CN109150051B - Flux linkage observation method and system for electrically excited synchronous motor - Google Patents
Flux linkage observation method and system for electrically excited synchronous motor Download PDFInfo
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- CN109150051B CN109150051B CN201811149907.9A CN201811149907A CN109150051B CN 109150051 B CN109150051 B CN 109150051B CN 201811149907 A CN201811149907 A CN 201811149907A CN 109150051 B CN109150051 B CN 109150051B
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- excited synchronous
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/141—Flux estimation
Abstract
The invention discloses a flux linkage observation method and a flux linkage observation system for an electrically excited synchronous motor, wherein the flux linkage observation method comprises the following steps: establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system; constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to a state equation and a preset feedback matrix; acquiring d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and acquiring d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor; and observing the flux linkage of the electrically excited synchronous motor by using a full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator. Therefore, the full-order flux linkage model is established to observe the flux linkage of the electrically excited synchronous motor, the steady-state precision and the dynamic performance are excellent, and the high-performance control of the motor control system is guaranteed.
Description
Technical Field
The invention relates to the field of high-power alternating current transmission, in particular to a flux linkage observation method and system of an electrically excited synchronous motor.
Background
Compared with an asynchronous motor, the electro-magnetic synchronous motor has the advantages of high power factor, high motor efficiency, high overload multiple, small rotational inertia and the like, so that the electro-magnetic synchronous motor is widely applied to the field of high-power alternating-current transmission. At present, there are two main control modes of an electrically excited synchronous motor: vector control based on magnetic field orientation and direct torque control based on torque. In order to realize the control strategy of the motor control system with high performance, the two control modes both need to acquire the flux linkage of the electrically excited synchronous motor, and the accuracy of the acquired flux linkage determines the control performance of the system to a great extent, so that the accurate flux linkage observation method is very critical to the control performance of the system.
In the prior art, the flux linkage observation models of the electrically excited synchronous motor mainly include two types: open-loop flux linkage models and mixed flux linkage models based on voltage and current. For the open-loop flux linkage model, the open-loop flux linkage model adopts an open-loop flux linkage observation method which is easily influenced by motor parameters, and the motor parameters can change along with the change of temperature and working conditions, so that the accuracy of the open-loop flux linkage model in observing flux linkages is low. For the hybrid flux linkage model, the hybrid flux linkage model is essentially a reduced-order flux linkage model, the steady-state precision and the dynamic performance are not excellent enough, and the high-performance control of the motor control system cannot be ensured.
Therefore, how to provide a solution to the above technical problem is a problem that needs to be solved by those skilled in the art.
Disclosure of Invention
The invention aims to provide a flux linkage observation method and system for an electrically excited synchronous motor, wherein a full-order flux linkage model is established to observe flux linkages of the electrically excited synchronous motor, and compared with an open-loop flux linkage model and a mixed flux linkage model, the method has excellent steady-state precision and dynamic performance, so that the high-performance control of a motor control system is ensured.
In order to solve the technical problem, the invention provides a flux linkage observation method of an electrically excited synchronous motor, which comprises the following steps:
establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system;
constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to the state equation and a preset feedback matrix;
acquiring d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and acquiring d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor;
and observing the flux linkage of the electrically excited synchronous motor by using the full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator.
Preferably, the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C is the coefficient matrix,. phisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer is specifically:
Preferably, the process of obtaining the d-axis component and the q-axis component of the stator voltage of the electrically excited synchronous motor specifically includes:
setting a phase voltage reconstruction relational expression in advance according to direct-current side voltages and pulse vectors corresponding to a three-phase inverter in a control system of the electrically excited synchronous motor;
and reconstructing phase voltage input by the stator by using the phase voltage reconstruction relational expression, and carrying out coordinate transformation on the phase voltage to obtain a d-axis component and a q-axis component of the stator voltage.
Preferably, the phase voltage reconstruction relation is specifically as follows:
wherein u isan、ubn、ucnCorresponding to the a-phase component, the b-phase component, the c-phase component and the U-phase component of the stator voltage of the electrically excited synchronous motor in an abc three-phase static coordinate systemdcIs the DC side voltage, SjAs a function of three-level switchinga、ib、icThe phase-a component, the phase-b component and the phase-c component of the stator current of the electrically excited synchronous motor in the abc three-phase static coordinate system correspond to each other, and delta U is a preset error voltage.
Preferably, the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically includes:
and acquiring the excitation voltage of the electrically excited synchronous motor by using a voltage sensor.
Preferably, the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically includes:
reconstruction of relation u by means of preset excitation voltagef＝0.9*u1(1+ cos α) 0.5 reconstructing the excitation voltage of the electrically excited synchronous machine; wherein u isfIs an excitation voltage u1And alpha is a control angle, and is the peak value of the alternating current input voltage corresponding to the power supply of the rotor.
Preferably, the preset feedback matrix is specifically:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, it is set according to the pole positions configured for the full-order flux linkage observer.
In order to solve the above technical problem, the present invention further provides a flux linkage observation system of an electrically excited synchronous motor, including:
the system comprises a state equation establishing unit, a state equation calculating unit and a state equation generating unit, wherein the state equation establishing unit is used for establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system;
the observer constructing unit is used for constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to the state equation and a preset feedback matrix;
a voltage and current obtaining unit, configured to obtain d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and obtain d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor;
and the flux linkage observation unit is used for observing the flux linkage of the electrically excited synchronous motor by using the full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator.
Preferably, the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the outputIn variable, y is the output variable, A, B, C is the coefficient matrix, #sdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer is specifically:
Preferably, the preset feedback matrix is specifically:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, it is set according to the pole positions configured for the full-order flux linkage observer.
The invention provides a flux linkage observation method of an electrically excited synchronous motor, which comprises the following steps: establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system; constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to a state equation and a preset feedback matrix; acquiring d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and acquiring d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor; and observing the flux linkage of the electrically excited synchronous motor by using a full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator. Therefore, the full-order flux linkage model is established to observe the flux linkage of the electrically excited synchronous motor, and compared with an open-loop flux linkage model and a mixed flux linkage model, the stable-state precision and the dynamic performance are excellent, so that the high-performance control of the motor control system is ensured.
The invention also provides a flux linkage observation system of the electrically excited synchronous motor, which has the same beneficial effect as the flux linkage observation method.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed in the prior art and the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
Fig. 1 is a flowchart of a flux linkage observation method of an electrically excited synchronous motor according to the present invention;
fig. 2(a) is a d-axis equivalent circuit diagram of an electrically excited synchronous motor provided by the present invention under a dq two-phase rotation coordinate system;
fig. 2(b) is a q-axis equivalent circuit diagram of an electrically excited synchronous motor provided by the present invention under a dq two-phase rotating coordinate system;
FIG. 3 is a space vector diagram of an electrically excited synchronous motor according to the present invention;
fig. 4 is a circuit diagram of a connection circuit between a three-phase three-level inverter and a motor stator according to the present invention;
fig. 5(a) is a comparison graph of an observed value and an actual value of a d-axis component of an air gap flux linkage of an electrically excited synchronous motor according to the present invention;
fig. 5(b) is a comparison graph of an actual value and an observed value of a q-axis component of an air gap flux linkage of an electrically excited synchronous machine according to the present invention;
fig. 6 is a schematic structural diagram of a flux linkage observation system of an electrically excited synchronous motor according to the present invention.
Detailed Description
The core of the invention is to provide a flux linkage observation method and system of an electrically excited synchronous motor, a full-order flux linkage model is established to observe the flux linkage of the electrically excited synchronous motor, and compared with an open-loop flux linkage model and a mixed flux linkage model, the method has excellent steady-state precision and dynamic performance, thereby ensuring the high-performance control of a motor control system.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, fig. 1 is a flowchart of a flux linkage observation method of an electrically excited synchronous motor according to the present invention.
