A control method of electric spring based on sliding mode control

Abstract

The present invention discloses a power spring control method based on sliding mode control, comprising the following steps: determining that the transmission line current satisfies a relational expression when the voltage on the key load side reaches a reference value, and an expression for the transmission line current amplitude; calculating the reference value of the transmission line current and the reference value of the output voltage of the power spring according to the detected grid voltage and various circuit parameters; obtaining the final reference value of the output voltage of the power spring; calculating the error between the reference value of the sine wave of the output voltage of the power spring and the actual sine wave of the output voltage of the power spring, and performing sliding mode control. The present invention controls the output voltage of the power spring so that the voltage of the key load is stabilized to the reference value, thereby achieving system stability.

Description

Technical Field

[0001] The invention relates to the technical field of power electronic inverter control, and in particular to an electric spring control method based on sliding mode control. Background Art

[0002] In recent years, the renewable energy industries such as wind energy and solar energy have developed rapidly. Although they have brought a lot of clean energy, their intermittent and unpredictable characteristics have affected the voltage stability in microgrids and posed a threat to the stability of the power system. In order to solve the problem of load voltage fluctuations caused by renewable energy, Professor Xu Shuyuan of the University of Hong Kong proposed the concept of power springs in 2012, applying the principle of mechanical springs to the power field, and dividing the loads into critical loads and non-critical loads, sacrificing the voltage stability of non-critical loads. By controlling the output voltage of the power springs, active power and reactive power compensation are provided to the system, achieving the purpose of stabilizing the voltage of critical loads and improving the power quality of the system. However, the existing technology is not good enough in anti-interference. Summary of the invention

[0003] The object of the present invention is to provide a method for realizing voltage compensation of a key load by an electric spring by an electric spring control method based on sliding mode control.

[0004] The technical solution to achieve the purpose of the present invention is:

[0005] An electric spring control method based on sliding mode control comprises the following steps:

[0006] Step 1: Establish a mathematical model of the electric spring according to the circuit structure of the electric spring. The mathematical model of the electric spring is:

[0007]

[0008] where v g is the grid voltage; v es is the output voltage of the power spring; L1 is the equivalent inductance of the transmission line; R1 is the equivalent resistance of the transmission line; Z1 is the equivalent impedance of the transmission line; Z C is the critical load resistance; Z2 is the non-critical load resistance; C is the AC measurement filter capacitor, L is the AC measurement filter inductor; v i is the inverter AC side output voltage; v c is the power spring critical load voltage; i0 is the inductor current; i1 is the transmission line current; i2 is the non-critical load current; i3 is the critical load current;

[0009] Step 2: Determine the voltage v at the critical load side c Reach the reference value v c-ref When the transmission line current I1 satisfies the relationship:

[0010] (I r -K1) 2 +(I i -K2) 2 =ε 2

[0011]

[0012] Among them I r , I i are the real and imaginary parts of the transmission line current respectively; K1 and K2 are the grid voltage v g The real and imaginary parts of the ratio of the line impedance Z1; ε is the critical load voltage reference value V c-ref The ratio of the line impedance modulus |Z1| satisfies:

[0013]

[0014] Step 3: Determine the transmission line current amplitude I 1M The expression is:

[0015]

[0016] Among them I r , I i are the real and imaginary parts of the transmission line current, respectively;

[0017] Step 4: According to the detection grid voltage signal v g , line impedance, and the relationships and expressions in steps 2 and 3 to determine the reference value of the transmission line current I 1M-ref :

[0018] (1) When the grid voltage modulus |v g |Less than the critical load voltage reference value v c-ref hour:

[0019]

[0020]

[0021] At this time, the transmission line current amplitude I 1M Set to:

[0022]

[0023] (2) When the grid voltage modulus |v g |Greater than the critical load voltage reference value v c-ref hour:

[0024]

[0025] At this time, the transmission line current amplitude I 1M Set to:

[0026]

[0027] Step 5: Determine the reference value v of the output voltage of the electric spring es-ref and phase angle reference value θ es-ref :

[0028]

[0029]

[0030] where v es-ref is the reference value I of the transmission line current in step 4 1-ref Substitute the following formula:

[0031]

[0032] in:

[0033]

[0034]

