esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Semantic Expression of Relational Data Provenance
### Representation of Provenance Data
As show in Figure 2, \(Q_{1}\) is a typical SQL query, and the corresponding relational algebra is \(\prod_{Sno,Jno}(\mathit{Suppliers}\ \mathcal{S}\mathcal{S}\mathcal{S} \mathcal{S}\mathcal{S}\mathcal{S}\mathcal{S}\mathcal{S}\mathcal{S}\mathcal{S} \mathcal{S}\mathcal{S}\mathcal{S}\According to Definition 2, the provenance of \(u_{1}(\text{S1},\text{J4})\), \(u_{2}(\text{S3},\text{J4})\), and \(u_{4}(\text{S5},\text{J3})\) in the result of \(Q_{1}\) can be represented as \(\mathit{TupWhere}(Q_{1},u_{1})=\{s_{1},j_{4}\}\), \(\mathit{TupWhere}(Q_{1},u_{2})=\{s_{3},j_{4}\}\), and \(\mathit{TupWhere}(Q_{1},u_{4})=\{s_{5},j_{3}\}\), respectively. Using where-prov, if a tuple \(u\) is fully or partially copied to compute the output tuple \(t\), then \(u\) is the provenance data of \(t\). Compared with the value-level where-prov, a schema is at a high level of granularity. Similarly, if tuples of relation table \(R_{1}\) contribute to tuples of relation table \(R_{2}\), we can intuitively infer that the schema \(\mathbf{U}\) for \(R_{1}\) contributes to the schema \(\mathbf{T}\) for \(R_{2}\) at the schema level. Consequently, the standardized definitions of field-level and schema-level provenance data can be obtained (Definitions 3 and 4). **Definition 3** (_FProv_): _The provenance data of field \(A\): \(\mathit{FProv}(A)=\cup\{B|u[B]\in\mathit{Where}(Q_{i},t[A])\}\), \(i=1,2,\ldots n\), where \(Q_{i}\) is any query containing \(A\) in the list of target fields._  
Definition 3 demonstrates that all fields contributing to the value of every tuple on field \(A\) constitute the field-level provenance of field \(A\). For example, \(\mathit{FProv}(\mathit{Sno})=\{Supplies.Sno\}\). **Definition 4** (_SProv_): _The provenance data of schema \(\mathbf{T}\): \(\mathit{SProv}(\mathbf{T})=\cup\{\mathbf{R}_{i}|u\in\mathit{TupWhere}(Q_{i},t)\), \(U\in R_{i},u\in U,t\in T\},\ i=1,2,\ldots n\), where \(Q_{i}\) is any query inserting its querying results to table \(T\)._  
Under the copy contribution semantics, if tuples of relation table \(R_{i}\) contribute to tuples of relation table \(T\) and \(u\in\mathit{TupWhere}(Q,t),t\in T,u\in R_{i}\), then \(\mathbf{R}_{i}\) contributes to \(\mathbf{T}\) at the schema level.
## 2 Materials and Methods  
### System Components  
Highway condition-sensing devices are often deployed only at key points like ramps and toll booths, leading to inadequate monitoring over the entirety of the highway network. To enhance the monitoring capabilities across all highway segments and to assist road management authorities in actively alerting and managing abnormal conditions on the road surface, this paper introduces a fusion solution that integrates robotic technology, edge computing, and advanced object detection, as shown in Figure 1. This solution primarily consists of an intelligent patrol robot, equipped with an enhanced object detection algorithm, in conjunction with a cloud-based early warning platform.  
The intelligent patrol robot is comprised of four key components: a real-time monitoring module, an anomaly recognition module, a positioning module, and a module for reporting and storing anomalies. Imagine a workflow spanning \(T\) moments in time. The real-time monitoring module's primary role is to capture the highway surface information at each moment \(t\) as the robot traverses a specified highway segment. The collected road surface data are then transmitted to the anomaly recognition module. Within this module, the neural network model proposed in this paper conducts object detection on the real-time road imagery. If the detection results align with any predefined anomalous states in the database, the positioning module is activated to relay this information to the highway maintenance authorities. Moreover, the storage module archives images of road anomalies on a local forensic server. This enables maintenance authorities to remotely access the server, ensuring the traceability and verifiability of the reported data.  
