A better quality of high-speed software encoder for an aerogenerator-based PMSM machine

Abstract

Wind energy systems are based on a synchronous machine, which can support a high-speed rotation case due to possible high wind coming speeds. The machines used are affiliated with permanent magnet machines, and it seems that when the speed becomes high, speed detection can be difficult if a software application is adapted. This difficulty appears when the high speeds come, as the motor temperature will increase, which can influence motor parameters, especially the stator resistance. This will influence the proposed speed software estimator robustness. The proposed high-speed estimator algorithm is based on the model reference adaptive system MRAS estimation method, which can be used for motor speed estimation. The proposed MRAS concept was based on the reactive power model, which ensures the robustness of the estimator in facing any possible stator resistance variation, even at very high speeds. This MRAS estimator was tuned by the particle optimization algorithm to avoid the regulator parameter identification problem. So, this concept was modelled and mathematically defined, and then tested by implementation on the Matlab tool and on a real machine prototype which can operate a high-speed rotated load. The stability analysis of the overall speed encoder is also shown in various speed regions, and practice lab application is presented and discussed to show the success of the proposed high-speed control scheme. The results were depicted under 42000 rpm (eq to 600 Hz), and the proposed speed estimator demonstrated good behavior, and a lesser estimator error was evaluated at 50 Hz as the maximum speed error.

Keywords

Nyquist speed encoder wind energy system high speed vector control algorithm

Introduction

Research background

Total Wind or hybrid wind systems are widely based on electrical motors as an official torque source for starting and accelerating. Numerous motor types are exposed for uses in these systems, such as the direct current motor, the brushless AC or DC Motors, the Interior permanent synchronous motor (IPMSM), the simple permanent synchronous motor (PMSM), and the switched reluctance motors (Hu et al., 2023; Sun et al., 2023). A comparative study between these electrical machines, in relation to the global efficiency, robustness, cooling, given torque, and max limitation, has been resumed in Fang et al. (2023), demonstrating that the induction permanent magnet synchronous machine is the most used due to their advantages such as the wide power region and high power density of the PMSM, especially for its high efficiency (Wang et al., 2023a; Zhang et al., 2021).

Selecting the appropriate motor type is essential for making a robust and efficient wind energy production system, but monitoring this motor with the best functioning is a surely important objective. In the majority of research works, induction motors can be operated by two essential strategies, the first being the vector control method and the second being the direct torque control method. Each method presents its advantages and disadvantages. Referred to works such as Aguirre et al. (2011) and Ishikawa et al. (2013). After identifying these different strategies, the vector control topology seems to be the simplest architecture, facing the others and can be used in many induction machine applications (Zhang et al., 2023). So, to achieve high performance and maximum motor yield, the vector control strategy is developed and applied in this work to control the motor speed so that the wind system can face the external effects.

Discussion of PMSM-related problem

The vector control strategy principle is classified as an AC motor control method where it’s possible to control the motor speed or torque by decomposing the motor flux into a direct and quadrature component (Ishikawa et al., 2013; Zhang et al., 2023). The operation principle is based on two essential current controllers, which we can use to generate the exact stator voltages, the direct and the quadrature components. However, the problem or complexity is related to the current regulation of the quadrature component, where it’s impossible to start without referencing the current quadrature stator (Lin et al., 2005).

Generally, this component is directly related to the electromagnet torque reference that will be calculated by another controller using the speed information. Effectively, after obtaining the real and the reference speed, the controller will generate the desired torque component. However, the difficulty is related to the real speed value and how it is possible to identify the rotor position.

The rotary encoder or resolver is used in conventional motor control methods. This method gives an ideal rotor position information and touches the control objective with the best performance. However, in the real application, the overall system will be exposed to disadvantages such as the high cost, oversized face, and the available machine size. Basically, it is related to the wiring schema, the encoder position, and external effects from dust, vibration, and even the external temperature that can appear. So, the robustness and dependability of the PMSM drive systems will drop.

Referring to the cited speed encoder problems and based on the new research, the new processor technologies, and high performances, a software speed encoder becomes the greatest solution that can be applied to this system.

Speed estimator: problem and solution

Different rotor positions/speed sensorless are exposed in the literature, as the sensorless based on artificial intelligence (Lin et al., 2005) sliding mode observer (Guo and Panda, 2015) or model reference adaptive system (MRAS) (Flah and Sbita, 2012; Teja et al., 2015). The efficiency of these software speed encoders is presented in the cited works in specific conditions and a specific speed zone. However, the verified robustness was proved under specific speed regions, which did not consider the high-speed range.

As a knower of the PMSM, and as presented in our previous work (Flah and Sbita, 2012), I know that this kind of electrical motor can be operated at high-speed zones and can touch 200% of the rated speed. This can be assured if the filed weakening mode is activated. Due to this special running mode, many parameters, especially the magnet flux and the stator resistance variable, can be changed. These parameter modifications or variations will normally affect the sensorless speed mathematical model, influencing system stability, effectiveness, and robustness (Ding et al., 2011; Novák et al., 2011).

This test condition is required in many applications that can use high-speed regions. In the case of wind system applications, some systems can exceed the nominal speed motors in an overtaken phase or other possible conditions. Then, the system’s dysfunction will be out at this stage, and the overall loop will be out.

In this work, we have taken into consideration this case, and we desire to present a software speed encoder based on a robust MRAS technique that can be operated at high speeds with good behavior.

On the other hand, it is mandatory to mention that for an MRAS estimator, the Popov criteria is used based on a PI controller that needs to be adapted to the system configuration. However, this point presents weaknesses in the related MRAS algorithm adaptation as the studied system is nonlinear and managing the PI parameters needs a complicated adaptation calculator (Fei et al., 2024; Wang et al., 2024). This can be resolved if a dynamic calculator is adapted, and the optimization algorithm seems the most adapted.

In this work, this problem was resolved by adapting the Popov criteria to the particle swarm optimization algorithm.

Paper organization

This paper is organized into four parts. After a general introduction, the field weakening phenomenon and the method for operating the motor in the high-speed zone will be explained. The principles of the speed observer are presented in the third part, and then, in the fourth section, the stability analysis will be exposed. In the fifth part, the experimental results will be presented and discussed. Finally, a conclusion concludes this work.

Permanent magnet machine: design and modelling

As the application model is based on the induction machine, the corresponding electrical machine needs to be identified and mathematically understood in the case of the wind system. As explained in the introduction section, high-speed control is vital to this application. In the nominal situation, increasing the stator input voltage over the nominal one is impossible for operating at a high speed. This condition corresponds to the nominal speed of the motor running. The plan is to find the best control method and ensure motor security and speed goals. Based on our previous study, the concept of field weakening can be operated to resolve the high-speed running phenomenon (Flah et al., 2018).

The idea behind this technology is comparable to that of a DC machine, in which the flux can be controlled separately. Therefore, achieving a high-speed region requires flux minimization. The flux generated by the rotor magnet (λm) is the issue that has emerged, making it challenging to minimize the overall motor flux. Generally speaking, maintaining zero direct stator current ensures the rated speed mode (Wang et al., 2024). The direct flux component must be decreased to influence the high-speed mode, according to the flux formulas shown in (1). Lowering the direct stator component to the negative zone will ensure this action.

{\begin{cases} I_{d}^{2} + I_{q}^{2} \leq I_{\max}^{2} \\ V_{d}^{2} + V_{q}^{2} \leq V_{\max}^{2} \end{cases}

(1)

The issue that has emerged during this phase has to do with the theory that is required to generate the requisite direct stator current in order to ensure that this running mode is safe. The concept relates to voltages and currents that are less than a maximum. The limit system of equations takes into consideration the maximum voltage and maximum current, as stated in (Flah and Sbita, 2013) which is typically determined by the inverter. The maximum inverter phase-current and phase-voltage amplitudes are represented by the values Imax and Vmax, respectively.

These limit equations allow for the field weakening zone to be utilized. Two different kinds of circles—one for the voltage limitation condition and one for the current limitation—are shown in Figure 1 (Wang et al., 2023b). The speed inverses determine the voltage limitation’s radius. In actuality, the voltage circle radius shrinks as speed rises. Additionally, the PMSM settings determine the voltage circle center.

Figure 1.

Diagram of a field weakening plan.

As a first step, it is mandatory to try to express the related stator current expression in the “direct” component, as it is the only variable that can be used to decrease the flux inside the machine.

Equation (3) exposes this expression. This relation was depicted from the voltage equation model as it is presented in equation (2). So, if supposing that the saturation effect is null and if supposing that the hysteresis iron loss is absent, it will be able to expose the high-speed control loop, which will calculate the necessary direct stator current component as it is in Figure 2.

