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Scientific Reports volume 15, Article number: 43600 (2025) Cite this article
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In recent years, the growing interest in renewable energy has increased attention on photovoltaic systems. While traditional photovoltaic systems are typically built on the ground, floating photovoltaic power generation involves placing photovoltaic panels on floating platforms in water. When these platforms are on the sea surface, the solar radiation received by the photovoltaic array changes periodically due to ocean waves, leading to fluctuations in the maximum power point temperature and light radiation. This results in varying power generation capacities and an unbalanced energy supply at different locations. The current fixed DC bus voltage further exacerbates this issue, reducing power generation efficiency. A new multi-winding permanent magnet synchronous motor (MWPMSM) system for distributed energy is proposed to address these challenges. This system features multiple independent DC buses, each operating at a different voltage level to ensure compatibility with the energy absorbed by each part of the photovoltaic array. The MWPMSM system is designed with a specific structure and mathematical model, and its structure parameters are carefully chosen and verified through finite element analysis. A control strategy for the MWPMSM is then established, and an experimental platform is used to demonstrate that the system maintains high efficiency and unchanged output power while ensuring a balanced power ratio (the Maximum error of winding power ratio is 6.7%).
With the increasing energy demand, the siting of photovoltaic power stations worldwide is mainly based on land. However, land resources are extremely precious, which poses a significant barrier to the promotion of photovoltaic power stations. Floating photovoltaic systems, due to their low cost, ease of installation and maintenance, and high-power generation efficiency, have become a hot topic of research. Many countries and regions have begun to apply this technology on a large scale^1,2. The PV characteristic curve is shown in Fig. 1, The blue dashed line represents the MPPT curve. To enhance the value of photovoltaic utilization, maximum power point tracking (MPPT) technology is very important³. The V-I curve of photovoltaic cells is similar to a parabola. When the voltage increases from zero, the current remains constant, and when it increases to the maximum power point (MPP), the current begins to decrease as the voltage increases, so it is very necessary to find the maximum power point⁴.
PV characteristic curve under temperature and light intensity variations.
Figure 2 shows the offshore work platform is powered by different offshore floating photovoltaic arrays, and the offshore floating power supply at different locations. When the floating body swings under the action of ocean waves, the equivalent light intensity on the surface of each photovoltaic cell changes accordingly, and with the change of light intensity, the V-I of the photovoltaic array also changes, and the maximum power point also changes^5,6,7,8,9. Since the light and wave floating conditions are different, as shown in Fig. 3, the tradition is to import the power supply into the same voltage busbar, adopt a single busbar voltage, and then use it for the work platform water pump motor¹⁰. The problem with this form is due to adopting a single bus voltage, where different floating photovoltaic arrays cannot operate at their respective maximum power points¹¹. This situation complicates energy scheduling and collaborative motor control, ultimately reducing the overall efficiency of the energy management system¹².
Offshore floating photovoltaic power generation system.
Traditional offshore work platform powered from floating photovoltaic arrays.
The solution is to adopt the idea of power distribution and management of distributed generation and nearby conversion¹³, with energy balance and energy flow efficiency as the optimization goals, split the control model of the energy management system into multiple subsystems, and implement the distributed collaborative control method to make each module work together to maintain power balance and improve energy utilization efficiency. Since the energy management system uses distributed generation, the motor should also be in the form of multiple modules, as shown in Fig. 4(such as division into three parts).
Multiple modules powered from floating photovoltaic arrays.
In Fig. 4, the DC bus voltage is no longer fixed at a single value as shown in Fig. 3. The photovoltaic arrays in different regions can track their own MPP due to changes in irradiance caused by factors such as waves and shading, The power-distribution controller allocates power to each winding based on the conditions of different areas. Thereby improving the overall efficiency of the system.
