CN109842307B - Direct power boundary control method based on three-phase three-opening two-level rectifier - Google Patents

Direct power boundary control method based on three-phase three-opening two-level rectifier Download PDF

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CN109842307B
CN109842307B CN201910130134.8A CN201910130134A CN109842307B CN 109842307 B CN109842307 B CN 109842307B CN 201910130134 A CN201910130134 A CN 201910130134A CN 109842307 B CN109842307 B CN 109842307B
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马辉
田鹏辉
韩笑
田宇
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China Three Gorges University CTGU
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Abstract

基于三相三开两电平整流器的直接功率边界控制方法，先建立两相同步旋转坐标系下三相三开两电平整流器的数学模型；结合瞬时功率理论，并采用电压定向原则，建立旋转坐标系下整流器的功率模型；以直流侧电压作为相平面的横轴，交流侧电流作为相平面的纵轴，建立标准相平面，分析标准相平面内整流器交流侧电流降低和升高时，整流器自然轨迹的变化；以功率量为基础，利用边界控制条件来创造一种新型直接功率控制，首先以交流侧电流降低和升高时整流系统的自然轨迹为基础，选择边界控制的自然开关面，然后使用这个自然开关面更新直接功率控制中功率滞环比较器输出的规则，最终得到直接功率边界控制方法。本发明针对实际应用中的载负突变问题，有效提高三相三开关两电平整流器直流侧的动态性能。

Figure 201910130134

Based on the direct power boundary control method of the three-phase, three-open, two-level rectifier, the mathematical model of the three-phase three-open two-level rectifier in the two-phase synchronous rotating coordinate system is first established; The power model of the rectifier in the coordinate system; take the DC side voltage as the horizontal axis of the phase plane and the AC side current as the vertical axis of the phase plane, establish a standard phase plane, and analyze the rectifier when the AC side current of the rectifier decreases and increases in the standard phase plane. The change of natural trajectory; based on the amount of power, a new type of direct power control is created by using boundary control conditions. First, based on the natural trajectory of the rectifier system when the AC side current decreases and increases, the natural switching surface of boundary control is selected. This natural switching surface is then used to update the rules for the output of the power hysteresis comparator in direct power control, resulting in a direct power boundary control method. The invention can effectively improve the dynamic performance of the DC side of the three-phase three-switch two-level rectifier, aiming at the sudden change of load in practical application.

Figure 201910130134

Description

Direct power boundary control method based on three-phase three-opening two-level rectifier
Technical Field
The invention relates to the technical field of three-phase three-opening two-level rectifier control, in particular to a direct power boundary control method based on a three-phase three-opening two-level rectifier.
Background
In recent years, due to rapid development of economy, the demand for energy is increased, low-carbon energy conservation becomes a common requirement of all countries in the world, and green and low-carbon development of electric energy has great significance for energy conservation and environmental protection. Therefore, how to obtain high-quality electric energy becomes the focus of current research, and in order to solve the problem of harmonic pollution, a PWM technology is introduced into a rectifier to generate a PWM rectifier, which has the advantages of sinusoidal network side current, theoretically realizable unit power factor, low network side current distortion rate and the like. Currently, the grid-side current control strategy of the three-phase PWM rectifier is divided into an indirect current control strategy and a direct current control strategy, wherein the latter is dominant. Hysteresis current control, feedforward decoupling PI control, predictive current control, direct power control and the like are common direct current control strategies at present.
Direct Power Control (DPC) is one of the most efficient control strategies for three-phase PWM rectifiers, and has the following advantages over other PWM rectifier control strategies: operating with unit power factor; secondly, the dynamic response is very fast; and thirdly, the structure is simple and clear. The switching state of the Direct Power Control (DPC) strategy is selected by a switching table according to the instantaneous power error and the input voltage vector position, and the direct power control is improved by using an updated switching table, adaptive control, fuzzy logic selection, sliding mode control, duty cycle optimization or prediction method, which can cope with the problem of uncertain parameters, improve the anti-interference capability, etc., but these methods have limited improvement on the dynamic performance of the dc output voltage.
Boundary control is a geometry-based control method suitable for power electronic converters with switching action, which finds application in many power electronic converters. Various studies have been made on different switching planes, such as first, second and higher order switching planes, in which the natural switching plane has good dynamic properties. However, most of the articles only study the boundary control scheme of the single-phase power electronic converter, and the boundary control of the three-phase PWM rectifier, especially the natural switch surface is rarely studied.
