meanwhile, a discrete system stability analysis method aiming at different electromagnetic transient simulation algorithms is provided. The method comprises the following steps:

step 1: analyzing the operation principle of the DAB converter, establishing a simplified circuit of the DAB converter, and solving a state equation of the DAB converter through a kirchhoff voltage and current law.

Step 2: the stability of the physical system formed by the DAB converter was demonstrated by the Lyapunov second method.

And step 3: and aiming at the DAB converter electromagnetic transient simulation algorithm, a stability analysis method of the discrete system is provided.

2. The method according to claim 1, wherein the step 1 to the step 3 are based on the execution of the next step, and the 3 modeling steps are executed in a loop-by-loop and sequentially, and are an organic, indivisible whole.

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