Complexity

Volume 2017, Article ID 7539089, 10 pages

https://doi.org/10.1155/2017/7539089

## Structural Evaluation for Distribution Networks with Distributed Generation Based on Complex Network

^{1}Department of Electrical and Electronic Engineering, Xi’an Jiaotong-Liverpool University, No. 111 Ren’ai Road, Suzhou Industrial Park, Suzhou, China^{2}SDIC Baiyin Wind Power Co., Ltd., Lanzhou, China^{3}Politecnico di Torino, Torino, Italy

Correspondence should be addressed to Fei Xue; nc.ude.ultjx@eux.ief

Received 16 May 2017; Revised 1 September 2017; Accepted 12 September 2017; Published 17 October 2017

Academic Editor: Zofia Lukszo

Copyright © 2017 Fei Xue et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Structural analysis based on complex network theory has been considered promising for security issues of power grids. At the same time, modern power distribution networks with more Distributed Generations (DGs) and Energy Storage Systems (ESS) have taken on more challenges in operation and security issues. This paper proposed a dedicated metric named as Power-Supply-Ability for power distribution networks based on net-ability. Special features of DGs, such as relations of capacities, identification of effective supply area, and limitation in continuous power supply, have been considered in definition. Furthermore, a novel opinion is proposed that the extent of improvement for operation and security by adding DGs also depends on the original structure of the distribution networks. This is an inherent ability of the original networks and could be quantitatively analyzed. Through case studies, this method has been proved to be effective in identifying potential structural vulnerabilities of distribution networks; particularly the impact of DGs on security has been studied. Furthermore, it can help in site selection for DGs by providing different priorities of locations compared with results of other works. This can help to complement other methods to construct a more comprehensive methodology by considering aspects of security, economy, and quality.

#### 1. Introduction

The networks of power system, also named as power grids, are a critical infrastructure in modern social livings [1]. Serious outages of electrical power systems can impact the whole society [2, 3]. For instance, recent blackouts have occurred in the USA and Europe directly causing losses up to billions of dollars [4]. These serious consequences have drawn much attention to electrical security problems such as accidental or intentional attacks [4, 5].

However, with the increasing size and complexity in power grids [6], as well as increased consumption of power and other social developments, it is becoming more difficult and complex to analyze a large scale of whole power system and the complicated interconnectivity precludes us from understanding and evaluating an overall power system [6]. Complex network theory is a popular method to analyze networked systems in terms of a set of lines with connected nodes and fortunately recent studies have found that several properties of complex network (CN), such as small-world [7] and the characterization of scale-free [8], were related to power networks. It then allows structural analysis of power grids through pure topological metrics and brings a new analyzing method to overcome the above problems [9, 10]. In the theory of CN, Global Efficiency is a metric to measure the efficiency of the network for information transmission between vertices [10] and later is popularly referred to in assessing the vulnerability of power grids [5, 11–15]. Furthermore, with consideration of specific features in electrical engineering, it was updated as net-ability to evaluate power transmission networks [2, 4]. Based on complex network concept, net-ability analyzes the performance of transmission networks through considering extra physical features such as power flow limits, electrical distance, and contributions of all involved transmission paths.

Although net-ability is effective in analyzing power transmission networks, due to different structural features among transmission and modern distribution networks, it could not be directly utilized for modern distribution networks. In conventional distribution networks, the main differences from transmission networks are their radial topology and impedance to resistance ratio. But it is not a problem for complex network theory to analyze any network structure including radial topology, and it is not a problem to adapt net-ability with appropriate impedance model. However, in modern power distribution networks, Distributed Generation (DG) and energy storage devices may increase its complexity. DGs, simply defined as small-scale electricity generation within distribution networks or on the customer side of the networks, are currently undergoing an increasing amount to relieve environmental problems, such as greenhouse gases from traditional electricity generation [16–23]. There are various categories of DGs, such as photovoltaic cells installed at homes or wind turbines on a farm land. Although these DGs could improve power supply to local loads, compared to conventional generation, they are highly dependent on climates or weather and could not provide continuous electricity [16, 17]. So battery Energy Storage Systems (BESS) can also be widely applied to improve power stability and demand/supply balance [17].

Up to now, to our best knowledge, few papers have considered direct applying of complex network approaches for analyzing modern distribution networks, especially to include impacts from DG and BESS. By comparing with conventional power distribution stations, [24, 25] consider DG with relevant small capacity and being placed to load node. Reference [24] pointed out that the power supply performance of DG should decrease rapidly with the increases of distance. Based on complex network concept, they raise some metrics to reflect that DG performance would decrease rapidly with increase of distance. The metrics used exponential form to show that DG contributed more power to relatively local load demand and less to remote loads, but exponential form cannot be fully justified and specific electrical features, such as impedance, power capacities of different devices, and contribution of different paths, were not fully considered. In this paper, the main impacts from DG on structural analysis of distribution networks are considered according to the channel capacity, supplying distance as well as intermittency and fluctuation of primary energy. These will be discussed in detail in Sections 2 and 3.

The rest of paper is organized as follows: global efficiency and net-ability will be discussed with their limitations for applying in distribution networks in Section 2. In Section 3, a new concept of Power-Supply-Ability (PSA) and its application in evaluating power distribution networks will be proposed. In Section 4, a novel opinion will be discussed to evaluate the inherent ability of original network structure to be improved by adding DGs. Simulation and results of application of PSA are shown in Section 5 with some examples and Section 6 contains some conclusions.

#### 2. From Global Efficiency to Net-Ability

Global efficiency from the CN theory was initially defined by Latora [2, 4, 10] and was later widely used to evaluate performance of network, such as vulnerability assessment or location of critical components [4, 26]. It was also utilized in analyzing cascading failures for assessing power systems [27–29]. The definition for global efficiency can be written as

is the distance (length of the shortest path) between the pair of node and node , and is the number of all nodes in the network. This formula is aimed at measuring network efficiency of information transmission by considering that the efficiency for sending information between a pair of nodes and is proportional to the reciprocal of their geodesic distance. For obtaining the general efficiency of the whole network, performance between each pair of nodes should be assessed to calculate an average value.

However, when applying this metric to evaluate power grids, the original concept of distance in (1) is not meaningful in electrical engineering [2, 4, 30]. Distance in power grids should be adjusted as the ability to overcome difficulties of transferring power between the pair of generator node and load node . Through considering the economic and technical aspects, power transmission difficulties should depend both on power flow capacity and on impedance. According to the electrical circuit theory, the equivalent impedance between bus and bus can be expressed as, , and are corresponding elements of the impedance matrix of the network.

Furthermore, the maximum power flow limit from to should also be considered, which can be calculated as

is power transmission capacity between the generator-load (-*d*) pair. is the set of all lines connecting and ; is the maximum power flow capacity for line ; is the power transfer and distribution factor (PTDF) when transferring power from bus to . PTDF here has overcome the assumption of transferring physical quantity only through the shortest path in global efficiency. Therefore, with the new definition of distance in power grids and taking into account power flow capacity characterized by PTDF, net-ability for power transmission network was defined as [3, 4, 9]

and are, respectively, the sets of generator buses and load buses. is the number of generator buses and is the number of loads buses.

With fast development of smart grid technologies, distribution networks with DGs and BESS have become a hot topic in research and engineering. However, up to now, pure structural analysis has seldom been applied to this field. In fact, the evaluation of power supply security with penetration of DGs and BESS is meaningful and necessary; and site allocation for DGs and BESS from structural perspective can also contribute to real system planning and operation.

Although net-ability has been applied to evaluate structure vulnerabilities of power transmission network as an effective approach, it is not reasonable to directly apply it for modern distribution networks.

Firstly, only the capacity of transmission channel between any pair of generator bus and load bus was considered, because net-ability only targeted features of network and did not consider generators or loads as a part of networks. However, the power capacities of power sources and loads may impact on the final power supply performance if they are much different from the capacity of channel, especially for distribution networks where the capacities of power sources are not comparable with transmission networks. Therefore, the connotation of structural analysis should not be limited to pure topological features but should also include some static physical features of devices, such as capacities of power sources and BESS.

