Research on Cooperative Planning of Distributed Generation Access to AC/DC Distribution (Micro) Grids Based on Analytical Target Cascading

Abstract

With the wide application of distributed generation (DG) and the rapid development of alternating current/direct current (AC/DC) hybrid microgrids, the optimal planning of distributed generation connecting to AC/DC distribution networks/microgrids has become an urgent problem to resolve. This paper presents a collaborative planning method for distributed generation access to AC/DC distribution (micro) grids. Based on the grid structure of the AC/DC distribution network, the typical interconnection structure of the AC/DC hybrid microgrid and AC/DC distribution network is designed. The optimal allocation models of distributed power supply for the AC/DC distribution network and microgrid are established based on analytical target cascading. The power interaction between the distribution network and microgrid is used to establish a coupling relationship, and the augmented Lagrangian penalty function is used to solve the collaborative programming problem. The results of distributed power supply allocation are obtained, solving the problem so that distribution generation with different capacity levels is connected to the power grid system in a single form.

1. Introduction

An alternating current-direct current (AC-DC) hybrid microgrid provides an effective way to solve the problems caused by large-scale distributed generation and DC load access, and this microgrid has become the mainstream of distribution network terminal development [1,2,3]. With the large-scale operation of distributed generation, the progress of power electronics technology and the large amount of DC load access, the traditional AC distribution network has been unable to meet the demand for power system development. The DC distribution network has certain advantages in energy transmission and fast control, which can improve system stability and reduce the utilization of power electronic devices such as converters. Therefore, to meet the demand for a high proportion of distributed generation access and a large amount of DC load access, collaborative optimization planning between AC/DC hybrid microgrids and AC/DC distribution networks has become a research hotspot in recent years [4,5,6]. However, research on the interconnection structure, operation control and fast protection of the two hybrid power grids by domestic and foreign scholars is still in the initial stage, and a large number of problems of coordinated planning and control need to be solved urgently.

When an AC/DC hybrid microgrid is interconnected with an AC/DC distribution network, the system has flexible network structure, multiple connection modes and operation modes, which effectively improves the reliability of the AC/DC hybrid distribution (micro) grid system. Faced with the changeable structure and wide application of a hybrid power grid, the design of hybrid distribution (micro) grid topology under different scenarios is the basis and focus of AC/DC distribution (micro) grid research. When high-proportion distributed power is connected to AC/DC hybrid distribution (micro) grid, its access mode and location are uncertain, that is, the power supply can selectively access the micro-grid system or distribution network system according to its voltage level, installed capacity and other characteristics. Therefore, the method and capacity planning of distributed generation connecting to hybrid power grid are also difficulties in current research.

At present, domestic and overseas scholars focus on the AC/DC distribution network for the study of the interconnection structure between microgrids and distribution networks. The grid structure of the AC/DC distribution network is mainly divided into AC and DC parts. The main structure of the AC distribution network is the radiation structure, which is widely used in the current power system, so the structural distinction of the AC/DC distribution network is embodied in the DC part. According to the structure of the DC distribution network, the current mainstream structure of the AC/DC distribution network is radiation, ring structure, and two-terminal power supply (hand-in-hand type). The AC distribution network and DC distribution network are connected by a high-voltage AC/DC converter [7,8]. In the case of an AC/DC hybrid microgrid connected to the AC/DC distribution network, there are interactions between the microgrid and distribution network, AC/DC interactions and so on, which make the structure of the whole system more complex, and this structure will become the development trend of future power systems. This paper presents a typical structure of an AC/DC hybrid microgrid interconnected with an AC/DC distribution network, and this structure is universal, as shown in Figure 1.

As shown in Figure 1, AC and DC distribution networks are interconnected by AC/DC converters. Under this structure, large-scale and centralized distributed generators are connected to AC or DC distribution network systems through converters, which reduces the use of converters and improves the access capacity and generation efficiency of distributed generators [9,10,11]. The microgrid in the system can exist in many forms, mainly depending on the type of load and load demand. For pure AC or DC load systems, AC or DC microgrids can be established to supply power. If AC and DC loads need a power supply at the same time and the load cannot be transferred, it is the most economical choice to construct an AC/DC hybrid microgrid, which can effectively reduce system costs and losses and improve the power supply capacity of the system.

The typical structure of the AC/DC hybrid microgrid is powered by both ends of the AC and DC distribution networks; the DC bus of the hybrid microgrid is interconnected with the DC distribution network, and the AC bus is interconnected with the AC distribution network. Therefore, the structure has many operation modes, including ring network operation, DC distribution network operation, AC distribution network operation, hybrid microgrid islanding operation, AC/DC sub-microgrid islanding operation, and AC/DC sub-microgrid disconnection operation, which greatly improve the reliability and flexibility of hybrid microgrids. When the size of a sub-microgrid in the AC/DC hybrid microgrid is small, it can be disconnected from the corresponding distribution network and supplied by a single distribution network that can meet the stability requirements of the system.

At present, scholars at home and abroad have carried out a great deal of research on DC distribution networks and even AC/DC distribution networks [12,13,14,15,16]. One study presented a mathematical method to determine the minimum required efficiency of power electronic converters in a DC distribution network and concluded that a DC system can only be considered when the minimum required efficiency can be economically achieved [12]. In Reference [13], the economic efficiency of hybrid AC/DC distribution systems was evaluated and compared with conventional AC systems, and the proposed methodology determined the optimal AC/DC distribution substation location and size and AC/DC feeder routing, as well as the length and capacity of AC/DC feeders on both the low-voltage and medium-voltage sides. One paper presented an AC/DC hybrid smart power system, and the DC bus voltage was maintained within an acceptable range by applying power consumption control with the droop characteristic [16].

