esa-sceva/satcom-chunk-collection huggingface dataset:
## 5 Discussions
### Summary of the Impacts of the Orbital Parameters on the LEO-LEO Occultation Events  
The impacts of the orbital parameters of inclination, RAAN, height, and AP on the number and global coverage of LEO-LEO occultation events were investigated using the variable separation approach based on a pair of Rx and Tx satellites. The numerical experiment results reveal that: 1 the inclination and RAAN are the main impact parameters followed by orbital height, while the impact of AP is small; 2 co-planar and counter-rotating Rx and Tx satellites constitute an ideal two-satellite LEO-LEO constellation to form the occultation geometry easily; 3 for the polar orbit constellation, when the RAAN difference of the Rx and Tx is 180 deg,meaning that the orbits are co-planar and counter-rotating, it is easy to form the occultation geometry; 4 the polar orbit and NPO constellations easily achieve global coverage of occultation events; and 5 for the NEO constellation, when the Rx and Tx inclinations are supplementary, it is easy to form the occultation geometry, and the occultation events are mainly distributed in the low and middle latitude zones.  
It should be noted that the results on the inclination, RAAN, and height shown in Figure 2 were obtained for polar orbit constellations without the effect of the RAAN precession, while the results for the inclination experimental group were affected by the inclination and RAAN precession. The inclination and RAAN define the relative position and running direction of the Rx and Tx satellites and are key parameters of LEO-LEO  
Figure 16: Accumulated time dependence of the global coverage fraction (GCF) (blue lines) and the occultation event number (orange lines) for the 2 Rx/2 Txorbit, 4 Rx/4 Txorbit and 6 Rx/6 Txorbit constellations with the Rxi98 and Txi98 inclination orbital planes.  
occultation orbital design, so it is necessary to carefully design the satellite orbit's inclination and RAAN to obtain more LEO-LEO occultation events and a better distribution.  
The RAAN precession is an important orbital perturbation that cannot be neglected in the LEO-LEO occultation orbital and constellation design. The RAAN precession affects the number and distribution of LEO-LEO occultation events by changing the Rx and Tx RAANs. For particular constellations, the RAAN precession period may cause the repetition of the behavior and characteristics of the LEO-LEO occultation events as shown in Figure 4.
# Internet of Things for Modern Energy Systems: State-of-the-Art, Challenges, and Open Issues
## 4 Illustrative Examples
### IoT-Driven Smart Cities  
To apply IoT systems in smart cities, some fundamentals need to be defined in advance. The first indispensable necessity is communication infrastructure. Then, people interaction with the system should be enabled. In smart cities, IoT is not only for energy management purposes, but also for many different goals, such as smart parking, transportation and vehicular traffic, healthcare, etc.--all of which can be monitored and controlled via a unified IoT system, while a different level of accessibility, privacy, security, BD, and even communication technologies must be enabled based on the services' specifications [133]. To apply IoT in smart cities, still an architecture must be used to categorize every component in a category and to define their connections. In [106], a three-layer architecture including perception, network, and application layer is used in order to implement IoT systems into smart cities. Many of the implemented IoT systems in smart cities are reported in [106; 134], which include Amsterdam, Barcelona, Fujisawa, etc. In all of the mentioned attempts, one or two services like controlling streetlights are implemented. Although these attempts are appreciated, a global IoT system including most IoT services mentioned in the literature with different control and monitor level, and real-time accessibility for consumers is a matter of research and has not been implemented yet.
# An Unsupervised Deep Learning System for Acoustic Scene Analysis
## 2 The Proposed Method
### Auto-Encoder Network  
An auto-encoder network is a powerful unsupervised dimensionality-reduction technique. Different from handcraft features, an auto-encoder network can learn an internal representation automatically by the optimization method. As illustrated in Figure 2, a deep auto-encoder network consists of two modules, an encoder and a decoder. The encoder \(f_{E}\) produces a low-dimensional representation \(x\) from the high-dimensional input \(\omega\); i.e., \(x=f_{E}(\omega)\). Then the encoded vector \(x\) is fed to the decoder \(f_{D}\) to reconstruct the original input \(\omega\) as faithfully as possible; i.e., \(\hat{\omega}=f_{D}(x)\), where \(\hat{\omega}\) is an estimate of \(\omega\)[17]. The network is trained by minimizing the loss \(L(\omega,\hat{\omega})\) between \(\omega\) and \(\hat{\omega}\). Thus, it does not need manual labels of training data during the network training. There is an overlap between the encoder and decoder, named the _bottleneck_, which is the narrowest hidden layer of the entire network. The output of the bottleneck is called the _bottleneck feature_, i.e., \(x\), which used as a compact representation of \(\omega\)[18].  
Our auto-encoder network consists of five fully connected layers. Table 1 shows the detailed architecture of the network. Specifically, we expand each input frame with adjacent frames by a contextual window and reduce the dimensionality of the input with a discrete cosine transform so as to avoid overfitting. Batch-normalization layers are added for the rapid and stable convergence of the network training. Mish [19] is used as the activation function which is represented as:  
\[f(z)=z\tanh(\ln(1+e^{z})). \tag{1}\]  
This state-of-the-art activation function leads to a faster convergence rate and better performance than conventional activation functions. Note that the activation function at the bottleneck layer is still the sigmoid function, which is designed to produce a reasonable probability distribution.  
Figure 1: Block diagram of the proposed system, where the term “BR” refers to binaural representation, “AE” refers to an auto-encoder, “SC” refers to spectral clustering, “AHC” is short for agglomerative hierarchical clustering, and \(N_{s}\) is the number of acoustic scenes for clustering.  
We set the dimensions of both the input layer and output layer of the auto-encoder \(N_{I}\) to 576. The neuron number of the bottleneck \(N_{B}\) is set to 40, and the neuron numbers \(N_{H}\) of all other hidden layers are set to 500 respectively. Finally, we average the 40-dimensional frame-level bottleneck features of each audio clip in dimensions for a segment-level feature \(x\).
## 4 Simulation Results and Analysis
### Radiation Pattern
#### 4.3.3 Far-Field 3D Radiation Pattern  
The 3D radiation pattern shown in Figure 8 confirms a highly directional beam with maximum radiation in the +Z direction. Side lobes appear symmetric, implying effective phasing and power division. Peak gain matches the previous value of 9.9 dBi, indicating simulation consistency. The Theta and Phi orientation suggests the array radiates with the dominant contribution in the \(Z\)-axis, with well-controlled side lobes. The series-fed architecture with uniform spacing (\(\sim\)0.5\(\lambda\)) and a symmetrical layout helps to preserve the main beam direction across the operating bandwidth. Simulation data confirms that the main lobe deviates less than \(\pm\)3\({}^{\circ}\) within the 27.5-29.5 GHz range, supporting stable directional performance over the entire band. The 3D far-field plot confirms the antenna's ability to form a stable directional beam suitable for beam steering, which is critical for mm-wave applications.
## Appendix A Derivation of Equation (20)  
The \(\sigma_{\text{p}}^{2}\) of the \(\alpha\)-\(\beta\)-\(\eta\)-\(\theta\) filter is now derived from Equations (1)-(4); \(x_{\text{ts},k}\) represents the motion of the constant-velocity target:  
\[x_{\text{ts},k}=x_{\text{ts},k-1}+Tv_{\text{ts},k-1}, \tag{10}\]  
where \(v_{\text{ts},k}\) is the true velocity. With Equations (1) and (10), the predicted error is calculated as:  
\[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\] \[=E[(x_{\text{s},k-1}-x_{\text{ts},k-1})^{2}]+2 TE[(x_{\text{s},k-1 }-x_{\text{ts},k-1})(v_{\text{s},k-1}-v_{\text{ts},k-1})]\] \[\quad+T^{2}E[(v_{\text{s},k-1}-v_{\text{ts},k-1})^{2}]. \tag{11}\]  
Thus, it is necessary to derive the error variance and covariance in the smoothing process to obtain \(\sigma_{\text{p}}^{2}\). The quantities \(x_{\text{ts},k}\) and \(v_{\text{ts},k}\) can be expressed as:  
\[x_{\text{ts},k} =(1-\alpha)x_{\text{ts},k}+\alpha x_{\text{ts},k}+T\eta(v_{\text {t},k}-v_{\text{t},k}), \tag{12}\] \[v_{\text{ts},k} =(1-\theta)v_{\text{ts},k}+\theta v_{\text{ts},k}+(\beta/T)(x_{ \text{t},k}-x_{\text{t},k}). \tag{13}\]  
Using Equations (3), (4), (12) and (13), we have:  
\[x_{\text{s},k}-x_{\text{ts},k} = (1-\alpha)(x_{\text{p},k}-x_{\text{ts},k})+\alpha(x_{\text{o},k}- x_{\text{ts},k}) \tag{14}\] \[+T\eta((v_{\text{o},k}-v_{\text{t},k})-(v_{\text{p},k}-v_{\text{ t},k})),\] \[v_{\text{s},k}-v_{\text{ts},k} = (1-\theta)(v_{\text{p},k}-v_{\text{ts},k})+\theta(v_{\text{o},k}- v_{\text{ts},k})\] (15) \[+(\beta/T)((x_{\text{o},k}-x_{\text{t},k})-(x_{\text{p},k}-x_{ \text{t},k})). \tag{16}\]  