Disclosure of Invention
In order to improve the dynamic performance of the direct-current output voltage of the three-phase PWM rectifier, the invention provides a direct power boundary control method based on a three-phase three-throw two-level rectifier, which can effectively improve the dynamic performance of the direct-current output voltage of the three-phase PWM rectifier. The control method is based on a mathematical model under a dq coordinate system, and deduces a natural track of a rectifying system when the current on the d-axis alternating current side is lowered and raised; combining with instantaneous power theory to obtain P, Q-variable direct power control model, and outputting S to direct power hysteresis comparatorqAnd a new rule is adopted, and the analyzed natural track is used as a switch surface, so that the effect of boundary control is achieved.
The technical scheme adopted by the invention is as follows:
the direct power boundary control method based on the three-phase three-opening two-level rectifier comprises the following steps of:
step 1: analyzing the working process of the three-phase three-switch two-level rectifier, and establishing a mathematical model of the rectifier under a synchronous rotation dq coordinate system by using coordinate transformation;
step 2: combining an instantaneous power theory, converting a mathematical model of the rectifier under the synchronous rotation dq coordinate system into a power model with P and Q as variables under the dq coordinate system;
and step 3: analyzing the boundary control conditions of the three-phase three-switch two-level rectifier, namely establishing a standard phase plane by taking the voltage at the direct current side as the horizontal axis of the phase plane and the current at the alternating current side as the vertical axis of the phase plane; in a standard phase plane, the rectifier has different natural tracks in different states, and the natural tracks of the rectifier when the current on the alternating current side is reduced and increased are analyzed;
and 4, step 4: based on the power quantity, firstly, a natural switch surface of boundary control is selected according to a natural track of the rectifier when the alternating current side current is reduced and increased, then the rule of the output of a power hysteresis comparator in direct power control is updated by using the natural switch surface, and finally the direct power boundary control method based on the three-phase three-switch two-level rectifier is obtained.
Step 1, analyzing the working process of the three-phase three-switch two-level rectifier, defining a switch function, and establishing a mathematical model of the three-phase three-switch two-level rectifier under a three-phase static coordinate system; because a mathematical model under a three-phase static coordinate system is complex, coordinate transformation needs to be introduced into a modeling process of the system, and the mathematical model of the three-phase three-switch two-level rectifier under a synchronous rotation dq coordinate system is obtained by utilizing the coordinate transformation.
In step 2, obtaining a calculation formula of instantaneous active power and instantaneous reactive power based on a dq coordinate system according to an instantaneous power theory; and (3) adopting the voltage orientation of the power grid, selecting the initial phase angle of the d axis to be equal to the initial phase angle of the a phase, and substituting the calculation formula into the mathematical model under the synchronous rotation dq coordinate system established in the step 1 to obtain a power model with P and Q as variables under the dq coordinate system.
And 3, establishing a phase plane by taking the voltage at the direct current side as the horizontal axis of the phase plane and the current at the alternating current side as the vertical axis of the phase plane, and obtaining the natural tracks of the rectifier when the current at the alternating current side is reduced and when the current is increased in the standardized phase plane through simple standardized calculation.
In step 4, in the direct power boundary control method, the reactive power hysteresis comparator outputs SQNumerical valueThe rule and the switching vector table are the same as the traditional direct power control method, and only the output S of the direct active power hysteresis comparatorPThe rule of the values is different from the conventional direct power control method.
The invention discloses a direct power boundary control method based on a three-phase three-opening two-level rectifier, which has the following technical effects:
1: direct power control is created by using boundary control conditions based on power quantities, using a new rule to control the power hysteresis comparator output SpThe numerical value of (c).
2: aiming at the problem of load sudden change in practical application, the dynamic performance of the direct-current side voltage of the three-phase three-throw two-level rectifier can be effectively improved.
Drawings
Fig. 1 is a topology structure diagram of a three-phase three-switch two-level rectifier.
Fig. 2 is a natural track diagram of a rectification system when the current on the alternating current side of the three-phase three-switch two-level rectifier is reduced.
Fig. 3 is a natural track diagram of a rectifying system when the current on the alternating current side of the three-phase three-switch two-level rectifier rises.
Fig. 4 is a boundary condition diagram for direct power control of a three-phase three-switch two-level rectifier.
Fig. 5 is a waveform diagram of the a-phase voltage and current on the ac side under rated load of the rectifier.
Fig. 6 is a waveform diagram of the a-phase current on the ac side when the rectifier suddenly loads 1 time from the rated load.
Fig. 7 is a diagram showing waveforms of voltage and current on the dc side when the rectifier is loaded 1 times from the rated load.
Detailed Description
Step 1: analyzing the working process of the three-phase three-switch two-level rectifier, and establishing a mathematical model of the rectifier under a synchronous rotation dq coordinate system by using coordinate transformation;
step 2: combining an instantaneous power theory, converting a mathematical model of the rectifier under the synchronous rotation dq coordinate system into a power model with P and Q as variables under the dq coordinate system;
and step 3: analyzing the boundary control conditions of the three-phase three-switch two-level rectifier, namely establishing a standard phase plane by taking the voltage at the direct current side as the horizontal axis of the phase plane and the current at the alternating current side as the vertical axis of the phase plane; in a standard phase plane, the rectifier has different natural tracks in different states, and the natural tracks of the rectifier when the current on the alternating current side is reduced and increased are analyzed;
and 4, step 4: based on the power quantity, firstly, a natural switch surface of boundary control is selected according to a natural track of the rectifier when the alternating current side current is reduced and increased, then the rule of the output of a power hysteresis comparator in direct power control is updated by using the natural switch surface, and finally the direct power boundary control method based on the three-phase three-switch two-level rectifier is obtained.
Step 1, analyzing the working process of the three-phase three-switch two-level rectifier, defining a switch function, and establishing a mathematical model of the three-phase three-switch two-level rectifier under a three-phase static coordinate system; because a mathematical model under a three-phase static coordinate system is complex, coordinate transformation needs to be introduced into a modeling process of the system, and the mathematical model of the three-phase three-switch two-level rectifier under a synchronous rotation dq coordinate system is obtained by utilizing the coordinate transformation.
In step 2, obtaining a calculation formula of instantaneous active power and instantaneous reactive power based on a dq coordinate system according to an instantaneous power theory; and (3) adopting the voltage orientation of the power grid, selecting the initial phase angle of the d axis to be equal to the initial phase angle of the a phase, and substituting the calculation formula into the mathematical model under the synchronous rotation dq coordinate system established in the step 1 to obtain a power model with P and Q as variables under the dq coordinate system.
And 3, establishing a phase plane by taking the voltage at the direct current side as the horizontal axis of the phase plane and the current at the alternating current side as the vertical axis of the phase plane, and obtaining the natural tracks of the rectifier when the current at the alternating current side is reduced and when the current is increased in the standardized phase plane through simple standardized calculation.
In step 4, in the direct power boundary control method, the reactive power hysteresis comparator outputs SQThe rule of the numerical value and the switching vector table are the same as the traditional direct power control method, and only the direct active power hysteresis comparator outputsGoes out of SPThe rule of the values is different from the conventional direct power control method.
The method comprises the following specific steps:
step 1: as can be seen from the analysis of the topology structure of the three-phase three-switch two-level rectifier shown in fig. 1, the three-phase three-switch two-level rectifier is a PWM rectifier, the rectifying circuit includes three switching tubes, and the output voltage at the dc side is only vdcAnd-vdcTwo types of three-phase three-switch two-level rectifiers have the characteristics of simplicity, strong robustness, easy acquisition of power modules and auxiliary devices and the like.
ea、eb、ecThe three-phase static coordinate system is the power grid electromotive force; i.e. ia、ib、icThree-phase current at the alternating current side under a three-phase static coordinate system; l isA、LB、LCIs an AC side inductor, LA＝LB＝LCL; r is an equivalent resistance of an alternating current side circuit; c is a direct current side capacitor; rLIs a direct current side load; v. ofdcIs a direct current side voltage; e.g. of the typed、eq、id、iqThe voltage and current of the AC side under the two-phase synchronous rotating coordinate system.
In order to establish a general mathematical model of a three-phase three-opening two-level rectifier, the following assumptions are made: 1) the electromotive force of the power grid is an ideal three-phase sine wave; 2) the alternating current filter inductor is linear and is not saturated; 3) the power switch tube ignores dead time and is an ideal switch.
Defining a switching function:
Figure BDA0001975012870000041
a. b and c represent a three-phase stationary coordinate system.
Establishing a general mathematical model of a three-phase three-switch two-level rectifier:
Figure BDA0001975012870000042
Sa、Sb、Screpresenting abc three-phase switching functions, respectively.
In addition, kirchhoff's current law is applied to the positive node of the direct current measurement capacitor, and the following results are obtained:
Figure BDA0001975012870000043
c represents a DC capacitor, RLRepresenting a dc load.
And (3) adopting coordinate transformation to the equations (2) and (3), transforming the three-phase stationary coordinate system (a, b, c) to the two-phase synchronous rotating coordinate system (d, q), and obtaining a mathematical model of the three-phase three-switch two-level rectifier as follows:
Figure BDA0001975012870000051
in the formula: w is angular velocity, Sd、SqIs a switching function transformed into dq coordinate system.
