summary
This paper selects a back-to-back dual PWM converter as the research object for a direct-drive permanent magnet wind power inverter. The control strategies for the generator-side converter are studied separately. For the generator-side mathematical model, a dual closed-loop decoupling control strategy is adopted. This paper uses a sliding mode observation algorithm to estimate the generator rotor position angle, which has good robustness and effectively improves the stability and reliability of the system. A simple and easy-to-implement positioning method is proposed for the generator-side control. Experiments show that the control strategy for the generator-side inverter achieves good control results.
1 Introduction
China's rapidly developing economy is driving increasing energy demand. Faced with shortages of traditional energy sources and pressure to meet global environmental commitments, China's wind power technology lags behind other developed countries. However, given its vast wind energy reserves, wind power has seen faster development compared to other renewable energy sources, and its future prospects are promising. This paper first reviews the current status and prospects of wind power globally and in China, then elaborates on the technical solutions for permanent magnet direct-drive wind power systems. Finally, it selects a back-to-back dual PWM converter, which allows for flexible control of the turbine side, as the research object to study the control strategy of the turbine-side converter.
Early wind power systems used a constant speed and frequency operation strategy, but this strategy has gradually been phased out with the development of the wind power industry. Modern wind power systems mostly adopt a variable speed and constant frequency operation mode. When the system operates below the rated wind speed, it operates at a fixed pitch, and the generator speed is controlled by the inverter on the motor side of the wind turbine system, adjusting the tip speed ratio of the wind turbine blades to achieve maximum wind energy capture. When operating above the rated wind speed, the wind turbine pitch angle is adjusted, changing the power of the wind turbine to absorb wind energy. This effectively changes the wind energy utilization coefficient, ensuring the generator operates at its rated speed and preventing damage to the generator due to excessive wind speed exceeding its rated speed. This control strategy effectively controls the speed and power of the wind turbine, preventing it from exceeding its operating limits.
2 Mathematical Model of Permanent Magnet Synchronous Motor
Figure 2-1 shows a simplified physical model of a two-pole surface-mounted permanent magnet synchronous motor. The A-axis is taken as the spatial reference coordinate of the ABC axis system, and the counterclockwise direction is taken as the positive direction of the speed and electromagnetic torque, while the load torque is opposite to it.
Figure 2-1 Physical model of a two-pole surface-mounted permanent magnet synchronous motor
Fig.2-4The physical model of permanent magnet synchronization generator
As shown in Figure 2-1, under the ABC axis system, the stator current space vector is defined as:
(2-1)
The fundamental part of the excitation magnetic field generated by the rotor permanent magnet is taken as the excitation space vector, which rotates together with the rotor. Its phase in the ABC coordinate system is determined by the electrical angle.
Therefore, we can write the stator voltage vector equation in the ABC axis system:
(2-2)
In the formula, is the stator voltage space vector; is the stator phase resistance; and is the equivalent synchronous inductance.
The axis of the permanent magnet's fundamental excitation magnetic field is selected as the axis, and the electrical angle leading the rotor's rotation direction is selected as the axis. The shaft system rotates with the rotor at an electrical angular velocity, and the coordinates of the shaft system are determined by the electrical angle between the axis and the A-axis. Thus, Figure 2-1 can be further represented as Figure 2-2.
Figure 2-2 Physical model in rotating coordinate system
Fig.2-2The physical model in axes
Replacing the three-phase stator windings with two stator coils on the shaft system, because the power constant constraint needs to be satisfied, the effective number of turns of the shaft stator coils should be a multiple of the effective number of turns per phase of the original three-phase windings. Equation (2-2) can be transformed into the voltage equation expressed in the shaft system as follows:
(2-3)
(2-4)
The equation for the magnetic flux linkage of the shaft system is expressed as:
(2-5)
(2-6)
In the formula, is the differential operator.
This is the leakage inductance of the coil, which consists of the self-inductance and magnetizing inductance of the shaft electronic coil.
