esa-sceva/satcom-chunk-collection huggingface dataset:
# Study of the Phenolic Compound Profile of _Arbutus unedo_ L.
## 3 Results and Discussion
### Analysis of Phenolic Compounds by HPLC-TQ-MS/MS  
#### 3.3.1 Development of the HPLC-TQ-MS/MS Method  
Firstly, the fragmentation patterns of the 21 target PC were determined by direct infusion of pure standard solutions of each compound in the ESI source. The analyte signals exhibited higher intensities in negative, than in positive ion mode. Therefore, all compounds were ionized in negative ion mode. A cone voltage of 40 V was used to generate the precursor ion ([M-H]\({}^{-1}\)) of each compound. The predominant ion was selected as the precursor ion to obtain the product ion spectra. The collision energy to generate each product ion was also optimized. Table 3 shows the precursor ion, product ions, and optimal collision energy for each compound. To enhance detection sensitivity, the most intense product ion obtained for each analyte (in MRM mode) was used for quantification (Table 3), while the other product ions were monitored for confirmatory purposes to improve detection specificity. Moreover, for confirmation, it was also checked that the relation of product ions in the mass spectra of the samples was maintained in comparison with the mass spectra of the standard solutions. Additionally, the retention time was also used as a confirmation parameter. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Origin**} & \multirow{2}{*}{**Harvest year**} & \multirow{2}{*}{**Moisture (\%)**} & \multicolumn{2}{c}{**TPC**} & \multicolumn{2}{c}{**RSA**} & \multicolumn{1}{c}{**TAC**} \\  & & & **mg GAE/100g DW** & **mg TE/100g DW** & **mg Cyn-3-glu/100g DW** \\ \hline Möstoles & 2018 & 72.5 \(\pm\) 0.8 \({}^{\text{b}}\) & 1309 \(\pm\) 99 \({}^{\text{a}}\) & 2258 \(\pm\) 212 \({}^{\text{a}}\) & 76 \(\pm\) 8 \({}^{\text{ab}}\) \\ Losar de la Vera & 2018 & 69.6 \(\pm\) 0.5 \({}^{\text{a}}\) & 1965 \(\pm\) 96 \({}^{\text{b}}\) & 3256 \(\pm\) 281 \({}^{\text{b}}\) & 91 \(\pm\) 27 \({}^{\text{b}}\) \\ Möstoles & 2016 & 76.1 \(\pm\) 0.9 \({}^{\text{c}}\) & 2018 \(\pm\) 60 \({}^{\text{b}}\) & 4800 \(\pm\) 161 \({}^{\text{c}}\) & 69 \(\pm\) 2 \({}^{\text{ab}}\) \\ Madrid & 2016 & 77.1 \(\pm\) 0.9 \({}^{\text{c}}\) & 1943 \(\pm\) 62 \({}^{\text{b}}\) & 4730 \(\pm\) 151 \({}^{\text{c}}\) & 72 \(\pm\) 8 \({}^{\text{ab}}\) \\ Manzanares el Real & 2016 & 71.0 \(\pm\) 0.5 \({}^{\text{ab}}\) & 1895 \(\pm\) 25 \({}^{\text{b}}\) & 2338 \(\pm\) 82 \({}^{\text{a}}\) & 50 \(\pm\) 12 \({}^{\text{a}}\) \\ \hline \end{tabular}  
* Data are expressed as mean \(\pm\) standard deviation (\(n=4\)); DW: Dry weight; GAE: Gallic acid equivalents; TE: Trolox equivalents; Cyn-3-glu: Cyanidin-3-glucoside equivalents, \({}^{\text{a,b,c,d,e,f,g}}\) mean values within a column followed by different superscript letters are significantly different when subjected to statistical analysis (\(p\leq 0.05\)).  
\end{table} 
Table 2: Total phenolic compounds (TPC), total anthocyanin compounds (TAC), and radical scavenging activity (RSA) for _A. unedo_ L. berries harvested at an intermediate ripening stage in different years and from different geographical locations *.
