**2. AC/DC Distribution Network Model**

The AC/DC distribution system generally consists of three main components: an AC distribution network, a DC distribution network, and a voltage source converter (VSC).

The main function of the VSC is to realize the bi-directional flow of active power on the AC side and the DC side, and at the same time to regulate the reactive power. The control mode of the converter mainly includes master-slave control and droop control [15–17]. This paper mainly studies the distribution network DG planning method when the converter adopts master-slave control mode.

To study the AC/DC distribution network trend, we must first establish a VSC model. When the VSC model is obtained, the power flow additional equation of the DC system should be given to consider the different control modes of the converter, so that the power flow of the AC/DC power distribution system can be solved. In the AC/DC distribution network described in this paper, the quasi-steady state model is used to equivalently process the DC part. The model not only effectively reflects the power characteristics of the DC converter, but also accurately and fully meets the actual engineering needs. The specific modeling process is as follow [18].

*2.1. AC Distribution Network Power Flow Model*

$$P\_{jk} = P\_{ij} - \frac{r\_{ij}[(P\_{ij})^2 + (Q\_{ij})^2]}{\left(V\_i\right)^2} - P\_j \tag{1}$$

$$Q\_{jk} = Q\_{ij} - \frac{\varkappa\_{ij}\left[\left(P\_{ij}\right)^2 + \left(Q\_{ij}\right)^2\right]}{\left(V\_l\right)^2} - Q\_j \tag{2}$$

$$\mathbb{E}\left(V\_{\bar{j}}\right)^{2} = \left(V\_{\bar{i}}\right)^{2} - 2\left(r\_{\bar{i}\bar{j}}P\_{\bar{i}\bar{j}} + \mathfrak{x}\_{\bar{i}\bar{j}}Q\_{\bar{i}\bar{j}}\right) + \frac{\left[\left(r\_{\bar{i}\bar{j}}\right)^{2} + \left(\mathfrak{x}\_{\bar{i}\bar{j}}\right)^{2}\right]\left[\left(P\_{\bar{i}\bar{j}}\right)^{2} + \left(Q\_{\bar{i}\bar{j}}\right)^{2}\right]}{\left(V\_{\bar{i}}\right)^{2}}\tag{3}$$

$$P\_{\bar{\jmath}} = P\_{\bar{\jmath},L} - P\_{\bar{\jmath},\mathsf{DG}} \tag{4}$$

$$Q\_{\rm j} = Q\_{\rm j,L} - Q\_{\rm j,DG} \tag{5}$$

$$Q\_{\rm j,DG} = P\_{\rm j,DG} \tan \varphi \tag{6}$$

where *V<sup>i</sup>* and *V<sup>j</sup>* are the voltage amplitudes of node *i* and node *j* respectively; *rij* and *xij* are the branch resistance and reactance between node *i* and node *j*, respectively; *Pij* and *Qij* are the active and reactive power of branch *ij*, respectively; *Pj*,*L*, *Pj*,DG, *Qj*,*L*, and *Qj*,DG are the load active power, DG active power, load reactive power, and DG reactive power at node *j*, respectively. *ϕ* is the power factor angle.
