Traditional distributed generators (DGs) planning methods take network loss minimization as the main objective to optimize DG sites in feeders. The use of load supply capability (LSC) in DG planning will precisely answer the questions how many DGs should be integrated, which transformer they should be connected to, and which type of DGs should be adopted. The main work of this paper is to analyze the impact of DGs on LSC so as to answer the three key questions. It resolves the planning problem through three steps: (i) two LSC models considering DGs’ access are developed, in which two different transfer strategies are considered: direct load transfer and indirect load transfer; (ii) the method of combined simple method and point estimate method is proposed. At last, based on a base case, when the configuration of DGs is changing, the impact of DGs on system LSC is studied. After the case study, the conclusion concerning the impact of load transfer strategy, DG capacities, and DG types on LSC is reached.
Distributed generation (DG) is widely used in the distribution power system nowadays in order to take its advantages of cleaner energy, less loss, and local power supply. However, there are many problems such as intermittency, bidirectional power flow, and controlling strategy, coming along with the DG integration. The problems have challenged the traditional network planning [
The concept of load supply capability (LSC) [
At present, researches that apply LSC into DG planning are not very common. Reference [
As a result, an LSC evaluation method that considers N1 contingency of transformers is necessary in DG planning. In it, the main impacts of DGs on LSC include DG types, DG capacity, and the transformer DGs are connected to, but the sites of DG in feeders have very little impact on LSC. Therefore, it can decide how many DGs and what types of DGs can access into the power system and which transform they access to according to LSC analysis. Then the detailed sites of DGs can be determined with traditional planning methods considering network losses. The process mentioned above is shown in Figure
The relationship between LSC and traditional DG planning.
This paper presents a novel model of LSC considering the access of DGs and then investigates the impact of DGs on LSC. The proposed approach is extremely valuable for DG planning. The main types of DGs in wide use, including photovoltaic (PV), wind turbines, and storage as supplement, are analyzed in this paper.
When there is one unit (such as transmission lines, substations) lost, the system should immediately restore to supply the demand.
Under N1 contingency, the lack of supply capacity needs to be filled by neighbor spare units. As a result, the spare capacity is indispensable to satisfy the system operation consistently. The quantity of spare capacity decides the incremental cost because inadequate spare capacity leads to the discrepancies of N1 contingency while overfull one leads to largescale investment. To resolve the dilemma, the concept of load supply capability is introduced.
Under the requirement of N1 contingency, the total load that the distribution power system can supply is defined as its load supply capability (LSC). Accordingly, LSC in the distribution system is decided by loading factors and the spare capacity of all units in the system.
The LSC in the distribution power system increases with DG integration, but the incremental LSC is random because of DGs’ intermittency.
As discussed earlier, the proper spare capacity, which is influenced by the load restoration in N1 contingency, determiners the LSC of a system. Thus, the process in which the loads of one transformer are restored by another is defined as load transfer. Inner substation load transfer is initiated first when the failed and the functional transformers are in the same substation. It is followed by intersubstation load transfer, when the failed and functional transformers are in different substations.
To model LSC, it is necessary to build a proper description of DGs. It is found that DGs could be treated as an intermittent supply unit in calculating LSC to transfer load impacted by unit failure for calculation efficiency. So, the concept of DG route is defined.
Turbine output curve [
Weibull distribution [
The PV modelling is similar to wind turbine modelling. The output of PV is decided by solar radiation [
Beta distribution [
Energy storage is an essential supplement to DGs. In this research, leadacid battery is considered. The output of a leadacid battery is determined by its state of charge. Kinetic Battery Model (KiBaM) [
As discussed above, the value of LSC is influenced by the strategy of load transfer. In this paper, the main strategy is divided into direct load transfer and indirect load transfer.
When N1 contingency occurs, loads impacted by the failure can only be transferred to the transformers inside a substation and the transformers that have direct feeder connection with the failed transformer.
When N1 contingency occurs, the load transfer will be divided into 2 steps. In the first step, load impacted by the failure can be transferred to the transformers in the same substation and the transformers that have direct feeder connections with the failed transformer. The functional transformers in the substation can overload for a short time (usually a few hours) defined by a coefficient
The process of the 2 transfer strategies.
The overloading factor and duration are influenced by the manufacturing techniques of transformers, the top oil temperature of the transformers, and the operation guidelines. In the operation guideline of China, the overloading factor and duration are shown in Table
The overloading factor and duration.
Overloading factor  Overloading duration 

(%)  (minute) 
110  180 
120  150 
130  120 
140  45 
150  15 
According to the strategy of direct load transfer, the model of LSC is established in formulae (
Constants and variables in the model.
Symbol  Data type  Variable type  Dimension  Description 


Number  Constant  1  Transformer number 



Vector  Constant 

Transformer capacity 





Vector  State variable 

Transformer loading factor 




Tr  Matrix  Free variable 

Load transfer capacity 





Matrix  Constant 

Connection feeder capacity 





Probabilistic vector  Constant 

DG route capacity 





Matrix  Constant 

Identity matrix 



Vector  Constant 

Vector full of 1 
In the model, formula (
Under indirect load transfer, the model of LSC is established in the following formulae:
In this model, formula (
These two models can determine, when the LSC reach the maximum, which transformers the loads can be transferred to and how many loads should be transferred.
The model of LSC is linear but with random variables. The method combining simple and point estimate methods is used to resolve this problem. The calculation flow is shown in Figure
Calculation flow of LSC with DGs.
Taking the base case shown in Figure
Connection structure of MV network in the case.
The transformer capacities and connection feeder capacities of the base case are provided in Table
Capacities of the transformers and connection feeders.
Connection feeder capacity 
Tran. 1  Tran. 2  Tran. 3  Tran. 4  Tran. 5  Tran. 6 

20 MVA  20 MVA  20 MVA  20 MVA  31.5 MVA  31.5 MVA  
Tran. 1  
20 MVA  0  20  0  0  0  0 
Tran. 2  
20 MVA  20  0  8  0  3  0 
Tran. 3  
20 MVA  0  8  0  20  5  3 
Tran. 4  
20 MVA  0  0  20  0  5  5 
Tran. 5  
31.5 MVA  0  3  5  5  0  31.5 
Tran. 6  
31.5 MVA  0  0  3  5  31.5  0 
In the base case, there are five feeders to which the DGs are connected. The configuration of DGs in the feeders of transformer 1 is shown in Figure
DGs integration in feeders of transformer 1.
In this study, the impact of load transfer strategy is studied. A configuration of DGs shown in Table
Installed capacities of DGs in feeders.
Feeder  Transformer  DG integration  Turbine capacity 
PV capacity 
Battery capacity 

Feeder 1  1  7  1 685  1 380  970 
Feeder 2  1  9  2 720  2 010  1 530 
Feeder 3  2  7  2 080  1 200  1 380 
Feeder 4  5  7  2 145  1 500  970 
Feeder 5  6  8  1 965  1 480  1 170 
The calculation separately considers direct load transfer and indirect load transfer, where the results are shown in Table
Comparison between direct and indirect load transfer.
LSC expectation 
Direct load transfer  Indirect load transfer  

90.3599  101.143  
Tran.  Loading factor 
Loading factor 
Loading factor 
Loading factor 
1  55.75  0.97  69.89  0.31 
2  47.16  0.84  63.02  0.39 
3  77.53  0.18  69.9  0.30 
4  72.47  0.18  75.53  0.38 
5  64  6.46  72.18  0.25 
6  55.75  0.97  72.18  0.00 
According to Table
97.5% confidence interval of available transformer loading factors with direct load transfer strategy.
97.5% confidence interval of available transformer loading factors with indirect load transfer strategy.
DGs’ intermittency causes the available loading factors to be probabilistic. In Figure
Based on the configuration in Figure
The LSC with different DG sites.
Access to tran. 1  Basic case  Access to tran. 3  Access to tran. 6  

LSC expectation  101.82  101.14  100.53  101.12 
MVA  
LSC standard deviation  0.33  0.14  0.04  0.23 
MVA  

101.45  100.91  100.32  100.87 
MVA 
LSC expectation with different DG sites.
LSC standard deviation with different DG sites.
The green column in Figure
Based on the configuration in Figure
LSC expectation change trend with storage capacity.
LSC standard deviation change trend with storage capacity.
Figure
In this paper, two LSC models in distribution power system considering DGs are proposed, with which the impact of DGs on LSC is studied. Through the analysis, the following conclusions are reached.
DGs’ integration increases system LSC. It is influenced by the strategies of load transfer. Indirect load transfer produces higher LSC and makes the incremental LSC more stable.
It also proves that the transformers which the DGs are connected to have a direct impact on LSC. In order to make full use of LSC, DGs need to be connected to transformers which have fewer connection feeders and larger capacity.
The study also illustrates that the more the storage in the system, the more stably the LSC increases. When the percent of storage capacity reaches around 80%, the most stable incremental LSC can be achieved.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by Project of National Natural Science Foundation of China (Approval 51107085, 51261130473) and National HighTech R&D Program of China (“863” Program) (Approval 2011AA05A106). This research is also supported by Technology Project of State Grid Corporation—Active Distribution System Technology and Application Research of Coordinated Planning for LargeScale DG and Diversity Load Integration.