[\frac{v_{d}}{v_{q}}] = [\begin{array}{c} R_{s} + {p L}_{d} & {- ω L}_{d} \\ {ω L}_{d} & R_{s} + {p L}_{q} \end{array}] [\begin{array}{l} i_{d} \\ i_{q} \end{array}] + [\begin{array}{c} 0 \\ {ω λ}_{m} \end{array}]

(2)

i_{d}^{*} = \frac{\sqrt{V_{\max}^{2} - {(ω L_{q} i_{q})}^{2}} - {ω λ}_{m}}{{ω L}_{d}}

(3)

Figure 2.

High-speed algorithm (HSA).

This block is incorporated into the vector control algorithm to generate the necessary stator voltage. Following the speed controller block, the quadrature reference current is obtained, and the HAS algorithm calculates the direct stator current. We can generate the reference stator voltages using two more Pi controls.

MRAS-reactive power speed observer design

One type of efficiency estimation methodology is the model reference adaptive system technique. This method can be considered the most proficient when compared to the Back-EMF and state observer methods (Song et al., 2022a). Some authors link this one to intelligent estimating techniques in other literature, where fuzzy and neural solutions may also be appealing. Nevertheless, these systems’ drawbacks are the need to understand database information (Babes et al., 2022; Song et al., 2022b; Zhang et al., 2024). As a result, the majority of published research based on techniques made use of mathematical models like MRAS and Lunberger, and the outcomes demonstrate the effectiveness of the suggested solutions in (Fei et al., 2024; Flah et al., 2018; Flah and Sbita, 2013).

The two mathematical equations, as reference and adjustable matehmatical model, which are shown in Figure, form the foundation of the MRAS principle (3). The results will be contrasted and applied to a certain algorithm in order to determine or approximate a specified parameter. This output signal is typically utilized in the adjustable model as well. The issue with the MRAS estimator has to do with the stability phenomena, which can cause the global system to become unstable if the mechanisms for adaptation and adjustment are not carefully chosen and identified. It is possible to fix this issue using Popov’s hyperstability criterion (Figure 3).

Figure 3.

General design of the model reference adaptive system.

In relation to the desired application specification, the PMSM machine speed will be estimated online, as the main objective is to replace the mechanical speed encoder with the software application. So, as a first work step, the adaptable mathematical model needs to be built and formed by using the different previous equations. However, if referring to the literature, more than one type of MRAS observer can be applied as the Back-EMF (E-MRAS), reactive power (Q-MRAS), and active power (AMRAS). However, the selection of the best solution depends on knowing the specifications of the interior machine design. Here, each selected MRAS model has its advantages and drawbacks.

If concentrating on the related cited works as is in (Flah and Sbita, 2012; Flah and Sbita, 2013), some standard MRAS estimators have a sensitivity to some parameters variation as the stator resistance. This parameter depends on the electrical motor’s existing temperature. Even if the temperature is high, the stator resistance changes and this can make the estimated parameters, such as the stator resistance value, wrong and different from the reality. Therefore, the present model has an advantage over other exposed solutions in the cited references, where the proposed solution is independent from that parameter. In relation to high-speed mode, where the high speed comes with a high temperature, increasing the motor temperature might result in an increase in the motor stator resistance value. It seems that the exposed Q-MRAS resolves this issue.

Starting with the basing relation of the reactive power, as it is in equation (4);

Q_{s} = v_{q} i_{d} - v_{d} i_{q}

(4)

if based on the previously equations of the stator voltages, the reactive power expression can be formulated as it is in equation (5).

Q_{s} = ω (L_{d} i_{d}^{2} + L_{q} i_{q}^{2}) + (L_{d} i_{d}^{2} \frac{{d i}_{q}}{d t} - L_{q} i_{q} \frac{{d i}_{q}}{d t}) + ω i_{d} λ_{m}

(5)

In the permanent regions, where the torque and the motor speeds are constant then, it is possible to migrate equation (5) to what is in equation (6), where all currents can be supposed to be constant.

Basing the stator currents as the direct and transversal components, the adjustable Q-MRAS model is illustrated in equation (7).

