## 6 Conclusions  
In this paper, a new approach based on a regression model was proposed to utilize all the available measurements to improve the DSSE results. The DSSE results have widely been dependent on traditional measurements before the installation of smart measurement devices in ADNs. As part of grid modernization efforts toward an advanced grid, smart measurement devices have progressively been installed to manage and control the dynamic behaviors of ADNs. However, all traditional measurement devices cannot be substituted with advanced ones over a short time, and it is essential to utilize different kinds of measurements using an appropriate method. The method we presented can be used to effectively model distribution systems throughout a grid modernization process. Conventional measurements have low update rates, unlike smart measurement devices, which collect measurements at high frame rates. The difference in frame rates requires interpolation between the traditional measurements to allow for synchronization between the traditional and advanced sensors.  
In this study, the WLS method was initially performed using traditional measurements to calculate the state variables, i.e., the bus voltage magnitudes and phase angles. Then, a network configuration was modified toward a modernized DN by installing smart measurement devices to improve the DSSE results and observability analysis. Since traditional and smart measurements have different sampling rates, the DSSE results using a traditional measurement before smart measurement devices were added to the system, and their data were used to train a machine-learning-based regression approach. This training model was used to predict the traditional measurements when these measurements were not available between their refreshing times after the installation of smart measurement devices.  
The proposed regression method works effectively for DSSE calculations, but it requires the model to be updated regularly in order to be robust in a dynamic environment. In this work, we compared the results of the proposed method to the results obtained when traditional measurements were incorporated into the DSSE calculation using a sample-and-hold technique after smart measurement installation. The effectiveness of the proposed method was validated using two case studies in the presence of DGs.  
The DSSE results given in the paper illustrate that the proposed method is better than the sample-and-hold method after advanced measurement installation. The proposed method could be used in advancing distribution grid modernization to enhance DN performance and capabilities.  
In future work, we aim to focus on other aspects of grid modernization challenges, such as how to identify and correct for False Data Injection Attacks (FDIAs) on PMU or SCADA measurements.  
Figure 6: (**a**) Actual and estimated values of voltage magnitudes at bus 20 for 145 consecutive samples and (**b**) actual value and estimated values for all buses at a given time.  
**Author Contributions:** Conceptualization, S.R. and T.V.; methodology, S.R. and T.V.; software, S.R., T.V. and K.L.; validation, T.V., K.L. and B.M.W.; writing--original draft preparation, S.R.; writing--review and editing, T.V., B.M.W. and H.N.; visualization, S.R.; supervision, B.M.W.; project administration, H.N.; funding acquisition, H.N. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was partially supported by the US National Science Foundation under Award 1806184 and by Montana State University.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.