Millimeter Wave Based Real-Time Sag Measurement and Monitoring System of Overhead Transmission Lines in a Smart Grid

Overhead transmission line sag is a crucial parameter that needs to be measured for safe and efficient power transmission. Due to this reason, real time measurement of transmission line sag is necessary in a smart power grid. The ability of smart grid to facilitate real-time monitoring of different power system parameters allows sag measurement and monitoring of overhead transmission lines to be integrated with smart grid system. In this paper, two sag measurement methods based on millimeter wave (mmWave) signals are proposed. The performance of the proposed methods is analyzed and compared for practical 132 kV, 230 kV and 400 kV overhead power transmission lines. The first method uses single transceiver, whereas, the second method uses multiple transceivers for measuring sag. Simulation results demonstrate that the second method shows significantly better accuracy than the first method. The performance of the communication network for establishing sag related information exchange among the devices in the proposed methods is also evaluated in this paper. Moreover, trade-offs between latency and sensitivity with bandwidth, and latency and percentage average error with number of samples are also rigorously investigated.


I. INTRODUCTION
Smart grid a self-monitoring advanced grid that integrates information and communication technologies to improve decision making, as well as enables efficient operation of the power system network. Moreover, it offers reliability, flexibility-through intelligent load management, automated maintenance, coordinated operation, and so on [1], [2]. Furthermore, energy flow pattern in a smart grid is more flexible compared to a traditional grid. The Energy subsystem of a smart grid can be classified into three categories: power generation [3]- [8], transmission grid [9], [10] and distribution grid [11]. Smart grid enables innovative features The associate editor coordinating the review of this manuscript and approving it for publication was Derek Abbott . like advanced monitoring, control, optimization and machine learning to be included to ensure efficient transmission of power from generators to the end users. Communication technologies of a smart grid can be wireless [12]- [22] and wired [23]- [25]. The optimal operation of a smart grid system requires accurate monitoring of power system parameters. One important parameter for safe and effective operation of power system is transmission line sag, measured by the difference in height between the points of support for the transmission line and the lowest point on the conductor [26].
The placement of a transmission between two line supports can create tension on the transmission tower. If this tension crosses its limit, it can cause damage to the tower. To reduce the tension, a sag is intentionally provided in transmission line [27]. However, the sag of a line is not constant over the time. In a power system, when power flows through an overhead transmission line, it heats up the line. As a result, the conductor gets extended, which increases the transmission line sag. Temporal variation of weather parameters also play role in change of sag of transmission line [28], [29]. Real-time monitoring of this variation in transmission line sag is crucial for efficient, safe and uninterrupted power transfer [30]- [32]. For instance, several studies found that the nature of rating of a transmission line is dynamic, so that capacity utilization gain can be increased between 10-30% by monitoring sag and other parameters [29], [30], [33]. Moreover, it is important to ensure a minimum ground clearance for stable and secure grid operation [34]. Increased transmission line sag can increase the chances of faults and in effect, damage the power system infrastructures. These facts necessitate real-time monitoring of the overhead high voltage transmission line sag.
On the other hand, Wireless technology is considered as the major contender for smart grid communications [1], [35]. In this essence, millimeter wave (mmWave) based wireless communication has emerged as an appropriate promising technology for real-time, fast, reliable and accurate monitoring of smart grid [36]. mmWave is the band of frequencies lies in between 30 GHz to 300 GHz. This frequencies can be used for real-time monitoring of different parameters of the system, as it offers availability and bandwidth. Moreover, size of antenna and associated network devices can be greatly reduced by incorporating mmWave in smart grid [37].
In our previous works [38], [39] on mmWave based overhead transmission line sag measurement, preliminary results have been shown on sag calculation accuracy where the impact of distance and shadowing is considered. In this paper, we present a detailed analysis of the mmWave based sag measurement methods for practical systems, under different physical system settings for three phase transmission lines. Moreover, network parameters including latency and sensitivity associated with the proposed methods are also studied rigorously in this paper. The key contributions of this paper are summarized as follows: • Two sag measurement methods based on millimeter wave based transmission are proposed. The first method uses a transmitter and a transceiver and the second method uses an angle of arrival (AoA) sensor in addition to the transmitter and the transceiver for measuring sag of an overhead transmission line.
• Analytical models for calculating transmission line sag are developed for the proposed methods. These models incorporate the channel, device and physical system as well as communication network parameters.
• Performance of the proposed methods is evaluated and compared for practical 132 kV, 230 kV and 400 kV overhead power transmission lines in Bangladesh. In addition to the impact of channel, device and physical system parameters on sag measurement performance, the performance of the communication network in terms of latency and power consumption is also thoroughly investigated.
• The proposed mmWave methods are compared with the existing methods of measuring overhead transmission line sag.
The remainder of the paper is organized as follows. Section II describes the mmWave based sag measurement methods. Section III focuses on the performance evaluation of the methods under different system settings. Section IV demonstrates the performance of the methods from communication network perspectives, followed by a summary of the paper reflected in Section V.