How to access the distribution network of a DC microgrid or AC/DC hybrid microgrid has been discussed in [17,18,19,20,21,22]. A method of forming a DC network by replacing some AC lines with a DC line is proposed. Compared with the pre-engineered project, the construction of the DC microgrid significantly reduces the transmission cost of the AC/DC hybrid microgrid, and further optimizes the grid loss and voltage stability indicators in [17]. A hybrid planning model of distributed energy and power generation system is proposed, and the type of microgrid is selected according to economic factors [18]. In Reference [19], considering the impact of line investment cost and interaction power cap on the planning results, the capacity and location of distributed power resources are optimized. For the distributed grid technology [20], the topology structure of synchronous AC/DC hybrid microgrid and the basic working principle of microgrid under different operation modes are proposed. Combined with power electronics technology, the modular multi-interface structure of power router is applied. AC-DC hybrid microgrid and proposed control strategy. In the above research results, there are few studies on the distributed generation access optimization planning of AC/DC distribution networks. In the established mathematical model, the interaction between the microgrid and the distribution network was not considered, and how to select the distributed generation access mode in the variable hybrid mode was not analysed.

When researching the optimal planning method of distributed generation access to AC/DC distribution (micro) grids, it is necessary to coordinate the resource requirements of microgrids and distribution networks, so a hierarchical programming model is needed to solve the problem [23,24,25,26,27]. A multi-agent system was introduced to deal with the problem of source-network-load coordination caused by a high proportion of renewable energy access to a distribution network. Optimization models of the distribution network layer, direct coordination layer and indirect coordination layer were constructed, and coordination was carried out among different levels through price leverage [23]. In Reference [24], aiming at the randomness of distributed generation output, a two-level programming model for an active distribution network was designed; this model considered the influence of energy storage access to determine the optimal installation capacity of distributed generation. To solve this problem, this paper establishes two hierarchical distributed generation planning models of AC/DC distribution networks/microgrids, respectively, uses the coupling variables between them to solve iteratively, and obtains the coordinated optimal planning results.

In view of the above problems, this article proposes a collaborative optimization planning method for distributed generation access to AC/DC distribution (micro) grids, realizing the collaborative optimal allocation of distributed generation in microgrids and distribution networks and improving the economy and reliability of hybrid systems. Based on the grid structure of the AC/DC distribution network, this paper designs a typical interconnection structure between the AC/DC hybrid microgrid and the AC/DC distribution network. The optimal allocation models of distributed generation connecting to AC/DC distribution networks and AC/DC hybrid microgrids are established. The analytical target cascading (ATC) method is used to establish the interactive power coupling relationship between the microgrid and distribution network, and the parallel collaborative optimization planning calculation is carried out. Finally, an example is given to verify the accuracy and efficiency of the proposed method and model.

The remainder of this work is organized as follows: Section 2 introduces the optimization planning mathematical model for distributed generation access to AC/DC distributed (micro) grids. Section 3 presents the method for solving the optimization model. Section 4 employs an actual example to analyse the optimal planning results. Section 5 presents the conclusions.

2. Optimization Planning Model for Distributed Generation Access to Alternating Current/Direct Current (AC/DC) Distributed (Micro) Grids

In the AC/DC hybrid distribution (micro) grid system, the AC/DC hybrid microgrid, as a local unit, combines distributed power generation and low-voltage AC/DC load closely to realize the local absorption of renewable energy. When the capacity of the microgrid is excessive or insufficient, the system stability is maintained by power interaction with the distribution network. Therefore, in the planning stage, it is necessary to plan the distributed power supply capacity connected to the distribution network and the microgrid, so as to minimize the cost of the microgrid system. At the same time, the distribution network can satisfy the stable operation of the microgrid and reduce its own operating costs. As different stakeholders, the microgrid and distribution network have different economic indicators, but there is a certain power interaction between them, which has a strong coupling in actual operation. Therefore, the AC/DC hybrid distribution (micro) grid planning model can be established by coupling relationship.

Based on the objective cascade analysis method, this paper studies the cooperative optimization planning of distributed generation access to AC/DC distribution (micro) grids. The optimal allocation models of the distributed generation supply for the AC/DC distribution network and AC/DC hybrid microgrid are established, and then the relationship coupling between the microgrid and distribution network is realized by the interactive power between the two grids. The mathematical model of the specific optimization planning is described below.

2.1. Optimal Model of Distributed Generation Access to AC/DC Distribution Network

Large-scale distributed generations (such as photovoltaic plants, wind farms, and energy storage systems) are connected to the distribution network and have a great impact on the distribution network system. Therefore, the AC/DC distribution network planning is mainly aimed at optimizing the operation cost of access to distributed generations. This paper chooses the operation cost and sale cost of distributed generation as the objective function and considers power balance, power output constraints, tie-line transmission power constraints, etc., to optimize the planning of distributed generation access to the AC/DC distribution network.

(1) Objective function

Aiming at minimizing the cost of operation and maintenance and the cost of purchasing and selling electricity, this paper takes the distributed generation capacity and real-time electricity price of access distribution network as decision variables, and establishes an optimal planning model.

$$\min F_{DS}={\displaystyle \sum _{i=1}^M{\displaystyle \sum _{m=1}^{N_m}{\displaystyle \sum _{t=1}^T{k}_i{p}_{ibt}}}}-{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1}^J\lambda (t)p_j(t)}}$$

(1)

where $F_{DS}$ is the comprehensive cost of the AC/DC distribution system; M is the type of distributed generation connected to the AC/DC distribution network; Nm is the amount of power supply in class m; T is the running time; k_i is the operation and maintenance coefficient of distributed generation in group i; $p_{ibt}$ is the power access capacity; J is the number of microgrids; $\lambda (t)$ is the electricity price at time t; and $p_j(t)$ is the energy interactive power between the distributed network and microgrid at time t; when the distribution network transfers energy to the microgrid, this value is positive, and conversely, this value is negative.