Step 2: and (3) balancing the three-phase power grid, and obtaining the calculation formula of instantaneous active power and instantaneous reactive power under the dq coordinate system by combining an instantaneous power theory:
P＝edid+eqiq，Q＝eqid-ediq (5)
by using grid voltage orientation, e is obtainedqWhen the above formula is substituted by formula (5), 0 can be obtained:
P＝edid，Q＝-ediq (6)
multiplying both sides of the formula (4) by edAnd obtaining a power model with P and Q as variables under the dq coordinate system as follows:
Figure BDA0001975012870000052
and step 3: firstly, two axes of a phase plane are selected, and according to the existence and uniqueness theory of differential equation solutions, under the condition that any initial data condition is selected, a phase track is required to correspond to the phase plane on the phase plane. For a rectifying system, any of its states corresponds to a point in the phase plane, so that system motion can be represented in the phase plane. The movement of points on the phase plane corresponds to the change of the system state with time, and these movement trajectories are the phase trajectories. The switch surface used by the boundary control of the invention is a natural switch surface, so that the alternating current side current is selected as the longitudinal axis of the phase plane, the direct current side voltage is selected as the transverse axis of the phase plane, the phase plane is established, and the natural track is selected as the phase track.
To obtain the specific power factor, i is controlledqWhen the inductance equivalent resistance R is negligibly small, i.e., R is 0, equation (4) can be simplified as:
Figure BDA0001975012870000061
v in formula (8)Sd＝vdcSd，
Figure BDA0001975012870000062
According to the operating principle of three-phase three-switch two-level rectifiers vSdThe maximum value of (d) is:
Figure BDA0001975012870000063
when the AC side current decreases, vSdShould be positive, i.e.
Figure BDA0001975012870000064
Order to
Figure BDA0001975012870000065
Substituting the compound in the formula (8) to obtain:
Figure BDA0001975012870000066
by using the following trigonometric identity:
Figure BDA0001975012870000067
Figure BDA0001975012870000068
equation (10) can be transformed into the following form:
Figure BDA0001975012870000069
wherein k is and ide、vdcInitial value-dependent constants.
Let vn＝vdc，
Figure BDA00019750128700000610
edn＝ed，
Figure BDA00019750128700000611
And substituting the natural path lambda of the rectifying system when the alternating current side current is reduced in an expression (11)downComprises the following steps:
Figure BDA00019750128700000612
in the normal phase plane, λ is shown in FIG. 2downIs one to
Figure BDA00019750128700000613
A circle with a radius of l as the center of the circle.
When the AC side current rises, vSdShould be negative, i.e.
Figure BDA0001975012870000071
The natural track lambda of the rectifying system is obtained when the current of the alternating current side rises by adopting the same derivation method when the current of the alternating current side fallsupComprises the following steps:
Figure BDA0001975012870000072
in the normal phase plane, λ, as shown in FIG. 3upIs one to
Figure BDA0001975012870000073
A circle with m as the radius as the center of the circle.
And 4, step 4: since only the active power has an effect on the DC output voltage, and inCan be represented by a change in the instantaneous active power P, and a change in the state of the switch will cause a change in P. Therefore, the system operation track can be controlled by the method.
In order to obtain the direct power boundary control rule of the three-phase three-switch two-level rectifier, the following definitions are firstly made:
Figure BDA0001975012870000074
Figure BDA0001975012870000075
i in formulae (14) and (15)n_T、vn_TAre the current and voltage at the operating target point on the phase plane.
By natural trajectory λ when the alternating side current is reduceddownAnd a natural locus lambda of when the alternating-current side current risesupThe selected boundary condition natural switch surfaces are:
Figure BDA0001975012870000076
RT_downindicating a falling boundary resistance
Figure BDA0001975012870000077
ednRepresenting the voltage to ground on the DC side, RT_upRepresenting the rising boundary resistance.
The α β plane is divided into 12 vector sectors, each of which is 30 degrees in the α β plane, and the phase angle range thereof can be represented by equation (18).
Figure BDA0001975012870000078
When the space where the grid voltage vector is located needs to be determined, the phase angle of the grid voltage vector E is calculated firstly
Figure BDA0001975012870000081
eα、eβThe interval of the grid voltage vector E is determined by using an equation (18) for the alternating-current side voltage in the alpha beta coordinate system.
Reactive power hysteresis comparator output S in direct power boundary control algorithm of three-phase three-throw two-level rectifierQThe rules for the values are the same as the conventional direct power control rules:
Figure BDA0001975012870000082
in the formula (19), q is an instantaneous reactive power estimated value, qrFor instantaneous reactive power reference value, HqThe hysteresis width of the reactive power hysteresis comparator. Generally, the hysteresis width of the hysteresis comparator is affected by parameters in the main circuit, such as the inductance L on the ac side and the voltage v on the dc sidedc. If the hysteresis width is too small, the switching frequency is too high, and as a result, the loss of the system switch is increased, and the aging of the switch is accelerated; if the hysteresis width is too large, the power tracking is too slow to satisfy real-time control. Therefore, when designing a system, the size of the hysteresis loop width should be selected to meet the system requirement and meet the practical requirement.
Active power hysteresis in direct power boundary control algorithm of three-phase three-switch two-level rectifierOutput S of loop comparatorPThe value adopts a new rule:
i: if v isdc<vn_TOnly when σdown<At 0, S P1, otherwise SP＝0；
II: if v isdc>vn_TOnly when σup>At 0, S P0, otherwise SP＝1。
Firstly, a sector where a power grid voltage vector is located is judged by adopting a formula (18), and then S is output according to a power hysteresis comparatorP、SQThe sector of the grid voltage vector and the S outputP、SQAnd sending the switching vector into a switching table to select the switching vector.
The switch table used in the direct power boundary control algorithm of the three-phase three-switch two-level rectifier is the same as the switch table used in the traditional direct power control:
TABLE 1 direct power boundary control algorithm switching table for three-phase three-switch two-level rectifier
Figure BDA0001975012870000083
Figure BDA0001975012870000091
Setting line parameters of a three-phase three-switch two-level rectifier: the effective value of the three-phase circuit is 220V/50Hz, and the input inductance L at the alternating current sideA＝LB＝LCThe line equivalent resistance R is 0.1 Ω, the dc-side filter capacitance C is 3300 μ F, the load R is 30 Ω, the switching frequency is 20kHz, and at 0.15s, the load is doubled on the dc side.
When the load is rated, the waveform diagram of the A-phase voltage current at the AC side of the three-phase three-switch two-level rectifier is shown in figure 5, and the current at the network side of the three-phase three-switch two-level rectifier adopting a direct power boundary control algorithm can be obtained from the waveform diagram, so that the sine is realized, the voltage current is basically in the same phase, and the power factor is close to 1.
When the load is suddenly changed to 2 times of load from the rated load, the A-phase current waveform diagram of the AC side of the three-phase three-switch two-level rectifier is shown in fig. 6, and the current of the network side of the three-phase three-switch two-level rectifier adopting the direct power boundary control algorithm can quickly reach a stable state when the load fluctuates.
When the load suddenly changes from the rated load to 2 times of the load, the voltage and current waveform diagram of the direct current side of the three-phase three-switch two-level rectifier is shown in fig. 7, and the direct current side voltage and current of the three-phase three-switch two-level rectifier adopting the direct power boundary control algorithm can be obtained from the diagram and reach the stable state again in a short time when the load fluctuates, so that the three-phase three-switch two-level rectifier has good dynamic performance.
From the analysis of the oscillogram, the direct power boundary control algorithm based on the three-phase three-switch two-level rectifier can effectively improve the dynamic performance of the direct current output current and the direct current output voltage of the three-phase three-switch two-level rectifier, achieves the expected experimental result and has certain practical value.

