Graph Computing based Parallel Power Flow Algorithm and ... · requires higher efficient data management methods and faster power flow solutions [1]. To achieve the goal of efficient

Graph Computing based Parallel Power Flow Algorithm and Graph Visualization for Power

Distribution Networks

Jun Tan*, Yi Lu§, Kewen Liu**, Hong Fan*, Guangyi Liu*, Renchang Dai*, and Zhiwei Wang*

*Global Energy Interconnection Research Institute North America, San Jose, CA 95134, USA **Global Energy Interconnection Research Institute, Beijing, 102209, China

§Sichuan Electric Power Corporation, China [email protected]

Abstract—With the emergence of the graph database and the graph computing technologies, the power system is facing a new era of technology development. Meanwhile, the fast-growing power distribution systems with increased size and complexity require more efficient data management systems and faster power flow solving algorithm. These challenges could be well solved by applying the graph data model (GDM) and graph computing technologies as the GDM provides more efficient data management methods and the graph computing is suitable for the node based parallel computing. This paper proposes a GDM based power distribution network modeling approach. Then a graph computing based parallel power flow algorithm and a graph visualization based power flow software have been developed based on it. The proposed parallel power flow algorithm is implemented on a graph database platform and the simulation results show that it is able to effectively reduce the computing time of the power flow with large test systems. Moreover, the power flow software is able to provide vivid data visualization and perform flexible data analysis and data management functions.

Index Terms—Graph computing, parallel power flow, graph visualization, backward forward sweep.

I. INTRODUCTION

With the fast-growing penetration of the renewable resources such as solar and wind generations, the power distribution systems are becoming more complex and it requires higher efficient data management methods and faster power flow solutions [1]. To achieve the goal of efficient data management and faster computation, new modeling methods for the power systems are required to break through the limits brought by traditional relational database. Graph computing is a new technology which constructs the power network from the viewpoint of a graph. The graph database also provides more efficient data management approaches by storing the information directly on vertices and edges. Its graph structure for connecting the vertices and edges also demands less processing time for retrieving data at any depth [2]. Different types of graph platforms have been developed in the market

such as Pregel [3], Neo4j [4], Giraph [5], TigerGraph [6], etc. for various applications.

Many research has been conducted in the field of graph computing and its application in power systems [7]-[11]. Reference [7] adopts a graph theory based network flow analysis in real time power system operations to improve network connectivity visualization. A graph based computational framework for coupled infrastructure networks’ optimization has been proposed in [8]. Paper [9] proposes a graph partition based mixed integer linear programming approach for power system islanding operation. A graph theory based optimal power quality monitors planning approach is presented in [10]. Reference [11] applies factor graphs for distributed power system state estimation.

However, very few study has been carried out in the field of graph computing based parallel power flow algorithm and the graph based visualization of power distribution networks. Thus, this paper will propose a graph data model (GDM) based power distribution network modeling approach which is able to provide fast parallel power flow platforms, efficient data management approaches, and graph based data visualizations. Base on the GDM of the power distribution network, a graph computing based parallel power flow algorithm has been proposed. The parallel power flow algorithm adopts the hierarchical group synchronization (HGS) parallel computing mechanism in bulk synchronous parallel (BSP) [12] computing model and it is able to effectively reduce the computing time for the power flow when dealing with large systems. Finally, a software package has been developed based on the GDM of the power distribution network. The graph visualization based software is able to provide vivid data visualization and perform flexible data analysis and data management functions such as voltage profile along the feeder, network reconfiguration, etc.

This study has made contributions in several major aspects by: (1) proposing a GDM based power distribution network modeling approach; (2) proposing a graph computing based

This work was supported by State Grid Corporation technology project 5455HJ180018.

parallel power flow algorithm; (3) developing a graph visualization based power flow software.

II. GRAPH BASED SYSTEM MODELING

A. Graph Database

In the context of graph computing, a graph database is defined as a database that applies semantic queries with vertices, edges and attributes to store data in a graph structure [13]. In a graph database, each vertex or edge represents an entity, and the relationships among these entities are represented by the graph structure. Thus, various kinds of scenarios such as power system network, transportation network, social network, etc. can be modeled into graphs by properly defining the vertices and edges.