(2) Constraints

For the AC/DC distribution system, the constraints include system energy conservation, power quality and access characteristics of renewable energy.

1) System power balance constraints.

$${\displaystyle \sum _{m=1}^{N_m}{p}_{ibt}}-{\displaystyle \sum _{j=1}^J{p}_j(t)}=P_{load}^{DC\text{-}DN}(t)$$

(2)

where $P_{load}^{DC\text{-}DN}(t)$ is the load value at time t.

2) Tie-line load level constraints

$$P_{\min }^L\le P_j^L(t)\le P_{\max }^L$$

(3)

where $P_{\min }^L$ and $P_{\max }^L$ are the upper and lower limits of the tie-line load level and $P_j^L(t)$ is the tie-line flow power at time t.

3) Distributed generation output constraints

The distributed generation in distribution network system is centralized power station, such as photovoltaic power station, wind farm, etc. Therefore, the constraints on the distribution network layer are centralized.

Photovoltaic power plants output constraints:

$$P_{PV}{(t)}_{\min }\le P_{PV}(t)\le P_{PV}{(t)}_{\max }$$

(4)

Wind-turbine output constraints:

$$P_{Wi}^{\min }\le P_{Wit}\le P_{Wi}^{\max }$$

(5)

where $P_{PV}(t)$ is the output of photovoltaic power plants at time t; $P_{Wit}$ is the wind turbine output at time t; $P_{PV}{(t)}_{\min }$ and $P_{PV}{(t)}_{\max }$ are minimum and maximum output of photovoltaic power station; $P_{Wi}^{\min }$ and $P_{Wi}^{\max }$ are minimum and maximum output of wind farm.

4) Distributed generation capacity constraints for access to distribution network

When the distributed generation is connected to the AC/DC distribution network in the form of a large-scale and high-capacity connection, its installed capacity and voltage level also meet certain requirements. Distributed power sources such as photovoltaic power plants and wind farms connected to distribution networks need to meet certain upper and lower capacity limits. Distributed generation with limited capacity is allowed to access the distribution network, otherwise they can only access the micro-grid level or abandon the power supply.

$$P_{DN\text{-}\min }\le P_{DG}\le P_{DN\text{-}\max }$$

(6)

where $P_{DG}$ is the distributed generation capacity for planned access to the power grid; $P_{DN\text{-}\min }$ and $P_{DN\text{-}\max }$ are the upper and lower limits of distributed generation capacity allowing access to the distribution network.

2.2. Optimal Model of Distributed Generation Access to AC/DC Hybrid Microgrid

For an AC/DC distribution network system, a microgrid has more flexibility when it is connected to a distribution network, and there is more choice of access mode and location. In the AC/DC distribution network, a DC-dominated AC/DC hybrid microgrid or DC microgrid can be connected to the DC distribution network; an AC microgrid or AC-dominated AC/DC hybrid microgrid can be connected to the AC distribution network. Aiming to minimize the investment cost, operation cost and purchase and sale costs of microgrids, this paper establishes an optimal configuration model of distributed generation at the level of microgrids, taking into account the constraints of microgrid system power balance, output of distributed generation, battery charge and discharge, and access capacity of distributed generation.

(1) Objective function

In the objective function of the microgrid level, this paper takes into account the economic index of distributed generation in microgrid system. Distributed generation cost per unit of electricity and electricity price at different times will have a greater impact on the planning results and play a decisive role.

$$\min F_{HMG}={\displaystyle \sum _{i=1}^K(F_{ins}^i+F_{op}^i+F_{buy}^i)}$$

(7)

where $F_{ins}^i$ is the microgrid investment cost in group i; $F_{op}^i$ is the microgrid operation cost in group i; $F_{buy}^i$ is the microgrid costs of purchasing and selling electricity from the distribution network in group i; and K is the number of microgrids.

The expression of each cost is shown in formulae (8)–(10).

$$F_{ins}={\displaystyle \sum _{z=1}^Z{N}_z{C}_{DGz}\frac{\delta {(1+\delta )}^{Y_z}}{{(1+\delta )}^{Y_z}-1}}+{\displaystyle \sum _{i=1}^K{C}_{con}}\frac{r{(1+r)}^n}{{(1+r)}^n-1}$$

(8)

where $F_{ins}$ is the microgrid investment cost; M is the new distributed generation types; $N_z$ is the number of installations of distributed generation in group m; $C_{\mathit{DG}z}$ is the purchasing cost of distributed generation in group m; $Y_m$ is the lifetime of distributed generation in group m; $\delta$ is the discount rate, taken as 10%; K is the number of installed converters; $C_{con}$ is the purchase cost of converters; and r is the discount rate, taken as 10%.

$$F_{op}={\displaystyle \sum _{m=1}^M{\mathsf{\Omega }}_m{E}_{\mathit{DGm}}}+\phi P_{\mathit{con}}$$

(9)

where $F_{op}$ is the microgrid operation cost; ${\mathsf{\Omega }}_m$ is the distributed generation consumption unit operation and maintenance costs in group m; $E_{DGm}$ is the total annual power generation of distributed generation in group m; $\phi$ is the unit power converter operation and maintenance costs; and $P_{\mathit{con}}$ is the total power of the installation converter.

$$F_{buy}={\displaystyle \sum _{t=1}^T{(-1)}^n{k}_t{P}_{gridt}}$$

(10)

where $F_{buy}$ is the microgrid costs of purchasing and selling electricity from the distribution network; n is constant; when the microgrids purchase electricity from the distribution network, n = 0, and when the microgrids transmit power to the distribution network, n = 1. $k_t$ is the electricity price at time t, and $P_{gridt}$ is the interactive power between the microgrid and the distribution network at time t.