From Equations (1), (2) and (10) and defining \(\Delta x_{\text{s},k}\equiv x_{\text{s},k}-x_{\text{ts},k}\), \(\Delta v_{\text{s},k}\equiv v_{\text{s},k}-v_{\text{ts},k}\), \(\Delta x_{\text{o},k}\equiv x_{\text{o},k}-x_{\text{ts},k}\) and \(\Delta v_{\text{o},k}\equiv v_{\text{o},k}-v_{\text{ts},k}\), we calculate:  
\[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]0 \[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]1Thus, the variances of the errors in the smoothed positions can be calculated using Equation (A7) as:  
\[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]2 \[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]3 \[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]4 \[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]5 \[\sigma_{\text{p}}^{2} =E[(x_{\text{p},k}-x_{\text{ts},k})^{2}]\]6  
Because we have assumed \(k\rightarrow\infty\), the variances and covariances of errors do not depend on \(k\).
# Satellite-Observed Global Terrestrial Vegetation Production in Response to Water Availability
## 5 Conclusions
The following are available online at [[https://www.mdpi.com/article/10.3390/rs13071289/s1](https://www.mdpi.com/article/10.3390/rs13071289/s1)]([https://www.mdpi.com/article/10.3390/rs13071289/s1](https://www.mdpi.com/article/10.3390/rs13071289/s1)), Figure S1: Geographical patterns of the annual ensemble mean LUE model GPPs from 1982 to 2015, Figure S2: The comparison between monthly flux site measurement of GPP and monthly LUE GPP, Figure S3: Geographical patterns of the dependence and response time of vegetation productivity to water availability in different seasons, Figure S4: Spatial distribution of global LUE GPP values at 10 th (a), 20 th (b), 30 th (c) and 40 th percentiles (d) during June-August, Figure S5: Spatial distribution of global LUE GPP values at 10 th (a), 20 th (b), 30 th (c) and 40 th percentiles (d) during September-November, Figure S6: Spatial distribution of global LUE GPP values at 10 th (a), 20 th (b), 30 th (c) and 40 th percentiles (d) during December-February, Figure S7: Conditional probabilities of vegetation productivity losses under different drought scenarios in June-August, Figure S8: Conditional probabilities of vegetation productivity losses under different drought scenarios in September-November, Figure S9: Conditional probabilities of vegetation productivity losses under different drought scenarios in December-February, Figure S10: Conditional probabilities of vegetation productivity losses under different scenarios in June-August, Figure S11: Conditional probabilities of vegetation productivity losses under different scenarios in September-November, Figure S12: Conditional probabilities of vegetation productivity losses under different scenarios in January-August, Figure S13: Conditional probabilities of vegetation productivity losses under different scenarios in January-August, Figure S14: Conditional probabilities of vegetation productivity losses under different scenarios in different land cover types when the GPP \(\leq\) 40 th percentile in September-November, Figure S15: Conditional probabilities of vegetation productivity losses under different scenarios in different land cover types when the GPP \(\leq\) 40 th percentile in December-February, Table S1: Univariate margin distribution functions, Table S2: Common two-dimensional copula function families. * 4. Data curation, Y.C. ; Supervision, B.F.; Validation, X.W. ; Writing--original draft, Y.Z. ; Writing--review & editing, X.F. and B.F. All authors have read and agreed to the published version of the manuscript. * 5. This research was funded by the National Key Research and Development Program of China (2017 YFA0604700), National Natural Science Foundation of China (41991233) and Chinese Academy of Sciences (QYZDY-SSW-DQC025 and 2019 DC0027). * 6. Not applicable. * 7. Data Availability Statement: The data used in the study can be downloaded through the corresponding link provided in Section 2.1.