[0035] The relationship obtained; v es-refr and v es-refi They are v es-ref The real and imaginary parts of

[0036] Step 6: Set the phase angle reference value θ of the power spring output voltage es-ref , generate a sinusoidal signal through a sin function signal generator, and use the amplitude reference value of the output voltage of the electric spring Multiplying with the sinusoidal signal gives the final electric spring output voltage sinusoidal wave:

[0037]

[0038] where v ref The output voltage of the electric spring is a sine wave;

[0039] Step 7: Perform sliding mode control on the error between the output voltage sine wave of the electric spring in step 6 and the actual output voltage sine wave of the electric spring. From the modeling in step 1, it can be seen that:

[0040]

[0041] Where D represents the sum of parameter perturbation, electromagnetic interference and unknown interference;

[0042] Define the error variable of the system as e, and its expression is:

[0043] e=v ref -v es

[0044] where v es is the output voltage of the electric spring, and the first-order derivative of the error variable is obtained by taking its derivative:

[0045]

[0046] Considering that the tracking error e finally converges to zero, the sliding mode variable s is defined as:

[0047]

[0048] Where λ (λ>0) is a constant, and the first-order derivative obtained by differentiating the sliding mode variable is:

[0049]

[0050]

[0051] Step 8: The sliding mode variable structure controller of the single-phase power spring system adopts the Lyapunov direct method and selects the Lyapunov function:

[0052]

[0053] Derivative it yields:

[0054]

[0055] The sliding mode variable structure controller expression is obtained as follows:

[0056]

[0057] Where η is a constant greater than zero, sign(s) is the sign function, and we have:

[0058]

[0059] To verify the rationality of the controller design, we have:

[0060]

[0061] To ensure convergence, It can make η≥|D|, when When s≡0, according to Lyapunov principle, the closed-loop system is asymptotically stable. Within a certain period of time, the sliding mode variable s converges to the sliding surface s=0, and the closed-loop dynamic error will gradually decrease, be limited to the sliding surface, and gradually converge to 0. The convergence speed depends on the size of the parameter η.

[0062] Compared with the prior art, the present invention has the following significant advantages: on the premise of stabilizing the key load voltage, the present invention can reduce external interference and quickly achieve the purpose of stabilizing the key load voltage. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is the block diagram of electric spring control based on sliding mode control.

[0064] Figure 2 System topology diagram for power spring application.

[0065] Figure 3 It is the effective value of the key load voltage under the control method of the present invention and the actual effective value waveform of the key load voltage when ES is not introduced. DETAILED DESCRIPTION

[0066] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0067] like Figure 1 As shown, the electric spring control method based on sliding mode control of the present invention comprises the following steps:

[0068] Step 1: According to Figure 2 The circuit structure diagram of the electric spring is shown, and the mathematical model of the electric spring is established. The model is:

[0069]

[0070] in:

[0071] where v g is the grid voltage; v es is the output voltage of the power spring; L1 is the equivalent inductance of the transmission line; R1 is the equivalent resistance of the transmission line; Z1 is the equivalent impedance of the transmission line; Z C is the critical load resistance; Z2 is the non-critical load resistance; C is the AC measurement filter capacitor, L is the AC measurement filter inductor; v i is the inverter AC side output voltage; v c is the power spring critical load voltage; i0 is the inductor current; i1 is the transmission line current; i2 is the non-critical load current; i3 is the critical load current.

[0072] Step 2: Determine the voltage v at the critical load side c Reach the reference value v c-ref When the transmission line current I1 satisfies the relationship:

[0073] (I r -K1) 2 +(I i -K2) 2 =ε 2

[0074]

[0075]

[0076] Among them I r , I i are the real and imaginary parts of the transmission line current respectively; K1 and K2 are the grid voltage v g The real and imaginary parts of the ratio of the line impedance Z1; ε is the critical load voltage reference value V c-ref The ratio of the line impedance modulus |Z1| satisfies:

[0077]

[0078] Step 3: Determine the transmission line current amplitude I 1M The expression is:

[0079]

[0080] Among them I r , I i are the real and imaginary parts of the transmission line current, respectively;

[0081] Step 4: According to the detection grid voltage signal v g , line impedance, and the expressions in steps 2 and 3 to determine the reference value of the transmission line current I 1M-ref :

[0082] (1) When the grid voltage modulus |v g |Less than the critical load voltage reference value v c-ref hour:

[0083]

[0084]

[0085] At this time, the transmission line current amplitude I 1M Set to:

[0086]

[0087] (2) When the grid voltage modulus |v g |Greater than the critical load voltage reference value v c-ref hour:

[0088]

[0089] At this time, the transmission line current amplitude I 1M Set to:

[0090]

[0091] Step 5: Determine the reference value v of the output voltage of the electric spring es-ref and phase angle reference value θ es-ref :

[0092]

[0093]

[0094] where v es-ref is the reference value I of the transmission line current in step 4 1-ref Substitute the following formula:

[0095]

[0096] in:

[0097]

[0098]

[0099] The relationship obtained; v es-refr and v es-refi They are v es-ref The real and imaginary parts of .

[0100] Step 6: Set the phase angle reference value θ of the power spring output voltage es-ref , generate a sinusoidal signal through a sin function signal generator, and use the amplitude reference value of the output voltage of the electric spring Multiplying with the sinusoidal signal gives the final electric spring output voltage sinusoidal wave:

[0101]

[0102] where v ref The output voltage of the electric spring is a sine wave;

[0103] Step 7: Perform sliding mode control on the error between the output voltage sine wave of the electric spring in step 6 and the actual output voltage sine wave of the electric spring. From the modeling in step 1, it can be seen that:

[0104]

[0105] Where D represents the sum of parameter perturbation, electromagnetic interference and unknown interference.

[0106] Define the error variable of the system as e, and its expression is:

[0107] e=v ref -v es

[0108] where v es is the output voltage of the electric spring, and the first-order derivative of the error variable is obtained by taking its derivative:

[0109]

[0110] Considering that the tracking error e finally converges to zero, the sliding mode variable s can be defined as:

[0111]

[0112] Where λ (λ>0) is a constant, and the first-order derivative obtained by differentiating the sliding mode variable is:

[0113]

[0114]

[0115] The above completes the selection of the sliding surface of the sliding mode controller. Next, the specific expression of the variable structure controller is derived based on the sliding surface.

[0116] Step 8. In order to verify the stability of the sliding mode controlled single-phase electric spring system control system, it is necessary to select an appropriate Lyapunov energy function. By designing a sliding mode variable structure controller for the single-phase electric spring system and ensuring that the energy function converges, it can be proved that the system is stable. The sliding mode variable structure controller for the single-phase electric spring system in this paper adopts the Lyapunov direct method, and the selected Lyapunov function is:

[0117]

[0118] Taking the derivative of it, we get:

[0119]

[0120] The sliding mode variable structure controller expression is obtained as follows:

[0121]

[0122] Where η is a constant greater than zero, sign(s) is the sign function, and we have:

[0123]

[0124] To verify the rationality of the controller design, we have:

[0125]

[0126] To ensure convergence, we need It is possible to make η≥|D|, that is, η needs to be greater than or equal to the maximum value of the absolute value of the sum of system interference. When s≡0, according to Lyapunov principle, the closed-loop system is asymptotically stable. Within a certain period of time, the sliding mode variable s converges to the sliding surface s=0, and the closed-loop dynamic error will gradually decrease, be limited to the sliding surface, and gradually converge to 0. The convergence speed depends on the size of the parameter η.

[0127] Through the above theoretical analysis, it can be seen that the design of the sliding mode variable structure controller designed in the present invention is reasonable and correct, which provides a theoretical basis for the subsequent simulation experiment analysis.

[0128] Example

[0129] In order to verify the effectiveness of the solution of the present invention, a simulation model was built in MATLAB / Simulink, and simulation experiments were carried out using a discrete time and fixed step simulation mode.

[0130] The sampling time is 5e-5s, and the component parameters used in the simulation are shown in Table 1.

[0131] Table 1 Simulation component parameters

[0132]

[0133] The transmission line current and key load voltage compensation electric spring control method proposed in the present invention is compared with the traditional electric spring control method. When the voltage on the grid side fluctuates, the control method proposed in the present invention is adopted. When the active power injected into the grid by the renewable energy system is lower than the operating condition, the grid voltage is lower than 220V. We set the grid voltage to 210V, and conduct simulation experiments in this state to verify its supporting role, and obtain the effective value waveform of the key load voltage under the action of the electric spring, which gradually reaches the reference voltage value of 220V.