The flux linkage observation method of the electrically excited synchronous motor comprises the following steps:
step S1: and establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system.
Specifically, firstly, a mathematical model of the electrically excited synchronous motor in a three-phase stationary coordinate system is converted into a dq two-phase rotating coordinate system for analysis, and the mathematical model of the electrically excited synchronous motor in the dq two-phase rotating coordinate system is as follows:
the flux linkage equation:
voltage equation:
the torque equation:
Te＝ψsdisq-ψsqisd；
the equivalent circuit of the electrically excited synchronous motor under the dq two-phase rotating coordinate system can be obtained according to a mathematical model of the electrically excited synchronous motor under the dq two-phase rotating coordinate system. Referring to fig. 2(a) and fig. 2(b), fig. 2(a) is a d-axis equivalent circuit diagram of an electrically excited synchronous motor provided by the present invention in a dq two-phase rotation coordinate system, and fig. 2(b) is a q-axis equivalent circuit diagram of an electrically excited synchronous motor provided by the present invention in a dq two-phase rotation coordinate system.
By combining the above analysis, a space vector diagram of the electrically excited synchronous motor can be obtained, please refer to fig. 3, and fig. 3 is a space vector diagram of the electrically excited synchronous motor provided by the present invention. In FIG. 3,. omega.r＝ω。
Wherein psisFor stator flux linkage psisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, #δIs an air gap flux linkage psiδdIs the d-axis component, psi, of the air-gap flux linkageδqIs the q-axis component of the air gap flux linkage, LsdIs stator d-axis synchronous inductance, LsqFor stator q-axis synchronous inductance, LadIs d-axis armature reaction inductance, LaqIs q-axis armature reaction inductance, LfIs a rotor synchronous inductor, LDTo damp d-axis synchronous inductance, LQTo damp the q-axis synchronous inductance, LslAs stator leakage reactance, isIs stator current, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifFor exciting current, iadFor d-axis armature reaction current, iaqFor q-axis armature reaction current, iDTo damp the d-axis component of the current, iQTo damp the q-axis component of the current, usIs the stator voltage usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage uDTo damp the d-axis component of the voltage, uQTo damp the q-axis component of the voltage, RsIs stator resistance, RfIs rotor resistance, RDTo damp the d-axis component of the resistance, RQTo damp the q-axis component of the resistance, ωrAngular velocity, T, of the motoreIs the torque of the motor.
Based on this, considering that the flux linkage of the electrically excited synchronous motor is a key variable in the motor operation, a state equation of the electrically excited synchronous motor is established by taking the stator flux linkage, the rotor flux linkage and the damping flux linkage as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system, and the state equation may specifically be:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable;
wherein, the coefficient matrix A, B, C is:
Step S2: and constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to the state equation and a preset feedback matrix.
It should be noted that the preset of the present application is set in advance, and only needs to be set once, and the reset is not needed unless the modification is needed according to the actual situation.
Specifically, according to a state equation of the electrically excited synchronous motor and a feedback matrix set in advance, a full-order flux linkage observer of the electrically excited synchronous motor can be constructed by utilizing a modern control theory, and the specific result is as follows:
wherein ^ represents the state observed quantity, and G is a feedback matrix. For a full-order flux linkage observer, the feedback matrix determines the performance of the full-order flux linkage observer, and in order to accurately observe the flux linkage value of the electrically excited synchronous motor, the feedback matrix needs to be reasonably designed.
Step S3: the d-axis component and the q-axis component of the excitation voltage and the stator voltage of the electrically excited synchronous motor are obtained, and the d-axis component and the q-axis component of the excitation current and the stator current of the electrically excited synchronous motor are obtained.