Permanent magnet synchronous motors (PMSM) have many advantages, such as energy saving, high power density, high efficiency, and fast dynamic response. It is very suitable for offshore working platforms with high requirements for energy saving and fast response. Sun P. et al. proposed that the two sets of windings are with double winding hybrid exciters; these exciters are on the stator and rotor, respectively. In this drive system, two Converters and heat dissipation-related challenges require that the inner rotor winding cannot be ignored. Jiang X et al. proposed double-winding Fault-tolerant machines, in which double windings were backed up to have the same polar pair numbering as each other. Reliability, however, the drive system is improved at the expense of torque density. The motor is not conducive to a floating photovoltaic distributed power generation system. Hui‑Min Wang proposed the single‑winding arrangement for arbitrary multiphase bearingless permanent magnet synchronous motor^14,15. Most of these motors adopt a multiphase structure. Inaccurate position detection can easily lead to torque imbalance¹⁶. Shaoshuai Wang et al. proposed the flux-modulated multi-winding PM machine (FMM-PMM) for electric vehicles, by adopting two stator windings with different pole-pairs aiming to achieve multiple harmonics utilization with high efficiency. Due to the technical features of harmonic utilization and magnetic gear effect, the torque density of the proposed PM machine can be improved without worsening the power factor¹⁷. Furthermore, increasing the number of phases will bring complexity to the design of stator and rotor structures, which is not conducive to multi-modular design. In this paper, a new type of outer rotor permanent magnet synchronous motor is proposed to reduce the unbalanced torque caused by multiple modules, and it can well meet the requirements of distributed power supply.
Considering the floating photovoltaic distributed power generation system application scenario, the motor has a disc-type outer rotor structure, as shown in Fig. 5, and the winding adopts a design scheme of the same phase¹⁸. At the same time, due to its redundant structural design, three sets of accumulators can be independently powered and generated using a motor controller PWM The signal directly drives three sets of inverters in parallel, ensuring that the three sets of windings of the MWPMSM have three times the output power of the conventional permanent magnet synchronous motor when driven by stator current at the same frequency and phase. In this way, the MWPMSM reduces the number of turns per set of stator windings compared to conventional permanent magnet motors of equal power by 1/3, while the total number of turns of the stator winding remains unchanged. Moreover, the working characteristics of the MWPMSM are better when analyzed from the point of view of the actual driving capability. Each of the three sets of stator windings of the motor is arranged in a phase-free angle difference arrangement and is not electrically connected Y.Y. Type connection. The schematic diagram of the stator structure is shown in Fig. 5b. So, the motor has a total of nine outlet ends, which need the controller to provide each phase stator current, and at the same time, the control strategy must be used to ensure the same frequency and phase. At the same time, from the perspective of motor design and operation, this structure can ensure the balance of forces on the motor shaft, reduce the uneven rotation of the motor rotor, and reduce the vibration and noise generated by the motor. The winding motor winding electromagnetic wire is in the form of multiple strands and is insulated between each strand. The motor wire turns and outlet ends are evenly divided according to the number of strands 3 Sections, each of which may be used as a separate motor winding, A1B1C1 Composition of motor windings 1, A2B2C2 Composition of motor windings 2, A3B3C3 Composition of motor windings 3, are all controlled by an independent controller¹⁹. Each part of the power is designed for 100W, the motor operating voltage is set at 35V ~ 100V.
Overall structure diagram of MWPMSM.
The MWPMSM is a non-linear system with multi-variable, multi-input features. To facilitate the analysis and the establishment of the model, the following ideal assumptions are made²⁰:
1. The three-phase windings are symmetrically distributed, and the windings are arranged symmetrically in spatial position.
2. Ignoring core saturation, excluding eddies and hysteresis phenomena.
3. The magnetic potential generated by the stator winding current in the air gap is sinusoidally distributed, ignoring the higher harmonics.
Mathematical model of MWPMSM under a stationary coordinate system. Voltage Eq. (1):
Magnetic flux Eq. (2):
where:
where, u_ai, u_bi, and u_ci (i = 1,2,3) are the three-phase stator voltages of windings, respectively. i_ai, i_bi, i_ci, (i = 1,2,3)are three-phase stator currents of windings; R_s is the winding resistance of the stator per phase; ψ_ai, ψ_bi, ψ_ci, (i = 1,2,3) are three-phase stator fluxes of windings, respectively. The flux coefficient matrix γ represents the position distribution relationship of each phase winding; θ represents the electrical angle between the rotor pole position and the winding shaft of the stator phase A; L_s represents the motor inductance coefficient matrix, respectively. L_m1, L_m2, and L_m3 are the mutual inductance coefficients between winding 1 and winding 2, winding 1 and winding 3, and winding 2 and winding 3, respectively. L_r1, L_r2, and L_r3 are the leakage inductance coefficients of windings 1,2, and 3. ψ_f is the flux of a permanent magnet.
