Convex Model for Estimation of Single-Phase Photovoltaic Impact on Existing Voltage Unbalance in Distribution Networks  
[PERSON]  
Department of Electrical Engineering and Automation, Aalto University, Maarintie 8, 02150 Espoo, Finland; [EMAIL_ADDRESS]  
[PERSON]  
The  
Numerous works have been done on assessing VU levels in networks with PVs or any other kind of distributed generation. In [3], authors proposed simple, yet effective methodology for VU assessment. The proposed method does not require load flow calculations and just estimates VU based on negative sequence current contribution of each PV. Different single-phase PV connection strategies were shown and extensive sensitivity analysis was showcased on several sized networks. The model, however, did not represent simulations over a week-long period. A probabilistic modelling of distribution network was demonstrated in [4]. Time series of PV generation and load were analysed and utilized in quasi-sequential Monte Carlo simulation for the further assessment of voltage-level and unbalanced violations. The importance of the cumulative duration of violations was emphasized in the article, since network standards set the violation tolerance on one week basis. Another probabilistic analysis of VU based on the Monte Carlo simulation is presented in [5]. The contribution of several VU sources was utilized to prospect possible VU mitigation possibilities. The impact of network line configuration on VU and power factor of PVs was demonstrated. A VU sensitivity analysis was performed in [6] for different PV sizes and location in case of typical networks in Spain. Probabilistic PV and load models were utilized to assess VU in rural networks. It showcased lower VU levels at urban networks, while rural networks sustain severe VU. To properly evaluate network standard requirements, a recommended PV size was derived based on one-year simulations on 10-minute mean resolution. Randomness of PV installations, such as number of PVs, PV location and others, was modelled with Monte Carlo simulation. An evaluation of VU mitigation by PVs is analyzed in [7]. Mitigation schemes were modelled with probabilistic approach in a Monte Carlo simulation. The study is focused on long-term operation of networks concerning VU mitigation schemes. Calculations are supported by a three-phase load flow algorithm and utilize historical metered data. A comprehensive analysis of PV impact on distribution network and its hosting capacity (HC) was carried out in [8]. The study covered 50,000 real low-voltage distribution networks and considered several limiting constraints, including VU. The hosting capacity was presented in risk-based analysis, where the network HC is represented as a probability value. Thus, it is possible to derive a risk level that a network operator is willing to take. Moreover, traditional Monte Carlo simulations were carried out in [9; 10] to assess VU and its extent to PV hosting capacity. Several works focused on the contribution of many VU sources at customer buses. An extensive analysis was carried out in [11], which divided VU contributors into downstream and upstream (background) sources. The Thevenin approach was utilized to allocate contributors into two parts and then each part was individually split down into sub-units. An aggregation of VU components was studied in [12]. A wide range of VU factors was modelled and their contribution at every distribution network bus was evaluated. Voltage unbalance estimation by Monte Carlo simulation can predict possible VU levels and is useful in determining solar HC of distribution networks. As observed in the articles previously, most of the Monte Carlo simulations have fixed PV output and the exact value of HC remains unresolved. On the other hand, an optimization routine with PV output as a decision variable changes the direction of the VU estimation and permits new possibilities for HC studies. Exact HC value, that would satisfy VU constraint, can be found.