Claims (7)

1.基于三相三开两电平整流器的直接功率边界控制方法，其特征在于包括以下步骤：1. based on the direct power boundary control method of three-phase three-open two-level rectifier, it is characterized in that comprising the following steps: 步骤1：分析三相三开关两电平整流器的工作过程，运用坐标变换，建立同步旋转dq坐标系下整流器的数学模型；Step 1: Analyze the working process of the three-phase three-switch two-level rectifier, and use coordinate transformation to establish the mathematical model of the rectifier in the synchronously rotating dq coordinate system; 步骤2：结合瞬时功率理论，将同步旋转dq坐标系下整流器的数学模型，转换成dq坐标系下以P，Q为变量的功率模型；Step 2: Combine the instantaneous power theory, convert the mathematical model of the rectifier in the synchronously rotating dq coordinate system into a power model with P and Q as variables in the dq coordinate system; 步骤3：分析三相三开关两电平整流器的边界控制条件，即以直流侧电压作为相平面的横轴，交流侧电流作为相平面的纵轴，建立标准相平面；在标准相平面内，不同状态下整流器具有不同的自然轨迹，分析交流侧电流降低和升高时整流器的自然轨迹；Step 3: Analyze the boundary control conditions of the three-phase three-switch two-level rectifier, that is, take the DC side voltage as the horizontal axis of the phase plane and the AC side current as the vertical axis of the phase plane to establish a standard phase plane; in the standard phase plane, The rectifier has different natural trajectories in different states, analyze the natural trajectories of the rectifier when the AC side current decreases and increases; 步骤4：以功率量为基础，首先以交流侧电流降低和升高时整流器的自然轨迹，选择边界控制的自然开关面，然后使用这个自然开关面更新直接功率控制中功率滞环比较器输出的规则，最终得到基于三相三开关两电平整流器的直接功率边界控制方法；Step 4: Based on the amount of power, first select the natural switching surface of boundary control based on the natural trajectory of the rectifier when the AC side current decreases and increases, and then use this natural switching surface to update the output of the power hysteresis comparator in direct power control. rules, and finally a direct power boundary control method based on three-phase three-switch two-level rectifier is obtained; 有功功率滞环比较器输出Sp数值则采用规则如下：The active power hysteresis comparator output Sp value adopts the following rules: I：若vdc＜vn_T，只有当σdown＜0时，Sp＝1，其他情况下Sp＝0；I: if v dc <v n_T , only when σ down < 0, Sp = 1, in other cases, Sp = 0; II：若vdc>vn_T，只有当σup>0时，Sp＝0，其他情况下Sp＝1；II: If v dc >v n_T , only when σ up >0, Sp = 0, otherwise Sp = 1; 基于三相三开关两电平整流器的直接功率边界控制方法如下：The direct power boundary control method based on three-phase three-switch two-level rectifier is as follows: 先做如下定义：First make the following definitions:
Figure FDA0002720136850000011
Figure FDA0002720136850000011
Figure FDA0002720136850000012
Figure FDA0002720136850000012
 式(14)、(15)中in_T、vn_T是相平面上运行目标点的电流和电压；In equations (14) and (15), i n_T and v n_T are the current and voltage of the operating target point on the phase plane; 通过交流侧电流降低时的自然轨迹λdown和交流侧电流升高时的自然轨迹λup，选择的边界条件自然开关面为：Through the natural trajectory λ down when the AC side current decreases and the natural trajectory λ up when the AC side current increases, the natural switching surface of the selected boundary condition is:
Figure FDA0002720136850000013
Figure FDA0002720136850000013
Figure FDA0002720136850000014
Figure FDA0002720136850000014
 将αβ平面划分为12个矢量扇区，在αβ平面内，每个扇区均为30度，其相角范围可由式(18)来表示；Divide the αβ plane into 12 vector sectors, in the αβ plane, each sector is 30 degrees, and its phase angle range can be represented by equation (18);
Figure FDA0002720136850000021
Figure FDA0002720136850000021
 当电网电压矢量所在空间需要被确定时，先计算电网电压矢量E的相位角
Figure FDA0002720136850000022
eα、eβ为αβ坐标系下的交流侧电压然后利用式(18)确定电网电压矢量E所在区间；When the space where the grid voltage vector is located needs to be determined, first calculate the phase angle of the grid voltage vector E
Figure FDA0002720136850000022
e α and e β are the AC side voltage in the αβ coordinate system, and then use the formula (18) to determine the interval where the grid voltage vector E is located; 三相三开两电平整流器的直接功率边界控制算法中无功功率滞环比较器输出Sq数值的规则为：The rules for the output S q value of the reactive power hysteresis comparator in the direct power boundary control algorithm of the three-phase three-open two-level rectifier are:
Figure FDA0002720136850000023
Figure FDA0002720136850000023