# Error Modeling of Fiber Optic Gyroscope Universal Time Measurement
## 3 UT1 and the Instantaneous Angular Velocity of the Earth's Rotation
A drift phenomenon exists in the FOG device itself; it follows that the error will be continuously accumulated by integrating, so that the solution result will be shifted from the real value. Therefore, the model parameters need to be calibrated periodically with UT1 results published by IERS. When the difference between the UT1 solution and VLBI observation data exceeds a certain threshold, recalibration of the parameters is necessary. The selection of this threshold is related to the measurement accuracy of the FOG. For a giant FOG with an accuracy of 2 \(\times\) 10\({}^{-10}\) rad/s, the maximum theoretical error value for this accuracy is 230 ms; therefore, the threshold is chosen to be within \(\pm\)230 ms.
# Second-Harmonic Generation of Blue Light in GaN Waveguides
###### Abstract  
Second-harmonic generation was studied in III-metal-polar GaN films grown on sapphire substrates by metalorganic chemical vapor deposition and formed into ridge waveguides. Broadband near-IR femtosecond pulses of an optical parametric amplifier system were injected by end-fire coupling and the nonlinear response was measured while tuning the central wavelength. A prominent peak was found at 450 nm for 1140 nm thick and 10 \(\upmu\)m wide GaN waveguides. The measured second-harmonic peak was in agreement with the modal-dispersion phase matching condition calculated using the dispersion of the extraordinary refractive indices of GaN obtained by prism coupling.  
GaN waveguides; second-harmonic generation; modal-dispersion phase matching
# Evaluation of Green Strategies for Prolonging the Lifespan of Linear Wireless Sensor Networks
## 7 Discussion  
This section discusses the reasons why certain energy-saving techniques that work in traditional WSNs are not suitable for LWSN monitoring applications. It also presents a comparative analysis of the energy consumption in LWSNs and traditional WSNs and the integration of user requirements and operational constraints in LWSN energy management.  
Challenges Adapting Energy Management Techniques from Traditional WSN to LWSN Monitoring Applications  
To discuss why these techniques designed for traditional WSNs may not work for LWSNs, it is important to recap the difference between traditional WSNs and LWSNs. The main difference between WSNs and LWSNs lies in the deployment of the nodes. In typical WSNs, nodes are randomly deployed, whereas, in LWSNs, the network topology is predetermined. LWSNs necessitate a linear arrangement of sensor nodes, with data relayed to a central base station through daisy-chaining via neighboring sensor nodes. However, this approach introduces significant energy inefficiencies and imbalances, resulting in data transmission delays and complex application and service management [153]. While some energy-saving techniques have proven effective in traditional WSNs, their applicability in LWSN monitoring applications poses unique challenges [8]. Several factors contribute to the incompatibility of certain energy-saving techniques of traditional WSNs in the context of LWSNs [154]. In this section, we explore the reasons why certain energy-saving techniques that work in traditional WSNs are not suitable for LWSN monitoring applications.
# Biological Properties of Sandalwood Oil and Microbial Synthesis of Its Major Sesquietrepenoids
## 5 Metabolic Engineering Strategies to Increase the Yield of Santalene and Santalol in S. cerevisiae
### Engineering of the Key Enzymes in the MVA Pathway  
To increase the supply of IPP and DMAPP, efforts have been made to manipulate the MVA pathway in _S. cerevisiae_ (Table 3). This involves overexpression and increasing  
Figure 3: The biosynthetic pathway of \(\alpha\)-santalene and \(\alpha\)-santalols in _S. cerevisiae_. The black arrows represent the steps catalyzed by native enzymes, and the red arrows represent the steps catalyzed by exogenous enzymes. Meanwhile, the dashed arrow represents a step that is depressed. (ERG10: acetoacetyl-CoA thiolase; ERG13: HMG-CoA synthase; HMG-CoA: 3-hydroxy-3-methyl-gluraryl-CoA; tHMG1 and tHMG2: a truncated HMG-CoA reductase; ERG12: mevalonate-5-kinase; ERG8: phosphomevalonate kinase; ERG19: mevalonate pyrophosphate decarboxylase; ERG20: (E, E)-FPP synthase; ERG9: squalene synthase; SanSyn: \(\alpha\)-santalene synthase; CYP: cytochrome P450 monooxygenase; CPR2: NADPH-cytochrome P450 reductase. the transcript levels of key genes in the MVA pathway. The conversion of HMG-CoA to mevalonate is a crucial step in this context; HMGR is a highly regulated enzyme recognized as responsible for controlling the flow in the MVA pathway [88]. Also, HMG-CoA reductase is an important enzyme that regulates sterol synthesis by interacting with sterol trigger sensors of the endoplasmic reticulum membrane, eliminating the sterol regulation feedback. This is achieved by expressing an improved form of HMGR, a truncated (tHmg1) lacking the NH2-terminal. Overexpression of the HMG1 has been successfully used earlier and revealed to have the most significant impact on producing alcohols in _S. cerevisiae_ via the MVA pathway [89; 90]. ERG20 catalyzes the condensation reaction of IPP to form GPP and FPP. It has been identified that converting IPP to FPP in _S. cerevisiae_ is a flux-regulatory step that is firmly controlled in the MVA pathway [94; 95]. FPP is a universal precursor not limited only to sesquiterpenes but also acts as an intermediate substance for many other compounds,
# Study on Fire Smoke Distribution Characteristics in Mountain Spiral Highway Tunnels
## 2 Materials and Methods  
### Fire Dynamics Simulator  
The fire dynamics simulator developed by the US National Institute of Standards and Technology was applied in this study to study the temperature and velocity fields in fires [23; 24; 25]. A series of numerical models of highway tunnels was established with a large-eddy simulation model [26]. Many previous studies proved the reliability of FDS applied to simulate the behaviors of tunnel fire [27; 28]. The following are the key equations of the FDS basic theory, where Equation (1) is the mass conservation equation, Equation (2) is the momentum conservation equation, Equation (3) is the energy conservation equation, Equation (4) is the component transport conservation equation, and Equation (5) is the ideal gas state equation.  
\[\partial\rho/\partial t+\
abla\cdot\rho u=0, \tag{1}\]  
\[\partial\Big{(}\dot{\rho}\dot{u}\Big{)}/\partial t+\
abla\cdot\rho uu+\
abla p =\rho g+f+\
abla\cdot\tau_{ij}, \tag{2}\]  
\[\partial(\rho h_{s})/\partial t+\
abla\cdot\rho h_{s}u=Dp/Dt+\dot{q}^{\prime \prime\prime}-\
abla\cdot\dot{q}^{\prime\prime}+\Phi, \tag{3}\]  
\[\partial(\rho Y_{i})/\partial t+\
abla\cdot\rho Y_{i}u=\
abla\cdot\rho D_{i} \
abla Y_{i}+m_{i}^{\prime\prime\prime}, \tag{4}\]  
\[p=\rho RT/\overline{W}. \tag{5}\]  
where, \(\rho\) is the fluid density; \(u\) is the fluid velocity; \(g\) is the gravitational acceleration; \(f\) is external force; \(\tau_{ij}\) is the viscous stress tensor; \(h_{s}\) is the sensible enthalpy; \(p\) is fluid pressure; \(\dot{q}^{\prime\prime\prime}\) is the rate of heat release per unit volume; \(\dot{q}^{\prime\prime\prime}\) is the heat flux; \(\Phi\) is the dissipation function; \(Y_{i}\) is the mass fraction of the \(i\) component in the total component; \(D_{i}\) is the diffusion coefficient of the \(i\) component; \(m_{i}^{\prime\prime\prime}\) is the formation rate per unit volume mass of the \(i\) component; \(T\) is the fluid temperature; \(R\) is the ideal gas constant; and \(\overline{W}\) is the relative molecular mass of the fluid.
# A Family of ACO Routing Protocols for Mobile Ad Hoc Networks
## 1 Introduction
The rest of the paper is structured as follows: Section 2 performs a review of the state of the art of the ACO routing protocols for mobile ad hoc networks observing that there are not representative protocols whose functioning metrics are degraded little or nothing in scalable environments. This review has included a comprehensive analysis of the AntHocNet protocol, the indisputable reference in the area. The study of the literature has also picked up a compilation of the major parallelization techniques of ACO algorithms, which is especially interesting if you want to provide a scalable solution. Section 3 comments on the AntOR-based protocol and its main phases. Section 4 presents a family of ACO routing protocols for mobile ad hoc networks: Disjoint Link Routes (AntOR-DLR), Restrictive Disjoint Link Routes (AntOR-RDLR), Unicast Disjoint Link Routes (AntOR-UDLR), AntOR-v2 and Hybrid ACO Routing (HACOR). Section 5 shows a comparative study between these protocols based on AntOR. Section 6 presents the main lines of research of this work. Finally, the conclusions are exposed in Section 7.