Different from the relational database, data in a graph database is directly related and linked together stored in a graph as shown in Fig. 1. For relational databases, the data tables retrieved from the database are the same as they were first stored. Its data retrieving process needs complex join operations of the tables. However, for graph databases, the relationships among the data are constructed into a graph structure in the database. When the data is retrieved from the graph database, the relationships among the data are also retrieved with one simple operation. Thus, the data retrieval, data update and data communication efficiency is greatly enhanced by using the graph database.

Figure 1. Data storage in relational database and graph database.

The benefits of using graph database is obvious, especially in handling the topology traversal problems in systems with complex hierarchical structures. One of such applications is to analyze the voltage profile along a feeder in a power distribution system. This kind of analysis is very important to power distribution system operators/planners to perform necessary operations to improve the power quality and it can be efficiently realized in a graph database as shown in Fig. 2(c).

Fig. 2 illustrates that how a power distribution network is represented in both relational database and graph database. For the example of the IEEE 13 node test feeder as shown in Fig. 2(a), the relational database needs to build a node table with 13 records, a branch table with 12 records and a bridge table with 24 records while the graph database only needs to create 13 vertices and 12 edges. As shown in Fig. 2(b), a bridge table needs to be created to represent the relationship between the nodes and branches as the relational database does not support Many-to-Many relationship between tables. However, in the graph database, the connectivity information is directly

represented in the graph structure as shown in Fig. 2(c). To retrieve the voltage information along the feeder from node 650 to node 675 as an example, the graph database only needs to traverse the highlighted path by finding the father node of each traversed node in the path. It only takes 4 steps to locate all the nodes in the path from node 675. However, this process is very complex for relational database as shown in the highlighted path in Fig. 2(b). It takes 8 join operations to find all the nodes in the path. These join operations are both compute and memory intensive and its time cost grows exponentially with the increase of the system size. Thus, the graph database is very effective in the application of data management in power distribution systems.

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and graph database. (a) IEEE 13 node test feeder, (b) data expression in relational database, (c) data representation in graph database.

B. Modeling Power Distribution Networks with Graph Data Model

The power distribution network is essentially a graph, thus it can be easily modeled as a graph network in graph computing as shown in Fig. 3. To construct the GDM for a distribution network, we need to define the network as �(�, �) where � is the set of vertices and � denotes the set of edges. Intuitively, the load points, voltages regulators, switches and shunt capacitors can be modeled as vertices while the line segments and transformers can be modeled as edges. Both the vertices and edges have a set of attributes denoted as �(��, ��) . Thus, the data for power flow computing and the computed results can be stored in the graph database. As the graph database is already loaded in the computer memory, the graph computing does not need to waste time on communication between the power flow program and the database. Moreover, the data retrieval is more effective for graph database as it does not need the time consuming on join operations in the traditional relational database. For instance, all the data associated with the load point such as load demand, voltage, connected bus, etc. are stored in the vertices and it does not need to join the tables of load demand, network topology, and power flow results to retrieve the information for the load point. The graph structure also provides an opportunity for the application for the node synchronization based parallel computing. As a result, graph

database is able to benefit the power system by providing fast parallel power flow calculations together with efficient data management and data analysis.

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III. GRAPH COMPUTING BASED PARALLEL POWER FLOW

A. Graph Computing Formulation with MapReduce based Parallel Mechanism

The graph computing is efficient in data retrieval and storage, flexible in modeling network connections and effective in model exploration. Graph computing is carried out directly on the vertices and edges of the graph. Thus, we need all the vertices and edges to be able to perform power flow calculations. Additional, we need to add virtual nodes S and T to indicate the start point and terminal point of a distribution network. These virtual nodes can also be viewed as the separation points for different sections of the power distribution network. First we define two relative concepts, child node set and father node set as shown in Fig. 4. Child node set is the nodes we are currently working on, while the father node set are preceding nodes directly connecting with child node set. For instance, if child node set is T0, then father node set is T1.

Figure 4. The mechanism of graph based parallel computing.

After obtaining the GDM, the parallel computing is able to be carried out on the graph as shown in Fig. 4. As shown in the figure, the generation of the GDM and resource allocation is in phase 1, the MapReduce [14] based parallel computing is in phase 2, and phase 3 is used to obtain the results. The BSP model has a Master to control the operation processes in each phase. First, the graph is divided into several parts by partition process and each partition is assigned to an independent worker in phase 1. Then, each worker divides the job into multiple maps in phase 2. There are two different parallel computing mechanism in this phase. The first one is the node

based parallel mechanism. As shown in the figure, each map has one father node and several child nodes. The power flow calculations for the child nodes are carried out in parallel and the result information is provided to their father node. This is also the process of MapReduce. The other parallel mechanism is the hierarchical parallel. We can observe from the figure that the maps at the same level are paralleled. Thus, the child nodes at the same level (for instance: nodes 4, 5, 6 in T0, and nodes 2, 3 in T1) are calculated in parallel.

B. Graph computing based three-phase unbalanced backward-forward power flow algorithm

Fig. 5 shows the process of MapReduce in the three phase unbalanced power flow calculation of radio distribution network with backward forward sweep [15]. In the backward forward sweep, the mapping process is to calculate the current node voltage and current, and the reduction process is to find out the father node voltage and current. Note that currents injecting to farther node set are calculated by aggregating branch currents which can be considered as Reduce phase. In forward sweep, node voltages are updated in a concurrent way as well while there is no current calculation involved in the sweep.

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IV. GRAPH BASED VISUALIZATION OF DISTRIBUTION

NETWORK POWER FLOW

In this section, we will introduce the graph computing based power flow software which is developed based on the proposed parallel power flow approach in Section III. We will also demonstrate its advantages for both data visualization and data analysis.

A. Software Architecture

The developed graph computing based fast distribution system power flow software is a web-based software. It includes 15 different web pages for case retrieval, power flow setting, results display, data analysis, graph management, etc. As shown in Fig. 6, the developed software adopts a frontend-backend design and it features a 3-level structure including frontend, backend and database. The frontend uses Angular as framework and leverage HTML, CSS and JavaScript to develop components for different applications. The backend is responsible for communications between sever, applications

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C. Yuan, M. Illindala, A. Khalsa, “Coresource planning in community microgrids,” Energy

C. Vicknair, M. Macias, Z. Zhao, X. Nan, Y. Chen, and D. Wilkins,comparison of a graph database and a relational database: A dataprovenance perspective,” in Conf.

G. Malewicz processing,” in2010, pp. 135

“Neo4jhttp://neo4j.com/

C. Avery, “Giraph: LargehadoopAvailable:http://www.slideshare.net/averyching/20110628giraphhadoop-summit

“TigerGraph: The first native parallel graphhttps://www.tigergraph.com/.

T. Werhoconnectivity monitoring using a graph theory network flow algorithmIEEE Trans. Power

J. Jalving, S. Abhyankar, K. Kim, M. graphof coupled infrastructure networks," in& D

T. Ding, K. Sun, C. Huang, Z. Bie, and F. Li, programmingoperation considering network connectivitypress

D. J. Won and S. quality monitors considering system topologyDelivery,

P. Chavali and A. Nehorai, using factor graphspp. 2864

Leslie G. Valiant, Communications of the ACM

G. Ravikumar andoriented graph database framework for power systemsPower Systems,

J. Dean and S. Ghemawat, large clustersJan. 2008.

W. H.2002.

“Distribution Test Fieee.org/


s paper modelsGDM which provideefficient data Based on power flow algorithm and a power flow software have been developed. effectively reduce

s efficientvisualization

authors are gracoding work at the early stage of this research.

C. Yuan, M. Illindala, A. Khalsa, “Coresource planning in community microgrids,” Energy, vol. 8, no. 4, pp. 1351C. Vicknair, M. Macias, Z. Zhao, X. Nan, Y. Chen, and D. Wilkins,comparison of a graph database and a relational database: A dataprovenance perspective,” in Conf.,2010, Art. no. 42G. Malewicz processing,” in2010, pp. 135“Neo4j: An open source graph databasehttp://neo4j.com/C. Avery, “Giraph: Largehadoop,” in Available:http://www.slideshare.net/averyching/20110628giraphhadoo

summitTigerGraph: The first native parallel graph

https://www.tigergraph.com/.Werho

connectivity monitoring using a graph theory network flow algorithmIEEE Trans. Power J. Jalving, S. Abhyankar, K. Kim, M. graph-based computational framework for simulation and optimisation of coupled infrastructure networks," in& DistributionT. Ding, K. Sun, C. Huang, Z. Bie, and F. Li, programmingoperation considering network connectivitypress. D. J. Won and S. quality monitors considering system topologyDelivery,P. Chavali and A. Nehorai, using factor graphspp. 2864Leslie G. Valiant, Communications of the ACMG. Ravikumar andoriented graph database framework for power systemsPower Systems,J. Dean and S. Ghemawat, large clustersJan. 2008.

H. Kersting,2002. Distribution Test F

ieee.org/


s paper modelsGDM which provideefficient data managementBased on graph database and graph computingpower flow algorithm and a power flow software have been developed. The simulation reseffectively reduce

efficientvisualizations.


C. Yuan, M. Illindala, A. Khalsa, “Coresource planning in community microgrids,”

, vol. 8, no. 4, pp. 1351C. Vicknair, M. Macias, Z. Zhao, X. Nan, Y. Chen, and D. Wilkins,comparison of a graph database and a relational database: A dataprovenance perspective,” in

2010, Art. no. 42G. Malewicz processing,” in2010, pp. 135

: An open source graph databasehttp://neo4j.com/C. Avery, “Giraph: Large

,” in Available:http://www.slideshare.net/averyching/20110628giraphhadoo

summit/. TigerGraph: The first native parallel graph

https://www.tigergraph.com/.Werho, V. Vittal, S. Kolluri, and S. M. Wong,

connectivity monitoring using a graph theory network flow algorithmIEEE Trans. Power J. Jalving, S. Abhyankar, K. Kim, M.

based computational framework for simulation and optimisation of coupled infrastructure networks," in

istributionT. Ding, K. Sun, C. Huang, Z. Bie, and F. Li, programmingoperation considering network connectivity

D. J. Won and S. quality monitors considering system topologyDelivery, vol. 23 no. 1, pp. 288P. Chavali and A. Nehorai, using factor graphspp. 2864-2876, Jun. 2015.Leslie G. Valiant, Communications of the ACMG. Ravikumar andoriented graph database framework for power systemsPower Systems,J. Dean and S. Ghemawat, large clustersJan. 2008.

Kersting,

Distribution Test Fieee.org/ soc/pes/dsacom/testfeeders/


s paper modelsGDM which provide

managementgraph database and graph computing

power flow algorithm and a power flow software have been The simulation res

effectively reduceefficient data management services and




2010, Art. no. 42G. Malewicz et al.processing,” in Proc. 2010 ACM SIGMOD Int. Conf. Manage. data2010, pp. 135–146

: An open source graph databasehttp://neo4j.com/.C. Avery, “Giraph: Large

,” in Proc. Hadoop SummitAvailable:http://www.slideshare.net/averyching/20110628giraphhadoo

TigerGraph: The first native parallel graphhttps://www.tigergraph.com/.

, V. Vittal, S. Kolluri, and S. M. Wong, connectivity monitoring using a graph theory network flow algorithmIEEE Trans. Power J. Jalving, S. Abhyankar, K. Kim, M.


istribution, vT. Ding, K. Sun, C. Huang, Z. Bie, and F. Li, programming-based splitting strategies for power system islanding operation considering network connectivity

D. J. Won and S. quality monitors considering system topology

vol. 23 no. 1, pp. 288P. Chavali and A. Nehorai, using factor graphs

2876, Jun. 2015.Leslie G. Valiant, Communications of the ACMG. Ravikumar andoriented graph database framework for power systemsPower Systems, vol. 32, no. 4, pp. 2560J. Dean and S. Ghemawat, large clusters”, Communication of the ACM

Kersting, Distribution system modeling and analysis

Distribution Test Fsoc/pes/dsacom/testfeeders/


VI.

s paper modelsGDM which provide



effectively reduces the computing time of power flow and data management services and

Aauthors are gra

coding work at the early stage of this research.