Secondly, in definition of net-ability, all generator buses are supposed to have large capacity to support long distance transmission, so any generator can be a power source for any load bus in the same network. However, in distribution networks, most DGs have much smaller power capacity and may only be effective power sources for a range of local loads. Therefore, DGs cannot be considered as equal power sources in set with other traditional sources and cannot be an effective power source for any load bus in the network.

Thirdly, most DGs are renewable power generation, such as wind power or solar power. The output power of such power sources greatly depends on the availability of primary energy. Therefore, with intermittency and fluctuation, these power sources cannot supply continuous full rated output power for any required time period. Similar problem exists for BESS, which have to operate in charging and discharging modes in turn and cannot supply continuous full rated power for any required time period. As these features can seriously impact on the power supply performance of the distribution networks, they should not be neglected in structural analysis.

#### 3. Power-Supply-Ability for Distribution Networks

To address the problems mentioned above, a new metric named as Power-Supply-Ability (PSA) dedicated to distribution networks is proposed based on net-ability.

To address the first problem mentioned in Section 2, the capacity of power source will be compared with the capacity of transmission channel defined in (3), and the minimum one will be applied in evaluating Power-Supply-Ability:

If the capacity of power source is smaller than the channel capacity, that means the channel capacity cannot be fully utilized by the power source, so it cannot be directly used in evaluating Power-Supply-Ability.

As for the second problem in Section 2, with development of renewable technology, focus of environmental-friendly energy, and demand/supply balance, new generation technologies of DG such as wind generation and energy storage are gradually considered in distribution networks [17, 31, 32]. However, according to their common small capacities [32, 33] and power generating efficiency, they should not be directly evaluated as above conventional power sources. So in definition of PSA, DGs will only be considered as backup or auxiliary power sources to improve power supply reliability and quality, which cannot be considered in a source-load pair in average calculation, but just as an additional compensation for a conventional source-load pair. Therefore, the net-ability can be extended aswhere is the set of DG buses which are effective power sources for load bus . And is capacity of DG at bus ; is power transmission capacity from bus to load , which can also be calculated by (3). is the equivalent impedance between and the supplied load bus .* The metric of net-ability calculates average network performance for all possible (generation + load) pairs. PSA considers a power supply layout in terms of main power source + load + auxiliary sources and calculates average power supply performance for all possible power supply layouts.* This means that when considering the power supply of one pair (*-d*), additional power supply from local power supplies (DGs) to that load will also be considered to improve the supply performance.

Since DGs in (6) are considered to have small capacities in this paper, it implies that DGs could not serve any load in the network like conventional power sources. It then needs a method to identify effective DG power sources for a load bus . From another point of view, we can say that we need a method to identify effective supply area of a DG bus . Then is the set of DG buses whose supply areas all include load . When considering effective supply area of DGs, the general idea is that, with the same impedance, higher power supply capacity increases the efficient supplying area; with the same power supply capacity, higher impendence reduces the efficient supplying area. Then, a criterion to identify effective supply area for a DG bus is proposed as

All DGs from satisfy criterion and . To be specific, when the criterion is satisfied, it means that the DG has the ability to supply power to load d with acceptable power quality. means that when analyzing power supplied to load , any DG directly installed at load bus will not be evaluated. The reason is that PSA in this paper is to evaluate the distribution network; once the DGs are placed at the load bus , to some degree, they could not be considered as a part of network because their interactions are not through the network frame, and the power supply from these DGs to load should be considered as an internal supply, which is isolated from the whole system performance. Additionally, *γ* is a parameter to define the DG supply area and it should be a value based on statistical analysis and simulation.

Figure 1 is a sketch to explain the meaning of effective supply area and power supply layout. A main power source G and a load bus D can be considered as a generation + load pair. There are three different DGs in the figure. Each DG could be considered as the center of a circle whose radius is *γ*. The circles could be considered as the effective area of each DG. The load bus D is inside the circles of DG1 and DG2 but outside of the circle of DG3. That means DG1 and DG2 are all effective auxiliary sources for D and should be included in . And DG3 is not an effective auxiliary source for D; it should not be included in . So the corresponding power supply layout could be (G + D + DG1 + DG2).