Electromagnetic Torque Eq. (9):
Since the motors designed herein are three sets of windings, all in phase Y. Shift 0° The electrical angles are arranged. At the same time, the electromagnetic coupling between the windings of this motor is small, and the difference between the self-induction coefficient, mutual induction coefficient, and leakage induction coefficient is minimal, so coordinate transformation and establishment are being carried out d-q Influences such as winding mutual inductance are ignored during analysis of coordinate systems²⁰. The electrical characteristics of each set of motor windings during operation are the same as those of ordinary PMSM²¹. Thus, only one set of windings needs to be mathematically modeled for subsequent analysis, such as coordinate transformation. Furthermore, the total electromagnetic torque Te of the MWPMSM is the vector sum of the three sets of windings superimposed on each other, so:
To control the motor more accurately, first of all, we need to consider the design structure of the motor, simulate the electromagnetic field, and analyze the finite element model of the motor according to the structural parameters and basic performance of the motor. This section mainly discusses the relevant technical indicators of multi-winding motor design and the boundary conditions of motor design, to study the calculation method of the motor magnetic circuit, and establish the finite element model of the motor.
The basic requirement of MWPMSM is to use a total of 2 motors on the left and right as the propulsion device, each motor includes 3 sets of windings, and each set of windings and its corresponding drive are a motor module. According to the project requirements, the motor system design basic requirement is shown in Table 1:
The MWPMSM is mainly composed of four parts: motor stator, rotor, winding, and permanent magnet. This section mainly discusses the design methods of these four parameters.
The stator parameters of the motor mainly include the parameters of the stator core and the parameters of the slot. The parameters of the stator core mainly involve the inner diameter of the stator punch, the outer diameter of the stator, and the effective length of the core. The size of the inner diameter of the stator and the effective length of the core are inextricably linked to the performance of the motor. Therefore, an important step in the design of a motor is to determine the main dimensions of the motor.
The parameters of the groove include the selection of the number of grooves and the determination of the size of the groove. The selection of the number of slots is closely related to the design of the motor winding. In terms of winding design, there are usually single- or double-layer windings. Single-layer winding refers to a slot in only one group of windings, only connected with the winding of another slot, forming a closed loop. For single-layer winding, the selection of the number of slots should meet the number of phases and the number of poles of the motor at the same time. Double-layer winding refers to a slot with two layers of windings, the windings are separated by insulating materials. For multi-layer windings, the selection of the number of slots should meet the Eq. (11) ²².
where Q₁ indicates the number of stator slots for the motor, k indicates a value greater than or equal to 1, a represents the number of winding layers.
In terms of motor rotor parameters, two aspects are mainly considered: the outer diameter of the rotor and the length of the rotor core. The selection of the outer diameter of the rotor should not be too small, as the outer diameter of the rotor is too small, there will be insufficient space to achieve the installation of the motor poles and rotating shafts.
Motor winding parameters:
where N_Ф1 represents the number of series conductors per phase of the motor, N_S1 represents the number of conductors per slot of the motor, and α₁ represents the number of parallel branches of the motor.
When designing PMSM, the magnetic field of PMSM is usually converted into a magnetic circuit for research and analysis, and a preliminary design is carried out to achieve the purpose of simplifying the calculation. Through the calculation of the magnetic circuit, the key parameters such as the magnetic flux of the motor and the magnetic density of the motor can be calculated. The following is a study of the magnetic circuit calculation in the case of no load of the motor. The expression for the calculated length of the stator tooth magnetic circuit is Eq. (13).
where h′_t1 represents the calculated length of the stator tooth magnetic circuit; hs₁, hs₂, and r represent the specific size parameters of the cogging.
The magnetic pressure drop of the stator tooth can be obtained by calculating the length of the stator tooth magnetic circuit, and its expression is Eq. (14).
where F_t1 represents the magnetic pressure drop of the stator teeth; H_t10 can query the DC magnetization characteristic table of stator material to obtain the parameter value, which indicates the degree of magnetization.
After a series of parameters about the stator teeth have been calculated, the parameters about the stator yoke need to be calculated. The stator yoke calculates the height expression in Eq. (15).
where h′_j1 denotes the calculated height of the stator yoke; D₁ denotes the outer diameter of the stator.
Before calculating the magnetic circuit, it is necessary to calculate the pole distance and relative recovery permeability of the motor:
The no-load working point of the permanent magnet that will be obtained b_m0, with the no-load work point set at the beginning, b′_m0 Compare and calculate, if the error value between the two Δb_m0 Less than 1%, it can be proved that the no-load working point set at the beginning meets the current requirements. If the current requirements are not met, one unloaded working point needs to be reassumed and a series of calculations performed. It’s error value Δb_m0 the expression in Eq. (17) ²³.