2010, Art. no. 42et al.Proc. 2010 ACM SIGMOD Int. Conf. Manage. data

146. : An open source graph database

. C. Avery, “Giraph: Large

Proc. Hadoop SummitAvailable:http://www.slideshare.net/averyching/20110628giraphhadoo


, V. Vittal, S. Kolluri, and S. M. Wong, connectivity monitoring using a graph theory network flow algorithmIEEE Trans. Power Systems,J. Jalving, S. Abhyankar, K. Kim, M.


, vol. 11, no. 12, pp. 3163T. Ding, K. Sun, C. Huang, Z. Bie, and F. Li,

based splitting strategies for power system islanding operation considering network connectivity

D. J. Won and S. II quality monitors considering system topology

vol. 23 no. 1, pp. 288P. Chavali and A. Nehorai, using factor graphs”,

2876, Jun. 2015.Leslie G. Valiant, “Communications of the ACMG. Ravikumar and S. A. Khaparde, oriented graph database framework for power systems

vol. 32, no. 4, pp. 2560J. Dean and S. Ghemawat,

Communication of the ACM

Distribution system modeling and analysis

Distribution Test Feederssoc/pes/dsacom/testfeeders/


VI.

s paper models the power GDM which provides fast parallel power flow platform,



the computing time of power flow and data management services and

ACKNOWLED

authors are grateful to Dr. Wenlei Bai for hiscoding work at the early stage of this research.



2010, Art. no. 42. et al., “Pregel: A system for largeProc. 2010 ACM SIGMOD Int. Conf. Manage. data

: An open source graph database

C. Avery, “Giraph: LargeProc. Hadoop Summit

Available:http://www.slideshare.net/averyching/20110628giraphhadoo


, V. Vittal, S. Kolluri, and S. M. Wong, connectivity monitoring using a graph theory network flow algorithm

Systems,J. Jalving, S. Abhyankar, K. Kim, M.


ol. 11, no. 12, pp. 3163T. Ding, K. Sun, C. Huang, Z. Bie, and F. Li,


Moon, quality monitors considering system topology

vol. 23 no. 1, pp. 288P. Chavali and A. Nehorai,

, IEEE Trans. Signal Processing,2876, Jun. 2015.

“A bridging model for parallel computationCommunications of the ACM

S. A. Khaparde, oriented graph database framework for power systems

vol. 32, no. 4, pp. 2560J. Dean and S. Ghemawat,



eederssoc/pes/dsacom/testfeeders/

ase of larger test systems. Thus, iresults that our proposed parallel power flow algorithm is very effective when dealing with large

C

the power fast parallel power flow platform,

management, and graph database and graph computing



CKNOWLED

teful to Dr. Wenlei Bai for hiscoding work at the early stage of this research.

REFERENCES


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CONCLUSIONS

the power fast parallel power flow platform, , and graph based

graph database and graph computingpower flow algorithm and a power flow software have been

The simulation results show that the software the computing time of power flow and

data management services and

CKNOWLED


EFERENCES


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ONCLUSIONS

the power distributionfast parallel power flow platform,

graph basedgraph database and graph computing

power flow algorithm and a power flow software have been ults show that the software


CKNOWLEDGMENT


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Proc. 48th Annu. Sout



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t can be concluded from the results that our proposed parallel power flow algorithm is very

systems.

ONCLUSIONS

distributionfast parallel power flow platform,




MENT


EFERENCES

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Documents

Graph Computing based Parallel Power Flow Algorithm and ... · requires higher efficient data management methods and faster power flow solutions [1]. To achieve the goal of efficient