Specifically, it is known that the flux linkage of the electrically excited synchronous motor can be observed only by knowing the voltage and current quantities of the rotor and the stator of the electrically excited synchronous motor in the full-order flux linkage observer, so that the d-axis component and the q-axis component of the excitation voltage and the stator voltage of the electrically excited synchronous motor are obtained, and the d-axis component and the q-axis component of the excitation current and the stator current of the electrically excited synchronous motor are obtained, so that the flux linkage of the electrically excited synchronous motor can be accurately observed by using the full-order flux linkage observer. As to the specific manner of obtaining the voltage and current quantities of the rotor and the stator, the present application is not particularly limited, and is determined according to the actual situation.
Step S4: and observing the flux linkage of the electrically excited synchronous motor by using a full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator.
Specifically, the flux linkage of the electrically excited synchronous motor can be observed by using a full-order flux linkage observer after the voltage and current of the rotor and the stator are acquired. Because the full-order flux linkage observer is adopted, the flux linkage observed value is slightly influenced by motor parameters, and the robustness is strong; the method has strong immunity to external signals and strong adaptability; and the steady-state precision and the dynamic performance are excellent, so that the high-performance control of the motor control system is ensured.
The invention provides a flux linkage observation method of an electrically excited synchronous motor, which comprises the following steps: establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system; constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to a state equation and a preset feedback matrix; acquiring d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and acquiring d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor; and observing the flux linkage of the electrically excited synchronous motor by using a full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator. Therefore, the full-order flux linkage model is established to observe the flux linkage of the electrically excited synchronous motor, and compared with an open-loop flux linkage model and a mixed flux linkage model, the stable-state precision and the dynamic performance are excellent, so that the high-performance control of the motor control system is ensured.
On the basis of the above-described embodiment:
as a preferred embodiment, the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C is the coefficient matrix,. phisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer specifically comprises:
Specifically, for the description of the present embodiment, the above-mentioned embodiments have been described in detail, and the detailed description of the present application is omitted here.
As a preferred embodiment, the process of obtaining the d-axis component and the q-axis component of the stator voltage of the electrically excited synchronous motor is specifically as follows:
setting a phase voltage reconstruction relational expression in advance according to direct-current side voltages and pulse vectors corresponding to a three-phase inverter in a control system of the electrically excited synchronous motor;
and reconstructing phase voltage input by the stator by using the phase voltage reconstruction relational expression, and transforming the phase voltage by coordinates to obtain a d-axis component and a q-axis component of the stator voltage.
Specifically, referring to fig. 4, fig. 4 is a circuit diagram of a connection circuit between a three-phase three-level inverter and a motor stator according to the present invention. The three-phase three-level inverter in the control system of an electrically excited synchronous machine comprises a power supply, an intermediate capacitor (C)1、C2) And each switch, the three-phase alternating current input to the motor stator is adjusted by changing the on state of each switch.
Based on this, in the process of acquiring the d-axis component and the q-axis component of the stator voltage of the electrically excited synchronous motor, in order to save cost, a voltage sensor is not installed on the stator side, and the stator voltage is reconstructed by the direct-current side voltage (i.e., the voltage across the intermediate capacitor) and the pulse vector (i.e., the switching function for controlling the on-state of each switch) corresponding to the three-phase inverter. Specifically, the phase voltage reconstruction relational expression is set in advance according to the direct-current side voltage and the pulse vector corresponding to the three-phase inverter. When the d-axis component and the q-axis component of the motor stator voltage are obtained, firstly, the phase voltage input by the stator (the stator voltage in a three-phase static coordinate system) is reconstructed by using a phase voltage reconstruction relational expression, and then the phase voltage is subjected to coordinate transformation (the three-phase static coordinate system-a two-phase rotating coordinate system) to obtain the d-axis component and the q-axis component of the motor stator voltage.