The above calculation of the magnetic circuit of the motor was carried out, based on the above formula, and at the same time, concerning the design of multi-winding motors at home and abroad, the main dimensions of each part of the motor and the materials used in each part were established, the basic parameters of the motor The numbers are as shown in Table 2.
According to the above motor design parameters and design requirements, the surface-mounted external rotor structure of the MWPMSM was finally established, and the finite element model was established by design software. Through the finite element software, you can quickly check whether the design parameters of each part of the motor meet the requirements, play a role in verification, and optimize and modify the motor in combination with the simulation results²⁴.
After modeling the motor, the design is first analyzed for a no-load simulation. The no-load state refers to no current excitation source, and only permanent magnets are excited separately²⁵. The following are the simulation results:
Figure 6 shows that the no-load air gap magnetic dense waveform has good waveform smoothness, the flux density waveform has two zero crossings within each cycle, which is a typical characteristic of PMSM and helps to produce stable torque, and the cogging torque has little influence, so the design is reasonable. The amplitude of the air-gap magnetic dense waveform is about 0.8 T when the motor is no-load, which meets the performance requirements of the motor²⁶.
Relationship between the magnetic density of the air gap and the angle of the rotor position.
Figure 7 is the vector magnetic potential distribution diagram at the 45-degree rotor position angle, from which it can be seen that the magnetic field distribution is relatively uniform, the magnetic field is not saturated, and the motor still has a large adjustment range²⁷.
Vector potential distribution at 45 degrees.
Figure 8 shows the relationship between the flux and the current of the DQ axis when the stator current of the motor changes, the flux value is within a reasonable range, the core has not reached saturation, and the torque and speed of the motor can be accurately controlled by controlling the current of the D axis and the Q axis. By adjusting the magnitude and phase of the current in the D-axis and Q-axis, the magnetic field-oriented control of the motor can be realized, thereby improving the efficiency and performance of the motor²⁸.
Relationship between DQ axis flux and DQ current.
Figure 9 shows the relationship between the DQ axis inductance and the stator current of the motor in a permanent magnet synchronous motor, the DQ axis inductance is a parameter that describes the internal inductance of the motor, and in a permanent magnet synchronous motor, the DQ axis inductance is usually nonlinear and related to the current magnitude and magnetic field distribution, it is a linear relationship within a certain range. By controlling the current in the D-axis and Q-axis, the inductance of the motor can be affected, and the performance and control characteristics of the motor can be affected²⁹.
Relationship between DQ axis inductance and DQ current.
Figure 10 shows the relationship between the control angle and the torque, and marks the working point of the motor at 30A. The control angle refers to the relative position between the magnetic field of the rotor and the magnetic field of the stator, controlling the motor. A reasonable selection of control angle can improve the efficiency, response speed, and stability of the motor; while reducing energy loss and vibration noise, As can be seen in Fig. 10, the torque at the working point is about 9.5Nm to meet the design requirements³⁰.
Relationship between control angle V.S. torque.
Figure 11 shows the relationship between the air gap magnetic field and the rotor position angle, and it can be seen from the air gap magnetic field curve that the magnetic field density amplitude meets the design requirements, which is about 0.9T, and there is a slight deformation at the individual peaks, which can be solved by optimizing the motor cogging in the later stage³¹.
Air gap magnetic field V.S. rotor position angle.
Figure 12 shows the relationship between output torque and speed, from which it can be seen that the motor can still maintain the maximum torque of 9.5Nm at 900r/min, and the torque is still greater than 3Nm when the motor reaches 2600r/min, which meets the design requirements³².
Output torque V.S. speed.
Figure 13 shows the relationship between the power factor of the motor and the speed, and it can be seen that in the whole speed range, the power factor varies between 0.974–1, the electric energy utilization rate of the motor is higher, the reactive power is smaller, and the motor efficiency is higher³³.
Motor power factor V.S. speed.
How to keep the current phase of the three sets of windings consistent is the core problem, the research on the control strategy of MWPMSM mainly includes the following aspects: first, the comparison and analysis of different controllers selected for multi-motor modules are carried out, and the reasonable parameters of the best controller are determined; Second, based on theoretical analysis, the tracking effect of the winding current of the remaining motor modules on the reference current phase after selecting different controllers is simulated and compared³⁴. The third is to carry out system simulation experiments of multi-winding motors to verify the feasibility of their coordinated operation³⁵.