 式(19)中q为瞬时无功功率估算值，qr为瞬时无功功率参考值，Hq为无功功率滞环比较器的滞环宽度。In formula (19), q is the estimated value of instantaneous reactive power, q r is the reference value of instantaneous reactive power, and H q is the hysteresis width of the reactive power hysteresis comparator. 2.根据权利要求1所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤1中，分析三相三开关两电平整流器的工作过程，定义开关函数，建立三相三开关两电平整流器在三相静止坐标系下的数学模型；将坐标变换引入到系统的建模过程中，利用坐标变换，得到三相三开关两电平整流器在同步旋转dq坐标系下的数学模型。2. the direct power boundary control method based on three-phase three-open two-level rectifier according to claim 1, is characterized in that: in step 1, analyze the working process of three-phase three-switch two-level rectifier, define switching function, establish Mathematical model of the three-phase three-switch two-level rectifier in the three-phase static coordinate system; the coordinate transformation is introduced into the modeling process of the system, and the coordinate transformation is used to obtain the three-phase three-switch two-level rectifier in the synchronous rotation dq coordinate system the mathematical model below. 3.根据权利要求1所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤2中，根据瞬时功率理论，得到基于dq坐标系下的瞬时有功功率和瞬时无功功率的计算式；采用电网电压定向，选取d轴的初始相角和a相初始相角相等，将上述计算式代入步骤1中所建立的同步旋转dq坐标系下的数学模型中，得到dq坐标系下以P，Q为变量的功率模型。3. the direct power boundary control method based on the three-phase three-open two-level rectifier according to claim 1, is characterized in that: in step 2, according to the instantaneous power theory, obtain based on the instantaneous active power under the dq coordinate system and the instantaneous no power. The calculation formula of power; adopt the grid voltage orientation, select the initial phase angle of the d-axis to be equal to the initial phase angle of the a-phase, and substitute the above calculation formula into the mathematical model under the synchronous rotation dq coordinate system established in step 1 to obtain dq A power model with P and Q as variables in the coordinate system. 4.根据权利要求1所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤3中，以直流侧电压作为相平面的横轴，交流侧电流作为相平面的纵轴，建立相平面，经过标准化计算，得到标准化相平面内交流侧电流降低时和电流升高时整流器的自然轨迹。4. the direct power boundary control method based on the three-phase three-open two-level rectifier according to claim 1, is characterized in that: in step 3, take the DC side voltage as the horizontal axis of the phase plane, and the AC side current as the phase plane. On the vertical axis, the phase plane is established. After standardized calculation, the natural trajectory of the rectifier when the AC side current decreases and when the current increases in the standardized phase plane is obtained. 5.根据权利要求2所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤1包括：5. The direct power boundary control method based on three-phase three-open two-level rectifier according to claim 2, is characterized in that: step 1 comprises: ea、eb、ec为三相静止坐标系下电网电动势；ia、ib、ic为三相静止坐标系下交流侧三相电流；LA、LB、LC为交流侧电感，LA＝LB＝LC＝L；R为交流侧线路等效电阻；C为直流侧电容；RL为直流侧负载；vdc为直流侧电压；ed、eq、id、iq为两相同步旋转坐标系下交流侧电压与电流；e a , e b , and e c are the electromotive force of the power grid in the three-phase static coordinate system; i a , ib , and ic are the three-phase currents on the AC side in the three-phase static coordinate system; L A , L B , and L C are the AC side Inductance, L A =L B =L C =L; R is the equivalent resistance of the AC side line; C is the DC side capacitance; R L is the DC side load; v dc is the DC side voltage; ed , e q , id , i q are the AC side voltage and current in the two-phase synchronous rotating coordinate system; 为建立三相三开两电平整流器的一般数学模型，做以下假设：1)电网电动势为理想三相正弦波；2)交流滤波电感线性无饱和；3)功率开关管均忽略死区时间，为理想开关；In order to establish the general mathematical model of the three-phase three-open two-level rectifier, the following assumptions are made: 1) The grid electromotive force is an ideal three-phase sine wave; 2) The AC filter inductor is linear without saturation; 3) The power switch tubes ignore the dead time, is an ideal switch; 定义开关函数：Define the switch function:
Figure FDA0002720136850000031
Figure FDA0002720136850000031
 a、b、c表示三相静止坐标系；a, b, c represent the three-phase stationary coordinate system; 建立三相三开关两电平整流器的一般数学模型：Establish a general mathematical model for a three-phase three-switch two-level rectifier:
Figure FDA0002720136850000032
Figure FDA0002720136850000032
 另外，对直流测电容正极节点处应用基尔霍夫电流定律，得：In addition, applying Kirchhoff's current law to the positive node of the DC measuring capacitor, we get:
Figure FDA0002720136850000033
Figure FDA0002720136850000033
 对式(2)、(3)采用坐标变换，则从三相静止坐标系(a、b、c)变换到两相同步旋转坐标系(d、q)，得三相三开关两电平整流器数学模型为：Using coordinate transformation for equations (2) and (3), the three-phase three-switch two-level rectifier is obtained by transforming from the three-phase static coordinate system (a, b, c) to the two-phase synchronous rotating coordinate system (d, q). The mathematical model is:
Figure FDA0002720136850000034
Figure FDA0002720136850000034
 式中：w为角速度，Sd、Sq为变换到dq坐标系下的开关函数。where w is the angular velocity, and S d and S q are the switching functions transformed to the dq coordinate system. 6.根据权利要求2所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤2包括：6. the direct power boundary control method based on three-phase three-open two-level rectifier according to claim 2, is characterized in that: step 2 comprises: 结合瞬时功率理论，得到dq坐标系下的瞬时有功功率和瞬时无功功率的计算式为：Combined with the theory of instantaneous power, the calculation formulas of instantaneous active power and instantaneous reactive power in the dq coordinate system are obtained as:
Figure FDA0002720136850000035
Figure FDA0002720136850000035
 采用电网电压定向，则可得到eq＝0，将上式代入式(5)中可得：Using the grid voltage orientation, e q = 0 can be obtained, and the above formula can be substituted into formula (5) to obtain: P＝edid，Q＝-ediq (6)P= ed i d , Q= -ed i q (6) 将式(4)两边同时乘以ed，得到dq坐标系下以P，Q为变量的功率模型为：Multiply both sides of equation (4) by ed at the same time to obtain the power model with P and Q as variables in the dq coordinate system:
Figure FDA0002720136850000041
Figure FDA0002720136850000041
 7.根据权利要求3所述基于三相三开两电平整流器的直接功率边界控制方法，其特征在于：步骤3包括：边界控制使用的是自然开关面，因此选择交流侧电流作为相平面的纵轴，直流侧电压作为相平面的横轴，建立相平面，选择自然轨迹作为相轨迹；7. The direct power boundary control method based on the three-phase three-open two-level rectifier according to claim 3, is characterized in that: step 3 comprises: what boundary control uses is the natural switch surface, therefore selects the alternating current side current as the phase plane The vertical axis, the DC side voltage is taken as the horizontal axis of the phase plane, the phase plane is established, and the natural trajectory is selected as the phase trajectory; 为了得到单位功率因数，需控制iq＝0，当电感等效电阻R小到可以忽略不计时，即R＝0，式(4)可以简化为：In order to obtain the unity power factor, it is necessary to control i q = 0. When the inductance equivalent resistance R is so small that it can be ignored, that is, R = 0, Equation (4) can be simplified as:
Figure FDA0002720136850000042
Figure FDA0002720136850000042
 式(8)中，vSd＝vdcSd，
Figure FDA0002720136850000043
根据三相三开关两电平整流器运行原理，vSd的最大值为：In formula (8), v Sd =v dc S d ,
Figure FDA0002720136850000043
According to the operating principle of the three-phase three-switch two-level rectifier, the maximum value of v Sd is:
Figure FDA0002720136850000044
Figure FDA0002720136850000044
 当交流侧电流降低时，vSd为正值，即
Figure FDA0002720136850000045
令
Figure FDA0002720136850000046
将代入式(8)中得：When the AC side current decreases, v Sd is positive, i.e.
Figure FDA0002720136850000045
make
Figure FDA0002720136850000046
Substitute into formula (8) to get:
Figure FDA0002720136850000047
Figure FDA0002720136850000047
 通过使用如下三角恒等式：By using the following trigonometric identities:
Figure FDA0002720136850000048
Figure FDA0002720136850000048
Figure FDA0002720136850000049
Figure FDA0002720136850000049
 式(10)可以变换成如下形式：Equation (10) can be transformed into the following form:
Figure FDA00027201368500000410
Figure FDA00027201368500000410
 式中k为与ide、vdc初值相关的常数；where k is a constant related to the initial values of i de and v dc ; 令vn＝vdc，
Figure FDA0002720136850000051
edn＝ed，
Figure FDA0002720136850000052
并将其代入式(11)中，得交流侧电流降低时整流系统的自然轨迹λdown为：Let v n =v dc ,
Figure FDA0002720136850000051
ed dn = ed ,
Figure FDA0002720136850000052
Substituting it into Equation (11), the natural trajectory λ down of the rectifier system when the AC side current decreases is:
Figure FDA0002720136850000053
Figure FDA0002720136850000053
 在标准相平面内，λdown是一个以
Figure FDA0002720136850000054
为圆心，以l为半径的圆；In the standard phase plane, λ down is a
Figure FDA0002720136850000054
is a circle with center and radius l; 当电流升高时，vSd应该为负值，即
Figure FDA0002720136850000055
采用和电流降低时同样的推导方法，得交流侧电流升高时整流系统的自然轨迹λup为：As the current increases, v Sd should be negative, i.e.
Figure FDA0002720136850000055
Using the same derivation method as when the current decreases, the natural trajectory λ up of the rectifier system when the AC side current increases is:
Figure FDA0002720136850000056
Figure FDA0002720136850000056
 在标准相平面内，λup是一个以
Figure FDA0002720136850000057
为圆心，以m为半径的圆。In the standard phase plane, λ up is a
Figure FDA0002720136850000057
is a circle with center and radius m.
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