[0134] The present invention proposes a power spring control method based on transmission line current and key load voltage compensation, which can ensure that the voltage on the key load side is stable to a reference value and achieve stability of the power system.

[0135] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An electric spring control method based on sliding mode control, characterized in that: The steps include: Step 1: Establish a mathematical model of the electric spring according to the circuit structure of the electric spring. The mathematical model of the electric spring is: where v g is the grid voltage; v es is the output voltage of the power spring; L1 is the equivalent inductance of the transmission line; R1 is the equivalent resistance of the transmission line; Z1 is the equivalent impedance of the transmission line; Z C is the critical load resistance; Z2 is the non-critical load resistance; C is the AC measurement filter capacitor, L is the AC measurement filter inductor; v i is the inverter AC side output voltage; v c is the power spring critical load voltage; i0 is the inductor current; i1 is the transmission line current; i2 is the non-critical load current; i3 is the critical load current; Step 2: Determine the voltage v at the critical load side c Reach the reference value v c-ref When the transmission line current I1 satisfies the relationship: (AND r -K1) 2 +(I i -K2) 2 =ε 2 Among them I r , I i are the real and imaginary parts of the transmission line current respectively; K1 and K2 are the grid voltage v g The real and imaginary parts of the ratio of the line impedance Z1; ε is the critical load voltage reference value V c-ref The ratio of the line impedance modulus |Z1| satisfies: Step 3: Determine the transmission line current amplitude I 1M The expression is: Among them I r , I i are the real and imaginary parts of the transmission line current, respectively; Step 4: According to the detection grid voltage signal v g , line impedance, and the relationships and expressions in steps 2 and 3 to determine the reference value of the transmission line current I 1M-ref : (1) When the grid voltage modulus |v g |Less than the critical load voltage reference value v c-ref hour: At this time, the transmission line current amplitude I 1M Set to: (2) When the grid voltage modulus |v g |Greater than the critical load voltage reference value v c-ref hour: At this time, the transmission line current amplitude I 1M Set to: Step 5: Determine the reference value v of the output voltage of the electric spring es-ref and phase angle reference value θ es-ref : where v es-ref is the reference value I of the transmission line current in step 4 1-ref Substitute the following formula: in: The relationship obtained; v es-refr and v es-refi They are v es-ref The real and imaginary parts of Step 6: Set the phase angle reference value θ of the power spring output voltage es-ref , generate a sinusoidal signal through a sin function signal generator, and use the amplitude reference value of the output voltage of the electric spring Multiplying with the sinusoidal signal gives the final electric spring output voltage sinusoidal wave: where v ref The output voltage of the electric spring is a sine wave; Step 7: Perform sliding mode control on the error between the output voltage sine wave of the electric spring in step 6 and the actual output voltage sine wave of the electric spring. From the modeling in step 1, it can be seen that: Where D represents the sum of parameter perturbation, electromagnetic interference and unknown interference; Define the error variable of the system as e, and its expression is: e=v ref -v es where v es is the output voltage of the electric spring, and the first-order derivative of the error variable is obtained by taking its derivative: Considering that the tracking error e finally converges to zero, the sliding mode variable s is defined as: Where λ (λ>0) is a constant, and the first-order derivative obtained by differentiating the sliding mode variable is: Step 8: The sliding mode variable structure controller of the single-phase power spring system adopts the Lyapunov direct method and selects the Lyapunov function: Derivative it yields: The sliding mode variable structure controller expression is obtained as follows: Where η is a constant greater than zero, sign(s) is the sign function, and we have: To verify the rationality of the controller design, we have: To ensure convergence, we need It can make η≥|D|, when When s≡0, according to Lyapunov principle, the closed-loop system is asymptotically stable. Within a certain period of time, the sliding mode variable s converges to the sliding surface s=0, and the closed-loop dynamic error will gradually decrease, be limited to the sliding surface, and gradually converge to 0. The convergence speed depends on the size of the parameter η.

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