## 4 Result and Discussion
### Delphi Result for Proposed MTOVE  
The proposed MTOVE metric and formula were included in the second- and third-round questionnaires. The purpose was to ask the panel members for their expert opinion. The participants were asked their opinions on the importance of the MTOVE metric through 5-point Likert scales. To analyze between-round Delphi results for the proposed MTOVE we employed [PERSON]'s kappa (\(\kappa\)) statistic using IBM SPSS version 26 software. [PERSON]'s kappa (\(\kappa\)) is often used to assess agreement of nominal data as a measure of inter-rater agreement or reliability [58]. The results in Table 8 show a kappa value of 0.75, and good agreement is indicated when the value is between 0.61 and 0.80. This demonstrated that respondents agreed to use the MTOVE formula to measure overall effectiveness.
## 3 Results
### Single-Factor Test Results
#### 3.1.1 Influence of Output Air Pressure on the Clamping Force of the Manipulator  
To investigate the influence of different output air pressures on the clamping force of the manipulator, a clamping force test was conducted. The gas storage tank is equipped with a pressure regulator, which can be adjusted with a screwdriver to adjust the output pressure. The output pressures of the test factors were selected to be 0.3 MPa, 0.4 MPa, 0.5 MPa, 0.6 MPa and 0.7 MPa for the clamping test, and each group of tests was performed 10 times. The clamping force data were recorded, and then the average clamping force was calculated. The diameter of the rape was chosen to be about 14 mm. The test results are shown in Table 4.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**No.** & **Output Air Pressure/MPa** & **Clamping Force of Manipulator/N** \\ \hline
1 & 0.3 & 109 \\
2 & 0.4 & 138 \\
3 & 0.5 & 182 \\
4 & 0.6 & 228 \\
5 & 0.7 & 263 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The influence of the output air pressure on the clamping force of the manipulator.  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Factors** & **Level Values** \\ \hline \(X_{1}\): output air pressure/MPa & 0.3, 0.5, 0.7 \\ \(X_{2}\): pulling angle/\({}^{\circ}\) & 60, 75, 90 \\ \(X_{3}\): pulling speed/cm\(\cdot\)s\({}^{-1}\) & 8, 10, 12 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Factors and levels of single-factor design.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Levels**} & \multicolumn{3}{c}{**Factors**} \\ \cline{2-4}  & **Output Air Pressure \(X_{1}\)/MPa** & **Pulling Angle \(X_{2}\)/\({}^{\circ}\)** & **Pulling Speed \(X_{3}\)/(cm\(\cdot\)s\({}^{-1}\))** \\ \hline \(-1\) & 0.4 & 60 & 8 \\
0 & 0.5 & 75 & 10 \\
1 & 0.6 & 90 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Test factors and levels.  
The test results show that the clamping force of the manipulator is significantly affected by the output air pressure, and there is a linear relationship between them. The clamping force of the manipulator increases with increasing output air pressure and decreases with decreasing output air pressure. When the output pressure is 0.3 MPa, the average clamping force of the manipulator is 109 N, and when the output pressure is 0.7 MPa, the average clamping force of the manipulator is 263 N.
# Advancements in the Intelligent Detection of Driver Fatigue and Distraction: A Comprehensive Review
## 3 Intelligent Detection Methods for Driver Fatigue and Distraction
### Intelligent Detection Methods Based on Driver's Facial Features
While people may display facial states similar to fatigue or distraction, such as yawning, blinking, or looking down, in everyday life, it does not necessarily mean they are truly in a state of fatigue or distraction. Therefore, judging whether a driver is fatigued or distracted based solely on facial features presents potential risks of misjudgment or omission.
## 3 Results and Analysis
### Effects of Different Additives on Microbial Community of Corn Stover
#### 3.2.1 Effects of Different Additives on Microbial Community Structure of Corn Stalk Silage
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & **Time** & **CK** & **LP** & **LPCE1** & **LPXE1** & **LPCE2** & **LPXE2** & **SEM** & **T** & **D** & **T \(\times\) D** \\ \hline pH & 30 d & 3.94 \({}^{\rm Aa}\) & 3.76 \({}^{\rm Ab}\) & 3.720 \({}^{\rm Abc}\) & 3.70 \({}^{\rm Abc}\) & 3.74 \({}^{\rm Abc}\) & 3.69 \({}^{\rm Ac}\) & & & & \\  & 60 d & 3.78 \({}^{\rm Ba}\) & 3.69 \({}^{\rm Ab}\) & 3.67 \({}^{\rm Ab}\) & 3.70 \({}^{\rm Ab}\) & 3.71 \({}^{\rm Ab}\) & 3.65 \({}^{\rm Ac}\) & 0.0061 & 0.4667 & 0.0016 & 0.0378 \\ NH\({}_{3}\)-N\% & 30 d & 0.7985 \({}^{\rm Aa}\) & 0.0397 \({}^{\rm Ab}\) & 0.0275 \({}^{\rm Ab}\) & 0.0263 \({}^{\rm Ab}\) & 0.0267 \({}^{\rm Ab}\) & 0.0213 \({}^{\rm Ab}\) & & & \\  & 60 d & 0.1562 \({}^{\rm Ba}\) & 0.0989 \({}^{\rm Ab}\) & 0.045 \({}^{\rm Abc}\) & 0.0545 \({}^{\rm Abc}\) & 0.0308 \({}^{\rm Abc}\) & 0.0200 \({}^{\rm Ac}\) & & & \\ LA & 30 d & 12.34 \({}^{\rm Ac}\) & 14.74 \({}^{\rm Abc}\) & 14.35 \({}^{\rm Be}\) & 14.21 \({}^{\rm Abc}\) & 16.01 \({}^{\rm Be}\) & 19.16 \({}^{\rm Ba}\) & & & & \\ (g/kgFM) & 60 d & 14.39 \({}^{\rm Ab}\) & 15.77 \({}^{\rm Ab}\) & 17.10 \({}^{\rm Aa}\) & 18.42 \({}^{\rm Aa}\) & 22.24 \({}^{\rm Aa}\) & 26.74 \({}^{\rm Aa}\) & 0.7495 \(<\)0.0001 & \(<\)0.0001 & 0.2251 \\ AA & 30 d & 1.14 \({}^{\rm Ba}\) & 0.76 \({}^{\rm Ab}\) & 0.63 \({}^{\rm Abc}\) & 0.56 \({}^{\rm Abc}\) & 0.61 \({}^{\rm Abc}\) & 0.53 \({}^{\rm Ac}\) & & & \\ (g/kgFM) & 60 d & 1.28 \({}^{\rm Aa}\) & 0.86 \({}^{\rm Ab}\) & 0.67 \({}^{\rm Ac}\) & 0.42 \({}^{\rm Ac}\) & 0.58 \({}^{\rm Ac}\) & 0.56 \({}^{\rm Aa}\) & 0.0434 & \(<\)0.0001 & 0.00014 & 0.0015 \\ PA & 30 d & 1.07 \({}^{\rm Ba}\) & 0.84 \({}^{\rm Ba}\) & 0.00 \({}^{\rm Ad}\) & 0.00 \({}^{\rm Ad}\) & 0.58 \({}^{\rm Be}\) & 0.00 \({}^{\rm Ad}\) & & & & \\ (g/kgFM) & 60 d & 1.89 \({}^{\rm Aa}\) & 1.37 \({}^{\rm Ab}\) & 0.00 \({}^{\rm Ad}\) & 0.00 \({}^{\rm Ad}\) & 0.73 \({}^{\rm Ac}\) & 0.00 \({}^{\rm Ad}\) & 0.1063 & \(<\)0.0001 & \(<\)0.0001 & \(<\)0.0001 \\ \hline  & & & & & & & & & & & \\ \end{tabular} Note. – (1) CK, no additive contro; LP, materials, NH\({}_{3}\)-N: ammonia nitrogen; LA: lactic acid; AA: acetic acid; PA: propionic acid. (2) Different lowercase letters within the same row show significant differences between different treatments at the same silage days (\(p<0.05\)). (3) Different capitalized letters within the same column show significant differences between different silage days for the same treatment (\(p<0.05\)); the same capitalized letters demonstrate no significant differences between treatments. (4) T: different additive treatments; D: different silage days; T \(\times\) D: interaction between additive treatment and silage days; SEM: standard error of mean.  
\end{table} 
Table 3: Effects of different additives on the fermentation quality of corn stover.
## 2 2 DOF IMC for SRM  
### Mathematical Model of the SRM  
Neglecting the magnetic saturation and mutual inductance, the self-inductance can be described by the Fourier series with DC and fundamental harmonic components:  
\[\left\{\begin{array}{l}L_{a}=L_{dc}+L_{ac}\cos\theta_{e}\\ L_{b}=L_{dc}+L_{ac}\cos\left(\theta_{e}-2/3\pi\right)\\ L_{c}=L_{dc}+L_{ac}\cos\left(\theta_{e}+2/3\pi\right)\end{array}\right. \tag{1}\]  
where \(L_{a}\), \(L_{b}\) and \(L_{c}\) are the A-, B- and C-phase self-inductance; \(L_{dc}\) and \(L_{ac}\) are the coefficients of DC and fundamental harmonic component. The \(\theta_{e}\) is the electrical rotor position, and the relationship between \(\theta_{e}\) and mechanical angle \(\theta_{m}\) can be expressed as:  
\[\theta_{e}=P\theta_{m} \tag{2}\]  
where the \(P\) is the number of rotor poles.  
The voltage balance equation of SRMs in the three-phase reference frame can be described as:  
\[\begin{bmatrix}u_{a}\\ u_{b}\\ u_{c}\end{bmatrix}=R\begin{bmatrix}i_{a}\\ i_{b}\\ i_{c}\end{bmatrix}+p\left(\begin{bmatrix}L_{a}&0&0\\ 0&L_{b}&0\\ 0&0&L_{c}\end{bmatrix}\begin{bmatrix}i_{a}\\ i_{b}\\ i_{c}\end{bmatrix}\right) \tag{3}\]  
where \(u_{a}\), \(u_{b}\) and \(u_{c}\) are A-, B- and C-phase voltage, \(i_{a}\), \(i_{b}\) and \(i_{c}\) are A-, B- and C-phase current, and \(R\) and \(p\) are the phase winding resistance and differential operator.  
By using [PERSON]'s transformation, the model in the rotating reference frame can be further obtained, and it can be denoted as:  
\[\begin{bmatrix}u_{d}\\ u_{q}\\ u_{0}\end{bmatrix}= R\begin{bmatrix}i_{d}\\ i_{q}\\ i_{0}\end{bmatrix}+\omega_{e}\begin{bmatrix}-L_{ac}\sin 3\theta_{e}&-L_{dc}-L_{ac} \cos 3\theta_{e}&0\\ L_{dc}-L_{ac}\cos 3\theta_{e}&L_{ac}\sin 3\theta_{e}&\frac{\sqrt{2}}{2}L_{ac}\\ 0&0&0\\ \end{bmatrix}\begin{bmatrix}i_{d}\\ i_{q}\\ i_{0}\end{bmatrix} \tag{4}\] \[+\begin{bmatrix}L_{dc}+\frac{1}{2}L_{ac}\cos 3\theta_{e}&-\frac{1}{2}L_{ ac}\sin 3\theta_{e}&\frac{\sqrt{2}}{2}L_{ac}\\ -\frac{1}{2}L_{ac}\sin 3\theta_{e}&L_{dc}-\frac{1}{2}L_{ac}\cos 3\theta_{e}&0\\ \frac{\sqrt{2}}{2}L_{ac}&0&L_{dc}\end{bmatrix}p\begin{bmatrix}i_{q}\\ i_{q}\\ i_{0}\end{bmatrix}\]  
where \(u_{d}\), \(u_{q}\) and \(u_{0}\) are the \(d\)-, \(q\)- and 0-axis voltage; \(i_{d}\), \(i_{q}\) and \(i_{0}\) are the d-, q- and 0-axis current. The \(\omega_{e}\) is the electrical rotor speed.  
The instantaneous torque \(T_{e}\) in the rotating reference frame is given as:  
\[T_{e}=\frac{\sqrt{2}P}{2}L_{ac}i_{0}i_{q}-\frac{P}{4}L_{ac}(i_{d}^{2}+i_{q}^{2 })\sin(3\theta_{e}+2\beta)) \tag{5}\]where the \(\beta\) is the advanced angle.  
From (5), it is obvious the second term makes no contribution to the average torque, and it is generally treated as the torque ripple. Hence, in this paper, to reduce the ripple term, the \(i_{d}=0\) strategy is adopted and the \(\beta=\frac{\pi}{2}\) is selected. Then, the \(T_{e}\) is simplified as:  
\[T_{e}=\frac{\sqrt{2}P}{2}L_{ac}i_{0}i_{q} \tag{6}\]