Predictive Voltage Control Method for Induction Motor Optimization Model

Abstract

The present invention discloses an induction motor optimization model predictive voltage control method. First, a mathematical model of the induction motor is established using the induction motor stator current and stator flux as state variables. Based on the stator voltage equation, a stator voltage reference value is calculated. Based on this, a reference voltage vector position angle is calculated, the sector where the reference voltage vector is located is determined, and a non-zero vector and a zero vector in this sector are selected as candidate voltage vectors. Assuming that the current moment is time k, the stator current at time k+1 is predicted to obtain a stator current prediction value corresponding to the candidate voltage vector. Based on this, a candidate voltage prediction value is calculated based on the stator current prediction value. A cost function is designed, and the stator voltage tracking error is used as a control variable. At the same time, an overcurrent protection link is designed in the cost function to ensure the normal operation of the system. The present invention effectively reduces the system computation load and improves the practicality of model predictive control.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-performance induction motor speed regulation control, and in particular relates to an induction motor optimization model prediction voltage control method. Background Art

[0002] Due to its many advantages such as low cost, high reliability, simple structure and low price, induction motors have been widely used in industrial and agricultural production, transportation, national defense and military, aerospace and other fields. At present, vector control is usually used for high-performance control systems of induction motors. However, the cascade structure in vector control and the links such as regulator parameter setting and pulse width modulation increase the complexity of control and limit the dynamic response speed of the system.

[0003] In recent years, model predictive control (MPC), as a novel control method, has garnered increasing attention and research in the field of AC motor control. Compared with vector control (VCC), MPC eliminates the need for an inner current loop, regulator parameter tuning, and pulse-width modulation (PWM). Compared with direct torque control (DTC), MPC selects the optimal voltage vector online, making its selection more accurate and efficient. In an induction motor MPC, setting an appropriate cost function can significantly improve control flexibility and simultaneously optimize multiple parameters (such as switching losses, switching times, reactive power control, and motor torque ripple). When the stator current is used as the control target in an induction motor MPC, the system is constructed as an induction MPC current control system.

[0004] Model-predictive current control for induction motors has several outstanding advantages. However, traditional model-predictive current control usually uses a method of traversing all voltage vectors to select the optimal vector to act on the inverter. This method is computationally intensive and occupies system resources, which limits the further development and application of model-predictive current control. Summary of the Invention

[0005] The purpose of the present invention is to provide an induction motor optimization model predictive voltage control method, which effectively reduces the system calculation amount and improves the practicality of model predictive control.

[0006] The technical solution adopted by the present invention is an induction motor optimization model predictive voltage control method, which is specifically implemented according to the following steps:

[0007] Step 1: Establish a mathematical model of the induction motor using the stator current and stator flux of the induction motor as state variables;

[0008] Step 2: Based on the mathematical model of the induction motor obtained in step 1, the stator voltage reference value is calculated according to the stator voltage equation. Based on this, the reference voltage vector position angle is calculated, the sector where the reference voltage vector is located is determined, and the non-zero vector and the zero vector in this sector are selected as the candidate voltage vectors;

[0009] Step 3: Based on the mathematical model of the induction motor obtained in step 1 and the candidate voltage vector obtained in step 2, assuming that the current moment is moment k, the stator current at moment k+1 is predicted to obtain a stator current prediction value corresponding to the candidate voltage vector. On this basis, a candidate voltage prediction value is calculated based on the stator current prediction value.

[0010] Step 4: Design a cost function, use the stator voltage tracking error as the control variable, and design an overcurrent protection link in the cost function to ensure the normal operation of the system.

[0011] The present invention is also characterized in that:

[0012] Step 1 is implemented as follows:

[0013] The mathematical model of the induction motor in the two-phase stationary coordinate system is as follows:

[0014]

[0015] in, x=[i s ψ s ] T , u=u s ,

[0016]

[0017]

[0018] in,

[0019] R s 、R r Indicates the stator resistance and rotor resistance of the motor;

[0020] ψ s represents the stator flux vector;

[0021] L s 、L r 、L m Indicates the motor stator inductance, rotor inductance, and mutual inductance;

[0022] ω r Indicates the motor rotor speed;

[0023] u s represents the stator voltage vector;

[0024] n p Indicates the number of motor pole pairs;

[0025] i s represents the stator current vector;

[0026] represents the cross product.