Q_{s} = ω (L_{d} i_{d}^{2} + L_{q} i_{q}^{2}) + ω i_{d} λ_{m}

(6)

\hat{Q_{s}} = \hat{ω} (L_{d} \hat{i_{d}^{2}} + L_{q} \hat{i_{q}^{2}}) + \hat{ω} \hat{i_{d}} λ_{m}

(7)

When the real and the estimated reactive power are confirmed, the adaptation protocol is built. The related graph is exposed in Figure 4 (Hamouda et al., 2019).

Figure 4.

Reactive MRAS power adaptation mechanism.

If using the two equations (4) and (7) and after doing a subtraction action, equation (8) can explain the power error value and the overall reactive power generated from the MRAS estimator. The related scheme is exposed in Figure 4.

e_{q} = Q_{s} - \hat{Q_{s}} = v_{q} i_{d} - v_{d} i_{q} - (L_{d} \hat{i_{d}^{2}} + L_{q} \hat{i_{q}^{2}}) - \hat{ω} \hat{i_{d}} λ_{m} = α + \hat{ω} β

(8)

Firstly, it is interesting to decompress the system of equations as it is in Figure 5. So, the Popov hyperstability condition can be validated and confirmed.

Figure 5.

Q-MRAS total structure improved by the PSO algorithm.

The working principle of the adaptation mechanism is based on the Popov conditions. Firstly, it is mandatory to verify that the linear model is strictly positive. The second Popov condition is supposed to have a nonlinear model which satisfies the inequality expressed in (10). Then, it is possible to validate the adaptation mechanism.

Based on the Popov theorem, the only related solution can be made if the sign block is adapted in the control loop. So, by using equation (11), the second stability condition is guaranteed.

We mention by W as it is expressed here:

w = - α - \hat{ω} β

(9)

\int_{0}^{t} v^{T} (w) d t \geq - γ_{0}^{2}

(10)

{\begin{cases} \int_{0}^{t} v^{T} (- α) d t \geq - γ_{0}^{2} \\ \int_{0}^{t} v^{T} (- \hat{ω} β) d t \geq - γ_{1}^{2} \end{cases}

(11)

The first part of the system (11) is guaranteed due to Lemma 1 (Stefanovski, 2014).

Lemma 1

α \leq 0 \Rightarrow - α \geq 0 \Rightarrow \int_{0}^{t} v^{T} (- α) d t \geq 0

(12)

Also, by applying the Lemma 2, The second part of the equation (11) will be justified.

Lemma 2

{\begin{array}{c} v = D_{e q,} \\ \hat{ω} = (k_{p} + \frac{k_{i}}{s}) v \end{array} \begin{array}{l} D i s t h e s i g n B l o c \end{array}

(13)

If all these conditions and rules are applied, the global reactive power-based MRAS estimator can be built, and then, it is figured out in Figure 5. PSO optimization tool is adapted for tuning the PI parameters that appear in the control loop (Antar et al., 2015).

After obtaining the speed observer, it is clear that the problem is linked to the choice of the PI controller parameters. In this application, the particle swarm optimization algorithm is used for online tuning related parameters and finding the optimal values.

Stability analysis of the reactive power MRAS estimator

The Q-MRAS scheme can be represented by this simple control loop, as presented in Figure 6. The PI controller is used to adjust the speed of a G(s) system.

Figure 6.

Simple control loop of Q-MRAS.

Started identifying the necessary mathematical expressions:

The PI input signal is defined by the error between the real and the estimated reactive power as expressed as follows:

e_{q} = Q_{s} - \hat{Q_{s}} = v_{q} (i_{d} - {\hat{i}}_{d}) - v_{d} (i_{q} - {\hat{i}}_{q})

(14)

We note by:

x = [\begin{array}{l} i_{d} & i_{q} \end{array}], u^{'} = [\begin{array}{l} v_{d} & v_{q}^{'} \end{array}], v_{q}^{'} = v_{q} + w \frac{λ_{m}}{L_{q}}

Referring to the previous error equation, the G(s) expression can be elaborated as indicated in equation (15).

\frac{e_{q}}{∆_{w}} = v_{q} (\frac{{∆ i}_{d}}{∆_{w}}) - v_{q} (\frac{{∆ i}_{q}}{∆_{w}}) = G (s)

(15)

Remained $\frac{{∆ i}_{d}}{∆_{w}} a n d \frac{{∆ i}_{q}}{∆_{w}}$ are expressed in (20) and (21).

