## 1 Introduction  
An electric power distribution network is constructed by distribution substations, distribution feeders, circuit breakers and interconnecting and sectionalizing switches. Historically, the distribution feeders, e.g., 6.6 kV feeders in Japan, have been expanded radially from the distribution substations to supply power to spreading power-consuming areas. The distribution feeders are divided into several load sections by the sectionalizing switches and each of the load sections is connected to multiple other feeders via the interconnecting switches. By closing or opening the switches appropriately, the distribution network can take different radial network topologies with a substation at its center. This is the multi-sectionalized and multi-connected distribution network [1].  
When situations such as power failure in the distribution network arise, the operators flip states of the switches to reform the distribution network from its original radial configuration to another one, which is the distribution network reconfiguration. Finding an appropriate set of the switch states is traditionally formulated as a combinatorial optimization problem and familiar in the electrical power field. The service restoration problem, which is to minimize outage loads in restorative phases [2, 3, 4, 5, 6], is well known as a typical example of a problem of distribution network reconfiguration. In addition, traditional and/or intelligent optimization algorithms have been applied to solve the reconfiguration problems. Dual-gradient methods [7], branch exchange methods [8, 9, 10]and simplex methods [11] are included in the former, while metaheuristics [12; 13; 14; 15] and artificial neural networks [16; 17] are in the latter. However, there is no established solution method for distribution network reconfiguration since distribution networks have a large number of switches.  
The recent growth in the penetration of photovoltaic generation systems (PVs) brings new challenges to distribution network reconfiguration [18; 19]. The output of the PVs strongly depends on weather conditions and cannot be monitored or controlled by the distribution network operators. Moreover, PVs connected to the outage load sections must be normally isolated from the distribution network to prevent their islanding operations [20; 21]. Most of the traditional service restoration problems require accurate information of the load sections, including the status of the PVs, while the PV installation is accompanied by additional uncertainty in the measurement and estimation of the section loads [22; 23; 24; 25]. That is, we cannot remove the uncertainty-originated operational risks of the overload and the voltage limit violation in the determined \"optimal\" restoration configuration. For these reasons, extended problem frameworks of the distribution network reconfiguration, which include applications of stochastic frameworks [26; 27; 28], have been attracting attention.  
This paper presents a problem framework and its solution method that finds the optimal restoration configuration under extensive PV installation. In the problem formulation, the application of robust optimization and two-stage stochastic programming enables us to deal with uncertainty using readily available information only. The robust optimization often gives conservative solutions. To mitigate this, the two-stage stochastic programming is combined with it. A parameter, the confidence coefficient, controls how they are combined. A particular value of this parameter turns the combined method to pure robust optimization. Furthermore, a solution method for the formulated problem is presented. Finally, the validity of the authors' proposal is verified through numerical simulations on a real-scale distribution network model and includes a discussion of their results.