By establishing a mathematical model for a permanent magnet synchronous motor, the permanent magnet can be equivalently represented as an excitation coil with the same number of effective turns as the stator coil. The equivalent excitation current is given, which generates the same fundamental excitation magnetic field as the permanent magnet. Therefore, the following relationship holds:
(2-7)
Therefore, the stator flux linkage equation can be expressed as:
(2-8)
(2-9)
Substituting equations (2-8) and (2-9) into equations (2-3) and (2-4), we get:
(2-10)
(2-11)
If we neglect the effect of temperature changes on the magnetizing capacity of the permanent magnet, it can be considered constant, i.e., a constant value. In equation (2-10), is actually the kinetic electromotive force generated in the shaft coil by the excitation magnetic field of the shaft permanent magnet, which is the no-load electromotive force. Under sinusoidal steady state, we have:
(2-12)
In the formula, is the effective value of the no-load electromotive force induced in the phase winding by the excitation magnetic field of the permanent magnet.
From equation (2-12), we can see that:
(2-13)
as well as
(2-14)
Therefore, it can be determined through an unloaded experiment; if it is known, it can be calculated.
If expressed in terms of no-load electromotive force, then:
(2-15)
(2-16)
If the operation is in a steady state, it can be further simplified:
(2-17)
(2-18)
Electromagnetic torque can be expressed as:
(2-19)
If expressed in terms of a shaft system, then:
(2-20)
(2-21)
Substituting equations (2-20) and (2-21) into equation (2-19), we get:
(2-22)
Substituting the flux linkage equations (2-5) and (2-6) into equation (2-22), we get:
(2-23)
As shown in Figure 2-5:
(2-24)
(2-25)
Substituting equations (2-24) and (2-25) into equation (2-23), we get:
(2-26)
or
(2-27)
In equations (2-26) and (2-27), the first term within the brackets is the electromagnetic torque generated by the interaction between the stator current and the excitation magnetic field of the permanent magnet, called the excitation torque. The second term within the brackets is caused by the rotor salient pole effect and is called the reluctance torque. For insert and embedded rotor structures, since there is a permanent magnet on the shaft magnetic circuit, and the permeability of the permanent magnet is very low (approximately equal to the permeability of air), therefore... For surface-mounted rotor structures, it is equivalent to installing the permanent magnet in the air gap, therefore, there is no reluctance torque.
For a surface-mounted permanent magnet synchronous motor, since , therefore we have:
(2-28)
or
(2-29)
When the axial component of the stator current is zero, it is orthogonal to both components, and the torque value generated per unit stator current is the maximum.
3. Machine-side inverter control strategy
This paper adopts a decoupled control method for active and reactive power, which can flexibly control the active and reactive power generated by the generator. In the shaft system, the shaft setpoint representing reactive power is usually set to 0, allowing the generator to output only active power. Further algorithms can be added by adjusting the shaft setpoint. In practical permanent magnet direct-drive wind power systems, the wind turbine and generator are coaxial. Due to safety and technical considerations, wind turbines are usually designed to operate at slower speeds, requiring the permanent magnet synchronous generator to also operate at a slower speed. Therefore, permanent magnet synchronous wind turbines are designed with multiple pole pairs. This brings another problem: too many poles increase the shaft diameter of the permanent magnet synchronous wind turbine, making it difficult to install photoelectric encoders. Therefore, accurately estimating the rotor position of the permanent magnet synchronous generator becomes a challenge in the control strategy. This paper uses a sliding mode algorithm to estimate the rotor position, achieving good control results. The entire control strategy is shown in Figure 3-1.