As a preferred embodiment, the phase voltage reconstruction relation is specifically:
wherein u isan、ubn、ucnCorresponding to the a-phase component, the b-phase component, the c-phase component, U of the stator voltage of the electrically excited synchronous motor in the abc three-phase static coordinate systemdcIs a DC side voltage, SjAs a function of three-level switchinga、ib、icThe method is characterized in that the method corresponds to a phase component a, a phase component b and a phase component c of stator current of an electrically excited synchronous motor in an abc three-phase static coordinate system, and delta U is preset error voltage.
Furthermore, the high-power circuit mostly adopts a three-level structure, the voltage reconstruction is described by taking the three-level structure as an example in the application, and other level structures can be analogized.
The three-level switching function is as follows:
the reconstructed phase voltages are:
in consideration of the fact that the dead time and the nonlinearity of the switching tube enable a small error to exist between the reconstructed phase voltage and the phase voltage input by the stator, the error voltage delta U is set in the phase voltage reconstruction relation so as to reduce the error between the reconstructed phase voltage and the phase voltage input by the stator.
As a preferred embodiment, the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically includes:
the excitation voltage of the electrically excited synchronous motor is obtained by using a voltage sensor.
Specifically, the excitation voltage of the electrically excited synchronous motor of the present application may be acquired by installing a voltage sensor.
As a preferred embodiment, the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically includes:
reconstruction of relation u by means of preset excitation voltagef＝0.9*u1Reconstructing the excitation voltage of the electrically excited synchronous motor by (1+ cos alpha) 0.5; wherein u isfIs an excitation voltage u1The peak value of the ac input voltage corresponding to the power supply of the rotor is denoted as α, which is a control angle.
Likewise, in addition to installing a voltage sensor to obtain the excitation voltage of the electrically excited synchronous machine, the present application may also reconstruct the excitation voltage. Specifically, the application sets an excitation voltage reconstruction relation u in advancef＝0.9*u1(1+ cos alpha) 0.5 (alpha determines the conduction time of the switch tube corresponding to the rotor, and further determines the input voltage of the rotor), and when the excitation voltage of the motor is obtainedAnd the excitation voltage of the motor can be reconstructed by using the excitation voltage reconstruction relational expression.
As a preferred embodiment, the preset feedback matrix specifically includes:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, the settings are based on the pole positions configured for the full-order flux linkage observer.
Specifically, given that the feedback matrix determines the performance of the full-order flux linkage observer, in order to obtain an accurate flux linkage value, the feedback matrix must be reasonably designed:
firstly, the form of a feedback matrix needs to be determined, because 5 state variables and 3 output variables exist, the feedback matrix can be determined to be a 5 x 3 matrix; meanwhile, the system is a 5-order system, so that the feedback matrix can be configured with 5 degrees of freedom. The rotor flux linkage is strongly related to the rotor current (namely the excitation current), the rotor flux linkage can be corrected by the error of the rotor current alone, and the rotor current is single-phase direct current, so that only one degree of freedom is needed; the stator flux linkage is strongly related to the stator current, and the stator flux linkage can be corrected by using the error of the stator current, and the stator current is symmetrical three-phase current, so that two degrees of freedom are required; because the damping current is not measurable, the damping current cannot be used for correcting the damping flux linkage, and meanwhile, two degrees of freedom remain in the feedback matrix, so that the damping flux linkage is corrected by adopting the error of the stator current, and the method is reasonable.
To sum up, for ease of calculation, the form of the feedback matrix can be obtained as follows:
then, the value of a feedback matrix is required to be determined, and the feedback matrix determines the pole position of the full-order flux linkage observer, namely the performance of the full-order flux linkage observer. In order to make the full-order flux linkage observer converge faster than the actual flux linkage of the motor, the pole of the full-order flux linkage observer can be arranged at k times of the original motor pole. Since the larger the value of k, the faster the convergence speed of the full-order flux linkage observer, but the more sensitive it is to external interference, the choice of k needs to be a compromise between rapidity and sensitivity to disturbance and noise, and is set empirically.
