Three-phase PWM rectifier starting impact current suppression strategy based on tracking differentiator

Abstract

The invention discloses a three-phase PWM rectifier starting impact current suppression strategy based on a tracking differentiator, and the strategy specifically comprises the steps: 1, calculating a relation between a shaft current instantaneous value and a DC bus voltage change rate based on a PWM rectifier mathematical model; and 2, aiming at reducing the change rate between a direct current bus voltage value and a direct current bus voltage reference value, adopting a slow start strategy based on a tracking differentiator, and taking a curve output by the tracking differentiator as the direct current bus voltage reference value to realize suppression of the starting impact current of the PWM rectifier.

Description

Technical Field

[0001] The invention belongs to the field of three-phase power supply, and in particular to a three-phase PWM rectifier startup impact current suppression strategy based on a tracking differentiator. Background Art

[0002] With the development of energy technology, PWM rectification technology has become a hot topic in research. The function of three-phase PWM rectifier is to generate a stable DC voltage from an AC voltage source. Its main advantages are bidirectional transmission of electric energy, single-power operation, adjustable DC side voltage, and low AC side current harmonic content. It has been widely used in renewable energy power generation systems.

[0003] The control strategy of the three-phase PWM rectifier usually adopts dual closed-loop direct current control based on PI regulator. This control strategy has a simple structure and fast response speed. However, during the startup process of the three-phase PWM rectifier, due to the large difference between the DC voltage reference value and the actual value, integral saturation is likely to occur after passing through the voltage outer loop. Therefore, the obtained shaft command current will be very large, resulting in a large impact current on the grid side. This current may damage the grid-side inductance and power devices. However, if the threshold current of the grid-side inductance and power devices is increased, the cost of the system will increase.

[0004] In response to the problem of starting impact current of three-phase PWM rectifier, some scholars have proposed corresponding suppression strategies. Some scholars have proposed a new load current feedforward control strategy to solve the problem of integral saturation of the voltage outer loop. However, this strategy requires adding a current sensor to measure the load current, which increases the system cost. Some literature has proposed a slow-set suppression method, but this method is only applicable to the start-up method of uncontrolled start-up and then controlled start-up, and the system stability is poor during direct start-up. The effect of this method in suppressing the starting impact current is proportional to the time from 0 to the given value. The longer it takes to reach the given value, the slower its dynamic response. There is also a starting method of pre-charging and slow-set mixed control. However, this method requires a series resistor on the grid side, which will increase the cost, reduce the efficiency, and cause system instability when the resistor is removed. In addition, some authors have proposed a slow-start method that sets the initial value of the reference voltage to the DC bus voltage in the uncontrolled rectifier state. This strategy still has the problem that the suppression effect is poor when the starting time is too short, the dynamic response of the DC bus voltage is slow when the starting time is too long. There are also documents that propose a capacitor voltage feedforward control strategy based on the d-axis current fundamental positive sequence decomposition method, which improves the stability of the grid-side current, but reduces the dynamic response of the bus voltage to a certain extent. Some scholars also inject an exponentially decaying DC quantity with an opposite constant time constant into the modulation wave during the startup process. This method suppresses the impact current to a certain extent, but the effect is not good. Summary of the invention

[0005] Purpose of the invention: In order to solve the problems existing in the above-mentioned prior art, the present invention provides a three-phase PWM rectifier starting inrush current suppression strategy based on a tracking differentiator.

[0006] Technical solution: The present invention provides a three-phase PWM rectifier startup inrush current suppression strategy based on a tracking differentiator, specifically including:

[0007] Step 1: Based on the PWM rectifier mathematical model, calculate the instantaneous value of the d-axis current i based on the model d (k) and DC bus voltage U dc the relationship between rates of change;

[0008] Step 2: In order to reduce the rate of change between the DC bus voltage value and the DC bus voltage reference value, a soft start strategy based on a tracking differentiator is adopted, and the curve output by the tracking differentiator is used as the DC bus voltage reference value to suppress the starting impact current of the PWM rectifier.