(2) Constraints

The optimal optimization of an AC/DC hybrid microgrid connected to a distribution network needs to meet the system power balance constraints, distributed generation output constraints and battery charge and discharge constraints.

1) System power balance constraints [19]

$$P_{\mathrm{load}}+P_{\mathrm{loss}}=P_{\mathrm{wind}}+P_{\mathrm{pv}}+P_{\mathrm{bat}}+P_{\mathrm{grid}}$$

(11)

where $P_{\mathrm{load}}$ is the system load power consumption, $P_{\mathrm{loss}}$ is the system loss, $P_{\mathrm{wind}}$ is the wind power, $P_{\mathrm{pv}}$ is the Photovoltaic (PV) power, $P_{\mathrm{bat}}$ is the energy storage battery power (if the energy storage battery stores energy, then the value is negative), and $P_{\mathrm{grid}}$ is the interactive power between AC/DC hybrid microgrid systems and the distribution networks (if the grid transmits energy to the microgrid system, then the value is positive, whereas if the microgrid system sends energy to the distribution network, then the value is negative).

2) Distributed generation output power constraints

In AC/DC hybrid microgrid, different types of distributed generation need to be connected to the system in order to meet the load demand. The uncertainties of distributed generation output will affect the system, so the power output should be constrained.

Photovoltaic and wind output power constraints:

$$\{\begin{array}{l}0\le P_{\mathrm{wind}}\le P_{\mathrm{wind}.\max }\\ 0\le P_{\mathrm{pv}}\le P_{\mathrm{pv}.\max }\end{array}$$

(12)

where $P_{\mathrm{wind}}$ is the output power of wind; $P_{\mathrm{pv}}$ is the output power of photovoltaic panels; $P_{\mathrm{pv}.\max }$ is the maximum output power of photovoltaic and $P_{\mathrm{wind}.\max }$ is the maximum output power of wind.

3) Battery charge and discharge constraints

$$\{\begin{array}{l}SO{C}_{\min }\le SOC\le SO{C}_{\max }\\ 0\le P_{\mathrm{char}.\mathrm{bat}}(t)\le P_{\mathrm{char}.\max }\\ 0\le P_{\mathrm{dischar}.\mathrm{bat}}(t)\le P_{\mathrm{dischar}.\max }\\ SO{C}_{\mathsf{\Delta }t}=SO{C}_t+{\eta }_C{P}_{\mathrm{char}\text{-}\mathrm{bat}}\Delta t/R_{\mathrm{bat}}-P_{\mathrm{dischar}\text{-}\mathrm{bat}}\Delta t/{\eta }_D{R}_{\mathrm{bat}}\end{array}$$

(13)

where $SO{C}_{\min }$ and $SO{C}_{\max }$ are the lower and upper limits of the state of charge, respectively; $P_{\mathrm{char}.\mathrm{bat}}(t)$ and $P_{\mathrm{dischar}.\mathrm{bat}}(t)$ are the charging and discharging power of the energy storage device at time t; $P_{\mathrm{dischar}.\max }$ and $P_{\mathrm{char}.\max }$ are the maximum discharging and charging power of the energy storage device, respectively; ${\eta }_C$ is the energy conversion efficiency in energy storage charging; ${\eta }_D$ is the energy conversion efficiency in energy storage discharging; $R_{\mathrm{bat}}$ is the energy storage capacity; and $\Delta t$ is the time step.

4) Distributed generation capacity constraints for accessing microgrid

The installed capacity of distributed generation connected to the microgrid is also limited and needs to meet a certain capacity range. If the installed capacity is too large and exceeds the overload capacity of the microgrid line, the distributed generation needs to be connected to the distribution network. If the capacity of distributed generation is too small, it is not appropriate to control the voltage level, which will affect the stability of the power grid; therefore, this kind of distributed generation should be centralized or abandoned. The specific threshold is shown below.

$$P_{MG\text{-}\min }\le P_{DG}<P_{MG\text{-}\max }$$

(14)

where $P_{DG}$ is the capacity of the distributed generation accessing to the microgrid; $P_{MG\text{-}\min }$ and $P_{MG\text{-}\max }$ are the upper and lower limits of distributed generation capacity allowing access to the microgrid.

3. Mathematical Model Solution of Analytical Target Cascading (ATC) Method

3.1. Analytical Target Cascading

First proposed by Professor Kim, ATC has become a part of multidisciplinary optimization design methods [28]. Its main principle is to use parallel structures to realize the design of complex programs and to solve them synchronously. When using the ATC method to optimize the calculation, ATC decomposes the system into several levels and solves the objectives of each level separately, which greatly reduces the calculation time of the system. Second, each hierarchical function receives the element values from its superior function and then optimizes the objective of the function. At this point, multiple solving processes can be computed in parallel, which effectively improves the efficiency of the system.