After the form of the feedback matrix and the positions of the expected poles are determined, the feedback matrix can be calculated by adopting a design method of a full-order state observer in modern control theory. Because the system is a 5-order system and the analytic expression of the feedback matrix is extremely large, the feedback matrix can be obtained by adopting the numerical calculation function of mathematical tools such as maple or matlab and the like, so that the flux linkage value of the motor can be accurately observed by the full-order flux linkage observer.
Referring to fig. 5(a) and fig. 5(b), fig. 5(a) is a comparison graph of an observed value and an actual value of a d-axis component of an air-gap flux linkage of an electrically excited synchronous machine according to the present invention, and fig. 5(b) is a comparison graph of an observed value and an actual value of a q-axis component of an air-gap flux linkage of an electrically excited synchronous machine according to the present invention. As can be seen from fig. 5(a) and 5(b), the air-gap flux linkage observed by the full-order flux linkage model can be consistent with the actual air-gap flux linkage of the motor in both the steady-state process and the dynamic process, i.e., the full-order flux linkage model has good steady-state precision and dynamic performance, which indicates the effectiveness and accuracy of the full-order flux linkage model.
Referring to fig. 6, fig. 6 is a schematic structural diagram of a flux linkage observation system of an electrically excited synchronous motor according to the present invention.
The flux linkage observation system of the electrically excited synchronous motor comprises:
the state equation establishing unit 1 is used for establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system;
the observer constructing unit 2 is used for constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to a state equation and a preset feedback matrix;
a voltage and current obtaining unit 3, configured to obtain d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and obtain d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor;
and the flux linkage observation unit 4 is used for observing the flux linkage of the electrically excited synchronous motor by using a full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator.
As a preferred embodiment, the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C is the coefficient matrix,. phisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer specifically comprises:
As a preferred embodiment, the preset feedback matrix specifically includes:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, the settings are based on the pole positions configured for the full-order flux linkage observer.
For the introduction of the flux linkage observation system provided by the present invention, reference is made to the above-mentioned embodiments of the flux linkage observation method, and the present invention is not described herein again.
It is further noted that, in the present specification, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (7)
1. A flux linkage observation method of an electrically excited synchronous motor is characterized by comprising the following steps:
establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system;
constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to the state equation and a preset feedback matrix;
acquiring d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and acquiring d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor;
observing the flux linkage of the electrically excited synchronous motor by using the full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator;
the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically comprises the following steps:
reconstructing the excitation voltage of the electrically excited synchronous motor by using a preset excitation voltage reconstruction relational expression;
the process of obtaining the d-axis component and the q-axis component of the stator voltage of the electrically excited synchronous motor specifically comprises the following steps:
setting a phase voltage reconstruction relational expression in advance according to direct-current side voltages and pulse vectors corresponding to a three-phase inverter in a control system of the electrically excited synchronous motor;
reconstructing phase voltage input by the stator by using the phase voltage reconstruction relational expression, and carrying out coordinate transformation on the phase voltage to obtain a d-axis component and a q-axis component of the stator voltage;
the phase voltage reconstruction relation is specifically as follows:
wherein u isan、ubn、ucnCorresponding to the a-phase component, the b-phase component, the c-phase component and the U-phase component of the stator voltage of the electrically excited synchronous motor in an abc three-phase static coordinate systemdcIs the DC side voltage, SjAs a function of three-level switchinga、ib、icThe phase-a component, the phase-b component and the phase-c component of the stator current of the electrically excited synchronous motor in an abc three-phase static coordinate system are corresponded, and the delta U is a preset error voltage.
2. The flux linkage observation method of an electrically excited synchronous machine according to claim 1, wherein the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C is the coefficient matrix,. phisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer is specifically:
3. The flux linkage observation method of an electrically excited synchronous machine according to claim 1, wherein the process of reconstructing the excitation voltage of the electrically excited synchronous machine using the preset excitation voltage reconstruction relational expression specifically includes:
reconstruction of relation u by means of preset excitation voltagef＝0.9*u1(1+ cos α) 0.5 reconstructing the excitation voltage of the electrically excited synchronous machine; wherein u isfIs an excitation voltage u1And alpha is a control angle, and is the peak value of the alternating current input voltage corresponding to the power supply of the rotor.
