*3.1. DG Timing Characteristics*

where μ is the DC voltage utilization under SPWM modulation, which is 0.866. **3. DG and Load Timing Characteristics**  *3.1. DG Timing Characteristics*  Distributed generator usually contains micro-turbine generators (MT), wind turbine generators (WGs), photovoltaics (PV), and so on. Different types of DG apply to different regions. For example, photovoltaics generate more electricity in areas with sufficient light; micro-turbine generators are more suitable for areas with high heat demand [19]. Different DGs contribute differently to the environment, PV and WG are cleaner distributed generators. However, the timing fluctuation characteristics of these two generators, increase the uncertainty and affect the stability of the system Distributed generator usually contains micro-turbine generators (MT), wind turbine generators (WGs), photovoltaics (PV), and so on. Different types of DG apply to different regions. For example, photovoltaics generate more electricity in areas with sufficient light; micro-turbine generators are more suitable for areas with high heat demand [19]. Different DGs contribute differently to the environment, PV and WG are cleaner distributed generators. However, the timing fluctuation characteristics of these two generators, increase the uncertainty and affect the stability of the system while improving environmental protection. We have fully considered the timing characteristics of PV and WG. If we do not, there is no essential difference between WG and PV, and we cannot reflect on the advantages of MT. Additionally, we do not need to install energy storage equipment in the distribution network as this is contrary to the reality. Therefore, for the DG planning problem, the timing characteristics must be taken into consideration.

VSC dc 3 3 *V V* = μ

while improving environmental protection. We have fully considered the timing characteristics of PV and WG. If we do not, there is no essential difference between WG and PV, and we cannot reflect on the advantages of MT. Additionally, we do not need to install energy storage equipment in the distribution network as this is contrary to the reality. Therefore, for the DG planning problem, the timing characteristics must be taken into consideration. We took the three types of DG mentioned above as the research objects because these three types of DG are highly representative: the MT has rated capacity; its output is controllable and does not change with time; and the PV and WG represent a type of DG whose capacity changes with time. We also selected these two types of DG to study the impact of timing characteristics on the distribution network planning in depth.

We took the three types of DG mentioned above as the research objects because these three types of DG are highly representative: the MT has rated capacity; its output is controllable and does not change with time; and the PV and WG represent a type of DG whose capacity changes with time. We also selected these two types of DG to study the impact of timing characteristics on the distribution network planning in depth. Wind speed has a great influence on the WG. Generally, wind speed is high in the evening and Wind speed has a great influence on the WG. Generally, wind speed is high in the evening and especially in the winter. Therefore, the output is highest in winter and the least in summer. Light intensity and temperature have a great impact on PV. During the day, solar energy is rich, and the PV output is strongest at noon. At night, PV does not generate electricity. In general, PV has the largest output in summer and the least in winter. PV and WG have a natural complementarity, which is the main reason for selecting these two DGs which have different timing characteristics. According to

is the main reason for selecting these two DGs which have different timing characteristics. According to meteorological data [20], wind speed curves and light intensity were obtained in different seasons,

and the PV and WG timing characteristics curves were obtained as shown in Figures 2 and 3.

especially in the winter. Therefore, the output is highest in winter and the least in summer. Light

meteorological data [20], wind speed curves and light intensity were obtained in different seasons, and the PV and WG timing characteristics curves were obtained as shown in Figures 2 and 3. *Appl. Sci.* **2019**, *9*, x FOR PEER REVIEW 5 of 16

*Appl. Sci.* **2019**, *9*, x FOR PEER REVIEW 5 of 16

**Figure 2.** Photovoltaics (PV) timing characteristics curve. **Figure 2.** Photovoltaics (PV) timing characteristics curve.

**Figure 3.** Wind turbine generators (WG) timing characteristics curve. **Figure 3.** Wind turbine generators (WG) timing characteristics curve.

### **Figure 3.** Wind turbine generators (WG) timing characteristics curve. *3.2. Load Timing Characteristics*

23:00, and the maximum load time is about 10:00.

23:00, and the maximum load time is about 10:00.