ATC is classified according to the object, target or module and other aspects to be solved. Mathematical models are established according to the different functions of different levels. The hierarchical structure of ATC is shown in Figure 2. The set of elements at each level contains all the elements at that level; at the same time, a set at higher levels contains all the factors at its sub-levels, such as the factors in C_j are included in C.

ATC is a modular and hierarchical optimization algorithm. Each level is composed of optimization design module P and analysis calculation module Q, as shown in Figure 3. The main purpose of the optimization design module P is to optimize the objective function, while the main purpose of the analysis calculation module Q is to calculate the elements. The information allocated at the above level is used as input, and the output information of the Q module is transmitted to the P module. The main idea of ATC is to distribute optimization objectives at different levels and then provide information as feedback from each sub-level system to the upper level, alternately optimizing until convergence is achieved.

By describing the mathematic model of coordinated planning of AC/DC distribution (micro) grids with distributed generators, it can be seen that the optimal planning of distributed generators for AC/DC hybrid microgrids and AC/DC distribution networks can be solved independently. In addition, for the whole power system, the power interaction between the distribution network and microgrid is realized through the connection line, so there must be a certain coupling relationship between them. We can use this coupling variable to obtain the optimal result of the system objective by optimizing the algorithm. The main idea of the ATC method is consistent with the cooperative optimization planning model of AC/DC distribution (micro) grids connected by distributed generators. Therefore, the mathematical model of cooperative optimization can be solved by the ATC method, and the optimal planning of distributed generators in a distribution network/microgrid system can be obtained.

3.2. Solving Process

When using the ATC method to optimize AC/DC distribution (micro) grid planning, the system should be divided into two levels, the microgrid and distribution network, and the coupling relationship between the two levels should be established as the connecting factor between the upper and lower levels. From Section 2.1 of this paper, we can see that there is a coupling relationship between the microgrid and the distribution network, that is, the power interaction between the microgrid and the distribution network; therefore, this element is regarded as the transfer variable of the system.

For the AC/DC distribution network, the coupling variable $P_{DM}$ can be attributed to the load connected to the distribution network and can interact with the distribution network to achieve energy interaction; conversely, for the AC/DC hybrid microgrid, the coupling variable $P_{MD}$ is equivalent to a power source. When the distribution network planning is solved independently, an optimization result can be obtained that is a quantitative value for the coupling variable $P_{DM}$. At this point, the fixed value should be transferred to the microgrid level as a parameter of microgrid optimization planning. Then, when optimizing the configuration of the AC/DC hybrid microgrid, the coordination between $P_{DM}$ and $P_{MD}$ should be considered at the same time. The goal is to obtain values of the two coupling variables that are approximately equal.

There are many methods to constrain coupling variables. Penalty function methods are mainly used today, including the quadratic penalty function form, Lagrange form [29], augmented Lagrange form [30], second-order diagonal form [31] and Lagrange dual form [32]. The augmented Lagrange penalty function has high accuracy and can achieve fast convergence. Therefore, the objective function of the AC/DC hybrid microgrid in this paper is adjusted as follows:

$$\min F_{HMG}+{\displaystyle \sum _{t=1}^T{\pi }_j(t)[P_{MD}(t)-\overline{P_{DMj}(t)}]}+{\displaystyle \sum _{t=1}^T{\lambda }_j(t){[P_{MD}(t)-\overline{P_{DMj}(t)}]}^2}$$

(15)

where ${\pi }_j(t)$ and ${\lambda }_j(t)$ are the corresponding weight coefficients of Lagrange’s first and second terms at time t, respectively; $P_{MD}(t)$ is the power transferred from microgrid to distribution network at time t; $\overline{P_{DMj}(t)}$ is the interactive power transferred from microgrid to distribution network by level j function.

Similarly, for the AC/DC distribution network, when K microgrids are connected, the objective function of the distribution network needs to introduce K penalty functions, whose expression is revised as follows:

$$\min F_{DS}+{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1}^K{\pi }_j(t)[P_{DM}(t)-\overline{P_{MDj}(t)}]}}+{\displaystyle \sum _{t=1}^T{\displaystyle \sum _{j=1}^K{\lambda }_j(t){[P_{DM}(t)-\overline{P_{MDj}(t)}]}^2}}$$

(16)

where $P_{DM}(t)$ is the power transferred from distribution network to microgrid at time t; $\overline{P_{MDj}(t)}$ is the interactive power transferred from distribution network to microgrid by level j function.

Therefore, for the collaborative planning model of the AC/DC hybrid microgrid/distribution network based on the ATC method, the optimal planning model of the AC/DC distribution network is composed of formula (16) and formulae (2)–(6), and the optimal allocation model of the AC/DC hybrid microgrid is composed of formula (15) and formulae (11)–(14). To solve the above model, iteration is alternately carried out until the convergence condition is reached, which is shown in formula (17).

$$\left|P_{DM}^k(t)-P_{MD}^k(t)\right|\le \epsilon$$

(17)

where $P_{DM}^k(t)$ is the power transferred from distribution network to microgrid in group k at time t; $P_{MD}^k(t)$ is the power transferred from microgrid to distribution network in group k at time t.

The flow chart of collaborative planning for distributed power supply access to the AC/DC distribution (micro) power grid based on the ATC method is shown in Figure 4, and the specific solution process is as follows:

(1) Count the system raw data, set coupling variables between the microgrid and distribution network and the initial value of the Lagrange multiplier, and set iteration number k = 1.

(2) Build the mathematical model of optimal planning for the AC/DC hybrid microgrid, solve the optimized model, and transfer the virtual power $P_{DM}$ to the DC distribution network.

