230 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 20, NO. 1, FEBRUARY 2005 Distributed Processing of Reliability Index Assessment and Reliability-Based Network Reconfiguration in Power Distribution Systems Fangxing Li, Member, IEEE Abstract—Parallel and distributed processing has been broadly generation and transmission systems by Monte Carlo simu- applied to scientific and engineering computing, including various lation [12]. These previous works can be classified into two aspects of power system analysis. This paper first presents a dis- categories: applications of parallel processing [4]–[6], [12] tributed processing approach of reliability index assessment (RIA) for distribution systems. Then, this paper proposes a balanced and applications of distributed processing [7]–[12]. It appears task partition approach to achieve better efficiency. Next, the dis- that more recent works focus on distributed processing. This tributed processing of RIA is applied to reliability-based network is probably due to the latest development in network hardware reconfiguration (NR), which employs an algorithm combining and software, which makes distributed processing faster, more local search and simulated annealing to optimize system reliability. broadly available, and easier-to-implement than before. Testing results are presented to demonstrate the speeded execution of RIA and NR with distributed processing. This paper presents distributed processing schemes of relia- bility index assessment (RIA) and reliability-based network re- Index Terms—Network reconfiguration, parallel and distributed configuration (NR) for distribution systems. Here, the radial dis- processing, power distribution systems, reliability index assess- ment, scalability, simulated annealing. tribution system is addressed, since the majority of U.S. distri- bution systems are radial. In addition, system-level reliability indices are addressed because they are the primary reliability I. INTRODUCTION concerns of utilities. The discussion shows that RIA can be ARALLEL and distributed processing [1], [2] has signif- easily de-coupled and executed in parallel among different pro- P icant contributions to scientific and engineering computa- cessors to achieve speedup in wall-clock running time. The dis- tions, especially for time-critical or time-consuming tasks. Par- cussion also shows NR is mainly composed of iterative runs of allel processing is usually carried out in dedicated multiproces- RIA. Therefore, NR can be executed in parallel based on the sors with a global clock and shared memory, while distributed distributed processing of RIA. The proposed implementation processing is usually carried out at multiple workstations or of distributed processing considers the unbalanced computing computers connected to a network without a central clock and ability of different processors, a typical feature of heterogeneous shared memory. In distributed processing, message passing is a computers connected to a LAN or a similar network. common technique to share information since there is no shared This paper is organized as follows. Section II presents a con- memory. Although the performance of networked computers is troller-worker model based on message passing to share the not as competitive as a dedicated parallel computer, networked data and coordinate the activity of different processors. Sec- computers are less expensive and more broadly available such as tion III first discusses the principle of an analytical approach to in local area networks (LANs). As such, distributed processing assess distribution reliability and why it is highly parallelizable; is sometimes referred to as the low-end parallel processing. then presents a coarse-grained distributed processing scheme for It should be noted that the term “parallel” is used occasionally RIA. Section IV discusses the balanced task partition among dif- in this paper to indicate the concurrent execution of a computing ferent processors in order to achieve better performance and ef- task. The discussion in this paper is essentially based on dis- ficiency. Section V presents and discusses the testing results for tributed processing. Especially, like many other distributed pro- distributed processing of RIA. Section VI applies the distributed cessing approaches, the proposed approach employs the mes- processing of RIA to reliability-based NR, which employs an sage-passing scheme for data sharing among collaborating pro- annealed local search and RIA. Test results are also provided. cessors. Section VII concludes the paper. Parallel and distributed processing has been applied to power system computing in various areas [3]–[12], such as load II. CONTROLLER-WORKER MODEL flows [4]–[7], optimal power flows [8], [9], state estimation FOR DISTRIBUTED PROCESSING [10], contingency analysis [11], and reliability evaluation for Distributed processing has two fundamental units: computa- tion and communication. Computation is referred to as the CPU activity to carry out the actual computing task, while commu- Manuscript received May 16, 2004. Paper no. TPWRS-00643-2003. nication is referred to as the overhead activity to transfer data The author is with ABB Inc., Raleigh, NC 27606 USA (e-mail: [email protected]; [email protected]). or share information among different collaborating processors. Digital Object Identifier 10.1109/TPWRS.2004.841231 Although communication is overhead indeed (and is desired to 0885-8950/$20.00 © 2005 IEEE LI: DISTRIBUTED PROCESSING OF RIA AND RELIABILITY-BASED NR 231 be minimum), it is normally a necessary part for distributed pro- cessing due to the lack of shared memory. This paper employs the controller-worker model [7] to co- ordinate computation and communication in distributed pro- cessing. As described in [7], the model is comprised of two types of processes, controllers and workers, which play different roles in the message-passing scheme. A controller is a process with the following responsibilities: • to accept user input; • to assign initial data to workers; • to invoke workers to execute tasks; Fig. 1. Input and output of RIA. • to send/receive intermediate data to/from workers; • to do system-wide, nonintensive calculations; (the failure on a component). Taking SAIFI as an example, this • to terminate the algorithm at the appropriate time and no- can be expressed as tify workers to stop. A worker is a process with the following responsibilities: • to receive initial data from a controller; (1) • to do intensive calculations upon a controller’s request; • to send/receive intermediate data to/from a controller; • to stop when notified. where In the approach here, there is only one controller, while there contribution to SAIFI from component ; are multiple workers. The controller is mainly responsible for total number of components. coordinating all workers and maybe some nonintensive compu- Since SAIFI is defined as the number of customer inter- tations, while workers are responsible for intensive computa- ruptions that an average customer experiences during a year, tions [7]. This model implies a coarse-grained distributed pro- is the number of customer interruptions at an average cessing, in which parallelism occurs at the level of subroutine customer caused by failures on component . Hence, or group of subroutines. can be written as [18] (2) III. DISTRIBUTED PROCESSING OF RIA where This work assumes N-1 contingencies. Further, only perma- failure rate per year of component ; nent component faults are considered in this section for sim- number of customers experiencing sustained interrup- plicity and illustration. tion due to a failure of component ; A survey of 205 U.S. utilities [13] showed that five relia- total number of customers. bility indices, SAIFI, SAIDI, MAIFI , CAIDI, and ASAI (or Combining (1) and (2), we have ), have been popularly employed in the utili- ties. The survey also mentioned other four less popular indices, CAIFI, CTAIDI, ASIFI, and ASIDI. This section takes SAIFI as an example to illustrate why the calculation of a reliability index can be divided into many parallelizable steps. The Ap- (3) pendix briefly illustrates that the other system reliability indices Since is a constant and is related to the component itself, can be assessed in a similar way. the above equation shows that the key to calculate SAIFI is to The purpose of RIA for distribution systems is to model each calculate . Since stands for the number of customers expe- system contingency and compute the reliability impact of each riencing sustained interruptions due to a failure of component contingency. It may be carried out through various approaches, , it can be evaluated by identifying which components will be such as analytical approach based on component contributions de-energized based on the system topology, protection scheme, [14], [15], failure mode and effect analysis (FMEA) [16], Monte and restoration. Although the evaluation of may be compli- Carlo simulation [17], [18], Markov modeling [19], and other cated, it is certain that the evaluation of is independent of practical approaches [20]. This work employs the analytical ap- . In other words, two processors can evaluate and proach in the previous work [14], [15] to evaluate reliability in- , respectively, in parallel, if both processors know the input of dices such as SAIFI, SAIDI, MAIFI , etc. Fig. 1 briefly illus- the system data. Hence, evaluation of SAIFI contributions from trates the input and output of RIA analysis. Appendix C also component and ,or and ,