After checking all the necessary expressions, the closed loop formula can be obtained as indicated in equation (16).

\frac{w}{\hat{w}} = \frac{G . (k_{p} + \frac{k_{i}}{s})}{1 + G . (k_{p} + \frac{k_{i}}{s})}

(16)

The demonstration of the presented equations is as follows:

Starting from the voltage equations expressed in (3), the system equation can be represented by:

{\begin{cases} \dot{x} = A x + B u^{'} \\ y = D x \end{cases}

(17)

After applying the lesser variation on the stator current, the new system equations can be formulated as follows:

\begin{array}{l} {\begin{cases} \dot{∆ x} = A ∆ x + ∆ A x_{0} \\ ∆ y = D . ∆ x \end{cases} \\ we note by \end{array}

(18)

∆ A = [\begin{array}{c} 0 & \frac{L_{q}}{L_{d}} \\ \frac{- L_{q}}{L_{d}} & 0 \end{array}] . ∆ w a n d b y D = [\begin{array}{l} 1 & 0 \\ 0 & 1 \end{array}]

The new output variation expression becomes as it is in (19).

∆ y = D {(s I - A)}^{- 1} ∆ A x_{0}

(19)

we mention by ∆ y = [\begin{array}{l} ∆ i_{d} \\ ∆ i_{q} \end{array}] . ∆ w a n d x_{0} = [\begin{array}{l} i_{d 0} \\ i_{q 0} \end{array}]

and

{(s I - A)}^{- 1} = \frac{1}{\det (s I - A)} [\begin{array}{l} s + \frac{R_{s}}{L_{d}} & w \frac{L_{q}}{L_{d}} \\ - w \frac{L_{q}}{L_{d}} & s + \frac{R_{s}}{L_{q}} \end{array}]

Then, the expressions of the stator current variations are exposed in the system of equations (20) and (21):

\frac{∆ i_{d}}{∆ w} = [- w {(\frac{L_{q}}{L_{d}})}^{2} i_{d 0} + (s + \frac{R_{s}}{L_{d}}) \frac{L_{q}}{L_{d}} i_{q 0}] \frac{1}{\det (s I - A)}

(20)

\frac{∆ i_{q}}{∆ w} = [- w {(\frac{L_{q}}{L_{d}})}^{2} i_{q 0} - (s + \frac{R_{s}}{L_{d}}) \frac{L_{q}}{L_{d}} i_{d 0}] \frac{1}{\det (s I - A)}

(21)

So, after checking the system G(s), the closed loop function can be represented by equation (20).

H (s) = \frac{β k_{p} s^{2} + (α k_{p} + β k_{i}) s + α k_{i}}{s^{3} + s^{2} (2 \frac{R_{s}}{L_{d}} + β k_{p}) + γ^{'} s + α k_{i}}

(22)

It is noted that the parameters:

γ^{'} = w^{2} + (α k_{p} + β k_{i}), ζ = (v_{q} i_{q 0} + v_{d} i_{d 0})

ζ^{'} = (v_{d} i_{q 0} - v_{q} i_{d 0}),

and

{\begin{cases} \begin{array}{l} α = a b ζ + ζ^{'} w b^{2} \\ \begin{array}{l} β = b ζ \\ a = \frac{R_{s}}{L_{d}} \end{array} \end{array} \\ b = \frac{L_{q}}{L_{d}} \end{cases}

The stability analysis was applied in different speed zones, starting from 5000 rpm and touching 42000 rpm, the maximum speed supported by the used motor. Figure 7 presents the obtained Nyquist graph. The results show the stability of the speed observer under high-speed variation. These results guarantee the overall observed system stability.

Figure 7.

Nyquist map for the Q-MRAS speed observer under different speeds.

Description of the experimental system and the system blocks

In this section, we want to present the experimental bank used to validate the high-speed control loop. The global material group can be shown in Figure 8. Basically, the permanent magnet synchronous motor is related to a compressor system, which can reach a very high speed by injecting a high-pressure oil. This is for simulating the high-speed regions. The specifications of the used electrical machine can be summarized in Table 1.

Figure 8.

Practice experiment tools.

Table 1.

Electrical machine parameters.