Figure 14 shows the block diagram of the MWPMSM control system and control strategy. Figure 14b gives the control strategy diagram. To simplify control, the (i_{d}^{ * } = 0) control method is adopted to achieve static decoupling control of active and reactive currents³⁶. After the Park transformation, the electromagnetic torque equation is (18):
Control system and control strategy diagram.
where Ω is motor angular velocity, The electromagnetic torque is proportional to i_q , and the electromagnetic power is proportional to T_e. Therefore, by proportionally distributing i_q , power can be proportionally distributed at a certain speed. K_PD1, K_PD2 are Power-distribution proportionality coefficients. i_A1 is multiplied by K_PD1 to serve as the basis for tracking current in winding 2, i_A1 is multiplied by K_PD2 to serve as the basis for tracking current in winding 3, and so on. Because the reference current i_A1 is an AC input signal, the use of PI control cannot improve the phase-locking accuracy, and there is a system steady-state error. Due to the wide speed range of the motor, the corresponding current frequency conversion range is large, so the current should be tracked over a wide range³⁷. As shown in Fig. 15, an SPLL based on an orthogonal signal generator controller can be used to realize the tracking of the current phase of the other two sets of windings to the phase of the reference current i_A1^38,39.
Structure diagram of SPLL based on orthogonal signal generator.
From Fig. 15, Small signal analysis is done using the network theory, the PLL closed-loop Phase transfer function can be written as follows: Eq. (19) ⁴⁰.
Comparing the closed-loop phase transfer function to the generic second-order system transfer function, the transfer function Eq. (20) can be obtained.
where T_i is the sample time.
Figure 16 shows the block diagram of Orthogonal signal generator of SPLL. The presented structure is based on a second-order generator integrator (SOGI), which is defined as Eq. (21).
Orthogonal signal generator of SPLL.
where ω_n represents the resonance frequency of the SOGI.
When the SPLL based on an orthogonal signal generator control strategy is used, the second-order generalized integrator closed-loop transfer function can be written in Eq. (22) ⁴⁰.
where k affects the bandwidth of the closed-loop system. Once the orthogonal signal is generated Park transform is used to detect the d and q components on the rotating reference frame. This is then fed to the loop filter, which controls the VCO of the PLL. Take the rotational speed 1500r/min with a current frequency is 450Hz as the working point⁴⁰.
Using the proposed method, the input signal is filtered, resulting in two clean orthogonal signals, due to the resonance frequency of the Orthogonal signal generator of SPLL at ω_n (grid frequency). The level of filtering can be set from k, as shown in Fig. 17, where there is a higher gain over a wide frequency range near the operating point. By selecting the parameters of k, comprehensively considering the stability performance and anti-interference ability of the SPLL based on the orthogonal signal generator controller system, and continuously optimizing the simulation model, the parameter values of SPLL are finally determined as follows: k = 3. The Bode plot is shown in Fig. 17 to optimize the control performance of the system.
Bode plot and step response of the closed-loop transfer function (H_d).
The simulated waveform based on the SPLL control current inner loop tracking strategy is shown in Fig. 18, after the current is stable, the tracking current i_A2 and the reference current i_A1 basically maintain the same phase and amplitude before 0.02s, and after the sudden load torque of 0.02s, the current increase of the two is still sinusoidally distributed, and there is almost no steady-state error, that is, the tracking current can effectively track the AC reference signal without static difference. After adopting the SPLL control strategy, the current phase of the tracking current i_A2 can quickly track the current phase of the reference current i_A1 with a very small error, and the simulation results are consistent with the theoretical analysis in the previous section, that is, the SPLL based on SOGI control can realize the static tracking of the AC input signal. At the same time, the phase synchronization between multiple winding currents is realized, which solves the problem that the phase needs to be consistent between multiple winding currents and improves the accuracy of phase locking.
Waveform diagram of tracking current and reference current under SPLL control.
Figure 18 illustrates the tracking current of module 2 following the implementation of the SPLL based on the SOGI control strategy. This method effectively mitigates the high-order harmonics of the output current, significantly enhancing the system’s steady-state accuracy. Additionally, it results in minimal phase shift between the tracking current waveform and the reference current waveform (phase lag of less than 0.005 rad) and enables error-free tracking without static error.