[0009] Furthermore, the expression of the PWM rectifier mathematical model in step 1 is:

[0010]

[0011] in, They are the d-axis and q-axis command currents, K vP , K vI are the proportional coefficient and integral coefficient of the voltage outer loop PI regulator, is the DC bus voltage reference value; S d , S q are the d-axis and q-axis components of the switching function respectively; K iP , K iI is the proportional coefficient and integral coefficient of the current inner loop PI regulator, s represents the differential; i d 、i q They represent the d-axis and q-axis components of the grid current, ω is the grid voltage angular frequency, L is the AC side inductance, and e d is the d-axis component of the grid voltage.

[0012] Furthermore, the instantaneous value of the d-axis current i d (k) and DC bus voltage U dc The relationship between the rates of change is expressed as follows:

[0013]

[0014] Where C is the DC bus capacitance, k is the time variable, T s is the control period, e d is the d-axis component of the grid voltage, i L is the load current.

[0015] Furthermore, the slow start strategy of the tracking differentiator is specifically as follows: a linear tracking differentiator is used, and an objective function is established by solving the linear tracking differentiator, and the objective function is solved to obtain an adjustable parameter r and time t of the linear tracking differentiator.

[0016] Furthermore, the expression of the linear tracking differentiator is:

[0017]

[0018] Where v represents the input signal of the linear tracking differentiator, x1 is the tracking signal of the input signal, x2 is the differential of x1, and U' dc =2.34 E , where E represents the effective value of the grid voltage;

[0019] Solving the linear tracking differentiator, we obtain: x1 = vv(1+rt)e -rt .

[0020] Furthermore, the objective function is:

[0021] min f=(1+rt)e -rt .

[0022] Furthermore, the Newton iteration method is used to solve the objective function:

[0023]

[0024] Among them, k1 represents the number of iterations, H is the Hessian matrix, is the gradient of the objective function, H and The expression is:

[0025]

[0026] Beneficial effects: The linear tracking differentiator proposed in the present invention effectively suppresses the starting impact current of the three-phase PWM rectifier. The present invention proposes to use the Newton iteration method to accurately calculate the parameters of the linear tracking differentiator. The present invention adds a voltage U' in the linear tracking differentiator. dc , when switching the controlled rectifier, add U' dc The initial value of the curve can be kept consistent with the actual initial value of the DC bus voltage to reduce the error. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flow chart of the present invention;

[0028] Figure 2 It is a three-phase voltage-type PWM rectifier main circuit topology structure of an embodiment of the present invention;

[0029] Figure 3 Schematic diagram of NTD and LTD output signals of an embodiment of the present invention, wherein (a) is a curve diagram of the x1 signal output by LTD, (b) is a curve diagram of the x1 signal output by NTD, (c) is a curve diagram of the x2 signal output by LTD, and (d) is a curve diagram of the x2 signal output by NTD;

[0030] Figure 4 is a structural block diagram of a linear tracking differentiator according to an embodiment of the present invention;

[0031] Figure 5 It is a control block diagram of a three-phase PWM rectifier startup inrush current suppression strategy based on a tracking differentiator according to an embodiment of the present invention;

[0032] Figure 6 is the optimal value of f and the optimal solution of variables r and t in the embodiment of the present invention;

[0033] Figure 7 This is a simulation waveform diagram of the starting voltage and current using step timing according to an embodiment of the present invention;

[0034] Figure 8 The embodiment of the present invention adopts a slow curve as a given starting voltage and current simulation waveform diagram;

[0035] Fig. 9 The embodiment of the present invention adopts a slow curve as the voltage and current waveform after the voltage is transformed at a given time;

[0036] Fig.10 The voltage and current experimental waveforms given by steps in the embodiment of the present invention are;

[0037] Fig.11 The embodiment of the present invention adopts a slow curve as the voltage and current experimental waveform at a given startup;

[0038] Fig.12 The embodiment of the present invention adopts a slow curve as the voltage and current experimental waveform after a given transformation. DETAILED DESCRIPTION

[0039] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0040] like Figure 1 As shown, the present invention comprises the following steps:

[0041] S1: Establish a mathematical model of PWM rectifier.

[0042] S2: Analyze the principle of generating starting impact current of PWM rectifier.

[0043] S3: A slow start strategy based on tracking differentiator is proposed, and the parameters are adjusted using Newton iteration method, thereby achieving the suppression of the starting impact current of the PWM rectifier.

[0044] The topology of the three-phase voltage type PWM rectifier main circuit is as follows Figure 2 As shown. a 、e b 、e c is the three-phase grid voltage, i a 、i b 、i c is the grid current, L is the AC side inductance, R is the equivalent internal resistance, C is the DC bus capacitance, U dc is the DC bus voltage, v a 、v b 、v c It is the input voltage of the rectifier AC side.

[0045] The mathematical model of the PWM rectifier in the three-phase stationary coordinate system under the ideal power supply is:

[0046]

[0047] In the formula, i L is the load current, S a , S b , S c They are switch functions respectively.

[0048] In the three-phase stationary coordinate system, the grid voltage and current are time-varying AC quantities, which is not conducive to the design of the control system. Therefore, through Clarke and Park transformation, the rectifier model in the three-phase stationary coordinate system is transformed into a mathematical model under two-phase stationary and two-phase rotating coordinates:

[0049]

[0050] Where ω is the grid voltage angular frequency, v d 、v q and v α 、v β are the dq axis component and αβ axis component of the rectifier AC side voltage, respectively. d 、e q and e α 、e β are the dq axis component and αβ axis component of the grid voltage respectively, i d 、i q and i α 、i β They are the dq axis component and αβ axis component of the grid current, S d , Sq and S α , S β They are the dq axis component and αβ axis component of the switching function respectively.

[0051] The corresponding transformation matrices are:

[0052]

[0053] In the formula, x α 、x β , x d 、x q (x=e,i,S) are x a 、x b and x c The components in the two-phase stationary coordinate system and the two-phase rotating coordinate system, x a 、x b and x c represents the state variable, ω is the angular velocity of rotation in the dq coordinate system, where θ=ωt.

[0054] Since there is cross coupling between the dq axis currents, the PWM rectifier uses a PI regulator based on feedforward decoupling as the controller of the voltage outer loop and the current inner loop. The PWM rectifier usually uses voltage-oriented control, so there is e q =0. Therefore, the corresponding mathematical model is:

[0055]

[0056] In the formula, K vP , K vI K is the proportional coefficient and integral coefficient of the voltage outer loop PI regulator. iP , K iI are the proportional coefficient and integral coefficient of the current inner loop PI regulator, is the DC bus voltage reference value, They are d-axis and q-axis command currents respectively, and s represents differential.

[0057] The equation after decoupling control is:

[0058]

[0059] In the first few switching cycles of the PWM rectifier, the DC bus voltage reference value is And feedback value U dc The error is large, so the d-axis current set value and change rate are large, resulting in a large impact current on the grid side.

[0060] In order to analyze the factors affecting the d-axis current of the rectifier after adding feedforward decoupling control, Discretization yields:

[0061]

[0062] Where T s is the control period, k is the time variable, and the discrete form of the mathematical model after decoupling control is:

[0063]

[0064] According to the above formula, we can get:

[0065]

[0066] In the formula,

[0067]

[0068] Since the PWM rectifier is usually in single power operation, i q (k)≈0, simplifying the above formula, we can get:

[0069]

[0070] In the formula,

[0071] Solving the above formula, we can get:

[0072]

[0073] The above formula is the discrete form of the d-axis current based on feedforward decoupling control. Since the response speed of the current inner loop is faster than that of the voltage outer loop, it is assumed that the d-axis current feedback value follows the command value, that is, From this we can get:

[0074]

[0075] In the formula,

[0076] Solving the above formula, we can finally get:

[0077]

[0078] From the above formula, we can know that the instantaneous value of the d-axis current is proportional to the instantaneous value of the DC bus voltage, the instantaneous value of the load current, and the rate of change of the DC bus voltage. In the first few switching cycles of the PWM rectifier, and U dc The rapid rise causes the d-axis current to rise rapidly, thereby generating an impact current. When starting with load, the starting impact current will be even greater.

[0079] From the above analysis, we can know that the main reason for the starting impact current is that the reference value of the DC bus voltage is given in steps. dc The rate of change of U is very large, which in turn generates a starting impact current. To address this problem, the DC bus voltage reference value is usually made to rise smoothly to the expected value according to a certain rule, which can reduce U dc Therefore, a new slow curve generation method is proposed to effectively suppress the starting impact current.

[0080] In ADRC, a transition process is usually arranged for the system input, and the purpose of arranging the transition process is to allow the system input to slowly approach the target point without stepping. That is, the transition process slowly generates a curve toward the target point. The transition process is completed by a nonlinear tracking differentiator (TD).

[0081] A nonlinear tracking differentiator is a nonlinear time-varying link that can obtain the differential form of the input signal. A typical nonlinear tracking differentiator is designed using the symbolic function sign, and its expression is:

[0082]

[0083] After the input signal v passes through TD, two output signals are generated, namely the tracking signal x1 of the input signal and the differential x2 of the tracking signal. The tracking speed of x1 is limited by the speed factor α, and the parameter α is difficult to determine.

[0084] In order to solve the problem that the parameters of the nonlinear tracking differentiator are difficult to confirm, the present invention adopts a linear tracking differentiator (LTD) to obtain a slow curve. The form of the linear tracking differentiator is:

[0085]

[0086] Among them, U' dc =2.34 E , where E represents the effective value of the grid voltage; where r is an adjustable parameter, in the present invention, a voltage U' is added to the linear tracking differentiator dc , when switching the controlled rectifier, add U' dc The initial value of the curve can be kept consistent with the actual initial value of the DC bus voltage to reduce the error.

[0087] Given an input signal v of 150, the output signals x1 and x2 of NTD and LTD can be obtained by building a Simulink model. Figure 3As shown. Both the nonlinear tracking differentiator and the linear tracking differentiator can obtain a gently rising curve x1. If the DC bus voltage reference value adopts curve x1, it can just solve the problem of the large rate of change of the DC bus voltage in the first few switching cycles when the PWM rectifier is just started, thereby suppressing the starting impact current. However, the curve obtained by NTD has an overshoot at the end of the curve. It can be seen from curve x2 that the rate of change of curve x1 at the start and end times is zero. However, the rate of change of curve x1 obtained by NTD is large during the rising process. And the maximum value of curve x2 obtained by NTD is difficult to determine. If its maximum value is too large, it will affect the d-axis current, thereby affecting the effect of suppressing the impact current. The structural block diagram of the linear tracking differentiator is shown as follows. Figure 4 The control strategy of the present invention is as shown in Figure 5 shown.

[0088] Solving the linear tracking differentiator yields:

[0089] x1=vv(1+rt)e -rt

[0090] Where t is time. The optimal solution of the function in the above formula can be transformed into the optimal solution of the minimum value of the objective function f in the following formula. The time variable t and the parameter r can be regarded as variables:

[0091] f=(1+rt)e -rt

[0092] There are many methods for finding the optimal solution of a function, such as gradient descent method, Newton iteration method, and numerical optimization method. The present invention chooses to use Newton iteration method to find the optimal solution. The partial derivative of f with respect to r and t is calculated as:

[0093]

[0094] From the above formula, the second-order partial derivative of f with respect to r and t can be calculated as:

[0095]

[0096] From the above formula, we can see that the gradient of the objective function is And the Hessian matrix H is:

[0097]

[0098] The update formula of Newton iteration method is:

[0099]

[0100] Assume that the maximum number of iterations is 1000 and the allowable error is 1×10 -6 .