Motor type	2AML406B-090-10-170
Manufacture	VUES Brno
Nominal speed	25 K rpm
Maximum speed	42 K rpm
Nominal current	11 A
Control strategy	FOC

In this application, the load charge is a turbocharger related to an oil pump, and its load torque is equivalent to the load of one road used in a wind system, where this load torque decreases when the speed rotation increases. The motor alimentation is from a three-phase inverter controlled by a DSP card throughout a PC.

The rectified voltage supplies an insulated gate bipolar transistor (IGBT) inverter. The inverter uses a power module SKM75GD124D and IGBT/MOSFET driver SKHI61, both from Semikron.

In the hardware implementation, a vector control strategy coupled with the software speed encoder is used to control the machine. As explained in the previous section, the speed software encoder called Q-MRAS requests a lot of motor information, such as currents and tensions in the (d, q) frame. Those signals are obtained from ADC blocks inserted in the control card.

In addition, in the motor operation loop, the high-speed algorithm (HSA) is used to verify the global system performance. Figure 9 gives more explanation.

Figure 9.

Vector control strategy and relation to the overall system blocks.

Results exposition and discussion

In this section, the results obtained are illustrated and discussed, and the overall system performance is tested and verified under high-speed running conditions, taking into account the performance of a wind system’s applied load. The system performance is tested and validated by the experimental materials.

As the vector control operation is adapted for controlling this prototype, it is mandatory to follow the control strategy and test if the related current and voltage variables are in the normal situation.

So, the principles of the vector control method are shown in Figure 10, where the direct current is approximately negative. So, the vector principle and high-speed theory are clearly verified. The existing ripples in those variables are related to the inverter model, which is characterized by 15 MHz as a commutation variable. If the inverter frequency is more than 15 MHz, then it is possible to have less ripples in those parameters.

Figure 10.

Currents and voltage results.

Those exiting ripples are not related to the only inverter specification, but they were dependent on the commutation blocks inserted in the HAS and the Q-MRAS. This presents the weakness of this software code.

In parallel to these results, the algorithm feedback must concentrate on the given speed specification as shown in Figure 11 and 12, which represent the obtained speed results and the obtained speed error.

Figure 11.

Speed performance (Hz): Red color: the real speed, blue color: the estimated speed.

Figure 12.

Speed error between the real and estimated MRAS speed.

Based on the given results, the efficiency of the proposed speed encoder is justified. However, it would be more interesting if it could be compared to other solutions in order to define the optimal solution.

Table 2 gives the performances of the proposed high-speed encoder. This is basing on the Sliding Mode observer as it is discussed in (Zhang et al., 2019), in (Gong and Zhu, 2021), the High-Speed Motors Based on a Polarity Switching Tracking Filter and Disturbance Observer is used. An ameliorated high-speed sliding-mode observer for the sensorless speed control of a PMSM is also used in Kim et al. (2011), and a second improved adaptive sliding mode speed observer is used in Xu et al. (2021).

Table 2.

The comparison involves five different speed observers.

Provider reference	Suggested speed sensor	Maximum speed (rpm)	Estimation error (%)
Guzinski et al. (2010)	Speed and load torque observers (LTOs)	1326	2
Xu et al. (2021)	Adaptive sliding mode (ASMO)	2000	1.2
Kim et al. (2011)	Modified SMO	3000	2
Gong and Zhu (2021)	Disturbance observer	8000	3
Zhang et al. (2019)	Interval sliding mode	3000	3.5
Proposed observer	Q-MRAS	32000	2.8

The comparison was based on error level for the high-speed regions for a similar motor specification.

The comparison reveals that the high-speed motor tests were not subjected to extreme conditions. However, as the motor speed increases, the speed error tends to grow. The proposed speed estimator demonstrates reliable performance with an acceptable error level of 2.8% at a very high speed of 42,000 rpm.

For proving the efficiency of the proposed speed observer, the rest of this section will demonstrate the efficiency of the global loop performance which is applied under two conditions: the given reference speed is equivalent to 32000 rpm (650 Hz) and the given load torque decreases proportionally. At t = 0.01 Te = 1.2 Nm and at t = 0.06 Te = 1 Nm.

Figure 11 presents the obtained speed results, under the cited previous condition. The real speed follows the desired one, with a chattering about the reference speed starting especially at t = 0.04 sec.

