## 5 Conclusions  
This paper tends to solve multi-stage OPF-based problems in PV-rich DN; therefore, the MINLP model is introduced. The concept of the paper comprises two main stages. The first stage is related to overvoltage problems, which occur with high PV integration. An approach to resolving this problem involves the existing voltage control components such as OLTC, without additional investment in new ones. After solving the overvoltage problem, the second stage strives to minimize losses using PV RPC. To preserve the original MINLP problem and not perform any transformation such as convexification and linearization, a co-simulation approach is used to obtain a solution. OLTC can effectively reduce overvoltages caused by PVs, but there is simultaneously a slight increase in energy  
Figure 12: Comparison of voltages at node 336 for all case studies and base case. losses by active power of 1.08% and energy losses by reactive power of 0.91%. The problem of OLTC occurs in unbalanced DN due to OLTC equally performing in all three phases. However, the shortcomings of OLTC can be solved with inverter-based sources such as PVs. PV RPC represents a promising solution for both voltage control and reducing losses. In the second stage, energy losses by active and reactive powers are reduced to 71.82% and 42.91%, respectively. Multi-stage optimization reduces energy losses by active power of 71.01% and energy losses by reactive power of 41.36%. Therefore, the question arises as to why to use OLTC when conditions can be achieved with a PV inverter. When a problem in the network occurs, DSO strives to solve it with its own resources, so OLTC imposes as a logical solution. DSO is not a reactive power producer, so a PV inverter can compensate for the lack of reactive power needed for loss minimization. According to the findings, the proposed model increases the flexibility of DN and represents an alternative control method in ADN. One disadvantage of this optimization model is the assumption that all PV inverters can control reactive power and engage in the optimization process. This assumption may not align with the practical constraints present in the real-world scenario. Also, the development of the communication infrastructure would improve the use of PV inverters. The central controller receives information about network issues and determines the specific inverter that should supply reactive power to address the problem. Lastly, except for technical conditions, future research would include an economic aspect of DN operation to satisfy both DSO and PV owners. Future expansion of this methodology would involve the problem of unbalance in LV DN. Conceptualization, M.D. and M.Z. ; methodology, M.D., M.Z. and K.F. ; formal analysis, M.D., M.Z. and D.T. ; investigation, M.D. ; writing--original draft preparation, M.D.and M.Z. ; writing--review and editing, K.F. and D.T. ; funding acquisition, D.T. All authors have read and agreed to the published version of the manuscript. The APC was funded by Croatian Science Foundation under the project \"Prosumer-rich distribution power network\" (project number: UIP-2020-02-5796). The work of doctoral student [PERSON] has been fully supported/supported in part by the \"Young researchers' career development project--training of doctoral students\" (DOK-2021-02-1257) of the Croatian Science Foundation. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. The authors declare no conflicts of interest. The following abbreviations are used in this manuscript: