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Outages are often unsuccessful due to ineffective advanced planning, which results in This is due to a combination of better instructions, easy access to parts, tools, Developing spreadsheets of piping systems that require blinds to be.
Table of contents
- Directions in Development
- Distributed Power-Line Outage Detection Based on Wide Area Measurement System
- Directions in Development
At this point, it is clear to see that by using Theorem 1, Equation 19 can be reduced to:. Next, we are concerned about how to address the updates of z n. As mentioned previously, we take the sub-differential over Equation 15b with respect to z n and the optimality condition becomes:. In a similar way, a closed-form solution for the updates of z n is obtained as follows:.
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- 1. Introduction.
The most computational-intensive step in Algorithm 1 is the update of x n given in Equation 17 , which, in essence, requires matrix inversion and multiplication for each PDC in every iteration. Nevertheless, a detailed look shows that the variables in Equation 17 may not change significantly within two consecutive iterations.
The previous ADMM iteration x n k often provides a good approximation to the results, which can be used as a warm start to update x n k. Now, if we look at the the minimization step in Equation 15a along with its minimizer in Equation 17 , it actually can be regarded as solving a system of linear equations:.
The least squares solution of Equation 25 is [ 24 ]:. We observe that Equation 17 is equivalent to finding the least squares solution with matrix A and vector b formed in the following:. At this point, we have changed the problem of x n -update in Equation 17 into finding a method to solve linear equations in Equation 25 with A and b defined in Equations 27 and 28 , respectively. To this end, we adopt the LSQR algorithm in this paper. Recall that I n , D n are diagonal matrices and that H n is sparse in general.
Thus, matrix A is also sparse. LSQR thus fits our need, since it is very efficient for solving sparse linear equations [ 25 ]. Interested readers, please refer to [ 25 ] for the details. We omit its introduction, here due to space limitation. In short, the modified distributed line detection algorithm with a warm start is described in Algorithm 2.
As discussed in Section 4. Thanks to the help of the cross-validation technique, we can have some portion of data for model validation. To evaluate the proposed centralized and distributed line change detection algorithms, we use an Intel Duo Core at 1. To solve the centralized algorithm in Equation 7 , we used CVX, a package for specifying and solving convex optimization problems [ 28 ]. In this section, the WSCC nine-bus test case system was used for our simulation. The diagram of the system is demonstrated in Figure 3.
There are three generators G1,G2,G3 , three transformers T1,T2,T3 and nine lines in which the line parameter information is listed in Table 1. From Table 1 , the line-to-bus admittance matrix Y fl can be formed, which is used for constructing the measurement matrix H in Equation 7. In this case, the size of the unknown vector is nine by one, and we place two PMUs at Bus 4 and Bus 6 with their line current measurements in 1—4 , 4—5 , 9—4 , 5—6 , 3—6 , 6—7. The system is assumed to be at steady state before and after the line change. We made the line change on the reactance of line 1—4 , which was altered from 0.
The above are all of the quantities considered as the input to our centralized line change detection algorithm. The result in Figure 4 shows that the faulty line 1—4 has been correctly detected by the algorithm. Note that initially, Branches 1—3, 5 and 9 have positive values, which means that they are all seen as a group of possible faulty lines. During Iteration 2—4, the values of Branches 1—3, 5 and 9 are actually decreasing, while an interesting point is that the decreasing speed of Branches 2, 3, 5 and 9 is much faster than Branch 1's. This observation is conformed with the theory part discussed previously, that the most likely set of branches should survive for the next iteration.
From Iteration 5, Branch 1 is almost the only one standing out. This implies that Branch 1 is considered to be faulty by our distributed line change detection algorithm. In other words, the distributed algorithm almost converges to the centralized version result we assume it as a benchmark in Figure 4 in just five iterations. The IEEE bus system is tested here for evaluating our algorithms in the case of a large network. There are branches in the test system, which will result in over 17, possible faulty topologies in just a double-line outage scenario.
All of the single line outage possibilities and double-line outage cases are randomly chosen for testing. We adopt the method in [ 29 ] as our pool of measurements and randomly select two thirds the number of measurements from it. The exhaustive search algorithm in [ 6 , 7 ] is compared with our proposed methods in Figure 6 in terms of the percentage of the correctly detected outage pattern.
It is impressive that both the centralized and distributed line outage detection methods perform very close to this optimal criterion. The running times of the developed algorithms are also tested on the IEEE bus test system. Following a Monte Carlo simulation method, the results for single and double-line outages are listed in Table 2.
It is found that as the system size and the number of line outages increases, the advantage of the warm-started D-LCD over distributed LCD becomes more sharper in terms of computational time. However, the exhaustive search approach does not scale well, as its running time jumps up in an order much higher than the others. In this paper, the proposed algorithms are assumed to work in transmission networks.
Nevertheless, theoretically, they can also apply to distribution networks. The current distribution networks usually lack measurements and have a low level of monitoring capabilities. Our proposed distributed algorithms involve the communication of neighboring PDCs. Each PDC only communicates with its neighbors by its estimates of the shared unknown variables.
Hence, if the PDC is unable to collect the neighbors's information, it will keep its value of estimates unchanged. In this paper, the proposed distributed algorithms are more robust than the centralized ones in the following sense: However, for the proposed distributed algorithms, the probability of having similar serious conditions is much smaller. A novel distributed line outage detection algorithm was developed based on WAMS, which has been an important component of smart grids. The proposed approach allows multiple line outage identification using limited PMU measurements.
The feature of low-complexity distributed processing in the proposed framework can enhance the efficiency, security and privacy level in smart grid monitoring. Numerical tests demonstrated the merits of the proposed schemes in coordinating the discovery of multiple line outages in a power grid.
Future research directions include the design and analysis of the control strategy considering the HVDCand FACTdevices involved after the localization of the faults and developing asynchronous the present paper is under a synchronous setting , distributed line outage detection algorithms, which are highly required in the environments of distributed systems, such as future smart grids.
The authors would like to thank Lang Tong Cornell University for his helpful suggestion and discussion in conducting the presented work. Liang Zhao made substantial contributions in proposing the problem formulation, designing the solution framework, performing the numerical analysis and manuscript preparation. Wen-Zhan Song made significant contributions in directing the related technical content and giving final approval of the version to be submitted. National Center for Biotechnology Information , U. Journal List Sensors Basel v. Published online Jul This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license http: This article has been cited by other articles in PMC.
Abstract In modern power grids, the fast and reliable detection of power-line outages is an important functionality, which prevents cascading failures and facilitates an accurate state estimation to monitor the real-time conditions of the grids. Related Work Existing PMU-based line outage detection methods typically use the internal-external network model for the whole interconnected system in which the goal is to identify external line outages using only measurements within the internal system [ 4 — 8 ]. Our key contributions in this paper can be summarized as follows: We formulate the line outage detection problem in a smart grid as a convex optimization problem, which can be solved efficiently in practice.
We propose a distributed algorithm to solve the aforementioned problem by using the alternative direction multiplier method ADMM. It overcomes the computational burden and privacy issues. This approach requires only simple matrix-vector operations, which is compatible with real power grids. Specifications for the Proposed Framework Our main idea is to devise a distributed and robust protocol that can be performed in WAMS for smart grid monitoring application.
Sensor Network Model Our proposed method is based on the hierarchical network of WAMS as shown in Figure 1 , which consists of a hierarchical structure, as follows. Open in a separate window. Hierarchical architecture of a wide area measurement system WAMS in a smart grid.
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Sensor Measurement Settings We consider a linear physical equation describing the relation between the measurable quantity and the set of unknown variables. Furthermore, an additional assumptions is made: For our purpose of detecting possible faulty lines, the number of measurements we have is relatively smaller than the number of unknown variables, which implies that the measurement matrix is under-determined. Problem Formulation In this section, we describe the detailed measurement equation and centralized line outage detection solution adopted in this paper.