(3) Optimize the planning of the distribution network according to the improved objective function and constraints after receiving the data transmitted by the hybrid microgrid, optimize the model itself while transferring values near the AC/DC hybrid microgrid level, and transfer the result of PDC to the microgrid.

(4) Check whether the convergence condition meets the requirement. If it is satisfied, stop the iteration process, obtain the optimal planning results, and output them to the outside; otherwise, increase the iteration number k, update the Lagrange multiplier, and return to step (2) for re-solving.

4. Example Verification and Discussion

4.1. Example System Description

Based on the aforementioned collaborative planning model of distributed generation access to AC/DC distribution (micro) grids, this paper takes the actual AC/DC distribution grid system in a certain area as an example and carries out the optimization analysis of distributed generation access to the AC/DC hybrid microgrid/distribution network according to the load demand, power distribution, and other factors. The basic architecture of the example system is shown in Figure 5. For each level of the power grid in the example system, the AC microgrid is the original structure of the system and needs to be expanded according to the load demand; because the system adds many DC loads, it needs to build a new AC-DC hybrid microgrid system to meet the load demand. For the microgrid system, the accessible distributed generation includes distributed PV, wind and small-scale energy storage systems; for the distribution network system, the accessible distributed generation includes centralized photovoltaic power stations and large-scale energy storage systems.

Figure 5 shows that the DC distribution network of the system is connected to a photovoltaic power station, energy storage system and AC/DC hybrid microgrid, and the AC distribution network provides power to AC loads and the AC microgrid at the same time. The new load of the system is mainly concentrated in the DC system, including a 1 MW high-voltage DC load, 400 kW low-voltage DC load and 450 kW AC load. Therefore, for the distribution network level, it is necessary to optimize the capacity optimization of PV power plants and energy storage systems, taking into account the AC load demand. For the AC/DC hybrid microgrid level, two microgrids are connected to the system, and the distributed generation in the microgrid should be optimized separately. In this paper, the upper limit of interactive power between the microgrid and distribution network is set at 500 kW. The distributed generation parameters [33], annual load curve and hourly tariff data [34] are shown in

Table 1. Distributed energy parameters.

Project	Single Machine Capacity	Installation Cost	Operational Management Coefficient	Service Life
PV	1 kW	1416.3 $/kW	0.0096	20 years
Battery	24 kWh	149.1 $/(kWh)	0.009	10 years
Wind	10 kW	1341.7 $/kW	0.0296	20 years

, Figure 6 and

Table 2. Time-of-day tariff data.

Time Interval	Electricity Purchase Price ($/kWh)	DG type	Electricity Sale Price ($/kWh)
Rush hours (19:00–21:00)	1.05	PV power station	0.45
Peak hours (8:00–11:00, 13:00–19:00, 21:00–22:00)	0.87	Household PV	0.43
Low hours (11:00–13:00, 22:00–Next day 8:00)	0.39	Wind farm	0.54

, respectively.

On the basis of the abovementioned example system, this paper carries out research on collaborative planning of distributed generation access to AC/DC distribution (micro) grids based on the ATC method. The program is built on the platform of MATLAB. It runs under Intel i5 3.4-GHz, 8 GB RAM, Windows 7 system and calls the function of MATLAB to solve the model.

4.2. Analysis of Optimal Configuration Results

The coupling variables between the AC/DC hybrid microgrid and the distribution network are updated alternately by the ATC method. After convergence, the optimal planning results of distributed generation are obtained, as shown in

Table 3. Configuration results of microgrid and distribution network DG collaborative planning.

	DG Type	PV Capacity	Wind Power Capacity	Battery Capacity
Power Grid Type
DC distributed network		1.2 MW	—	0.6 MWh
AC distributed network		0.5 MW	—	—
AC microgrid		450 kW	40 kW	25 kW
AC/DC hybrid microgrid		680 kW	12 kW	45 kW

.

This table shows that the capacity of the PV power station accessing the DC distribution network is larger than that of the AC distribution network, and a certain capacity of the energy storage device is installed on the side of the DC distribution network. The output power of photovoltaics is DC, and this power can be connected to a DC distribution network through a DC-DC converter, which has certain advantages in cost. The main purpose of the photovoltaic power station connected to the AC distribution network is to match the AC load and realize local absorption as much as possible. For energy storage devices, the current distribution network is mainly AC, while the DC grid is slightly weak; therefore, the charging and discharging of energy storage is connected to the DC distribution network to reduce the power supply on the DC side and the system loss. For the AC distribution network, when the PV power station generates more power than the AC side consumes electricity, it sells electricity at any time; in contrast, the AC distribution network directly supplies electricity and reduces the system cost by reducing the energy storage configuration.

For the microgrid system, the regional distribution network is connected to two microgrids, namely, an AC/DC hybrid microgrid and AC microgrid. Both microgrids are equipped with a certain amount of PV, wind and energy storage. Because of the weak wind resources in this area, the amount of wind access is small. For the PV power supply, the AC/DC hybrid microgrid not only supplies power to DC loads but also to some AC loads, which can increase the installed capacity and improve the system absorption capacity. The energy storage device can realize the storage of electric power and the island operation of the microgrid.

After the optimal planning of AC/DC hybrid distribution (micro) power grid, the whole system meets the stability requirements of the system. The variation of voltage amplitude of the main nodes is shown in Figure 7.

Figure 7 shows that the voltage amplitude of each node changes within the normal range, and the system remains stable. Voltage amplitude value is stable in the range of 0.98–1.0, and the voltage amplitude value of some nodes is 0.97, which is the permissible range of the system. Therefore, the stability of AC/DC distribution (micro) grid after optimization planning meets the requirements.

