## 1 Introduction  
As a core feature of smart distribution network (SDN), fast power-supply restoration after faults, which can reduce the adverse impacts of outage and abrupt faults, has important implications for both energy-supply companies and consumers. In recent years, technological advances and wide applications of distributed generators (DGs) provided powerful technical support for self-healing recovery of SDN. The self-healing of SDN with DGs supported is generally treated as a nonlinear combinatorial optimization model with multiple objects and multiple constraints [1; 2; 3; 4; 5; 6; 7; 8; 9]. Existing researches mainly focus on the following issues. (1) Total capacity of recovered loads [1; 2; 3; 4; 5; 6; 7; 8; 9]: As the basic goal of self-healing recovery, de-energized loads must be restored as quickly as possible. (2) Load/consumer priority [2; 3; 4; 5; 6; 9]: In actual distribution networks, priority of different loads is distinguished and the loads/consumers of higher priority shall be recovered preferentially. (3) Number of switching operations [6; 7; 9]: As switching operations are time consuming and have operational cost, the number of switching operations shall be minimized to realize faster recovery and lower cost. (4) Power loss [8; 9]: For economical operation, the smaller the power loss of a self-healing scheme, the better. Good results have been achieved in References [1; 2; 3; 4; 5; 6; 7; 8; 9]. However, existing strategies have two main shortcomings. The first, high-optimization dimension, results in low-optimization efficiency. The second, the effects of power quality issues, which are more serious in islanding and may further threaten the safe operation of islands, are usually neglected. With wide application of power electronic devices and access to various nonlinear loads, a series of power-quality issues, such as harmonic pollution and negative sequence component injection, widely exist. As the capacity of each operating island is smaller compared with normally operated SDN, these issues will be more serious and may affect the safe operation of islands. For synchronous generator-based DG, serious negative sequence currents may result in being out of service [10; 11]. For inverter-interfaced DG (IIDG), serious harmonic or negative sequence components may result in output oscillation or even in becoming out of service [12; 13; 14]. Serious harmonic component can lead to misoperation or could even cause harmonic sensitive load and equipment to stop working [15; 16]. Therefore, power-quality issues may result in power unbalance of island and further lead to recovery failure. Thus, to prevent potential recovery failures caused by power-quality issues, it is necessary to uniformly consider the influences of harmonic and negative sequence components in the analysis of self-healing of SDN. Furthermore, as the injections of harmonic and negative sequence sources are uncertain and fluctuant, it is necessary to employ the uncertainty analysis method to obtain an optimal self-healing scheme in accordance with the distribution network actual operation. In this paper, to realize faster, stronger, and safer recovery, a new self-healing recovery strategy is proposed. To improve optimization efficiency, a decoupled two-step optimization model of load-shedding and network-reconfiguration is established. To enlarge recovery capacity, the droop characteristic of DGs is considered in load-shedding within the permissible change in frequency. To prevent potential recovery failure caused by power-quality issues, a comprehensive set of power-quality restraints, including frequency constraint, uncertain constraints of harmonic, and negative sequence components, is established in the network reconfiguration optimization model. This paper is organized as follows: Section 2 puts forward the framework of the proposed self-healing recovery strategy. Detailed instructions of the load-shedding optimization model are illustrated in Section 3.