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Equivalent load density model of feeders

Liu Jian 1, Bi Pengxiang 2, Wu Xiaomeng 3 (1. Xi'an University of science and technology, Xi'an, Shaanxi 710054;

2. Xi'an Jiaotong University, Xi'an, Shaanxi 710049;

3. Xi'an Institute of petroleum, Xi'an, Shaanxi 710065) 1 Introduction

complex distribution is not only huge in scale, but also seriously lack of measurement 7 Beam lifting speed (mm/min): 0.01 ~ 500 data, so it is difficult to solve. In recent years, according to the characteristics of distribution, the research on establishing simplified models and carrying out simplified analysis is very active [1~7]. However, these research works can only obtain very rough results according to the statistical user load distribution [1], or determine the data of each load by dividing the feeder outlet load by the rated power of the distribution transformer [2], or treat the load as evenly distributed along the feeder [3], or generate an equivalent load according to the measurement results of each load on the feeder [4,5], These methods either have rough results or still need to rely on a large number of measured data. The method proposed in document [6] cannot calculate the voltage drop and power flow distribution along the distribution line. Reference [7] proposed a simplified analysis method to equivalent the distributed load on the feeder to an equivalent load at the appropriate position only according to the voltage at both ends of the feeder and the power flowing through both ends of the feeder. This method can get valuable analysis results without measuring each load on the feeder, but the error of its equivalent load model in calculating line loss is still large, because it is not ideal to use only a centralized load to represent multiple decentralized loads between feeder segments

in this paper, the equivalent load density model of distribution feeders is established, and the decentralized load of feeders is expressed in the form of load density along the line, and the distribution of load density is determined according to the measured data at both ends of feeders, which not only simplifies the distribution analysis, but also further improves the calculation accuracy of line loss compared with the equivalent load model in literature [7]

2 basic principle

Figure 1 shows a typical feeder. A and B are the sectionalizing switches at both ends of the feeder respectively. SA sap and Sb SBP are the power flowing through a and B respectively, s（ λ) It refers to the load of this feeder at the length of L from the B end. The total load without loss power along the line supplied by ab is expressed as s SP, and six load distribution forms along the line can be established as shown in Figure 2

for the six load distribution forms, the load distribution density function can be written separately to realize the utilization number on super large container ships, liquefied natural gas (LNG) ships and other high-tech ships ρ ( λ) Is

, where k=k 0, where k is a normal number, which is the amplitude of the characteristic value of load distribution, kva/km; The definition of L is shown in Figure 1, and its unit is km; L is the length of feeder AB, km. ① Assuming that the power factor of the load along the feeder is the same, there is sbp=sap=sp= θ； ② Assuming that the voltage change along the feeder is small, it can be approximately regarded as unchanged, which is expressed as uk=0.5 (ua+ub)

the voltage drop and line loss of feeders under different load distributions are given below. In the analysis process, the unit value of each parameter is adopted, in which the reference value of voltage is UK. According to hypothesis 2, the unit value of voltage along the line can be considered to be approximately 1

(1) load distribution 1, the situation of linear increase along the load distribution

according to formula (1) and hypothesis 1, there is

where Du is the voltage drop from a to B, R and X are the resistance and reactance per unit length of the feeder respectively, and R and X are the total resistance and total reactance of the feeder respectively. Further, there is

because the load distribution increases linearly, there is

(2) load distribution 2. The load distribution decreases linearly along the line

according to formula (2) and hypothesis 1, there is

according to formula (16), the loss power DS along the line is

because the load distribution decreases linearly, there is a univariate quadratic equation composed of

solution formula (23), which can obtain the value of K, which is expressed by kloss2

(3 landing platform) for increasing the political and military exchange cloth 3~6 for the load distribution, using a similar method, Kv3 ~ kv6 and kloss3 ~ kloss6 can be obtained

(4) modeling of load density model

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