Possible Centralized Solution for Line Outage Detection In this paper, we combine the measurements and the prior information on the branch currents to do the line outage detection. Then, the maximum likelihood ML estimation in a single control center can be formulated as: Remark 1 The centralized grid-wise measurement data collection the computation in implementing Equation 7 are inefficient due to bandwidth and time constraints or infeasible because of data privacy concerns; thus, distributed computations are strongly preferred or demanded.
Distributed Line Outage Detection In this section, we striveto solve the optimization problem in Equation 7 in a distributed manner. Remark 2 The criterion in Equation 9 will force some entries of the vector of branch currents x n equal to their mean values corresponding entries of x pn , which implies that they are consistent with their statistical distribution, and thus, these branches are recognized as in the normal condition.
Then, Equation 8 can be reformulated as: D n as a diagonal matrix with its m , m -th entry being 1;. I n denotes an identity matrix with its dimension being the number of states in n -th area. Theorem 1 For each pair of n , m in Equation 15c , the following holds for the updating Lagrange multipliers: Proof In Equation 15b , we note that the optimization task will be performed in n -th and m -th PDC in parallel for each adjacent pair n , m. Thus, we can obtain the following result by solving Equation 15b for n , m and m , n , respectively: Distributed Line Change Detection with Warm Start The most computational-intensive step in Algorithm 1 is the update of x n given in Equation 17 , which, in essence, requires matrix inversion and multiplication for each PDC in every iteration.
Now, if we look at the the minimization step in Equation 15a along with its minimizer in Equation 17 , it actually can be regarded as solving a system of linear equations: Numerical Tests To evaluate the proposed centralized and distributed line change detection algorithms, we use an Intel Duo Core at 1. Line parameters of the WSCC nine-bus system. Comparison of detection performance for the IEEE bus system. Running time comparison for the IEEE bus system. Discussion In this paper, the proposed algorithms are assumed to work in transmission networks. Conclusions and Future Work A novel distributed line outage detection algorithm was developed based on WAMS, which has been an important component of smart grids.
Author Contributions Liang Zhao made substantial contributions in proposing the problem formulation, designing the solution framework, performing the numerical analysis and manuscript preparation. Conflicts of Interest The authors declare no conflict of interest. De La Ree J. Synchronized phasor measurement applications in power systems.
Directions in Development
A multilevel state estimation paradigm for smart grids. Tracking changes in the external network model. External system line outage identification using phasor measurement units. Line outage detection using phasor angle measurements. Double line outage detection using phasor angle measurements. Sparse overcomplete representations for efficient identification of power line outages. Fault detection and localization in smart grid: A probabilistic dependence graph approach. Efficient identification method for power line outages in the smart power grid. Ambiguity group based location recognition for multiple power line outages in smart grids.
Power system line outage detection and identification—A quickest change detection approach. Distributed fault detection observer for rail vehicle suspension systems. HMRF-based distributed fault detection for wireless sensor networks. Wide-area monitoring, protection, and control of future electric power networks. Wikipedia Kirchhoff's Circuit Laws. A generalized likelihood ratio approach to the detection and estimation of jumps in linear systems. Here is a suggested planning timeline: Rough work list developed 18 to 24 months out: Work list reaches the budget, and planning commences 12 months out: Monthly outage meetings begin 6 months out: Work list is locked down.
Distributed Power-Line Outage Detection Based on Wide Area Measurement System
Post-Outage Critique meetings occur Successful maintenance organizations identify their outage work list from various sources, all of which should be in alignment with the outage objectives. The planning process can commence, once the outage work list has been established and approved. The key is that outage work task identification is critical and successful outage planning and scheduling depends on important events occurring far in advance.
In the timeline we state that the work list should be locked down six months prior to the outage. The lockdown date is essential to effectively managing and planning outage work. If a lockdown process is not in place there will be a never-ending flood of last-minute work items being added to the outage that will not be planned, and this will result in excessive costs, reactive response and increased probability of outage schedule overrun.
