## 1 Introduction  
With the shortage of fossil energy and the deterioration of the natural environment, renewable energy sources (RESs) represented by wind power and photovoltaic (PV) have been rapidly developed. With higher distributed energy resources integration, the traditional distribution network is gradually becoming an active distribution network (ADN) and the optimal operation of the distribution network is facing new challenges [1; 2; 3]. Active power optimization and reactive power optimization (RPO) are two important aspects of system optimization. Active power optimization is also called economic dispatch, which often aims to minimize the total day-ahead or real-time operation cost by deciding the output of distributed generations (DGs) and charge-discharge power in the distribution system. RPO is an important measure to ensure safe and economic operation of distribution network, which can regulate the system voltage profile and power flow, as well as reduce the active power losses [4; 5]. The RPO for ADN is often formed as a mixed integer nonlinear programming (MINLP) problem, which should deal with both continuous control variables such as DG output and discrete control variables, such as capacitor banks (CBs) and on-load tap changer (OLTC) [6; 7]. Meanwhile, the RPO problem is essentially nonconvex due to the nonconvex and nonlinear power flow equations, which are difficult to solve. Various methods have been proposed to cope with this problem, which can be divided into two categories: Heuristic algorithms and analytical methods [8]. The heuristic algorithms have attracted much attention because they are relatively easy to implement. A chaotic particle swarm optimization (PSO) was employed in [9] to minimize the system losses using voltages of wind power generator, tap changers, and shunt compensators. [PERSON] et al. [10] proposed a gravitational search algorithm for the reactive power scheduling, with the aim of minimizing the active power losses. A multi-objective reactive power scheduling model was proposed in [11], where the hybrid fuzzy multi-objective evolutionary algorithm was utilized to obtain the Pareto front. A novel cuckoo search algorithm was used in [12] to overcome optimal power flow problems and enhance the operation capacity of hydrothermal power systems. However, the obvious drawbacks of the heuristic algorithm are that they often require long calculation time and it is easy for them to fall into local optimum. Therefore, more researchers focus on the exploration of the analytical methods. Traditional analytical methods include gradient descent, interior point methods, quadratic programming, etc. However, due to the nonconvexity of power flow equations, these traditional methods can only guarantee a local optimal solution [13]. Thus, convex programming methods are more desirable. The second-order cone programming (SOCP) relaxation, which is based on the branch flow model, is a promising convexification method because of its lower computational complexity [14; 15]. The accuracy of SOCP relaxation has been verified in references [16; 17; 18]. Although a great number of methods have been proposed in the literature, they did not take the joint active and reactive power scheduling into consideration. Actually, the R/X ratio of the distribution system is large, the P-Q is not decoupled, and active power scheduling affects the voltage as well. In addition, apart from active power output, the inverter-based DG is allowed to provide reactive power as an ancillary service to further reduce power losses and improve the network voltage level [19; 20; 21]. Therefore, a joint dispatch of active and reactive resources for ADN is highly desired to take full advantage of renewable energies to reduce the operation cost and active power losses, as well as improve the voltage stability. It is worth noting that, with the large-scale wind power and PV access to distribution network, the random and intermittent nature of such resources may have an adverse effect on distribution network [22].