CN106229979A - Control Method of Active Power Filter based on fractional order sliding formwork - Google Patents

Abstract

The invention discloses a method for controlling an active power filter based on a fractional-order sliding mode, comprising: (1) establishing a mathematical model of the active power filter; (2) establishing a fractional-order sliding mode based on the active power filter The control law equation of the controller; (3) The active power filter is controlled by the output of the fractional-order sliding mode controller. The invention can ensure the real-time tracking of the harmonic current, strengthen the dynamic performance of the system, improve the robustness of the system, and can still maintain a good energy performance when the external load changes; the sliding mode variable controller is designed to ensure effective The source power filter runs along the sliding mode trajectory; the fractional order module is introduced in the sliding mode controller, which increases the adjustable items compared with the integer order and improves the overall performance of the system.

Description

Active Power Filter Control Method Based on Fractional Sliding Mode

technical field

The invention belongs to the technical field of active power filters, and in particular relates to a fractional-order sliding mode-based active power filter control method.

Background technique

Capacitors for compensating reactive power are widely used in the power grid. At a certain frequency, it may meet the condition of series or parallel resonance. When the harmonic is large enough, it will cause dangerous overvoltage or overcurrent, which often leads to electrical components and Equipment damage seriously affects the safe operation of the power system. In addition, the flow of harmonic currents in the grid will cause active power loss on the line. The additional line loss caused by the skin effect of the wire is relatively large; severe harmonic distortion reduces the breaking capacity of the circuit breaker and may damage the circuit breaker. In civil buildings, since the neutral line is generally thin (the new standard has increased When a large number of harmonics (usually the third harmonic) flow through it, it will overheat the wires, damage the insulation, and cause a short circuit, causing a fire.

At present, the commonly used ways to control harmonic pollution can be divided into two types: one is to improve the power electronic device itself to reduce harmonic generation in the process of electric energy conversion, and at the same time improve the power factor as much as possible. This method is suitable for power Where electronic equipment is the main source of harmonics. Second, use a power filter device to absorb the harmonics generated by the harmonic source nearby, which is the most effective and widely used measure for harmonic suppression at present. At present, passive filters are still mainly used in China to deal with harmonics in the power grid. However, the compensation characteristics of passive filters are single, and are easily affected by system impedance, causing resonance phenomena, amplifying harmonics, and then burning compensation devices, and can only effectively deal with specific harmonics. People gradually shift the focus of research to active power filter. Power grid purification products such as APF are standard products for smart grid construction. They can realize dynamic compensation of harmonics and reactive power, have fast response, are less affected by grid impedance, and are not easy to resonate with grid impedance; Suppressing flicker, compensating reactive power, compensation performance is not affected by grid frequency changes, and can effectively suppress harmonic pollution, so it has become an important means of harmonic control.

At present, the advanced control theory system of active power filter has not yet formed a system at home and abroad, and faces many problems that need to be studied and solved urgently. The modeling method of active power filter varies from person to person, and various control methods are used. There is a lack of system stability proof, and problems such as different system performance evaluation standards are common. Therefore, the research of active power filter has important scientific research significance and broad market prospect.

Contents of the invention

In view of the above problems, the present invention proposes an active power filter control method based on fractional-order sliding mode.

Realize above-mentioned technical purpose, reach above-mentioned technical effect, the present invention realizes through the following technical solutions:

A kind of active power filter control method based on fractional order sliding mode, comprises the following steps:

Step 1, establish the mathematical model of active power filter;

Step 2, establishing the control law equation of the fractional-order sliding mode controller based on the active power filter;

Step 3, using the output of the fractional-order sliding mode controller to control the active power filter.

In the step one, the active power filter mathematical model is:

$\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}$

Among them, x is the compensation current output by the active power filter, is the first derivative of x, k=1, 2, 3, v ₁ , v ₂ , v ₃ are three-phase active filter terminal voltage respectively, i ₁ , i ₂ , i ₃ are three-phase compensation current respectively, R _c is resistance, L _c is inductance, v _dc is the capacitor voltage, u is the control law output by the fractional-order sliding mode controller, d is the system disturbance, and t is the time.

In the second step, the control law equation of the fractional-order sliding mode controller is:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; b\&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&rsqb;</span>$

Among them, λ ₁ , λ ₂ , λ ₃ are adjustable parameters and are all positive numbers, x _d is the detection signal current, In order to detect the derivative of the signal current, D ^α e and D ^α-1 e are the fractional derivatives of the tracking error, α is any rational number; ρ is the upper bound of interference, and ρ is a positive number. The upper bound ρ satisfies the inequality ρ-|d|>σ ₁ , where σ ₁ is a positive number; s is a switching function, s=-λ ₁ e-λ ₂ ∫e-λ ₃ D ^α-1 e, the controller’s The goal is to make the compensation current x track the detection signal current x _d , where the tracking error e=x _d −x.

The third step is specifically: the active power filter collects the simulated load current in the main circuit, processes and outputs the corresponding control law through the fractional order controller, and controls the compensation current output by the compensation current generation module of the active power filter and The amplitude of the detection signal current is the same and the phase is opposite, and finally the desired power supply current is obtained.