The machine-side control strategy of a permanent magnet direct-drive wind power generation system requires the acquisition of analog quantities of the generator's two-phase current. Treating the motor as a closed node, according to Kirchhoff's current law, the motor outputs AC current, allowing for the reconstruction of the two-phase current. If the current sum is known, the current can be obtained. A Clark transformation is performed on the three-phase current from the three-phase coordinate system to the two-phase stationary coordinate system, followed by a Park transformation from the two-phase stationary coordinate system to the two-phase rotating coordinate system. This decomposes the current components in the two-phase rotating axis system. The theory of coordinate transformation is described in detail in many documents and will not be repeated here. The transformed axis current components are used by a PI controller to obtain the required sum component, which is then subjected to an inverse Park transformation to obtain the required sum component in the two-phase stationary coordinate system. Finally, this is fed into an SVPWM generator to obtain the switching signals of the six switching devices of the three-phase bridge in the machine-side converter. The electrical angle of the motor rotor position is required during the Park and inverse Park transformations. This system obtains the electrical angle of the rotor position using a sliding mode observation method, the principle of which will be explained in detail in the next section.
Figure 3-1 Control strategy for motor-side converter
Fig.2-7 The control strategy of the generator side converter
3.1 Rotor Position Observer Based on Sliding Mode Observation Algorithm
For a surface-mounted permanent magnet synchronous generator, the state equation in the stationary coordinate system can be expressed as:
(3-1)
In the formula:
The stator inductance component is , the stator resistance is , and the rotor flux linkage is . and represent the rotor speed and position angle, respectively.
Based on equation (3-1), the following sliding mode observer equation is adopted here:
(3-2)
In the formula:
Here, the symbol "^" represents an estimated value; "*" represents a given value.
After constructing the sliding mode observer, a certain estimated value must coincide with the actual value to achieve the same mathematical equations for the estimated model and the actual motor. Finally, the required angle value is obtained by solving the equation. Based on the mathematical model of the permanent magnet synchronous generator, the difference between the estimated stator current and the actual stator current is used as a switching function. This switching function is used to correct the deviation between the two until the deviation is zero. The signal in equation (3-2) is this switching function, which is a sign function of the current estimation error and can be expressed as:
(3-3)
The sliding surface is defined as the point where the value is zero, representing the ultimate goal of control. For the sliding observer to reach the sliding surface and perform sliding motion within a finite time, the following condition must be met: When sliding motion occurs, the estimated stator current and the measured stator current are equal. At this point, equation (3-1) is completely equivalent to equation (3-2), meaning the control signal includes the generator back electromotive force:
(3-4)
The rotor position angle can be calculated based on equation (3-4):
(3-5)
The control signal is a current error signal, which includes a sampled current signal and an estimated current signal. The sampled current signal is obtained by AD sampling and is a high-frequency signal. In particular, the calculated estimated current signal is also a high-frequency signal. Therefore, the control signal needs to be low-pass filtered to obtain the back EMF. The filtering equation is shown in equation (3-6):
(3-6)
The cutoff frequency of the low-pass filter in the formula is such that its value must be selected to ensure that high-frequency signal components are filtered out while low-frequency signal components are not affected. However, the filtering process will cause phase deviation, affecting the performance of the entire system. This is also a shortcoming of the sliding mode observer, which affects the application of the sliding mode observation algorithm in the field of high-precision servo systems. However, since the rotor position angle does not need to be precisely obtained in wind power generation systems, and the robustness of the sliding mode algorithm itself is suitable for estimating the position angle of low-speed permanent magnet synchronous electronic rotors.
In permanent magnet direct drive wind power generation systems, the wind turbine speed is generally not high. Theoretically, the sliding mode control signal requires an error between the actual current and the estimated current when switching. At low speeds, the degree of non-overlap between the estimated current and the actual current increases, which can lead to chattering problems. In order to improve the chattering problem of traditional sliding mode algorithms, improved sliding mode algorithms are usually used.
The improved sliding mode algorithm uses a saturation function control signal instead of the traditional switching control signal, as shown in Figure 3-2. In the improved sliding mode algorithm, the control signal is shown in equation (3-7):
(3-7)
In the formula.
In the improved sliding mode algorithm, the control signal still depends on the error between the estimated current and the actual current. Although there are still only two stable switching states, the use of a linear function in the transition range allows for smoother switching and reduces chattering. However, within this range, as the error between the estimated and actual current decreases, the gain also decreases, leading to a reduction in the control power of the sliding mode algorithm. In effect, some robustness is sacrificed to suppress chattering. To suppress chattering without sacrificing the robustness of the sliding mode algorithm, a multiplicative sliding mode algorithm can be used to observe the rotor position.
Figure 3-2 Control signals for the improved sliding mode algorithm
Fig.3-2The improved SMO signal
Discretizing equation (3-2) yields equation (3-7):
(3-7)
In the formula, is the sampling time, which is the same as the definition in formula (3-2).
The switch control quantity can be designed in the following form:
(3-8)
The initial state equations are:
Equation (3-8) describes the discrete form of the multiplexed sliding mode control signal. This method involves discrete integration of the sliding mode control signal. Because of the integral, a very small switching gain can be used to control the estimated current difference near the sliding surface. From equation (3-8), we can obtain:
(3-9)
Equation (3-9) shows that the switching gain selected by the multiplexed sliding mode method is the ratio of the difference between the sliding mode control signal and the switching signal for estimating the current difference in each sampling cycle. Since the control signal must approach zero, while the switching signal for estimating the current difference has only two states, a very small switching gain in the multiplexed sliding mode algorithm can control the estimated current difference near the sliding surface. Simultaneously, Equation (3-9) shows that because the control signal uses an integral form, it can be equivalently considered as increasing the logical switching states of the discrete control signal, making the system's switching near the sliding surface smoother and reducing system chattering. However, this algorithm also consumes computation time. It can be considered that the multiplexed sliding mode algorithm sacrifices system time to satisfy the robustness of the sliding mode algorithm and reduce system chattering. As signal processing chips become increasingly powerful, sacrificing processing time to meet system performance requirements is a very reasonable solution.
3.2 Research on generator-side converter providing power and positioning for generator
During system installation and commissioning, the motor rotor needs to be positioned. Since the permanent magnet synchronous motor rotor is a permanent magnet, rotating it during installation is difficult. Positioning the rotor while the generator is in motor mode can significantly reduce the installation workload. In ground experiments, two permanent magnet synchronous motors are used in a coupled-shaft drive for simulation, allowing for faster and better converter commissioning. One motor is used for driving, and the other for generating electricity. The converter topology used for driving and generating is the same, and it is also studied in this section.
This paper uses a simple and effective method to control the generator positioning using a generator-side converter. The control strategy is shown in Figure 3-3.
Figure 3-3 Rotor positioning control strategy for permanent magnet synchronous motor
Fig.3-3The allocation strategy of PMSG
This control method is an open-loop control. The rotating magnetomotive force (MF) controlling the generator's rotation can be decomposed into two-phase stationary coordinate axes, as shown in Figure 3-4. The rotor rotation angle is given by a ramp generator, slowly increasing from 0 to the given value, and ending when the given value is reached. The MF required for generator rotation is decomposed into two-phase stationary coordinate axis components, as shown in equations (3-10) and (3-11), and finally fed into the SVPWM generator to obtain the switching signals of the generator-side converter switching transistors.
(3-10)
(3-11)
Figure 3-4 Vector decomposition of rotor positioning coordinate system
Fig.3-4The space vector in axes
Because permanent magnet synchronous motors have a large number of pole pairs, each electrical angle corresponds to a very small mechanical angle of the rotor. Taking a 1.5MW permanent magnet synchronous wind turbine as an example, with 60 pole pairs, a mechanical angle of 360 degrees corresponds to an electrical angle of 21600 degrees. Conversely, a 1-degree electrical angle corresponds to only 0.01667 degrees of mechanical angle. As shown in Figure 3-3, the control method is open-loop control, and the initial angle of the generator rotor is unknown. When the ramp generator provides an initial angle of 0, the rotor, made of permanent magnets, may not be at the 0-degree electrical angle position, potentially causing generator rotation. The maximum electrical angle deviation is 180 degrees, corresponding to a mechanical angle of 3 degrees, which is only a small rotation and within an acceptable range.
Figure 3-5 Drive Motor Control Strategy
Fig.3-5The strategy of motor status
When the machine-side converter is used to drive the motor, the control method is shown in Figure 3-5.
When the converter drives the motor to rotate, the simulated angle is generated by a ramp generator and a simulated angle generator. Given the desired rotation frequency, the ramp generator gradually increases the frequency from 0 until the desired frequency is reached, at which point the simulated angle generator outputs a simulated electrical angle signal. Changing this signal alters the output torque. This control method is also an open-loop control, and therefore suffers from the problem of an unknown initial rotor angle. Due to the limitations of the experimental platform used in this paper, the permanent magnet synchronous motor cannot currently be equipped with an optical encoder. Therefore, this paper only conducted experiments on the open-loop control. A closed-loop speed control can be implemented later by installing an optical encoder or adopting a more complex control strategy.
4. Experimental Results
Figure 4-1a shows the dynamic waveforms of the current and DC bus voltage when the generator is operating at 60 rpm, from the uncontrolled rectification state to the shaft current setpoint of -0.1 (per unit value, calibration 1 corresponds to 100A), and then to the shaft current setpoint of -0.2. It can be seen that there is some overshoot in the current when transitioning from the uncontrolled state to the controllable state. After entering the controllable state, further increases in power current tracking show no significant overshoot, and the DC bus voltage rises smoothly without significant overshoot. The amplified waveform from the uncontrolled state to the controllable state is shown in Figure 4-1b. The amplified waveform from the shaft current setpoint of -0.1 to -0.2 is shown in Figure 4-1c. The steady-state waveform at the shaft current setpoint of -0.2 is shown in Figure 4-1d, with the bus voltage stabilizing at 300V and the current waveform showing good performance. With the shaft current setpoint still at -0.2, changing the motor speed to 120 rpm, the bus voltage continues to rise, finally stabilizing at 450V, with a very good sinusoidal current waveform, as shown in Figure 4-1e. The waveform from uncontrolled state to shaft setpoint -0.2 is shown in Figure 4-1f. It can be seen that there is no obvious overshoot during the state transition, and the DC bus voltage rises very smoothly, achieving a good control effect.
Figure 4-1 Experimental waveforms of the motor-side converter
Fig.4-1The experiment wave of generator-side
During the experiment, the CCS debugging tool was used to save the experimental data, and Matlab was used for data processing to plot the waveforms. The decoupling control effect of the motor-side converter is shown in Figure 4-2: the shaft current tracking is stable, the DC bus voltage is stable, and the motor phase angle observed by the sliding mode observer is stable, achieving the control objective. The phase angle observed by the sliding mode observer and the actual phase angle are shown in Figure 4-3. At the same speed, the deviation between the actual speed and the angle estimated by the sliding mode observer is small; there is only a jump when transitioning from the same cycle to the next cycle, which is actually an error effect and does not hinder control. It can be said that the sliding mode observer is accurate and practical for estimating the motor phase angle. The entire motor-side converter control strategy meets the expected requirements.
Figure 4-2 Experimental waveforms of the motor-side converter
Fig.4-2The experiment wave of generator-side
Figure 4-3 Sliding mode observer observation error
Fig. 4-3 The SMO-errors wave
5. Conclusion
The control strategy for the generator-side inverter was studied, employing a dual-closed-loop control strategy. The generator-side inverter primarily controls the generator output power, and the generator rotor positioning and motor state were also investigated to meet experimental and practical requirements. The generator-side inverter uses a sliding mode observation algorithm to estimate the generator rotor angle. Results show that the error between the estimated rotor position angle and the actual rotor angle obtained by the sliding mode observation method is very small, increasing the stability and reliability of the entire system. The generator-side inverter can control the generator output power and can decouple active and reactive power control separately. The generator-side inverter controls the generator output current to ensure a sinusoidal output current, guaranteeing smooth generator operation.