*3.2. Load Timing Characteristics*  At present, according to power planning and power industry statistics, the power load is generally divided into four typical loads, including industry, commerce, agriculture, and residents. Similar to DG, these loads also have particular timing characteristics. Moreover, the maximum output time of the DG is not always the same as the time of the maximum load. We took residential load and commercial load as the research objects of the distribution network, and their four seasonal load curves are shown in Figure 4 and Figure 5. The electricity consumption of residents is the lowest in the summer. The daily peak hours are generally at noon and in the evening. The daily maximum load time is about 20:00. The minimum load time, except in summer, is about 03:00, while the summer *3.2. Load Timing Characteristics*  At present, according to power planning and power industry statistics, the power load is generally divided into four typical loads, including industry, commerce, agriculture, and residents. Similar to DG, these loads also have particular timing characteristics. Moreover, the maximum output time of the DG is not always the same as the time of the maximum load. We took residential load and commercial load as the research objects of the distribution network, and their four seasonal load curves are shown in Figure 4 and Figure 5. The electricity consumption of residents is the lowest in the summer. The daily peak hours are generally at noon and in the evening. The daily maximum load time is about 20:00. The minimum load time, except in summer, is about 03:00, while the summer minimum load time is about 07:00 in the morning. The fluctuations in commercial electricity At present, according to power planning and power industry statistics, the power load is generally divided into four typical loads, including industry, commerce, agriculture, and residents. Similar to DG, these loads also have particular timing characteristics. Moreover, the maximum output time of the DG is not always the same as the time of the maximum load. We took residential load and commercial load as the research objects of the distribution network, and their four seasonal load curves are shown in Figures 4 and 5. The electricity consumption of residents is the lowest in the summer. The daily peak hours are generally at noon and in the evening. The daily maximum load time is about 20:00. The minimum load time, except in summer, is about 03:00, while the summer minimum load time is about 07:00 in the morning. The fluctuations in commercial electricity consumption over the four seasons are small, the power consumption period ranges from 09:00 to 23:00, and the maximum load time is about 10:00.

minimum load time is about 07:00 in the morning. The fluctuations in commercial electricity consumption over the four seasons are small, the power consumption period ranges from 09:00 to

consumption over the four seasons are small, the power consumption period ranges from 09:00 to

*Appl. Sci.* **2019**, *9*, x FOR PEER REVIEW 6 of 16

**Figure 4.** Residential loads timing characteristics curve. **Figure 4.** Residential loads timing characteristics curve.

**Figure 5.** Commercial loads timing characteristics curve. **Figure 5.** Commercial loads timing characteristics curve.

### **Figure 5.** Commercial loads timing characteristics curve. **4. DG Optimization Configuration Model of Distribution Network 4. DG Optimization Configuration Model of Distribution Network**

**4. DG Optimization Configuration Model of Distribution Network**  The objective function of this paper is to minimize the total annual system cost. Based on the distributed power supply capacity and voltage fluctuation range allowed by the distribution network The objective function of this paper is to minimize the total annual system cost. Based on the distributed power supply capacity and voltage fluctuation range allowed by the distribution network node, the location and capacity of the DG are finally determined. The objective function of this paper is to minimize the total annual system cost. Based on the distributed power supply capacity and voltage fluctuation range allowed by the distribution network node, the location and capacity of the DG are finally determined.

### node, the location and capacity of the DG are finally determined. *4.1. Objective Function 4.1. Objective Function*

*4.1. Objective Function*  The annual cost of the distribution network is The annual cost of the distribution network is

$$\min \mathcal{C}\_{TOL} = \mathcal{C}\_{\text{ow}} + \mathcal{C}\_{i} + \mathcal{C}\_{\text{loss}} + \mathcal{C}\_{f} + \mathcal{C}\_{\varepsilon} - \mathcal{C}\_{p} \tag{11}$$

where *CTOL* is the total annual cost of distribution system; *Com* is DG annual operation and maintenance costs; *Ci* is the DG annual equivalent investment cost; *Closs* is the system network loss cost; *C <sup>f</sup>* is the MT fuel cost; *Ce* is the pollution compensation cost; and *C <sup>p</sup>* is the maintenance costs; *Ci* is the DG annual equivalent investment cost; *Closs* is the system network loss cost; *C <sup>f</sup>* is the MT fuel cost; *Ce* is the pollution compensation cost; and *C <sup>p</sup>* is the environmental protection subsidy fee. where *CTOL* is the total annual cost of distribution system; *Com* is DG annual operation and maintenance costs; *C<sup>i</sup>* is the DG annual equivalent investment cost; *Closs* is the system network loss cost; *C<sup>f</sup>* is the MT fuel cost; *C<sup>e</sup>* is the pollution compensation cost; and *C<sup>p</sup>* is the environmental protection subsidy fee.

8760

8760

### (1) DG annual operation and maintenance costs ( ) *om om i C c Et* <sup>=</sup> (12) (1) DG annual operation and maintenance costs

(1) DG annual operation and maintenance costs

environmental protection subsidy fee.

$$\mathcal{C}\_{om} = c\_{om} \sum\_{t=1}^{8760} \sum\_{i \in \mathcal{N}\_{\rm DG}} E\_i(t) \tag{12}$$

power generation connected to the *i*-th node at time *t*, MW·h. (2) DG annual equivalent investment cost (2) DG annual equivalent investment cost where *com* is DG unit operation and maintenance costs, 10,000 yuan/(MW·h); and *Ei*(*t*) is the DG power generation connected to the *i*-th node at time *t*, MW·h.