Beneficial effects of the present invention:

The control method of the active power filter based on the fractional sliding mode of the present invention can ensure the real-time tracking of the harmonic current, enhance the dynamic performance of the system, and improve the robustness of the system. When the external load changes, it can still Maintain a good system energy; design the sliding mode variable controller to ensure that the active power filter runs along the sliding mode trajectory; introduce the fractional order module in the sliding mode controller, and increase the adjustable item compared with the integer order, Improve the overall performance of the system.

Description of drawings

Fig. 1 is a schematic diagram of a model of an active power filter in a specific embodiment of the present invention.

Fig. 2 is a working principle diagram of the fractional-order sliding mode control method of the active power filter of the present invention.

FIG. 3 is a time-domain response curve diagram of the actual output tracking the expected curve in a specific embodiment of the present invention.

Fig. 4 is a curve diagram of the voltage response of the DC side after the load is added stepwise in a specific embodiment of the present invention.

detailed description

In order to make the object, technical solution and advantages of the present invention more clear, the present invention will be further described in detail below in conjunction with the examples. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

The application principle of the present invention will be described in detail below in conjunction with the accompanying drawings.

A kind of active power filter control method based on fractional order sliding mode, comprises the following steps:

Step 1, establish the mathematical model of active power filter;

Step 2, establishing the control law equation of the fractional-order sliding mode controller based on the active power filter;

Step 3, using the output of the fractional-order sliding mode controller to control the active power filter.

What the present invention studies is the relatively widely used parallel voltage type active power filter. In daily life, the application of three-phase alternating current accounts for the majority, so it mainly studies the situation of being used in a three-phase three-wire system. As shown in Figure 1, its A model of an active power filter is represented.

The active power filter is mainly composed of three parts, namely the harmonic current detection module, the current tracking control module and the compensation current generation module. The harmonic current detection module usually adopts fast detection of harmonic current based on instantaneous reactive power theory. The compensation current of a three-phase three-wire active power filter (APF) is usually controlled by PWM. The compensation current should have the same amplitude as the detected harmonic current and the opposite phase to achieve the purpose of eliminating the harmonic component.

The basic working principle of the active power filter is to detect the voltage and current of the object to be compensated, and calculate the command signal of the compensation current through the command current operation circuit. The signal is amplified by the compensation current generation circuit to obtain the compensation current (that is, this In x) in the invention, the compensation current offsets the harmonics and reactive currents to be compensated in the load current (ie, the detection signal current in the invention), and finally obtains the desired power supply current.

Step 1. Establish the mathematical model of the active power filter:

According to circuit theory and Kirchhoff's theorem, the following formula can be obtained:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\\ {\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Among them, v _1M , v _2M , and v _3M are the voltages from terminal M to terminal a, b, and c, respectively, and v _MN is the voltage from terminal M to terminal N; v ₁ , v ₂ , and v ₃ are three-phase active power filters, respectively Terminal voltage, i ₁ , i ₂ , i ₃ are three-phase compensation current respectively, R _c is resistance, L _c is inductance;

Assuming that the power supply voltage on the AC side is stable, we can get:

${\mathrm{<span\; class="notranslate">\; \&nu;</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Among them, v _mM is the voltage from terminal M to terminals a, b and c respectively, m=1,2,3;

Define the switching function c _k to indicate the working state of the IGBT, which is defined as follows:

Among them, k=1,2,3.

At the same time, define v _kM = c _k v _dc , then formula (1) can be written as:

$\left\{\begin{array}{c}\frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\\ \frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\\ \frac{{\mathrm{<span\; class="notranslate">\; di</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}{\mathrm{<span\; class="notranslate">\; i</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; c</span>}}}{{\mathrm{<span\; class="notranslate">\; L</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 3</span>}}\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; 3</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, v _mM =c _m v _dc , c _m is the switch function, m=1,2,3;

Considering that there will be interference in the actual process, the three equations in formula (4) can be written in the following form:

$\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Among them, x is the compensation current output by the active power filter, x=[i ₁ ,i ₂ ,i ₃ ], is the first derivative of x,

k=1, 2, 3, v ₁ , v ₂ , v ₃ are three-phase active filter terminal voltage respectively, i ₁ , i ₂ , i ₃ are three-phase compensation current respectively, R _c is resistance, L _c is inductance, v _dc is the capacitor voltage, u, d are the amount of system disturbance, and t is the time.

2. Establish the control law equation of the fractional-order sliding mode controller based on the active power filter:

Set the upper bound of disturbance as ρ, ρ is a positive number, the system disturbance d and the disturbance upper bound ρ satisfy the inequality ρ-|d|>0, the goal of the controller is to make the compensation current x track the detection signal current x _d , where, Tracking error e= _xd -x.

The switching function s (that is, the fractional dynamic sliding mode surface equation) is defined as:

s=-λ ₁ e-λ ₂ ∫e-λ ₃ D ^α-1 e (6)

In the present invention, the function of the switching function is to make the tracking error gradually close to 0 when the system reaches the motion state.

make The corresponding equivalent control law equation can be obtained as:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; b\&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&rsqb;</span>$

Using the switching function u _sw =λ ₁ ρsgn(s) to replace λ ₁ d, the control law equation of the fractional sliding mode controller can be obtained as:

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; b\&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

3. Use the output of the fractional-order sliding mode controller to control the active power filter:

Specifically: the active power filter collects the simulated load current in the main circuit, processes and outputs the corresponding control law through the fractional-order controller, and controls the compensation current output by the compensation current generation module of the active power filter and the detection signal current. The amplitude is the same and the phase is opposite, and finally the desired power supply current is obtained.

4. Design the Lyapunov function:

$\mathrm{<span\; class="notranslate">\; V</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

but

$\begin{array}{c}\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\stackrel{<span\; class="notranslate">\; \&CenterDot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; b</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; b\&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; D.</span>}}^{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; \}</span>\\ <span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}\mathrm{<span\; class="notranslate">\; sgn</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&le;</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; )</span>\end{array}$

Because ρ-|d|>0, λ ₁ >0, so So the system can be stable.

5. Matlab simulation experiment

Combining the dynamic model of the active power filter and the fractional-order sliding mode control method, the main program is designed by Matlab/Simulink software.

The power supply voltage and frequency are V _s1 ＝V _s2 ＝V _s3 ＝220V, f＝50Hz, the nonlinear load is R＝10Ω, L＝2mH, the parameters of the active power filter are L＝100hH, R＝100Ω, C＝ 100 μF, λ ₁ =12, λ ₂ =3, λ ₃ =3, ρ=180000, α=0.9.

At 0.04S, the compensation circuit access switch is closed, and the active filter starts to work, and at 0.1S and 0.2S, an identical additional non-linear load is respectively connected.

The experimental results are shown in Figure 3 and Figure 4.

The beneficial effects of the present invention are:

The present invention designs a fractional-order sliding mode control method based on an active power filter, which can ensure real-time tracking of harmonic currents, enhance the dynamic performance of the system, and improve system robustness. Very good system performance; by designing the sliding mode variable controller to ensure that the active power filter runs along the sliding mode trajectory; the fractional order module is introduced in the sliding mode controller, which increases the adjustable items compared with the integer order, improving the overall performance of the system.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description only illustrate the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will also have Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (4)

1. a Control Method of Active Power Filter based on fractional order sliding formwork, it is characterised in that comprise the following steps:

Step one, set up the mathematical model of Active Power Filter-APF；

Step 2, the control law equation of foundation fractional order sliding mode controller based on Active Power Filter-APF；

Step 3, utilize fractional order sliding mode controller output control Active Power Filter-APF.

A kind of Control Method of Active Power Filter based on fractional order sliding formwork the most according to claim 1, its feature exists In: in described step one, Active Power Filter-APF mathematical model is:

$\stackrel{\&CenterDot;}{x}=f\left(x\right)+bu+d$

Wherein, x is the compensation electric current of Active Power Filter-APF output,It is the first derivative of x,K=1, 2,3, v₁,v₂,v₃It is respectively three-phase active power filter terminal voltage, i₁,i₂,i₃It is respectively three-phase and compensates electric current, R_cFor resistance, L_cFor Inductance,v_dcFor capacitance voltage, u is the control law of fractional order sliding mode controller output, and d is system interference amount, and t is Time.

A kind of Control Method of Active Power Filter based on fractional order sliding formwork the most according to claim 2, its feature exists In: in described step 2, the control law equation of fractional order sliding mode controller is:

$u=\frac{1}{{\mathrm{b\&lambda;}}_1}\&lsqb;-{\mathrm{\&lambda;}}_{1}f\left(x\right)-{\mathrm{\&lambda;}}_1\mathrm{\&rho;}sgn\left(s\right)+{\mathrm{\&lambda;}}_1{\stackrel{\&CenterDot;}{x}}_d+{\mathrm{\&lambda;}}_{2}e+{\mathrm{\&lambda;}}_3{D}^{\mathrm{\&alpha;}}e\&rsqb;$

Wherein, λ₁、λ₂、λ₃For customized parameter and be positive number, x_dFor detecting signal code,For leading of detection signal code Number, D^αe、D^α-1E is the Fractional Derivative of tracking error, and α takes arbitrarily for rational number；ρ is the interference upper bound, and interference upper bound ρ is just Number, system interference amount d and interference upper bound ρ meet inequality ρ-| d | > σ₁, wherein, σ₁For positive number；S is switching function, s=-λ₁e- λ₂∫e-λ₃D^α-1E, the target of controller makes compensation electric current x tracing detection signal code x exactly_d, wherein, tracking error e=x_d- x。

4. according to a kind of based on fractional order sliding formwork the Control Method of Active Power Filter described in claim 1 or 3, its feature It is: described step 3, particularly as follows: Active Power Filter-APF gathers the simulated load current in main circuit, passes through fractional order control Device processes and exports corresponding control law, control the compensation electric current compensating the output of electric current generation module of Active Power Filter-APF with Amplitude same phase in detection signal code is contrary, finally gives desired source current.