[0101] When the initialization starting point is set to [rt] = [300 0.04], the optimal value of f and the optimal solutions of variables r and t are as follows: Figure 6 As shown, the total number of iterations is 236, and the optimal solutions of r and t are 415 and 0.055 respectively.

[0102] In the embodiment of the present invention, the PWM rectifier DC bus reference voltage adopts a voltage and current simulation waveform given by a step, such as Figure 7 As shown, at the moment of startup with U dc The error is large, and the a-phase current and d-axis current command values ​​generate 16A and 19A of impact current respectively. The PWM rectifier DC bus reference voltage uses a slow curve as the given starting voltage and current simulation waveform as shown in Figure 8 As shown. When the reference voltage reaches the expected value at 0.055s, the impact values ​​of the a-phase current and d-axis current command values ​​are reduced to 7.5A and 8A respectively. The voltage and current waveforms after the PWM rectifier DC bus reference voltage adopts a slow curve as a given time. Fig. 9 As shown in the figure, the a-phase current has no obvious impact value. The d-axis current will produce an impact value of 5.67A.

[0103] The PWM rectifier DC bus reference voltage adopts a step-given voltage and current experimental waveform as shown in the figure. Fig.10 As shown, the DC bus reference voltage of the PWM rectifier adopts a slow curve as the given voltage and current experimental waveforms at startup and after transformation. Fig.11 and Fig.12 As shown in the above results, it can be seen that using the gentle curve obtained by the tracking differentiator as the DC bus voltage reference has a significant inhibitory effect on the starting impact current.

[0104] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

Claims

1. A three-phase PWM rectifier startup inrush current suppression strategy based on a tracking differentiator, characterized in that: Specifically include: Step 1: Based on the PWM rectifier mathematical model, calculate the instantaneous value of the d-axis current i based on the model d (k) and DC bus voltage U dc the relationship between rates of change; Step 2: In order to reduce the rate of change between the DC bus voltage value and the DC bus voltage reference value, a soft start strategy based on a tracking differentiator is adopted, and the curve output by the tracking differentiator is used as the DC bus voltage reference value to suppress the starting impact current of the PWM rectifier.

2. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 1, characterized in that: The expression of the PWM rectifier mathematical model in step 1 is: in, They are the d-axis and q-axis command currents, K vP , K vI are the proportional coefficient and integral coefficient of the voltage outer loop PI regulator, is the DC bus voltage reference value; S d , S q are the d-axis and q-axis components of the switching function respectively; K iP , K iI is the proportional coefficient and integral coefficient of the current inner loop PI regulator, s represents the differential; i d 、i q They represent the d-axis and q-axis components of the grid current, ω is the grid voltage angular frequency, L is the AC side inductance, and e d is the d-axis component of the grid voltage.

3. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 1, characterized in that: The instantaneous value of d-axis current i d (k) and DC bus voltage U dc The relationship between the rates of change is expressed as follows: Where C is the DC bus capacitance, k is the time variable, T s is the control period, e d is the d-axis component of the grid voltage, i L is the load current.

4. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 1, characterized in that: The slow start strategy of the tracking differentiator is specifically: using a linear tracking differentiator, solving the linear tracking differentiator to establish an objective function, and solving the objective function to obtain the adjustable parameters r and time t of the linear tracking differentiator.

5. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 4, characterized in that: The expression of the linear tracking differentiator is: Where v represents the input signal of the linear tracking differentiator, x1 is the tracking signal of the input signal, x2 is the differential of x1, and U' dc =2.34 E , where E represents the effective value of the grid voltage; Solving the linear tracking differentiator, we obtain: x1 = vv(1+rt)e -rt .

6. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 4, characterized in that: The objective function is: min f=(1+rt)e -rt 。 7. The three-phase PWM rectifier startup inrush current suppression strategy based on tracking differentiator according to claim 4, characterized in that: Newton iteration method is used to solve the objective function: Among them, k1 represents the number of iterations, H is the Hessian matrix, is the gradient of the objective function, H and The expression is:

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