[0027] Step 2 is implemented as follows:

[0028] Step 2.1: In the mathematical model of the induction motor, according to the stator voltage equation and the stator current reference value, the stator voltage reference value is obtained as follows:

[0029]

[0030]

[0031] in, is the given value of stator current,

[0032] Step 2.2: Set the reference voltage Converted into a two-phase stationary coordinate system through PARK inverse transformation And calculate the reference voltage vector position angle according to formula (4):

[0033]

[0034] Step 2.3: Each bridge arm in the two-level voltage source inverter circuit structure contains two switches. If only one voltage vector is generated in one control cycle, the two-level voltage source inverter contains 8 voltage vectors u i , i=0,1,2,3,4,5,6,7. From the voltage vector distribution of the two-level voltage source inverter, it can be seen that u0 and u7 are zero vectors, and u1, u2, u3, u4, u5, u6, and u7 are non-zero vectors. Among them, the six non-zero vectors divide the plane into six sectors, and each sector occupies an angle of π / 3. When the position angle θ is 0<θ<π / 3, the non-zero vectors to be selected are u1 and u2; when the position angle θ is π / 3<θ<2π / 3, the non-zero vectors to be selected are u2 and u3; when the position angle θ is 2π / 3<θ<π, the non-zero vectors to be selected are u3 and u4; when the position angle θ is π<θ<4π / 3, the non-zero vectors to be selected are u4 and u5; when the position angle θ is 4π / 3<θ<5π / 3, the non-zero vectors to be selected are u5 and u6; when the position angle θ is 5π / 3<θ<2π, the non-zero vectors to be selected are u6 and u1.

[0035] Step 3 is implemented as follows:

[0036] Step 3.1. According to the mathematical equation of induction motor, the stator current equation is expressed as:

[0037]

[0038] in,

[0039] Assuming that the current moment is k, the forward Euler discretization method is used to obtain the predicted value of the stator current at k+1 moment:

[0040]

[0041] in, represents the k+1-beat predicted value of the stator current, τ σ =σL s / R σ , σ is the magnetic leakage coefficient, T is the sampling time;

[0042] Step 3.2: Based on the predicted value of the stator current at time k+1 and the stator voltage equation, the predicted value of the stator voltage at time k+1 is:

[0043]

[0044]

[0045] in, represents the d-axis component of the stator voltage u d The k+1-shot predicted value, represents the q-axis component u of the stator voltage q The k+1-beat predicted value of

[0046] Step 4 is implemented as follows:

[0047] Step 4.1: Design a cost function based on the stator voltage prediction value at time k+1 obtained in step 3 and the stator voltage set value. Use the stator voltage tracking error as the control variable. The cost function expression is:

[0048]

[0049] Step 4.2: Overcurrent protection component in the cost function value at time k+1 is defined as

[0050]

[0051] If the estimated current absolute value corresponding to a voltage vector Greater than the set maximum current value |i max|, then the cost function value corresponding to the voltage vector is infinite. According to the selection principle of minimizing the cost function, the voltage vector will not be used as the output of the inverter, thus achieving the purpose of overcurrent protection;

[0052] Step 4.3, combining formulas (9) and (10), the cost function is modified to

[0053]

[0054] Step 4.4: Substitute the two candidate non-zero voltage vectors and the zero vector into the cost function shown in formula (11) respectively to obtain three cost function values. Sort these three cost function values and select the voltage vector that minimizes the cost function value as the output of the inverter.

[0055] Step 4.5: If the zero vector is selected based on the principle of minimizing the cost function, that is, the cost function value obtained by substituting u0 or u7 into formula (11) is the smallest, then u0 or u7 is selected based on the principle of minimum switching; in this way, the switching state only needs to be switched once, which is beneficial to reducing switching losses.

