5.1.1 Background and Motivation

The power transmission line is an important part of the power grid. It is critical for the control center to monitor the status of the transmission line (e.g. the working status of the key components, the voltage and phase of the power, etc.), and its surrounding environment (e.g. the temperature, the humidity, etc) so that necessary actions can be taken in time to prevent disastrous outcomes. However, monitoring the transmission line is not an easy task for a traditional power grid, because of its vast expanse as well as because parts of it are deployed in remote areas, such as deserts and mountains.

The smart grid, which integrates an advanced communication system to the traditional power grid [4, 6–8, 10, 34, 82–84], makes it possible to install and upgrade the monitoring equipment along transmission lines to obtain precise and timely status information. In the construction of power transmission lines, an optical ground wire (OPGW) [85] is usually installed alongside them [86]. Therefore, the monitoring data can be transmitted to the control center almost immediately once the data gets access to OPGW. However, it is not economical to deploy an OPGW gateway at each transmission tower. In practice, the gateways are deployed far away from each other (e.g. every 20 kilometers) [87].

In this chapter, we design a monitoring network for the transmissionline, based on the existing OPGW. The designed monitoring network consists of hundreds of wireless sensor nodes that are deployed on top of selected power line transmission towers. Each wireless sensor is a piece of comprehensive hardware which includes several physical sensors and a wireless transmission module. The physical sensors (e.g. current transformers [88, 89]) are deployed to measure the electric current status (e.g. electric flow, phase status, etc.) and line positions (e.g. sag) [90–92]. The wireless transmission module delivers the monitored data to the control center for further analysis. Wireless technology has been widely adopted in the smart grid. For example, the smart grid in China has been allocated a dedicated spectrum for wireless transmission [93, 94].

Although the transmission line carries electricity, it is too powerful to directly support a wireless sensor node. Therefore, we assume that the wireless sensors are powered by batteries coupled with green energy generation (e.g. solar power or wind turbines). Green energy and energy harvesting techniques have been studied to show their availability to support general wireless sensor networks as well as communication networks in the smart grid [10, 95, 96]. With green energy, the wireless monitoring network can be deployed in a more flexible way. Now that the sensors are powered by green energy, we need to design a proper power supply component (the size of solar panel and the capacity of the battery) for each sensor node so that the deployment and maintenance costs can be budgeted without much waste. Note that the physical sensors are assumed to be powered at a constant rate thus our focus is on the wireless transmission module.

The most imperative requirement of the transmission line monitoring network is timely delivery of data while being energy efficient. To tackle this issue, we propose several centralized schemes to estimate the power consumption of each sensor. Specifically, the first scheme is designed to minimize the total power consumption of all sensors. Due to its complexity, we relax the approach to minimizing the total transmission efficiency while meeting the latency requirement. We also introduce a game theoretical scheme for faster computation and two more schemes with partial fixed variables for practical application to a large network. The results of the centralized schemes are used as benchmarks for network deployment and operational settings. In practical field operations, the gathered/generated monitoring data is not always at its maximum for each sensor, and the frequency of gathering such data is lower than that of the worst‐case scenario considered in the centralized schemes. Moreover, centralized schemes are not applicable in practical operations due to the real‐time transmission of the monitoring network. Therefore, we propose an adaptive distributed power allocation scheme so that real‐time transmission can be achieved while each sensor can be more energy efficient by taking into consideration the dynamic transmitting data. The proposed distributed scheme is guaranteed to be more power efficient since it is bounded by the benchmark settings from the centralized schemes.

5.1.2 Related Work

The cyber‐physical system of the smart grid, which has been studied by many researchers [34, 6, 8, 10, 97] includes data transmission, power management, cybersecurity, etc. Only a few researchers works mention the monitoring network of the power line transmission system. In most cases, the monitoring systems for high‐voltage power transmission lines takes into consideration both electric current and the positions of the transmission lines so that overload, phase unbalance, fluctuation, etc. can be avoided or reduced, and some situations such as sagging and galloping can be tracked by the control center.

Current transformers (CTs) are typically used for current measurement [88, 89]. Some existing devices can directly or indirectly measure the sag of transmission lines. For example, Ren et al. proposed a dynamic line rating system to monitor the line sag under complex climates (e.g. heavy rains, heavy snow, strong wind, etc.) [90]. Huang et al. proposed an on‐line scheme to monitor the icing density and type of the transmission line [92]. Sun et al. proposed a high‐voltage transmission‐line monitoring system based on magnetoresistive sensors [91] that calculate both the current flow and the line positions from the magnetic field of the phase conductors. Although those monitoring systems work properly for a section of transmission lines, they lack a data transmission technology to deliver the measured data to the control center over long distances in a short period of time. Therefore, the control systems of the smart grid, such as updated supervisory control and data acquisition (SCADA) and general network operations center (NOC), are not fully utilized to provide real‐time monitoring and reaction.

Instead of monitoring technologies for a specific component or a section between two towers, our focus is on the long‐distance data delivery of the monitoring network's information to the control center so that the advance control system in the smart grid can take action quickly when necessary. Lin et al. proposed a power transmission line monitoring frame based on a wireless sensor netword [97]. A traditional wireless mesh sensor network was studied due to multiple sensors on each tower. Routing protocols and hybrid medium access control (MAC) were also proposed to increase the energy efficiency of the sensor network. However, a renewable energy source was not considered, and the transmission data rate was not guaranteed by the proposed schemes. Energy efficiency in wireless sensor networks and multiaccess networks has also been widely studied [74–76]. However, traditional approaches generally assume that the data is delay tolerant and the nodes are subject to unrecoverable failures (e.g. a fully discharged battery). Therefore, we cannot apply the power allocation schemes directly from those works. In our work, we propose a utility function that not only targets the energy efficiency of the wireless transmission module but is also adaptive to different link delay and data traffic requirements.

The rest of this chapter is organized as follows. In Section 5.2, we present the transmission line monitoring network model in the future smart grid. In Section 5.3, we propose several centralized power allocation schemes in which the results can be used as a benchmark for the sensor network design. We also propose a distributed scheme based on the benchmark to deal with dynamic traffic loads for practical cases. In Section 5.6, we show the analysis and numerical results for the centralized schemes. We also conduct a case study to demonstrate the performance of the distributed scheme. We conclude the work in Section 5.7.

5.4.1 Minimizing Total Power Usage

Since the sensor nodes in the multihop wireless portion of the monitoring network are powered by green energy, it is important to reduce the power consumption of the sensors to lower the hardware cost. Therefore, the first centralized scheme is designed to minimize the total power consumption of the sensors that upload data to the same gateway (e.g. ). The scheme is shown below.

(5.11)

subject to Eq. (5.5), Eq. (5.9), and Eq. (5.10), .

However, there is no polynomial time algorithm to solve . We then relax some of the constraints. As indicated before, the end‐to‐end delay requirement is very small (e.g. 10 ms), however is relatively large (e.g. 1 s), so the constraint in Eq. (5.9) is implicitly satisfied in general. For the end‐to‐end delay, intuitively, if gets higher, the solution to will be small, since each sensor is able to use less power to transmit and achieve the same delay requirement. Therefore, we relax the constraint shown in Eq. (5.10) to the following equation

(5.12)

Note that is a constant in in the worst‐case scenario. Therefore, Eq. (5.12) is an equation with variables . As discussed before, is an increasing function with respect to , and is also an increasing function with respect to if is given. Therefore, minimizing the total transmission power can be viewed as minimizing the summation of the normalized transmission data rate of each link. We write the relaxed problem into as shown below with constraints.

(5.13)

subject to Eq. (5.12) and

(5.14)

(5.15)

Constraint Eq. (5.14) is rewritten from Eq. (5.9) based on Eq. (5.1). It shows the lower bound of the normalized transmission rate of each link, below which the link would fail to deliver data before the transmission of new incoming data. Constraint Eq. (5.15) shows the upper bound of the normalized transmission rate of each link. The maximum SINR is achieved when . Since the objective is to minimize the summation of , we assume is estimated when for all . Now that is simpler compared with , it is faster to find the optimal solution. The numerical results in the later section will demonstrate that. However, there is still no polynomial algorithm to achieve the optimal solution to . Therefore, if the network size is large, then it will take much more computational time to get the solution.

5.4.2 Maximizing Power Efficiency

In order to quickly converge to a solution, we propose a game theoretical scheme. A noncooperative game is formed as , where is the set of sensors or players, is the strategy set of each player, and is the corresponding utility. In traditional multiaccess wireless networks, the utility function is generally defined as the effective transmission rate over transmission power. However, such modeling does not work for the proposed monitoring network for two reasons. One is that the proposed monitoring network has a much more stringent delay requirement, while the traditional multiaccess wireless network is assumed to be more delay tolerant. The other reason is that the link requirement (e.g. SINR) cannot be simply assumed as uniform or fixed if an optimal (or suboptimal) solution is the goal.

In our proposed game for the monitoring network, two additional requirements must be satisfied for the utility function compared with the traditional one. One is that the maximizer of the utility function must be delay sensitive. Specifically, when is lower, the maximizer should be larger so that the effective transmission rate will be higher to adapt to the lower delay. The other requirement of the utility function is that the maximizer must respond to the dynamic traffic flow. That is to say, when is higher, the maximizer should be larger for a higher effective transmission rate. Therefore, we update the utility function for sensor into the one shown below,

(5.16)

where is a weight factor and is the benchmark link delay, which can be the optimal solution to or .

For each sensor , the goal is to maximize the utility, as shown in .

(5.17)

subject to Eq. (5.5), Eq. (5.9),

(5.18)

Figure 5.4 illustrates the unique maximizer and the impact of dynamic and benchmark on the maximizer. Obviously, when gets higher or gets lower, the maximizer (if one uniquely exists) gets larger, and the corresponding effective transmission rate gets higher. Note that the unit of the utility function is not bit/joule.

Compared with and , the advantage of the proposed game theoretical scheme is that it is capable of finding the solution (the NE) quickly by finding for all and then computing the corresponding power allocation for all by solving a linear equation system. However, the disadvantage of the game theoretical scheme is that it must have the benchmark , which is the optimal solution from a centralized power allocation scheme. Moreover, it must have a carefully chosen weight factor so that the constraint in Eq. (5.18) is satisfied.

5.4.3 Uniform Delay

When the network size is large, it is time consuming to find the optimal solutions to and as benchmarks. Therefore, we further simplify the optimization problems so that a quick solution can be found. First, we assume that the delay for each link is uniform, that is, . Then the SINR for each link can be calculated from Eq. (5.3) and Eq. (5.8) as follows:

(5.20)

Moreover, Eq. (5.2) can be represented as follows:

(5.21)

Therefore, with a given for all , the set of power allocation can be easily calculated by solving a linear equation system where the number of equations and the number of variables are both . Note that the last link is required to have an effective transmission rate of . Compared with the first link, could be several times higher than . However, since the packet from each sensor is small, and is possibly several Kbps only, it is still reasonable for the monitoring network to apply equal delay in each transmission link.

5.4.4 Uniform Transmission Rate

If the data generated by a sensor node increases to some extent, a fixed link delay may no longer be a reasonable assumption. Alternatively, we can fix the transmission rate of each link, that is for all , as follows:

(5.22)

Without loss of generality, assume that , then . From Eq. (5.10) we can get

(5.23)

As stated before, Eq. (5.23) can be relaxed into equality, so that . With and given, can be easily computed and also . Then the corresponding power allocation can be found by solving the linear equation system Eq. (5.21).

5.6.1 Simulation Settings

The studied monitoring network with transmission line model is shown in Figure 5.5. Without loss of generality, we assume that the length of the power line between two neighboring towers is  km. However, the transmission towers are not necessarily installed in a straight line. To be more realistic, we assume that two neighboring towers have an angle of to the east. For simplicity, the elevation of the terrain is not considered in the settings, and the transmission line is assumed to be installed on a flat plain. Additionally, we assume that each is randomly chosen in . Practically, the sensors are deployed on the selected towers instead of all towers. In the simulation setting, we assume that the sensors are mounted at every towers. An example with is illustrated in Figure 5.5. Note that the wireless transmission distance between and is generally shorter than .

Without loss of generality, we assume that the multihop wireless sensor network (i.e. and ) is deployed on the towers with an end‐to‐end power line length of 10 kilometers. The rest of the setting are as follows: for all , we set  bit,  Kbps,  Hz. The end‐to‐end delay threshold  ms, the processing gain , the packet length  bit, the physical layer transmission rate  Mbps, and the transmission frequency  MHz.

5.6.2 Comparison of the Centralized Schemes

Assuming that the sensors operate in the f=230 MHz spectrum, it is practical for them to transmit over several kilometers. Therefore, without loss of generality, we evaluate from 1 to 10 if not otherwise specified. We first compare the results of and with the following settings:

• The towers are deployed with randomly chosen in the simulation setting.
• In each comparison with sensors, we generate 100 random topologies.
• For each generated topology, the power allocations are calculated by both and .
• The computation time is recorded.

The comparison is shown in Figure 5.6. Each result in the figure is an average value of the 100 solutions generated from 100 random topologies (excluding the largest and the smallest results for further accuracy) to the corresponding scheme. At we can see, solving for the optimal solution is much faster than solving . However, even when is a small number (e.g. ), finding the optimal solution is too expensive to be applied for real‐time operation of the monitoring system.

Second, we show the total transmission power for all the sensors with . In order to show the impact on the number of sensors more precisely, we place the transmission towers in a straight line (i.e. ). As shown in Figure 5.7, the relaxed scheme has almost the same power allocation results as scheme .

Third, we set and compare the results from different centralized schemes. Figure 5.8 shows the comparison of the normalized transmission efficiency of each sensor with different centralized schemes. We first calculate the solution to . The solution is then used as the benchmark value for the game theoretical scheme. In the game theoretical scheme, the weight factor is set as for all . As we can see, and have results close to each other, which indicates that the relaxation of remains a good approximation. The game theoretical scheme also has a result close to that of , because it is based on the benchmark setting from . The equal link delay scheme requires linearly increasing transmission efficiency as the link gets closer to the gateway, because the amount of data increases linearly as it is uploaded to the gateway. On the other hand, the equal transmission rate scheme results in a flat transmission efficiency.

Figure 5.9 shows the corresponding SINR for all of the centralized schemes. Note that the last link requires a much higher SINR in the scheme with equal link delay; therefore the last sensor requires a much larger power supply component, which will make the deployment more complicated.

Figure 5.10 shows the delay for each link achieved by the different centralized schemes. In comparison, all the schemes (except for the equal link delay one) have an increasing link delay as the sensors get closer to the gateway, because of the increase in aggregated data. The end‐to‐end delays for all the centralized schemes are the same as . The end‐to‐end delay for the game theoretical scheme is . The game theoretical scheme achieves a slight advantage because of its slightly higher transmission power.

Figure 5.11 shows results of total transmission power achieved by different schemes. Compared to the optimal solution generated by , and game theoretical scheme have close‐to‐optimal results. For practical purpose, the equal transmission rate scheme is recommended over the equal delay scheme, since its results are closer to optimal.

5.6.3 Case Study

In the case study, the transmission line is randomly deployed following the previous setting with sensors. It is then fixed throughout the discussion. At sensor , its monitoring data is assumed to be generated at a random rate , and the gathered data , . We first show the adaptive power allocation for sensor in 20 time slots () to demonstrate its adaptability to the dynamic traffic in Figure 5.12. In Figure 5.13, we show the link delay of link and the corresponding end‐to‐end delay . Note that the end‐to‐end delay is always below the required  ms; therefore, the distributed power allocation scheme is valid for practical operations.