Figure 19 shows the speed and torque of the motor. The initial speed is ω = 1200rad/s, the load torque remains unchanged at 10Nm, the speed increases to ω = 1600rad/s at 0.5s, the system simulation time is the same as 1s, and the waveform of the motor speed and torque is observed.
MWPMSM speed and torque during acceleration.
Based on the simulation results shown in Fig. 19, it is evident that following a sudden change in motor speed at 0.5s, the speed quickly stabilizes at a new set value of 1600 r/min and remains constant. Throughout the motor’s startup, speed adjustment, and stable operation phases, the motor speed remains relatively stable. Although there is a brief fluctuation in the electromagnetic torque at 0.5s, it quickly stabilizes at the initial value of 10Nm. While there is some pulsation in the electromagnetic torque when the speed increases at 0.5s, it is brief and does not impact the system’s stability or dynamic performance.
Figure 20 shows the experimental platform of a MWPMSM control system. The basic parameters of the motors used in the experiment are shown in Table 2. The voltage range of the DC bus is 35 ~ 100V, each motor module in the controller corresponds to a set of main control board and power drive board respectively, each power board has six drive signal circuits, and there is a power module on the bottom board, which sup-plies power to the main control board and the power drive board after voltage conversion.
Experimental platform for MWPMSM control system.
In this experimental platform, the host computer interface is used to simulate the new energy management system, and the speed command and winding power distribution command are issued to the motor controller. When a given DC bus voltage is input to the controller, configure the communication settings of the host computer monitoring system, select the corresponding host COM port, and then enter the operation control, and set the corresponding target speed to the power ratio of multiple windings, as shown in Fig. 21.
Host computer monitoring system interface.
The motor controller designed in this experiment consists of two sets of main control board and power drive board, because the winding current of module 2 and module 3 is obtained by the same control strategy and the same controller, the winding current of the two is the same, so only two sets of windings in the MWPMSM are used for experimental verification (i.e., winding 1 and winding 2). Each set of the main control board and power driver board can be directly connected with a set of motor windings to form a motor module. An external regulated source provides the DC bus voltage. After power-on, the MWPMSM does not rotate, and the controller forces the magnetic field orientation to ensure that the starting position of the two sets of windings is consistent, and the monitoring interface of the host computer shows that the magnetic field orientation is being carried out. After entering the starting state, the motor will increase the speed until it reaches the set speed and enters the stable operation state, and the power distribution can be adjusted after reaching the stable operation state.
The monitoring system of the host computer sets the speed of the MWPMSM to 1000r/rpm. Taking the C phase of the respective windings as an example, the current at the stage from 0 to 400 r/min during motor operation is shown in the Figure 22a, and the current at the stage from 400 r/min to a given speed of 1000 r/min is shown in Figure 22b. where 10mv represents a current of 10A.
(a) Current waveform at 0 to 400r/min (b) Current waveform at 400 to 1000r/min.
Figure 22 shows the current change, the analysis, and the comparison of the two figures. The winding current of module 1 is synchronized with the winding current of module 2 in the process of motor speed increase, which confirms the feasibility of theoretical verification. At the beginning of the motor, weak magnetic speed increases, when running to 400r/min, it will stay stable for a short time, at this time, the current waveform changes from Fig. 22a, b and the current amplitude decreases slightly, which is because it is in the forced commutation stage at this moment, the excitation current becomes the torque current, and the demagnetization is carried out, to achieve closed-loop torque control and ensure that the motor rises to a given speed. The frequency is gradually increasing, and the rotational speed is gradually increasing.
When the given speed is reached at 1000r/min, the monitoring interface of the host computer is displayed as normal operation, and the DC bus voltage of the two windings is set to 63.1V respectively. Figure 23 shows the current waveform when the power ratio of winding 1 and winding 2 is set to 1:1, 2:1, and 3:1, respectively. The monitoring interface of the upper computer can display the power occupied by each winding under different distribution ratios. The power ratio of the remaining windings is shown in Table 3.
(a) The current of phase C at 1000r/min with a winding power ratio of 1:1 (b). C-phase current with a 1000r/min winding power ratio of 2:1 (c). C-phase current waveform with a winding power ratio of 3:1 at 1000r/min.
In Table 3, the C-phase current was measured at various settings of the winding power ratio. When the motor operates normally and the power ratio of winding 1 to winding 2 is set to 1:1, the amplitude and phase of the current waveform for winding 1 and winding 2 are identical. This demonstrates the feasibility of a multi-winding motor with a 1:1 power ratio. In this configuration, the winding current of motor module 2 can accurately mirror the winding current of motor module 1, maintaining phase synchronization and achieving static tracking of the AC input signal. When the power ratio is set to 2:1, the current amplitude of winding 1 will increase immediately, and the current amplitude of winding 2 will decrease immediately, as shown in Fig. 23. It is estimated to be roughly 2:1 by the internal program, which corresponds to the set ratio of winding power. While changing the winding power ratio, the multi-winding motor maintains a given speed of 1000r/min, and the change of winding power is proportional to the change of torque, and the C-phase current and torque current are measured by the experiment and need to be transformed by Park, which is a nonlinear relationship. Therefore, from the experimental waveform of Fig. 23b above, it is not completely proportional to 2:1, but the current increases when the power of winding 1 increases. When the power of winding 2 is reduced, the current decreases, and the two still maintain the same frequency, and the current error is very small, maintaining the change trend of synchronization to meet the real-time performance of the power ratio. Similarly, when the power ratio is set to 3:1, as shown in Fig. 23c, the current of winding 1 continues to increase, the current of winding 2 decreases correspondingly, and the current still basically maintains the same frequency, and the phase error is small so that the current of winding 1 and the current of winding 2 are controlled and the current phase synchronization is maintained. It solves the difficulty of how to keep the phase synchronization between the currents of multiple windings and improves the phase-locking accuracy. From Table 3, the Maximum error of winding power ratio is 6.7%, and the error is less than 10%. At the same time, under the premise of ensuring the phase between the winding currents, the power of winding 1 and winding 2 can still be reasonably controlled according to the winding power ratio instruction, which proves that the MWPMSM control system has strong robustness, and verifies the feasibility and effectiveness of the design scheme in this paper.
In this paper, the structure of the new MWPMSM is analyzed and modeled in detail, the magnetic circuit of the MWPMSM is calculated in detail, its main parameters are determined, and the finite element model of the motor is built for simulation to verify the rationality of the parameter design.
The SPLL based on SOGI control strategy is used to track the phase of the reference current iA1, and the current tracking waveforms under SPLL based on SOGI control are given by simulation. The simulation results show that the SPLL based on the SOGI control strategy can accurately track the amplitude and phase of the reference current and prove the coordination between multiple motor modules. On this basis, the overall system simulation of the motor is carried out, and the simulation results show that the dynamic performance of the motor is well under the condition of load change and speed change, which verifies the correctness and feasibility of the scheme that each motor module in the MWPMSM control system can work independently and coordinated.
The MWPMSM control system was carried out, an experimental platform was built, and the upper computer simulated the new energy management system to issue the speed and the winding power ratio setting instructions of each motor module. Through experiments, it is proved that the winding currents of each motor module are in the same phase, the power setting ratio of different windings is changed, and the current amplitude of each motor module can be changed in real-time, and then the power size can be changed to meet the needs of the energy management system under different working conditions so that each motor module can work at the best working point and improve the overall system efficiency. This paper verifies the feasibility and effectiveness of the new MWPMSM system on floating photovoltaic distributed power generation.
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.
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This research is supported by the National Key Research and Development Program of China, Efficient and Safe Electrical System Design and Study on weather resistance of offshore floating photovoltaic (grant number 2022YFB4200703).
School of Electrical Engineering and Automation, Tianjin University of Technology, Tianjin, 300382, China
Peng Chen, Qiang Fu & Chunjie Wang
Tianjin Key Laboratory of New Energy Power Conversion, Transmission and Intelligent Control, Tianjin, 300382, China
Peng Chen, Qiang Fu & Chunjie Wang
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Peng Chen conducted the overall design and writing of the article, Qiang Fu designed the experimental system, and Peng Chen and Chunjie Wang analyzed the experimental data. All authors reviewed the manuscript.
Correspondence to Peng Chen, Qiang Fu or Chunjie Wang.
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Chen, P., Fu, Q. & Wang, C. Design and performance evaluation of a MWPMSM for distributed floating photovoltaic system. Sci Rep 15, 43600 (2025). https://doi.org/10.1038/s41598-025-25152-8
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Received: 26 November 2024
Accepted: 17 October 2025
Published: 08 December 2025
Version of record: 11 December 2025
DOI: https://doi.org/10.1038/s41598-025-25152-8
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