4. A flux linkage observation method of an electrically excited synchronous machine according to any one of claims 1 to 3, wherein the preset feedback matrix is specifically:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, it is set according to the pole positions configured for the full-order flux linkage observer.
5. A flux linkage observation system of an electrically excited synchronous motor, comprising:
the system comprises a state equation establishing unit, a state equation calculating unit and a state equation generating unit, wherein the state equation establishing unit is used for establishing a state equation of the electrically excited synchronous motor by taking a stator flux linkage, a rotor flux linkage and a damping flux linkage of the electrically excited synchronous motor as state variables according to a mathematical model of the electrically excited synchronous motor under a dq two-phase rotating coordinate system;
the observer constructing unit is used for constructing a full-order flux linkage observer of the electrically excited synchronous motor by utilizing a modern control theory according to the state equation and a preset feedback matrix;
a voltage and current obtaining unit, configured to obtain d-axis components and q-axis components of excitation voltage and stator voltage of the electrically excited synchronous motor, and obtain d-axis components and q-axis components of excitation current and stator current of the electrically excited synchronous motor;
the flux linkage observation unit is used for observing the flux linkage of the electrically excited synchronous motor by using the full-order flux linkage observer according to the acquired voltage and current of the rotor and the stator;
the process of acquiring the excitation voltage of the electrically excited synchronous motor specifically comprises the following steps:
reconstructing the excitation voltage of the electrically excited synchronous motor by using a preset excitation voltage reconstruction relational expression;
the process of obtaining the d-axis component and the q-axis component of the stator voltage of the electrically excited synchronous motor specifically comprises the following steps:
setting a phase voltage reconstruction relational expression in advance according to direct-current side voltages and pulse vectors corresponding to a three-phase inverter in a control system of the electrically excited synchronous motor;
reconstructing phase voltage input by the stator by using the phase voltage reconstruction relational expression, and carrying out coordinate transformation on the phase voltage to obtain a d-axis component and a q-axis component of the stator voltage;
the phase voltage reconstruction relation is specifically as follows:
wherein u isan、ubn、ucnCorresponding to the a-phase component, the b-phase component, the c-phase component and the U-phase component of the stator voltage of the electrically excited synchronous motor in an abc three-phase static coordinate systemdcIs the DC side voltage, SjAs a function of three-level switchinga、ib、icThe phase-a component, the phase-b component and the phase-c component of the stator current of the electrically excited synchronous motor in an abc three-phase static coordinate system are corresponded, and the delta U is a preset error voltage.
6. The flux linkage observation system of an electrically excited synchronous machine according to claim 5, wherein the state equation is specifically:
wherein, x is a state variable,
is the derivative of the state variable, u is the input variable, y is the output variable, A, B, C is the coefficient matrix,. phisdIs the d-axis component, psi, of the stator flux linkagesqIs the q-axis component of the stator flux linkage, #fFor rotor flux linkage psiDTo damp the d-axis component of the flux linkage, #QTo damp the q-axis component of the flux linkage, usdIs the d-axis component of the stator voltage, usqIs the q-axis component of the stator voltage, ufIs an excitation voltage, isdIs the d-axis component of the stator current, isqIs the q-axis component of the stator current, ifIs an exciting current;
the full-order flux linkage observer is specifically:
7. The flux linkage observation system of an electrically excited synchronous machine according to any one of claims 5 to 6, wherein the preset feedback matrix is specifically:
wherein, g1、g2、g3、g4、g5For 5 degrees of freedom of the feedback matrix G, it is set according to the pole positions configured for the full-order flux linkage observer.
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