Part delivery issues and labor availability become a problem when work is added after the lock down date. The implementation of a lockdown process is a concept that some individuals may find difficult to accept, especially if in the past they have been allowed to add work with no regard to the impact on the overall outage budget and schedule. A process to address add-on outage work must be developed and in place that requires the requestor to justify the need and identify what existing work items will be sacrificed. Management must seriously enforce the lockdown time frame, following the established process and gain agreement from all parties that it will be followed.
Any work proposed for addition after the lockdown date should be carefully scrutinized and justified before approval. It is important to remember that planning work is expensive. It is extremely wasteful to cancel a job that is already planned with parts on order or onsite , in order to do unplanned work.
As outage tasks are identified, the task scope has to be defined. In many instances the identified work task is all the scope that is provided. In this case workers assigned to accomplish the work are at a disadvantage, because they are left to determine the scope based on their knowledge, which may not be the intended scope at all. When this occurs, inefficiencies, delays and costly overruns usually result. Clearly defined work scope is essential to successful outage planning, scheduling and work execution. If the following questions are answered, a clear work scope will result:. As a part of defining and refining the scope of work, the planner will be required to conduct site visits at the location of the requested work to determine the five basic elements of work planning:.
To accomplish this level of planning it is very important that adequate personnel be dedicated full time to the planning of outage work packages. If this is not done, planners most likely will be placed in the role of supervisors, craftsperson, parts-chaser or all around go-fer. None of these activities will increase the efficiency of maintenance activities at the magnitude that effective advance planning will provide.
To meet this objective, advance planning must be thorough. The identification of job hazards, safety issues and obstacles that impact job progress is often overlooked. All can be avoided or taken into account if addressed during the planning process. These items cannot be fully considered if work planning is done on the fly or planners attempt to plan from their desk.
Site visits are an essential part of effective outage planning. As the planning process approaches the six month cutoff date, the outage work planning should be finishing up. Work packages should be fully planned and usually waiting on identified parts and materials to arrive. How do we determine that we have completed the planning process for the outage work? First, all of our outage work should be managed through our work order process. With that in place we can evaluate each work order with a series of questions that, if we answer them truthfully, will determine if the work order planning has been completed.
The evaluation process should include these questions:. The end result, when the work order is scheduled and executed, will be more work being executed with fewer people and in far less time. The repair quality will increase and the cost for each repair will significantly decrease. On average an unplanned repair work order that would take eight hours to complete can take less than two hours to execute when planned. This is due to a combination of better instructions, easy access to parts, tools, equipment, and materials, and better coordination of labor resources.
Experienced outage planners come up with great tricks of their trade. Identifying these tools help them to manage their time more efficiently thus allowing them to provide a better planned outage. Several of their experiences include:. An outage is a unique situation. All work that is placed on the outage schedule must be fully planned. If this is not done, it effectively places the burden of planning the job on the craftsperson. This slows the work tremendously and creates numerous opportunities for delays, mistakes, confusion and unsafe acts. We have covered four of the eight items that directly impact the effective execution of an outage.
Our discussion has specifically focused on the planning process and not on the scheduling process, because scheduling depends on knowing how much work is available, how long each task will take, how many labor resources are required per task, and the priority or criticality of the task.
Each of these factors is directly related to how effectively the planning has been performed. Effective outage planning will result in a meaningful schedule that can then be developed with a high percentage of probability that it will be successful. However, the success of a schedule depends on the execution of the work. Scheduled work expectations have to be communicated to the supervisors and workers responsible for work execution with progress monitored daily. Daily schedule updates are essential; without these updates, on-time completion of the outage is in jeopardy.
Outage management is an effective tool for reducing costs and increasing plant productivity. When the decision is made to identify major outage work far in advance and then carefully plan the work for maximum ease of execution, the result will be lower costs.
Directions in Development
If, at the same time, disruptions to the process such as late add-on work are kept under control, there will be sufficient resources available to continually refine and improve the outage model for even greater savings. References Kister, Timothy C. Maintenance Planning and Scheduling: