# Dynamic Voltage Optimization Based on In-Band Sensors and Machine Learning
## 5 Byproducts and Challenges
### Challenge: Sidelobes  
A major challenge in the deployment of in-band or on-wire sensor systems is the reactive nature of the distribution grid itself. Although some CVR deployments have noted the use of \"reverse path\" communications [36], these same studies and related technical documents have noted difficulties with the channel characteristics. Conventional solutions and products which attempt \"reverse path\" communication are well-known, however only a few attempts have been made at resolving the \"sidelobe problem\" which perturbs and distorts such low-frequency communications. Here, we briefly describe some of the challenges and possible solutions previously described by the authors [37; 39]. The distribution grid interacts with low-frequency communication signals to produce amplitude modulation which is coherent with the power signal itself. Predistortion of the communication signal prior to introduction to the channel has been shown to be effective in combatting these issues [37]. An example of this phenomenon, as well as the coherent predistortion technique, is shown in Figure 2. In Figure 2, the distorted communication signal is shown in the top plot along with the normalized (synchronous) power signal, \(p(t)\). The middle plot shows the synchronously predistorted signal, and the bottom plot shows the in-channel result, where the channel-induced distortion on the communication signal is minimized. Minimizing channel-induced distortion in this case is critical because of the harmonically related images of the modulated spectrum, which can be disastrous for multi-carrier communication schemes. The approach described in [37] estimates a phase-coherent distortion envelope \(q(t)\) from the power signal \(p(t)\) and applies the inverse of this envelope to the communication signal. The envelope is constructed as a linear combination of functions of the fundamental, or  
\[q(t,\boldsymbol{\alpha})=\sum_{j=1}^{N}\alpha_{j}\left[p(t)\right]^{j}, \tag{3}\]  
where coefficients \(\boldsymbol{\alpha}=(\alpha_{1},\ldots,\alpha_{N})^{\top}\) can be computed using any of several well-known techniques. This time-domain approach implicitly models the channel distortion with a very simple sampling technique, and does not require complex feedback loops or phase locking. The utility of this predistortion is displayed clearly in Figure 3 which overlays spectra of the idle channel, the channel with distorted input, and the compensated signal. The figure shows the distribution grid containing a low-rate communication signal with a carrier frequency near 900 Hz. When the pre-distortion scheme is not used, the images or sidelobes of the introduced signal are clearly evident in both figures at 120 Hz harmonic offsets from the carrier (i.e., 900 Hz \(\pm(n\times 120\) Hz). However, when the pre-distortion scheme is used, the images of \(x\) are suppressed significantly. Additionally, the differential distortion between the original communication signal and the pre-distorted signal is less than 0.5 dB. Estimation and inversion of the false message reduces to an optimization problem which depends on a linear combination of basis functions and the set of coefficients \(\boldsymbol{\alpha}\). Several well-known methods exist for optimizing coefficients of this form. Conventional optimization techniques have been explored, including Least Mean Squares (LMS), Recursive Least Squares (RLS), and so on. However, optimization of the coefficients \(\boldsymbol{\alpha}\) for the linear combination structure of the predistortion function \(q(t)\) produce secondary optimization issues. The suppression of image signals in low-frequency, narrowband PLC systems can be important. When optimized and deployed in a system which continuously re-optimizes the structure and outcome of the suppression envelope, the approach described in [37; 39] may yield significant benefits. As noted in [37], the optimal form of the pre-distortion problem is very difficult and the subject of considerable  
Figure 2: Time-domain perspective of synchronous predistortion.