[0056] The present invention has the beneficial effect of optimizing model-predictive voltage control for induction motors. This method uses the stator voltage equation to calculate a reference voltage vector. By determining the sector in which the reference voltage vector resides, the number of candidate voltage vectors is reduced to three, avoiding the computational complexity associated with eight predictions in conventional methods. Based on this, a voltage cost function is constructed to replace the conventional current cost function. The vector with the smallest error relative to the reference voltage is selected as the optimal voltage vector, which is ultimately applied to the inverter. By reducing the number of candidate voltage vectors, the calculation process is simplified, the system computational complexity is effectively reduced, and the practicality of model-predictive control is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a structural block diagram of the induction motor model prediction voltage control method of the present invention;

[0058] Figure 2 This is a circuit diagram of a two-level voltage source inverter according to the present invention;

[0059] Figure 3 This is the sector distribution of the two-level voltage source inverter of the present invention. DETAILED DESCRIPTION

[0060] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] The induction motor optimization model prediction voltage control method of the present invention is combined with Figure 1 , specifically follow the steps below:

[0062] Step 1: Establish a mathematical model of the induction motor using the stator current and stator flux of the induction motor as state variables;

[0063] Step 1 is implemented as follows:

[0064] The mathematical model of the induction motor in the two-phase stationary coordinate system is as follows:

[0065]

[0066] in, x=[i s ψ s ] T , u=u s ,

[0067]

[0068]

[0069] in,

[0070] R s 、R r Indicates the stator resistance and rotor resistance of the motor;

[0071] ψ s represents the stator flux vector;

[0072] L s 、L r 、L m Indicates the motor stator inductance, rotor inductance, and mutual inductance;

[0073] ω r Indicates the motor rotor speed;

[0074] u s represents the stator voltage vector;

[0075] n p Indicates the number of motor pole pairs;

[0076] i s represents the stator current vector;

[0077] represents the cross product.

[0078] Step 2: Based on the mathematical model of the induction motor obtained in step 1, the stator voltage reference value is calculated according to the stator voltage equation. Based on this, the reference voltage vector position angle is calculated, the sector where the reference voltage vector is located is determined, and the non-zero vector and the zero vector in this sector are selected as the candidate voltage vectors;

[0079] Step 2 is implemented as follows:

[0080] Step 2.1: In the mathematical model of the induction motor, according to the stator voltage equation and the stator current reference value, the stator voltage reference value is obtained as follows:

[0081]

[0082]

[0083] in, is the given value of stator current,

[0084] Step 2.2: Set the reference voltage Converted into a two-phase stationary coordinate system through PARK inverse transformation And calculate the reference voltage vector position angle according to formula (4):

[0085]

[0086] Step 2.3, according to the position angle θ, and Figure 2 and Figure 3 The two-level voltage source inverter circuit diagram and the voltage vector sector distribution diagram are shown respectively. The sector where the reference voltage vector is located is determined based on Table 1.

[0087] Table 1 Correspondence between position angle and selected non-zero vector

[0088]

[0089] Figure 2 The figure shows the circuit structure block diagram of a two-level voltage source inverter, where each bridge arm contains two switches. According to its circuit structure, if only one voltage vector is generated in one control cycle, the two-level voltage source inverter contains 8 voltage vectors u i , i=0,1,2,3,4,5,6,7. Figure 3 The figure shows the voltage vector distribution diagram of the two-level voltage source inverter. It can be seen that u0 and u7 are zero vectors, and u1, u2, u3, u4, u5, u6, and u7 are non-zero vectors. Among them, the six non-zero vectors divide the plane into six sectors, and each sector occupies an angle of π / 3. When the position angle θ is 0<θ<π / 3, the non-zero vectors to be selected are u1 and u2; when the position angle θ is π / 3<θ<2π / 3, the non-zero vectors to be selected are u2 and u3; when the position angle θ is 2π / 3<θ<π, the non-zero vectors to be selected are u3 and u4; when the position angle θ is π<θ<4π / 3, the non-zero vectors to be selected are u4 and u5; when the position angle θ is 4π / 3<θ<5π / 3, the non-zero vectors to be selected are u5 and u6; when the position angle θ is 5π / 3<θ<2π, the non-zero vectors to be selected are u6 and u1.