II. mmWAVE BASED SAG MEASUREMENT METHODS
We propose two methods for mmWave based sag measurement. The first method does not require an AoA sensor, whereas the second one utilizes AoA measurement.

A. METHOD 1: NO AOA SENSOR
In this method, a mmWave transmitter is placed at mid-point of transmission line and a transceiver is installed on the top ground wire or the shield in such way that is equidistant from the line support. The transmitter sends a signal using mmWave frequency and the transceiver receives the signal. The received power of the mmWave signal has a direct correlation between the transmitter and the transceiver, and this distance is a function of sag. Based on the sag related information, that is received power at the transceiver, the control center in smart grid computes transmission line sag. For complete sag information, this system needs to be installed at every span of transmission lines. A schematic view of information flow in the system is shown in Fig. 1.  Here, l is the span length between two adjacent towers and s is the sag of the transmission line. In Fig. 2 (b), R represents the distance between the transmitter and the transceiver. The horizontal distance between the ground wire and the transmission VOLUME 8, 2020 line is d. The vertical distance between the mid-point level of ground wire and the transmitter is Here, the distance S 1 can be expressed in the following manner: where, d 1 represents the vertical distance between the tip of ground wire support and the tip of line support, l I denotes the length of insulator and S 2 is the sag of the ground wire. Using this method, sag for all the three lines (phase 1, phase 2 and phase 3) can be calculated. However, in that case, three transmitters are needed to be placed on the lines. Applying Pythagorean Theorem, (2) can be extracted from Fig. 2 (b).
After some algebraic manipulations in (2), sag measurement equation can be obtained as: The transmitter and the transceiver has a pure line of sight (LoS) path in between. This path loss is calculated using 5GCM path loss model designed for urban micro scenario. Equation (4) shows the path loss equation defined in the 5GCM model, where d 3D is the distance between transmitter and transceiver, f c is the carrier frequency f of the transmitted signal and X σ is zero mean Gaussian distributed random variable with standard deviation σ [40].
After determining R based on received power or path loss from (4) and equating R with d 3D , transmission line sag can be determined using (3). This equation clearly indicates that this method is independent of span length, so the method is applicable for longer transmission lines as well.