The cloud-based early warning platform consists of two main components: a data storage module and a road anomaly information display module. Images of road surface anomalies and their corresponding location information, transmitted from the road patrol robots, are stored in the cloud database. The road anomaly information display module retrieves data from this storage module and presents it on a front-end interface for review by road management authorities.
# FPGA Implementation of Mutual Authentication Protocol for Medication Security System
## 4 Design and Implementation Results
### Verilog Simulation Results  
The proposed Medication Safety WSN authentication protocol (XOR method) was implemented in a hardware description language (Verilog) on the Altera Quartus II platform, as shown in Figure 5.  
The parameters of the design are reported in Table 2.  
Simulations of the proposed design were conducted in the Altera Quartus II design environment and implemented in an Altera Cyclone II EP2C70F896C6 FPGA on an Altera DE 2 board. The simulation results of the XOR-Padgen function as described in Section 4.1 are shown in Figure 6.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Family** & **Quartus II 8.0 Cyclone II** \\ \hline Device & EP2C70F896C6 \\ Logic elements & 1536/68,416 \\ Registers & 705 \\ PLLs & 0/4 \\ M4 Ks & 0/250 \\ Total memory bits (Total RAM block bits) & 0/1,152,000 \\ Logic array blocks (Block interconnects) & 2063/197,592 \\ I/O pins & 259/622 \\ Clock pins & 1/8 \\ Maximum fan-out & 705 \\ Total fan-out & 8410 \\ Average fan-out & 2.91 \\ Embedded multipliers & 0/300 \\ FPGA clock source (MHz) & 50 \\ Fmax (MHz) & 174.40 \\ Clock period (ns) & 6.281 \\ Longgest Path Delay (ns) & 5.512 \\ Worst Case Setup time (tsu) (ns) & 7.214 \\ Worst Case Hold time (th) (ns) & 0.496 \\ Total Power (mW) & 246.07 \\ Dynamic Power (mW) & 20.79 \\ Static Power (mW) & 155.13 \\ I/O Power (mW) & 70.15 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The parameters of Medication Safety WSN authentication protocol hardware (XOR method).  
Figure 5: Hardware chart of Medication Safety WSN authentication protocol (XOR method).  
The received user's identification and cover-code password are assumed to be UserID = 12345678 and CCPWD = 59 BF2F62. The two input numbers R1 and R2 for Padgen function are produced by XOR operation between two random numbers; for example, when R1 = Rt1 \(\oplus\) Rm1 = 66C3 and R2 = Rt2 \(\oplus\) Rm2 = F65A, the calculated result PAD1 = F272 at select = 0. When R1 = Rt1 \(\oplus\) Rm2 = EE0B and R2 = Rm1 \(\oplus\) Rt2 = F92, the calculated result PAD2 = C063 at select = 1. When R1 = Rt1 = 6003 and R2 = Rm1 = 06C0, the calculated result PAD3 = 9062 at select = 1. When R1 = PAD3 = 9062 and R2 = Rm1 = 6003, the calculated result PAD4 = CF6F at select = 2. When R1 = Rt2 = 7852 and R2 = Rm2 = 8E08, the calculated result PAD5 = 2340 at select = 3. When R1 = PAD5 = 2340 and R2 = Rt2 = 7852, the calculated result PAD6 = 1D4D at select = 5. PWD = ABCDF601 is gained by decoding CCPWD which is computation of CCPWD \(\oplus\) {PAD1, PAD2}. MsgM = 1234 is obtained by calculating in_CCMsgM = 8256 \(\oplus\) PAD3, and MsgL = 5678 is obtained by calculating in_CCMsgL = 9917 \(\oplus\) PAD4. out_CCMsgM = 3174 is gained by operating on MsgM \(\oplus\) PAD5, and out_CCMsgL = 4B35 is gained by operating on MsgL \(\oplus\) PAD6. Once out_CCMsgM and out_CCMsgL are produced, an internal signal is given to begin its CRC encoding, thus generating CCNgM \(\parallel\) CRC (=273B) and CCNgL \(\parallel\) CRC (=3 ABB).
## 4 Analysis of Numerical Simulation Results
### Results and Analysis
Under Figure 10a, Scheme 1, the surface curvature values are very small, with the maximum  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Monitoring** & **Scheme 1** & **Scheme 2** & **Monitoring** & **Scheme 1** & **Scheme 2** & **Monitoring** & **Scheme 1** & **Scheme 2** \\
**Point** & **(mm)** & **(mm)** & **Point** & **(mm)** & **(mm)** & **Point** & **(mm)** & **(mm)** \\ \hline BJ1 & 2.76 & 3.58 & HL4 & \(-21.29\) & 0.42 & YH4 & \(-21.29\) & \(-14.73\) \\ BJ2 & 2.93 & 2.61 & GL1 & \(-20.97\) & \(-2.40\) & **YH5** & \(-41.88\) & \(-39.38\) \\ BJ3 & \(-4.54\) & \(-5.75\) & GL2 & \(-20.27\) & \(-0.25\) & **YH6** & \(-53.98\) & \(-51.93\) \\ BJ4 & \(-3.94\) & \(-1.39\) & GL3 & \(-19.56\) & 0.92 & YH7 & \(-18.05\) & \(-14.89\) \\ BJ5 & 4.03 & 3.52 & GL4 & \(-14.43\) & 0.65 & **YH8** & \(-31.57\) & \(-29.89\) \\ BJ6 & 5.00 & 4.19 & GL5 & \(-4.04\) & 0.50 & YH9 & \(-20.50\) & \(-12.49\) \\ BJ7 & 4.40 & 3.43 & GC1 & \(-1.25\) & 0.48 & YH10 & \(-19.98\) & \(-11.49\) \\ BJ8 & 1.93 & 1.20 & GC2 & 0.63 & 0.51 & YH11 & \(-18.91\) & \(-9.47\) \\ BJ9 & 1.56 & 0.77 & GC3 & 1.36 & 1.05 & YH12 & \(-20.58\) & \(-11.53\) \\ BJ10 & \(-14.18\) & \(-11.19\) & GC4 & 1.62 & 1.13 & YH13 & \(-18.67\) & \(-8.44\) \\ BJ11 & \(-13.50\) & \(-1.97\) & GC5 & 1.99 & 1.69 & YH14 & \(-17.5  
curvature of 0.012 mm/m\({}^{2}\) occurring at monitoring point CZ2. Under Figure 10b, Scheme 2, the maximum curvature of 0.006 mm/m\({}^{2}\) occurs at monitoring point YH19. An analysis of Figure 10 reveals that increasing the backfill ratio in the YZS mining area has almost no effect on surface curvature. According to the stability criteria, the curvature values under both scenarios are far below the critical deformation limit of 3 mm/m\({}^{2}\), indicating that surface curvature has almost no impact on the ground under either scheme. (4) Lateral deformation  
Figure 11 shows the lateral deformation contour maps under the two scenarios. Under both Figure 11a,b, Scheme 1 and Scheme 2, the lateral deformation values on the surface are very small. Under Figure 11a, Scheme 1, the maximum deformation value of 0.37 mm/m occurs at monitoring point CZ2 among the 52 monitoring points. Under Figure 11b, Scheme 2, the maximum deformation value of 0.35 mm/m occurs at monitoring point BJ12 among the 52 monitoring points. However, the lateral deformation values are far below the standard requirements. As shown in Figure 11, distinct deformation centers are observed under both scenarios. Increasing the backfill ratio in the YZS mining area slightly reduces the lateral deformation within the mining area, indicating that raising the backfill ratio in the YZS mining area decreases lateral deformation, but the effect is not significant. Figure 11: Lateral deformation cloud map. Figure 10: Surface curvature cloud map.
# Regional Geomagnetic Field Modeling Based on Associated Legendre Polynomials
## 2 Principles and Methods  
### Associated Legendre Polynomials  
Associated Legendre equations are a type of ordinary differential equation frequently encountered in physics and various technical fields, particularly emphasizing orthogonality, computational accuracy, and speed in geophysics. The standard Legendre polynomials are a special case derived from solving an associated Legendre equation. When solving the associated Legendre equation, the solutions can be categorized into two main forms: one is the direct solution form, which involves explicit mathematical expressions to directly compute the solutions; the other is the recursive form, which is obtained through recurrence relations. Although these two forms are theoretically equivalent as solutions to the equation, they differ significantly in computational efficiency and numerical stability due to their structural differences. The direct solution form has precise mathematical expressions and can directly compute associated Legendre polynomials of any degree. However, for higher-degree polynomials, the computational cost of the direct solution increases dramatically and numerical instability may occur when the truncation level is large. This is because the calculation of higher-degree polynomials involves complex mathematical operations, which are susceptible to limitations in floating-point precision, leading to the accumulation of computational errors. In contrast, the recursive form--while less elegant in theoretical analysis--is highly suitable for efficient and stable numerical computations. Recurrence relations avoid the numerical instability issues that may arise in direct solutions, particularly excelling in the computation of higher-degree polynomials. In this study, the final recurrence formula for the associated Legendre polynomials we used is as follows [17]:  
\[(2k+1)xP_{k}^{m}(x)=(k+m)P_{k-1}^{m}(x)+(k-m+1)P_{k+1}^{m}(x)\quad(k\geqslant 1) \tag{1}\]  
The \(x\) in Equation (1) represents the longitude or latitude value, \(k\) denotes the degree of the associated Legendre polynomials, and m represents the ordinal number of the summed terms.
## 3 Optical Controlled Phased Sub-Array in Multi-Hop Bent-Pipe Payload
### Broadband Phased-Array Aperture Effect  
The broadband phased array aperture effect is mainly characterized by the constraint of the array antenna's crossing time \(T_{A}=Lsin\theta_{B}\) on the bandwidth of the transmitted signal, expressed as a certain deflection of the beam pointing by the wideband signal. The relationship between the deflection angle and bandwidth of a conventional phased array can be expressed as [43]:  
\[\Delta\theta_{f}=\frac{\Delta f}{f_{0}}tan\theta_{B} \tag{9}\]  
where \(f_{0}\) is the center frequency of the signal, \(\Delta f\) represents the bandwidth of the signal. As a result, the beam pointing skew caused by the change in signal frequency increasesas the bandwidth \(\Delta f\) and scanning angle become larger. The bandwidth criterion for phased-array antennas is the limit on \(\Delta f\). When \(\theta_{B}=60^{o}\), usually the maximum beam deflection is called to satisfy  
\[\Delta f_{max}\leq\theta_{1/2}(\theta_{B})/4. \tag{10}\]  
The \(\theta_{1/2}(\theta_{B})\) is the half power beam width (HPBW) when the beam is scanned to \(\theta_{B}\).  
\[\theta_{1/2}(\theta_{B})=\theta_{1/2}/cos\theta_{B} \tag{11}\]  
where \(\theta_{1/2}\) is the HPBW of the beam in the direction normal to the array plane. Therefore,  
\[\frac{\Delta f}{f_{0}}\leq\theta_{1/2}/4 sin\theta_{B} \tag{12}\]  
If the scanning angle \(\theta_{B}=60^{o}\) and the HPBW is \(2^{o}\), the limitation on the signal bandwidth is 0.02. For a 30 GHz phased array, the maximum instantaneous signal bandwidth allowed is 600 MHz, which is hardly enough to meet the requirements of current low-orbit communication satellites.  
If the antenna is divided equally into \(M\) sub-arrays, as shown in the figure, there are m antenna elements within each sub-array. The beam pointing of each subarray is still altered despite the subarray's continued exposure to the transition time and aperture effect; however, because each subarray's aperture represents only \(1/M\) of the total array, the subarray's aperture transition time will be decreased to  
\[T^{\prime}_{A}=T_{A}/M \tag{13}\]  
At this point, the system limit on the instantaneous signal bandwidth can be relaxed by a factor of \(M\). Equation (10) will be reduced to  
\[\frac{\Delta f}{f_{0}}\leq M\theta_{1/2}/4 sin\theta_{B} \tag{14}\]
# Future Perspectives for Gamma-ray Burst Detection from Space
## 11 Svom  
### Mission Overview  
The Space-based Variable astronomical Object Monitor (SVOM) mission is dedicated to gamma-ray burst studies and, in general, to time domain astrophysics, including multi-messenger science. It is optimized to detect and follow-up all types of GRBs, but particularly tailored for high-redshift GRBs thanks to its low-energy triggering threshold of around 4 keV. One of the main goals of SVOM is to produce a complete catalog of GRBs, including their redshift measurements. For this purpose, SVOM will follow an anti-solar pointing strategy and will avoid the galactic plane, in order to facilitate the observations from ground-based observatories and robotic telescopes. That is why SVOM is composed of a space segment, as well as a few ground-based dedicated follow-up facilities. SVOM alerts will be promptly transmitted to the ground through a dedicated network of VHF antennas and through the Chinese Beidou inter-satellite communications link. The goal is for ground observers to receive SVOM alerts less than 30 s after the GRB is detected on board. The SVOM satellite will be launched from China around mid-2024 with an LM 2-C rocket and injected in a low-Earth orbit (h\(\sim\)600 km) with an inclination of about 30\({}^{\circ}\). It will carry four co-aligned instruments. Two instruments (ECLAIRs and GRM) are sensitive in the hard X-/soft gamma-ray energy range and have a wide FoV, in order to monitor vast regions of the sky and detect gamma-ray transients. Two narrow FoV instruments (MXT and VT) will be used to follow-up and characterize the afterglow emission. The SVOM-integrated payload is shown in Figure 19.  
Figure 18: The expected cumulative on-board detection rate of canonical gamma-ray bursts (GRBs) and X-ray flashes (XRFs) by the _STROBE-X_/WFM as estimated by folding observed GRB and XRF spectra through the WFM responses and accounting for the effective field-of-view of the WFM. It will detect \(\sim\)100 long-duration GRBs, \(\sim\)7 short-duration GRBs, and \(\sim\)12 XRFs on-board per year. The onboard detection rate of long GRBs exceeds that of _Swift_/BAT, while the short GRB detection rate is comparable. A unique capability is the down-link of event data to the ground for the WFM, enabling sub-threshold searches to double the number of short GRB detections (purple shading). The detection rate of XRFs exceeds that of previous instruments and is a particular science focus for the WFM. The blue shading shows the region of the signal-to-noise ratio, where high-fidelity spectroscopy can be performed in the prompt X-ray for these sources.
## 3 Results
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Samples** & **145 Nd/144 Nd (\(\pm\)2**\(\sigma\times\) 10\({}^{6}\))** & \(\varepsilon\)**Nd** \\ \hline \multirow{8}{*}{ARA09C-St03} & 1 cm & 0.512169 (4) & \(-\)9.1 \\  & 37 cm & 0.512211 (5) & \(-\)8.3 \\  & 75 cm & 0.512070 (5) & \(-\)11.1 \\  & 85 cm & 0.511931 (4) & \(-\)13.8 \\  & 129 cm & 0.512199 (4) & \(-\)8.6 \\  & 160 cm & 0.512170 (6) & \(-\)9.1 \\  & 196 cm & 0.512231 (7) & \(-\)7.9 \\  & 289 cm & 0.512243 (11) & \(-\)7.7 \\  & 340 cm & 0.512228 (8) & \(-\)8.1 \\  & 375 cm & 0.512289 (8) & \(-\)8.0 \\  & 403 cm & 0.512151 (5) & \(-\)9.5 \\  & 424 cm & 0.512213 (5) & \(-\)8.3 \\  & 471 cm & 0.512174 (5) & \(-\)9.1 \\ \hline \multirow{2}{*}{East Siberian Sea} & Kolyma River & - & \(-\)6 \\  & Shelf sediment & & \(-\)10.5 \\ \hline \multirow{2}{*}{Canada Archipelago} & Central Ellesmere & - & \(-\)9.6 \\  & Shelf sediment & & \(-\)10.3 \\ \hline \multirow{2}{*}{Beaufort Sea} & Mackenzie River & - & \(-\)14.3 \\ \hline \multirow{2}{*}{Bering Sea basalt province} & - & \(+\)7.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Nd isotope data of core ARA09C-St03 and potential provenances from [PERSON] et al. [25].
# Computational-Intelligence-Based Spectrum-Sharing Scheme for NOMA-Based Cognitive Radio Networks
## 2 System Model and Problem Formulation
### NOMA-Assisted Power Allocation Scheme
#### 2.1.1 Time Slot 1  
In time slot 1, we can select the best receiver \(SU_{\text{self}}\) from the potential SUs based on the channel gain to retransmit the decoded signal to the user Q. The criteria for the selection of the SU can be mathematically expressed as \(k^{*}=arg\underset{k^{*}\in\Gamma}{\max}\left\lvert h_{k}\right\rvert^{2}\). The selected SU will re-transmit \(x_{0}\) of the previous frame to \(Q\). Simultaneously, PBS transmits \(x_{0}\) of the  
Figure 1: System Model.  
Figure 2: Time slot illustration for proposed communication process.  
current frame to the SR. Here it is important to mention that we develop a NOMA-assisted cooperative overlay spectrum-sharing framework comprising a primary transmission phase and a secondary transmission phase. Therefore, the SR can perfectly eliminate \(x_{0}\) of the previous frame after successful decoding and local caching. Thus, during the primary transmission phase, the signal received at the SR can be mathematically expressed as [31]:  
\[x_{SR}=\sqrt{P_{0}}h_{0}x_{0}+n_{SR} \tag{1}\]  
where \(n_{SR}\) is AWGN observed at the SR. From Equation (1), the achievable rate at the SR can be mathematically expressed as:  
\[R_{P}=log_{2}\Bigg{(}1+\frac{P_{0}|h_{0}|^{2}}{\sigma^{2}}\Bigg{)} \tag{2}\]  
where, \(\frac{P_{0}}{\sigma^{2}}\) is the transmit SNR. For successful decoding of \(x_{0}\) at the SR, the above rate should satisfy  
\[R_{P}\geq\gamma_{0} \tag{3}\]  
The corresponding minimum transmit power required at the PBS to achieve this rate can easily be obtained as:  
\[P_{0}\geq\sigma^{2}\bigg{(}\frac{2^{\gamma_{0}}-1}{|h_{0}|^{2}}\bigg{)} \tag{4}\]  
Finally, the distance between the PBS and the SR is kept sufficiently large to guarantee the successful transmission of \(x_{0}\).
# A Short-Circuit Current Calculation Model for Renewable Power Plants Considering Internal Topology
## 2 Classification and Control Strategies of N-SMSs
### LVRT Control Strategy  
During a short-circuit fault in the power grid, the terminal voltage of N-SMS drops, requiring these sources to supply reactive current to support the grid voltage. At this point, the voltage control outer loop is deactivated, and the reference values for the current inner loop are determined by the LVRT control strategy.  
Taking wind farms as an example, according to the grid connection standards [19], during symmetrical faults, the LVRT requirements specify the provision of reactive current during the voltage dip period:  
\[\Delta I_{\text{t}}\ =\ K_{1}\times(0.9-U_{\text{t}})\times I_{\text{N}},0.2 \leq U_{\text{t}}\leq 0.9 \tag{2}\]  
where  
* \(\Delta I_{\text{t}}\) represents the incremental dynamic reactive current injected by the wind farm;
* \(K_{1}\) is the proportional coefficient of the dynamic reactive current for the wind farm, with a value range of no less than 1.5 and preferably no greater than 3;
* \(U_{\text{t}}\) is the per-unit value of the voltage at the point of grid connection for the wind farm;
* \(I_{\text{N}}\) is the rated current of the wind farm.  
In this paper, \(K_{1}\) is set to 1.5, and because the wind farm operates under a unit power factor condition, the reference value for the reactive current during the LVRT period can be derived as follows:  
\[{I_{\text{q}}}^{*}\ =\ 1.5(0.9-U_{\text{t}})I_{\text{N}},0.2\leq U_{\text{t}} \leq 0.9 \tag{3}\]  
Due to the current limiting protection requirements of the inverter, the maximum value of the active current during the LVRT period is as follows:  
\[{I_{\text{dma}}}^{*}\ =\ \sqrt{{I_{\text{max}}}^{2}-{I_{\text{q}}}^{*2}} \tag{4}\]  
Figure 2: Diagram of grid connected inverter and its control system.  
where  
* \(I_{\text{dmax}}\)* is the upper limit of the active current;
* \(I_{\text{max}}\) is the current limit of the inverter,
* \(I_{\text{q}}\)* is the reference value of the reactive current.  
At this point, the command value of the active current is the minimum between the pre-fault active current command value and \(I_{\text{dmax}}\)*. Therefore, the current inner loop command value during the LVRT period is as follows:  
\[\left\{\begin{array}{c}{i_{\text{d}}}^{*}~{}=~{}\text{min}({i_{\text{d0}}},{I _{\text{dmax}}}^{*})\\ {i_{\text{q}}}^{*}~{}=~{}1.5(0.9-{U_{\text{t}}}){I_{\text{N}}}\end{array}\right. \tag{5}\]  
The complete control block diagram is shown in Figure 2.