[0090] Step 3: Based on the mathematical model of the induction motor obtained in step 1 and the candidate voltage vector obtained in step 2, assuming that the current moment is moment k, the stator current at moment k+1 is predicted to obtain a stator current prediction value corresponding to the candidate voltage vector. On this basis, a candidate voltage prediction value is calculated based on the stator current prediction value.

[0091] Step 3 is implemented as follows:

[0092] Step 3.1. According to the mathematical equation of induction motor, the stator current equation is expressed as:

[0093]

[0094] in,

[0095] Assuming that the current moment is k, the forward Euler discretization method is used to obtain the predicted value of the stator current at k+1 moment:

[0096]

[0097] in, represents the k+1-beat predicted value of the stator current, τ σ =σL s / R σ , σ is the magnetic leakage coefficient, T is the sampling time;

[0098] Step 3.2: Based on the predicted value of the stator current at time k+1 and the stator voltage equation, the predicted value of the stator voltage at time k+1 is:

[0099]

[0100]

[0101] in, represents the d-axis component of the stator voltage u d The k+1-shot predicted value, represents the q-axis component u of the stator voltage q The k+1-beat predicted value of

[0102] Step 4: Design a cost function, use the stator voltage tracking error as the control variable, and design an overcurrent protection link in the cost function to ensure the normal operation of the system.

[0103] Step 4 is implemented as follows:

[0104] Step 4.1: Design a cost function based on the stator voltage prediction value at time k+1 obtained in step 3 and the stator voltage set value. Use the stator voltage tracking error as the control variable. The cost function expression is:

[0105]

[0106] Step 4.2: When the motor starts or the load suddenly changes, the model predictive control system may experience overcurrent. To ensure the normal operation of the system, the overcurrent protection component at time k+1 in the cost function value is is defined as

[0107]

[0108] If the estimated current absolute value corresponding to a voltage vector Greater than the set maximum current value |i max |, then the cost function value corresponding to the voltage vector is infinite. According to the selection principle of minimizing the cost function, the voltage vector will not be used as the output of the inverter, thus achieving the purpose of overcurrent protection;

[0109] Step 4.3, combining formulas (9) and (10), the cost function is modified to

[0110]

[0111] Step 4.4: Substitute the two candidate non-zero voltage vectors and the zero vector into the cost function shown in formula (11) respectively to obtain three cost function values. Sort these three cost function values and select the voltage vector that minimizes the cost function value as the output of the inverter.

[0112] Step 4.5: If the zero vector is selected based on the principle of minimizing the cost function, that is, the cost function value obtained by substituting u0 or u7 into formula (11) is the smallest, then u0 or u7 is selected based on the principle of minimum switching; in this way, the switching state only needs to be switched once, which is beneficial to reducing switching losses.