At present, energy storage is a contradictory factor in microgrid planning because of its high cost and short service life, and its assembly capacity needs to be limited economically. However, the uncertainty of the output of distributed generation inevitably requires the operation of a certain capacity of energy storage to maintain the stability and improve the level of local absorption. By changing the installation cost and service life of energy storage system, the impact of energy storage on the optimal planning results of AC/DC hybrid distribution (micro) power grid is analyzed, as shown in

Table 4. Effect of energy storage factor on optimal configuration results.

NO.	Battery Parameters		AC Microgrid		AC/DC Hybrid Microgrid		PV Rejection Rate
	Installation Cost	Service Life	PV Capacity	ES Capacity	PV Capacity	ES Capacity
1	149.1 $/(kWh)	10 Years	450 kW	25 kW	680 kW	45 kW	0.2156
2	120 $/(kWh)	10 Years	480 kW	36 kW	760 kW	52 kW	0.2079
3	149.1 $/(kWh)	20 Years	475 kW	36 kW	755 kW	48 kW	0.2102
4	120 $/(kWh)	20 Years	505 kW	40 kW	890 kW	56 kW	0.1862

. The concept of PV rejection rate is introduced in the table, which means the ratio of abandoned photovoltaic energy to total photovoltaic power generation throughout the year.

It can be seen from the table that when the installation cost of energy storage is reduced or the service life is increased, the distributed power supply capacity accessed to the microgrid side increases, and the storage capacity increases accordingly. At this time, the penetration of distributed generation increases, and the PV rejection rate decreases significantly.

4.3. Comparisons of Algorithms in Advantages and Disadvantages

In this chapter, the ATC method is used to model and solve the AC/DC hybrid microgrid and AC/DC distribution network, respectively. The parallel computation of distributed generation optimal allocation is realized, which has significant advantages in the efficiency and stability of optimal planning. This paper discusses the advantages and disadvantages of the ATC method by comparing the ATC method with a traditional independent optimization method for microgrids and distribution networks.

As shown in

Table 5. Analysis of advantages and disadvantages between the ATC and distributed methods.

Contrasting Items		Microgrid Number K
		2	4	6
Computing Time/s	ATC	3.8	4.7	5.2
	Distributed	3.1	8.9	12.5
Total Costs/$	ATC	33,010.44	42,752.93	52,674.64
	Distributed	34,588.67	43,262.41	56,512.03

, by changing the number of access microgrids, the independent optimization and ATC methods are used for planning, and the advantages and disadvantages of these two methods are analysed and compared.

Table 5 shows that when the number of microgrids is small, distributed planning has a small advantage in computing time. However, when the number of microgrids increases gradually, the computing time of ATC increases slowly, while that of the distributed method increases greatly. Therefore, the ATC method has higher superiority in dealing with complex systems of multi-microgrids.

Additionally, this paper compares the ATC method with the distributed and bi-level programming methods and discusses the effectiveness of the ATC method in terms of the number of iterations. The analysis and comparison results are shown in Figure 8.

Figure 8 shows that the optimization performance of the distributed algorithm and bi-level programming algorithm is similar, and these algorithms converge prematurely after approximately 9 iterations and fall into a local optimum. Compared with the two methods mentioned above, the ATC method has strong climbing ability, and the convergence curve decreases quickly in the early stage of iteration, falls into a local optimum after approximately 2 iterations, jumps out of local optima after 5 iterations and 17 iterations, and continues to search iteratively. The final optimization result reduces the cost compared with that of the other two methods. In conclusion, the ATC method can balance the global and local search performance well and has obvious advantages in solving the co-optimization planning problem of AC/DC hybrid microgrids and AC/DC distribution networks.

At present, there are many researches on the interconnection between microgrid and distribution network, but most of them focus on an AC system. In this paper, the target cascade analysis method is used to study an AC/DC hybrid distribution (micro) power grid, which has certain advantages in model and algorithm. This paper chooses literature [35] as a comparison to analyse the advancement of the method proposed in this paper. The comparison results are shown in

Table 6. Comparative analysis with other literature.

TitleType	Simulation time/s
	One Microgrid	Two Microgrids	Three Microgrids
Reference	2.7	8.6	17.2
This paper	3.2	3.8	4.2

.

From the table, we can see that ATC method does not dominate when the number of microgrids is small, but when the number of microgrids connected to the distribution network is increasing, the calculation time of the method used in this paper is greatly reduced, and the advantage is obvious.

4.4. Analysis of Coupled Element Impact

The AC/DC hybrid microgrid and AC/DC distribution network are coupled by interactive power, and the ATC method also achieves parallel calculation of two-part planning by interactive power. Therefore, the size of the interactive power has a great impact on the planning results. Table 5 lists the cost calculation results for distribution networks and microgrids under different interactive power ratios. The interactive power ratio represents the percentage of the interactive power upper limit set to the initial value.

Table 7. Cost calculation results under different interactive power ratios.