## 3 Results
### Flat-roof Building
#### 3.1.3 Turbulence Intensity and Flow Acceleration
Arguably, the wind direction of 45\({}^{\circ}\) provides a suitable flow pattern for wind energy, as the turbulence intensities above the main diagonal of the roof are low, even at positions closer to the roof. Figure 8: Stream-wise (\(I_{UL}\)) and vertical (\(I_{W}\)) turbulence intensity, and normalised stream-wise velocity \(U\)/\(U_{ref}\) with uncertainty limits, as measured above the flat roof at 0\({}^{\circ}\), 15\({}^{\circ}\), 30\({}^{\circ}\) and 45\({}^{\circ}\). Measurement points include: (**a**) 18–50 (marked line z/D = 0.2), (**b**) 20–36 (marked line z/D = 0.5) and (**c**) 22–38–54 (z/D = 0.8). Free-stream reference values (at the inlet profile shown in Figure 3) are also marked for the turbulence intensity (\(\bullet\)). To compare the speed-up effect above the roof, Figure 8 additionally illustrates the normalised velocity profiles above the measuring points for the different wind angles. These profiles are normalised using the reference velocity (\(U_{\textit{ref}}\)). A similar normalisation is also shown in Figure 5.  
At 0\({}^{\circ}\), the zones of high turbulence intensity close to the roof are characterised by low values of normalised wind speed. Above, at heights z/\(D\) = 0.3 and z/\(D\) = 0.45, an increase in wind speed in the range of 20-30% can be observed. The highest value of \(\sim\)30% occurs above point 36 at z/\(D\) = 0.3, suggesting this is the upper limit of the separation zone. Similar to the previous case, at 15\({}^{\circ}\), a decrease in wind speed occurs due to the separation in the vicinity of the roof. In this case, an increase in the normalised velocity of \(\sim\)15-20% is identified above several measuring points from the height z/\(D\) = 0.3. At 30\({}^{\circ}\), normalised velocities at the lowest measurement height are mostly \(<\)1. At height z/\(D\) = 0.3, they are increased by the range of 10-20%, reaching 20% in the zone above the cone vortex development. For a wind angle of 45\({}^{\circ}\), even at the vicinity of the roof, all points at the main diagonal are experiencing an increase in wind speed of more than 15%. Yet, the maximum velocity increase of 20% occurs above the downstream point 54. These positions close to the roof are good candidates for wind harvesting due to their location and the fact that turbulence intensity levels are rather low for this wind direction. When all the cases are considered, the most favourable result regarding flow acceleration is detected above point 36 at a height of z/\(D\) = 0.3 at 0\({}^{\circ}\). Still, this region seems to be affected by slightly higher turbulence intensity levels, implying that for the adequate positioning of the wind turbine, an even higher location, just by a bit, should be considered.
# A Survey of Candidate Waveforms for beyond 5G Systems
## 3 Candidate Waveforms
### Filtered Orthogonal Frequency Division Multiplexing
#### 3.2.2 F-OFDM Receiver  
The F-OFDM receiver for each sub-band is similar to the CP-OFDM receiver. However each sub-band received signal is first filtered with the respective matched filter used upon transmission, i.e., \(f_{m}^{*}[n]\), resulting in the estimated signal, \(\bar{y}_{p}[n]\). This is followed by the CP (with \(N_{cp_{m}}\) length) removal and then the FDE (that performs an \(M\)-sized FFT operation) and finally the detection of the data symbols, \(\bar{S}_{k}\), and bitstream, \(\bar{\mathbf{b}}\).
# Energy Efficient GNSS Signal Acquisition Using Singular Value Decomposition (SVD)
## 4 Simulation and Performance
### Performance Metrics
#### 4.1.4 Probability of Detection (Pd) and Probability of False Alarm (Pfa)
In practice, to compute the probability of detection (\(Pd\)) this research assumes that because the non-coherent integration comprises the sum of many samples, the resulting probability distribution is close to Gaussian, derived from the central limit theorem [1] and the bell-shaped curve centered at the expected value of the correlation peak after non-coherent integration, and the probability of detection can then be computed by calculating the area under the curve and above the threshold and using Equation (29).
# Truss Structure Optimization with Subset Simulation and Augmented Lagrangian Multiplier Method
## 4 Test Problems and Optimization Results
### Planar 200-Bar Truss Structure  
The last test example regards the optimal design of the planar 200-bar truss structure shown in Figure 8. The modulus of elasticity is 30 Msi and the mass density is 0.283 lb/inch\({}^{3}\). The stress limit on all elements is \(\pm 10\) ksi. There are no displacement constraints. The structural elements are divided into 29 groups as shown in Figure 8. The minimum cross-sectional area of all design variables is 0.1 inch\({}^{2}\). The structure is designed against three independent loading conditions: (1) 1.0 kip acting in the positive \(x\)-direction at nodes 1, 6, 15, 20, 29, 34, 43, 48, 57, 62, and 71; (2) 10.0 kips acting in the negative \(y\)-direction at nodes 1, 2, 3, 4, 5, 6, 8, 10, 12, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 29,30, 31, 32, 33, 34, 36, 38, 40, 42, 43, 44, 45, 46, 47, 48, 50, 52, 54, 56, 57, 58, 59, 60, 61, 62, 64, 66, 68, 70, 71, 72, 73, 74, and 75; (3) loading conditions (1) and (2) acting together.  
This truss problem has been previously studied using SAHS [27], TLBO [34], ABC-AP [36], WEO [39], FPA [38], HPSACO [40], and HPSSO [41]. The optimized designs are compared in Table 10. SAHS, TLBO, HPSSO, and WEO generated feasible designs while HPSACO, ABC-AP, FPA, and ALSSO slightly violated the constraints. TLBO produced the best design for this test problem.  
Figure 7: Convergence curve obtained for the 72-bar truss problem with \(N=500\).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(N\) & **Best** & **Mean** & **Worst** & **SD** & **NSA** \\ \hline  & 100 & 379.7376 & 380.1562 & 382.8799 & 0.60467 & 62,292 (77,020) \\ ALSSO & 200 & 379.6001 & 379.7373 & 380.0177 & 0.100794 & 131,819 (115,840) \\  & 500 & 379.5922 & 379.7058 & 379.981 & 0.103908 & 260,928 (307,700) \\ \hline BBBC [33] & & 379.66 & 381.85 & N/A & 1.201 & 13,200 \\ SAHS [31] & & 380.62 & 382.85 & 383.89 & 1.38 & 13,742 \\ TLBO [34] & & 379.632 & 380.20 & 380.83 & 0.41 & 21,542 \\ CA [37] & & 379.69 & 380.86 & N/A & 1.8507 & 18,460 \\ FPA [38] & & 379.095 & 379.534 & N/A & 0.272 & 9029 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Comparison of statistical performance in the 72-bar truss problem.  
Statistical data listed in Table 11 prove that the present algorithm was also robust for this test problem. Figure 9 shows the convergence curve obtained for the last optimization run with \(N=500\).
# Advanced Metal Matrix Nanocomposites
## 5 Strengthening Mechanisms  
The strengthening mechanisms in the context of MMNCs are briefly introduced here. The effects that ceramic nanoparticles have on yield strength always include some different strengthening mechanisms that can act in varying degrees. The contributions to the strength increase can be summed up (Equation (6)) or the root of the sum of the squares can be regarded as an overall effect (Equation (7)). The summation method is used when the effects are assumed to be independent of each other, while the root of the sum of the squares is used when the individual effects do not act independently, the latter being more the case with larger particles. It is \(\Delta\sigma_{\rm Total}\), the total increase in yield strength; \(\Delta\sigma_{\rm GR}\), the yield strength increase caused by grain refinement; \(\Delta\sigma_{\rm OR}\), the Orowan contribution to yield strength increase; \(\Delta\sigma_{\rm CTE}\), the contribution to yield strength increase due to generation of geometrically necessary dislocations (GND), that are created during cooling due to mismatch of coefficient of thermal expansion (CTE) of particles and metal matrix; \(\Delta\sigma_{\rm Mod}\), the contribution to yield strength increase due to generation of GNDs, that are created during deformation due to different elastic moduli in a deformation process after casting; and \(\Delta\sigma_{\rm Load}\), the contribution to yield strength increase due to the simple presence of a reinforcement particles with higher strength, being well bonded to the surrounding matrix.  
\[\Delta\sigma_{\rm Total}=\Delta\sigma_{\rm GR}+\Delta\sigma_{\rm OR}+\Delta \sigma_{\rm CTE}+\Delta\sigma_{\rm Mod}+\Delta\sigma_{\rm Load} \tag{6}\]\[\Delta\sigma_{\rm Total}=\sqrt{\Delta\sigma_{\rm GR}{}^{2}+\Delta\sigma_{\rm OR}{} ^{2}+\Delta\sigma_{\rm CTE}{}^{2}+\Delta\sigma_{\rm Mod}{}^{2}+\Delta\sigma_{ \rm Load}{}^{2}} \tag{7}\]  
The individual contributions to increasing the yield strength will be discussed in more detail below.
# A New Architectural Approach to Monitoring and Controlling AM Processes
## 5 Case Study: In-Process Melt-Pool Monitoring
### Analyzing Data
#### 5.4.2 Find the Number of Clusters Automatically in the Dataset  
There are two well-known methods to find the appropriate number of clusters automatically: the elbow method and silhouette-analysis method [44]. In this study, we used the elbow method. The elbow method gives us a suitable (k) number of clusters based on the SSD between individual data points and the proposed centroid of the cluster. Algorithm (1) runs several times over the loop by increasing the number clusters and then (2) plots each proposed cluster's score as a function of the number of clusters. Elbow method can be articulated by SSD in the equation below [44].  
\[SSE=\sum_{k=0}^{k}\sum_{x_{i}\in S_{k}}\|X-C\|_{2}^{2}\]  
with k = many clusters formed, Ci = the ith cluster, and x = the data present in each cluster. The elbow method is used to find the value of (k) number of clusters in the given data set.
## 3 Bi-Level Optimal Model of a Distribution Network Comprising a Micro Energy Grid
### Optimal Model of the Distribution Network
#### 3.1.2 Constraint Conditions  
(1) Constraints for the balance of the electrical power  
\[P_{\text{gp1}}(t)+P_{\text{gp2}}(t)+P_{\text{ergrid}}(t)=P_{\text{load}}(t)+P_{ \text{loss}}(t), \tag{3}\]  
where \(P_{\text{load}}(t)\) is the electrical load, and \(P_{\text{ergrid}}(t)\) is the exchanged electrical power between the micro energy grid and the distribution network.  
(2) Constraints for the load flow equations  
\[\left\{\begin{array}{l}P_{i}=U_{i}\sum\limits_{j=1}^{N}U_{j}(G_{ij}\cos \theta_{ij}+B_{ij}\sin\theta_{ij})\\ Q_{i}=U_{i}\sum\limits_{j=1}^{N}U_{j}(G_{ij}\cos\theta_{ij}-B_{ij}\sin\theta_{ ij})\end{array}\right., \tag{4}\]  
where \(P_{i}\) is the injected active power of node \(i\); \(Q_{i}\) is the injected reactive power of node \(i\); \(U_{i}\) and \(U_{j}\) are the voltage magnitudes of nodes \(i\) and \(j\), respectively; \(G_{ij}\) is the conductivity between nodes \(i\) and \(j\); \(B_{ij}\) is the electrical susceptance; and \(\theta_{ij}\) is the phase difference between nodes \(i\) and \(j\).  
(3) Constraints for the electrical power of garbage power  
\[\left\{\begin{array}{l}P_{\text{gp1}}^{\text{min}}\leq P_{\text{gp1}}(t)\leq P _{\text{gp1}}^{\text{max}}\\ P_{\text{gp2}}^{\text{min}}\leq P_{\text{gp2}}(t)\leq P_{\text{gp2}}^{\text{ max}}\end{array}\right., \tag{5}\]  
where \(P_{\text{gp}}^{\text{min}}\) and \(P_{\text{gp}}^{\text{max}}\) are the minimum and maximum electrical powers of garbage power, respectively.  
(4) Constraints for the nodal voltage  
\[U_{i}^{\text{min}}\leq U_{i}(t)\leq U_{i}^{\text{max}}, \tag{6}\]  
where \(U_{i}^{\text{min}}\) and \(U_{i}^{\text{max}}\) are the minimum and the maximum values of nodal voltage, respectively.  
(5) Constraints for the voltage deviation  
According to the GB12325-2008-T allowable deviation of power-quality supply voltage, the voltage deviation was expressed as the following:  
\[\Delta U_{i}(t)=U_{i}(t)-U_{\text{R}},\;U_{i}\leq 0.93U_{\text{R}}\;\text{or}\;U_{i }\geq 1.07U_{\text{R}}. \tag{7}\]