Claims

1. An induction motor optimization model predictive voltage control method, characterized in that: Please follow the steps below to implement it: Step 1: Establish a mathematical model of the induction motor using the stator current and stator flux of the induction motor as state variables; Step 2: Based on the mathematical model of the induction motor obtained in step 1, the stator voltage reference value is calculated according to the stator voltage equation. Based on this, the reference voltage vector position angle is calculated, the sector where the reference voltage vector is located is determined, and the non-zero vector and the zero vector in this sector are selected as the candidate voltage vectors; The step 2 is specifically implemented according to the following steps: Step 2.1: In the mathematical model of the induction motor, according to the stator voltage equation and the stator current reference value, the stator voltage reference value is obtained as follows: in, is the given value of stator current, Step 2.2: Set the reference voltage Converted into a two-phase stationary coordinate system through PARK inverse transformation And calculate the reference voltage vector position angle according to formula (4): Step 2.3: Each bridge arm in the two-level voltage source inverter circuit structure contains two switches. If only one voltage vector is generated in one control cycle, the two-level voltage source inverter contains 8 voltage vectors u i , i=0,1,2,3,4,5,6,7. From the voltage vector distribution of the two-level voltage source inverter, it can be seen that u0 and u7 are zero vectors, and u1, u2, u3, u4, u5, u6, and u7 are non-zero vectors. Among them, the six non-zero vectors divide the plane into six sectors, and each sector occupies an angle of π / 3. When the position angle θ is 0<θ<π / 3, the non-zero vectors to be selected are u1 and u2; when the position angle θ is π / 3< When θ<2π / 3, the non-zero vectors to be selected are u2 and u3; when the position angle θ is 2π / 3<θ<π, the non-zero vectors to be selected are u3 and u4; when the position angle θ is π<θ<4π / 3, the non-zero vectors to be selected are u4 and u5; when the position angle θ is 4π / 3<θ<5π / 3, the non-zero vectors to be selected are u5 and u6; when the position angle θ is 5π / 3<θ<2π, the non-zero vectors to be selected are u6 and u1; Step 3: Based on the mathematical model of the induction motor obtained in step 1 and the candidate voltage vector obtained in step 2, assuming that the current moment is moment k, the stator current at moment k+1 is predicted to obtain a stator current prediction value corresponding to the candidate voltage vector. On this basis, a candidate voltage prediction value is calculated based on the stator current prediction value. The step 3 is specifically implemented according to the following steps: Step 3.

1. According to the mathematical equation of induction motor, the stator current equation is expressed as: in, Assuming that the current moment is k, the forward Euler discretization method is used to obtain the predicted value of the stator current at k+1 moment: in, represents the k+1-beat predicted value of the stator current, τ σ =σL s / R σ , σ is the magnetic leakage coefficient, T is the sampling time; Step 3.2: Based on the predicted value of the stator current at time k+1 and the stator voltage equation, the predicted value of the stator voltage at time k+1 is: in, represents the d-axis component of the stator voltage u d The k+1-shot predicted value, represents the q-axis component u of the stator voltage q The k+1-beat predicted value of Step 4: Design a cost function, use the stator voltage tracking error as the control variable, and design an overcurrent protection link in the cost function to ensure the normal operation of the system.

2. The induction motor optimization model predictive voltage control method according to claim 1, characterized in that: The step 1 is specifically implemented according to the following steps: The mathematical model of the induction motor in the two-phase stationary coordinate system is as follows: Among them, x=[i s ψ s ] T ,u=u s , in, R s 、R r Indicates the stator resistance and rotor resistance of the motor; ψ s represents the stator flux vector; L s 、L r 、L m Indicates the motor stator inductance, rotor inductance, and mutual inductance; ω r Indicates the motor rotor speed; u s represents the stator voltage vector; n p Indicates the number of motor pole pairs; i s represents the stator current vector; represents the cross product.

3. The induction motor optimization model predictive voltage control method according to claim 2, characterized in that: The step 4 is specifically implemented according to the following steps: Step 4.1: Design a cost function based on the stator voltage prediction value at time k+1 obtained in step 3 and the stator voltage set value. Use the stator voltage tracking error as the control variable. The cost function expression is: Step 4.2: Overcurrent protection component in the cost function value at time k+1 is defined as If the estimated current absolute value corresponding to a voltage vector Greater than the set maximum current value |i max |, then the cost function value corresponding to the voltage vector is infinite. According to the selection principle of minimizing the cost function, the voltage vector will not be used as the output of the inverter, thus achieving the purpose of overcurrent protection; Step 4.3, combining formulas (9) and (10), the cost function is modified to Step 4.4: Substitute the two candidate non-zero voltage vectors and the zero vector into the cost function shown in formula (11) respectively to obtain three cost function values. Sort these three cost function values and select the voltage vector that minimizes the cost function value as the output of the inverter. Step 4.5: If the zero vector is selected based on the principle of minimizing the cost function, that is, the cost function value obtained by substituting u0 or u7 into formula (11) is the smallest, then u0 or u7 is selected based on the principle of minimum switching; in this way, the switching state only needs to be switched once, which is beneficial to reducing switching losses.

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