Here, the system running frequency is equivalent to 650 Hz, this vast frequency variation influence on the commutation blocks inserted on the software speed encoder (the sign block inserted in Figure 5); therefore, we display here a big chattering at this frequency. As a recommendation, for this software speed encoder version we recommend 400 Hz as a maximum speed running. Figure 12, presents the speed error between the measured and estimated one.

However, the system’s robustness is not affected. These problems will take our research objective in future works.

Conclusion and future works

The PMSM control without a speed encoder is implemented in this study. The model reference adaptive system ensures the speed encoder after adjusting its PI controller by the PSO tool, which is based on reactive power characteristics. The vector control technique is employed to ensure motor control, and the high speed algorithm is used when operating in this mode. The selection of the speed observer is based on the robustness of the speed estimation tool phase and the motor parameters variation as the stator resistance. From the other side, and in relation to the specification of the wind system, which faces high-speed regions due to high wind speed, the motor speed observer has to be efficient enough in that speed characterization (Zhao et al., 2024).

The related speed observer is made on Matlab software tool and validated on a real prototype that has the possibility to be functioning in 42 K rpm. Based on the given results, and for 600 Hz, a maximum error equivalent to 8.5% is obtained.

In general, we can say that the proposed software speed encoder will be efficient in the wind system models, where the speed of the wind system doesn’t exceed 150 km/h.

Even the obtained results are accepted enough, it is mandatory to continue working on this observer by testing its specification on other motor parameters variations as the magnet flux level, which can also change due some external perturbation as temperature or vibration. From another perspective, the proposed speed observer can provide significant benefits for high-speed vehicles. So testing this speed observer in traction system and triboelectric systems can have future endeavors of this proposed prototype for resolving some common problems (Han et al., 2020).

Footnotes

Acknowledgment

The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2024/01/29320).

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study is supported via funding from Deanship of Scientific Research, The authors extend their appreciation to Prince Sattam bin Abdulaziz University for funding this research work through the project number (PSAU/2024/01/29320).

ORCID iD

Aymen Flah

References

Aguirre

Calleja

Lopez-de-Heredia

, et al. (2011) FOC and DTC comparison in PMSM for railway traction application. In: Proceedings of the 2011 14th European Conference on Power Electronics and Applications, pp. 1–10. IEEE.

Antar

Hassen

Babes

, et al. (2015) Fractional order PI controller for grid connected wind energy conversion system. In: 2015 4th International Conference on Electrical Engineering (ICEE), pp. 1–6, IEEE.

Babes

Hamouda

Kahla

, et al. (2022) Fuzzy model based multivariable predictive control design for rapid and efficient speed-sensorless maximum power extraction of renewable wind generators. Electrical Engineering & Electromechanics 3(3): 51–62.

Ding

Xiao

Zhang

, et al. (2011) Dynamic analysis of rotor system for magnetic levitation high-speed electrical machine. In: 2011 International Conference on Electric Information and Control Engineering, pp. 2129–2132, IEEE.

Fang

(2023) Torque improvement of Vernier permanent magnet machine with larger rotor pole pairs than stator teeth number. IEEE Transactions on Industrial Electronics 70(12): 12648–12659.

Fei

Zhang

Zhao

, et al. (2024) Optimal power distribution control in modular power architecture using hydraulic free piston engines. Applied Energy 358: 122540.

Flah

Sbita

(2012) An adaptive high speed PMSM control for electric vehicle application. Journal of Electrical Engineering 12: 13.

Flah

Sbita

(2013) A novel IMC controller based on bacterial foraging optimization algorithm applied to a high speed range PMSM drive. Applied Intelligence 38: 114–129.

Flah

Novak

Lassaad

(2018) An improved reactive power MRAS speed estimator with optimization for a hybrid electric vehicles application. Journal of Dynamic Systems, Measurment, and Control 140(6): 061016.

10.

Gong

Zhu

(2021) Vibration suppression for magnetically levitated high-speed motors based on polarity switching tracking filter and disturbance observer. IEEE Transactions on Industrial Electronics 68(6): 4667–4678.

11.

Guo

Panda

(2015) Design of a sliding mode observer for sensorless control of SPMSM operating at medium and high speeds. In: 2015 IEEE Symposium on Sensorless Control for Electrical Drives (SLED), pp. 1–6, IEEE.

12.

Guzinski

Abu-Rub

Diguet

, et al. (2010) Speed and load torque observer application in high-speed train electric drive. IEEE Transactions on Industrial Electronics 57(2): 565–574.

13.

Hamouda

Babes

Kahla

, et al. (2019) Real time implementation of grid connected wind energy systems: predictive current controller. In: 2019 1st International Conference on Sustainable Renewable Energy Systems and Applications (ICSRESA), pp. 1–6, IEEE.

14.

Han

Ding

Qin

, et al. (2020) A triboelectric rolling ball bearing with self-powering and self-sensing capabilities. Nano Energy 67: 104277.

15.

Wang

Chu

(2023) Novel Ramanujan digital twin for motor periodic fault monitoring and detection. IEEE Transactions on Industrial Informatics 19(12): 11564–11572.

16.

Ishikawa

Seki

Kurita

(2013) Analysis for fault detection of vector-controlled permanent magnet synchronous motor with permanent magnet defect. IEEE Transactions on Magnetics 49(5): 2331–2334.

17.

Kim

Son

Lee

(2011) A high-speed sliding-mode observer for the sensorless speed control of a PMSM. IEEE Transactions on Industrial Electronics 58(9): 4069–4077.

18.

Lin

Tang

Zhang

, et al. (2005) Artificial neural network modelling of driver handling behaviour in a driver-vehicle-environment system. International Journal of Vehicle Design 37(1): 24.

19.

Novák

Čeřovský

(2011) Experimental research of high-speed electrical motor supercharger dynamic properties. In: 2011 IEEE Workshop On Merging Fields Of Computational Intelligence And Sensor Technology, pp. 7–12, IEEE.

20.

Song

Mingotti

Zhang

, et al. (2022a) Accurate damping factor and frequency estimation for damped real-valued sinusoidal signals. IEEE Transactions on Instrumentation and Measurement 71: 1–4.

21.

Song

Mingotti

Zhang

, et al. (2022b) Fast iterative-interpolated DFT phasor estimator considering out-of-band interference. IEEE Transactions on Instrumentation and Measurement 71: 1–14.

22.

Stefanovski

(2014) Kalman–Yakubovič–Popov lemma for descriptor systems. Systems & Control Letters 74: 8–13.

23.

Sun

Lyu

Liu

, et al. (2023) Virtual current compensation-based quasi-sinusoidal-wave excitation scheme for switched reluctance motor drives. IEEE Transactions on Industrial Electronics 99: 1–11.

24.

Teja

AVR

Verma

Chakraborty

(2015) A new formulation of reactive-power-based model reference adaptive system for sensorless induction motor drive. IEEE Transactions on Industrial Electronics 62(11): 6797–6808.

25.

Wang

, et al. (2024) FI-NPI: exploring optimal control in parallel platform systems. Electronics 13(7): 1168.

26.

Wang

, et al. (2023a) Permanent magnet-based superficial flow velometer with ultralow output drift. IEEE Transactions on Instrumentation and Measurement 72: 1–12.

27.

Wang

Sun

Jiang

, et al. (2023b) A MTPA and flux-weakening curve identification method based on physics-informed network without calibration. IEEE Transactions on Power Electronics 38(10): 12370–12375.

28.

Zhao

, et al. (2021) An improved adaptive sliding mode observer for middle- and high-speed rotor tracking. IEEE Transactions on Power Electronics 36(1): 1043–1053.

29.

Zhang

Zhu

Jian

, et al. (2024) Fractional order complementary non-singular terminal sliding mode control of PMSM based on neural network. International Journal of Automotive Technology 25(2): 213–224.

30.

Zhang

Jiang

Yan

X-G

, et al. (2019) Incipient fault detection for traction motors of high-speed railways using an interval sliding mode observer. IEEE Transactions on Intelligent Transportation Systems 20(7): 2703–2714.

31.

Zhang

Chen

Gao

, et al. (2021) Cascade ADRC speed control base on FCS-MPC for permanent magnet synchronous motor. Journal of Circuits, Systems, and Computers 30(11): 2150202.

32.

Zhang

Gong

Zhao

, et al. (2023) Voltage and frequency stabilization control strategy of virtual synchronous generator based on small signal model. Energy Reports 9: 583–590.

33.

Zhao

Wang

Cui

(2024) Frequency-chirprate synchrosqueezing-based scaling chirplet transform for wind turbine nonstationary fault feature time–frequency representation. Mechanical Systems and Signal Processing 209: 111112.