Interactive Power Ratio	20%	40%	60%	80%	100%
DC distributed network cost/$	12,301.79	12,381.56	12,493.98	12,547.81	12,672.31
AC distributed network cost/$	10,490.08	10,531.23	10,594.6	10,639.18	10,657.52
AC microgrid cost/$	4021.674	3858.261	3623.279	3944.888	4286.923
AC/DC hybrid microgrid cost/$	7202.723	7122.06	6918.091	7340.64	7509.72
Total cost/$	34,016.27	33,893.11	33,629.95	34,472.52	35,126.47

shows that: (1) When the upper limit of interactive power increases, the costs of DC and AC distribution networks increase slowly. Because the increase in interactive power has little influence on the distributed generation connected to the AC/DC distribution network, the main responsibility of this power is to supply the load directly connected to the distribution network, and the distribution network hierarchy is less affected by the interactive power. (2) For the AC microgrid and AC/DC hybrid microgrid, the cost decreases first and then increases with increasing upper limit. When the interactive power value is small, the microgrid needs to rely on its own distributed power generation to meet the load demand, so the stability of the system can be achieved by increasing the cost of power supply; when the interactive power value is large, more energy interaction can be achieved between the microgrid and the distribution network, so the microgrid will invest a large number of distributed generators to generate electricity and gain benefits by selling electricity to the grid, and the cost of the microgrid will increase accordingly. (3) As far as the total cost of the system is concerned, the cost of the microgrid reaches the minimum when the ratio of interactive power is 60%. At this time, the total cost is the lowest and the system is the best. When the upper limit of power interaction is in the middle value, the power allocation of microgrid is low, and it is likely to meet the local absorption; at the same time, the power interaction with the distribution network is small, and the cost of power purchase is greatly reduced. At the same time, for the distribution network, there is no need to configure a large number of power sources to meet the needs of the micro-grid, which also reduces the cost of the distribution network, so the system is in the optimal state.

4.5. Analysis of the Capacity Limitation Effect of Distributed Generation

For distributed generation, different power scales are connected to different levels of the power grid. Low-capacity renewable energy sources, such as roof photovoltaics and small fans, are powered by the microgrid; large-capacity renewable energy, such as photovoltaic power plants and wind farms, can be directly interconnected with the distribution network to achieve grid connection. In this paper, the power capacity of the access microgrid and distribution network is constrained in the optimization planning model, and the upper and lower limits of the installed capacity of distributed generation are discussed below.

(1) In the case of $P_{MG\text{-}\max }=P_{DN\text{-}\min }{=P}_{IC}$ ($P_{IC}$ is constant )

Figure 9 shows that:

1) As the upper and lower limit values change from small to large, the cost of the distribution network decreases gradually. Because the lower limit of PV installed capacity is increased in the distribution network, the capacity of distributed generation directly connected to the distribution network is reduced, which directly leads to the cost reduction of the distribution network.

2) For the microgrid level, with the change in $P_{IC}$ value, the cost of the microgrid decreases first and then increases. When the upper limit of the microgrid power supply is small, the renewable energy capacity of the microgrid is small, and the microgrid needs to increase the purchased power to maintain the stability of the system. When the upper limit of the microgrid increases, the installed capacity of the power supply connected to the microgrid increases greatly, and the investment cost of the microgrid increases greatly.

3) For the total cost of the AC/DC hybrid microgrid and AC/DC distribution network system, when the constant term is small, the distributed generation is mainly connected to the distribution network, and the purchase cost of the microgrid is higher. With increasing $P_{IC}$, the installed capacity of the distributed power supply in the microgrid increases, and the cost of purchasing electricity and investing in the microgrid decreases, while the cost of the distribution network decreases. However, the full power operation of the microgrid with a large capacity of renewable energy cannot be realized, which causes the cost of the system to decrease first and then increase.

(2) In the case of $P_{MG\text{-}\max }\ge P_{DN\text{-}\min }$

When defining the capacity range of distributed generation in the power grid, there is a phenomenon that the definition is not clear. Partial capacity of the power supply can be connected to the distribution network or transmitted through the micro-grid. The upper limit of the microgrid and the lower limit of the distribution network may be $P_{MG\text{-}\max }\ge P_{DN\text{-}\min }$; but there cannot be $P_{MG\text{-}\max }<P_{DN\text{-}\min }$, in this case a distributed power supply with partial capacity will not be able to access the system. By changing the value of $P_{MG\text{-}\max }$ and $P_{DN\text{-}\min }$, this paper analyses the impact of upper and lower capacity limits on the results of optimal planning. The change of the total cost of the system is shown in Figure 10.

It can be seen from the figure that the system cost is higher when the upper limit value and the lower limit value of the distribution network are small, because at this time the distributed generation mainly connects to the micro-grid level, which improves the investment cost of the system. When the two thresholds are similar and float around 400 kW, the system cost changes little and the economic factors tend to be stable.

5. Conclusions

With a large number of distributed power supply access and DC load requirements, a single microgrid cannot meet the system requirements; moreover, power electronic equipment is constantly updated, and DC distribution networks are developing rapidly. In this context, based on the ATC method, this paper studies the optimal configuration scheme of distributed generation when an AC/DC hybrid microgrid and AC/DC distribution network are interconnected.

This paper proposes a collaborative optimization planning method of distributed generation accessing an AC/DC hybrid distribution (micro) grid, and based on the ATC method, the coupling relationship between the AC/DC hybrid microgrid and AC/DC distribution network is established. The mathematical model is solved iteratively by the augmented Lagrangian penalty function, and the results of the distributed generation configuration are obtained at two levels of the microgrid and distribution network. The optimal access location and capacity of distributed generation are planned, so the local absorption level of the system is improved and the cost is reduced. Through the analysis of practical engineering examples, the advantages and disadvantages of different optimization algorithms and the influence of system parameters on the planning results are compared.

The main contribution of this paper is that an interaction mechanism between AC/DC microgrids and distribution networks is established, and the collaborative planning of distributed generation at two system levels is realized. The ATC method can achieve the goal of fast convergence when multi-microgrids are connected to the distribution network. Therefore, the proposed model can be applied to actual projects.