B. METHOD 2: WITH AOA SENSOR
In this method, a transceiver along with an AoA sensor is placed on the transmission line at the end of the span and a transmitter can be installed at any point on the conductor. The mmWave signal is sent to the transceiver at regular intervals to identify any changes occurring in real-time.
The received power and the AoA of the signal changes with sag of the line. The AoA sensor determines the AoA of the incoming mmWave signal. The transceiver sends received power and AoA information to the control center of the smart grid. Depending on the received power level and AoA, location of the transmitter is determined to calculate the sag. The shape of a transmission line placed in between two transmission towers can be approximated as a parabola, assuming smaller sag compared to the span length of the line [27]. This approximation is considered for sag calculation in this method.   transceiver is y d , (x 1 , y 1 ) is the location of the transceiver and (x 2 , y 2 ) is the location of the transmitter. General equation of a parabola can be written as (5). Where, (h, k) is the vertex and a represents the coefficient.
In this method, the transceiver position (x 1 , y 1 ) is fixed and known but the transmitter position (x 2 , y 2 ) varies with sag. We use 5GCM path loss model according to (4) to calculate d based on the received power. Note that the variation in d will be smaller with small value of sag. However, for larger sag, the transmitter's position will change. Moreover, physical measurement of the sag with good accuracy may not always be possible. Thus, measuring distance from the path loss model can serve as an accurate and automated way for sag calculation.
Once d is determined, location (x 2 , y 2 ) of the transmitter is determined using: After the transmitter position is determined, sag is calculated from (11). As this method does not have any dependency on ground wire and distance between transmitter and transceiver is same for all the three phases of transmission line, impact of different parameters will be same for the lines. On the other hand, impact of different parameters is different for the lines in Method 1.

III. PERFORMANCE ANALYSIS: IMPACT OF SYSTEM PARAMETERS
In this section, we investigate how channel parameters like shadow fading, device parameters like number of samples influence the performance of the proposed methods. We also evaluate the impact of physical system parameters like span length, AoA and horizontal distance on sag measurement accuracy. To study the impact of these parameters, three practical transmission tower geometries are used for 132 kV, 230 kV and 400 kV transmission lines in Bangladesh are considered.

A. IMPACT OF SHADOW FADING
Shadow fading level is an important parameter that influences transmission line sag calculation. In any kind of wireless environment, path loss is subject to shadowing. Thus, calculation error increases with shadowing. In this analysis, we considered a shadow fading of 3.76 dB according to the path loss model in [40]. Then we also investigated how different levels of shadowing influence the sag calculation error. Fig. 6 shows the impact of shadow fading on sag calculation for phase 1 transmission lines in 132 kV, 230 kV and 400 kV systems when Method 1 is used. Similar analysis can be carried out for phase 2 and phase 3 lines as well. Fig. 7   number of samples, sag calculation accuracy increases. At the same time, it requires increased charge storing capacity of the devices. Fig. 8 and Fig. 9    this distance can vary for the three phases of the transmission line, depending on the support. Fig. 10 shows the impact of d on the calculated sag for phase 1 of 230 kV transmission

D. IMPACT OF ANGLE OF ARRIVAL (AoA)
Error in measurement of AoA θ e is an important factor for sag calculation accuracy in Method 2, whereas, Method 1 is free from this kind of error. When sag is small, small error in AoA measurement can amplify the error in the calculated sag. However, with higher value of sag, error decreases. Impact of AoA on the average error for σ = 0 dB and 20 samples is shown in Fig. 12. It is shown that the percentage error in calculated sag decreases with increase in sag and the error is significantly high for high AoA measurement error. For instance, percentage average error is 1.92 % for 132 kV line at AoA error of 0.1 degree, while the error is 9.62 % for the same line at 0.5 degree AoA error. However, error in AoA can be considered close to 0 degree at moderate SNR when multiple antenna elements are considered [41].

E. IMPACT OF SPAN LENGTH
Span length can be different for different sections of transmission lines. Span length of a section can have impact on the accuracy of the calculated sag in Method 2, whereas, Method 1 is free from the impact of span length. For long span length, distance between the transmitter and the transceiver increases slowly with the sag of the line. On the other hand, the distance between the devices increases at relatively higher rate for shorter span length. Due to this reason, percentage of error in calculated sag is relatively lower for transmission line with longer span length. Fig. 13 demonstrates the relation between span length and average sag calculation error for a transmission line considering 20 samples of received power, frequency of 30 GHz and shadow fading standard deviation of 3.76 dB. The transmitter is considered to be placed at 10 m away horizontally from the transceiver.

IV. PERFORMANCE ANALYSIS: NETWORKING PERSPECTIVE
In this section, we evaluate the communication network performance which is critical for sag related information transmission and sag calculation.

A. IMPACT OF FREQUENCY ON TRANSMIT POWER
For extracting the transmitted mmWave signal at the transceiver, a minimum transmit power is required for the transmitter. The minimum transmit power is dependent on the maximum distance that occurs during the variation of sag, receiver sensitivity and frequency. The maximum distance between the transmitter and the transceiver is different for 132kV, 230 kV and 400 kV lines. Fig. 14 shows minimum transmit power requirement for transmitter for variation of distance R between the transmitter and the transceiver for different frequencies f . For this simulation, the transceiver sensitivity is considered −150 dBm. For higher R and f , minimum transmit power requirement is higher.

B. COMMUNICATION FRAMES
For transferring sag related information to the control center, message frames are produced. For Method 1, sag related information is received power level, while, received power level and AoA are the sag related information for Method 2. Received power P r by the transceiver can be expressed as (14), where d i , i = 1, 2 . . . , 7 represents the digit of P r . Similarly, AoA can be expressed by (15), where A i , i = 1, 2. . . ,7 represents the digit of AoA. A 7 digit number and a 6 digit number can be represented by 24 bits and 20 bits, respectively.
Four digits after decimal point is taken for achieving resolution of 0.1 cm. Method 1 includes the digits of received power in the frame. On the other hand, Method 2 contains the digits of received power and AoA. A device identification (ID) number for the transceiver is also added to the frame. The control center has the information for the corresponding devices. Number of bits for device ID k is dependent on the number of transceiver under a control center. After extracting the transmitted information from the frame, sag is calculated using one of the two methods. Fig. 15 shows the frames for conveying sag related information in the two methods. After the communication frames are constructed at the transceiver, it sends the information using mmWave frequencies to the nearby small-cell base station, which supports short range communication. The small-cell base station can then use the core network to forward the message to the control center through the central server. The transmission technique is similar to the one adopted by 5G technologies. Given that this paper mainly focusses on sag calculation methods, further details are not discussed on data transmission as it is not within the scope of this paper.

C. LATENCY AND SENSITIVITY
In this subsection, we evaluate the latency and sensitivity of the sag measurement methods. For transmitting sag related information to the control center, a bandwidth B is allocated to the transceiver. Sensitivity of the receiver is dependent on the bandwidth of the signal. Equation (16) shows the relation of receiver sensitivity with bandwidth [42]. Where, S is the sensitivity of the receiver, NF is noise figure and SNR min is minimum SNR requirement. Sensitivity of a receiver decreases with increase in bandwidth. On the other hand, according to Shannon's capacity shown in (17), bit rate C is proportional to the bandwidth [43]. The latency is based on the frame duration. The transmission time is assumed to be negligible  compared to the frame duration. The latency is calculated using (18), where, L is latency, T b is bit duration, N b is number of bits in a frame and n is number of samples. Fig. 16 and Fig. 17 show the dependency of sensitivity and latency for a message frame in Method 1 and 2, respectively on the bandwidth. In this case, 3 dB SNR and 0 noise figure are considered. Bandwidth of the transmitted signal from the transceiver is varied from 1 kHz to 2 kHz and impact on the receiver sensitivity at the base station and latency per frame is observed. 100 number of segments of transmission line are considered for simulation. For 100 segments, number of transceivers is 100 for 132 kV lines and 200 for 230 kV and 400 kV lines in Method 1. So, value of k is 7 for 132 kV lines and 8 for 230 kV and 400 kV lines in this method. In Method 2, for 100 segments, there are 600 transceivers for all types of transmission lines in this method. So, value of k is 10 for 132 kV, 230 kV and 400 kV lines in this case.
As sensitivity of the receiver decreases and latency per frame increases with bandwidth, a trade-off is required for selecting optimum bandwidth for data transmission. From Fig. 16 and Fig. 17, optimum bandwidths can be found from the trade-off between the latency and sensitivity. In Method 1, optimum bandwidths are 1395 Hz for 132 kV lines and 1436 Hz for 230 kV and 400 kV lines. Sensitivity is −139.6 dBm and latency per frame is 11.11 ms for 132 kV lines. For 230 kV and 400 kV lines, sensitivity and latency per frame are −139.4 dBm and 11.14 ms, respectively in this method. On the other hand, optimum bandwidth is 1471 Hz, for which sensitivity is −139.3 dBm and latency per frame is 18.35 ms in Method 2.
In both methods, percentage error in sag calculation decreases and latency increases with number of samples. So, trade-offs are also required in these cases. Fig. 18 (a) and 18 (b) show the change of percentage error and latency with number of samples for phase 1 of 132 kV lines in Method 1 and for all 132 kV lines in Method 2, respectively. VOLUME 8, 2020

D. TRANSCEIVER TRANSMIT POWER
For a particular frequency transmit power requirement of a transceiver depends on the sensitivity of the receiver and the distance between the transceiver and the receiver. Transmit power requirement increases with increase distance between the transceiver and the receiver. For Method 1, receiver sensitivities are −139.6 dBm for 132 kV lines and −139.4 dBm for 230 kV and 400 kV lines. On the other hand, receiver sensitivity is −139.3 dBm for all lines in Method 2. So, the optimum sensitivities are almost same for all the lines in both methods. Due to this, variation of transceiver transmit power with distance is similar for both methods. Fig. 19 Shows the variation of the transceiver transmit power with the distance between the transceiver and the receiver for 132 kV line in Method 1 at 30 GHz frequency. For calculating path loss, 5GCM path loss model for non-line-of-sight as shown in equation (19) is used [40]. Here, standard deviation of shadow fading is 6.8.
A comparison between the mmWave based methods are shown in Table 1. It is clear that impact of shadowing is significantly lower for Method 2, compared to Method 1.
In the case of number of samples, better accuracy can be achieved with lower number of samples in Method 2. On the other hand, Method 2 faces error due to AoA error. Moreover, optimum bandwidth and frame duration are also relatively higher for Method 2.
A comparison between different techniques of measuring sag is presented in Table 2. The mmWave based methods are simple in operation and provide a very high resolution of 0.1 cm. Moreover, the mmWave based methods also allow real-time monitoring with low latency. However, accuracy of the proposed methods can be affected by natural factors, for instance, wind and ice loading. The environmental factors can also cause inaccuracies in distance calculation using the path loss model. Furthermore, data loss during transmission of sag related information has potential to cause error in sag calculation.

V. CONCLUSIONS
In this paper, two mmWave based overhead transmission line sag measurement methods have been proposed and performance of the proposed methods has been analyzed for practical 132 kV, 230 kV and 400 kV transmission lines. The methods are simple in operation and does not require any complex algorithm for calculation of sag. The methods also offer a very high resolution of 0.1 cm. Impact of different system parameters, namely, number of samples, shadow fading, horizontal distance between the transmitter and the transceiver, AoA error and span length has been thoroughly investigated for practical transmission lines. The effect of shadow fading is significantly lower in the case of Method 2, compared to Method 1. Method 2 allows more accurate sag calculation even with smaller number of samples. On the other hand, Method 2 faces errors in sag calculation due to AoA measurement error, while, Method 1 is free from this type of error. Moreover, the percentage error decreases with increase in span length in Method 2. Performance of the proposed methods from communication network perspective in terms of latency, bandwidth, etc. has also been investigated in this paper. Simulation results have demonstrated that latency per frame and sensitivity of the receiver decrease with bandwidth. Due to this, a trade-off has been obtained between latency and sensitivity to optimize bandwidth for transmission of frames to the control center. In future, the proposed methods will be tested over a network of transmitters and transceivers which will coordinate the sag estimations for a number of transmission line segments.