Clayton Barrows

Comparing the Topological and Electrical Structure of the North American Electric Power Infrastructure

The topological (graph) structure of complex networks often provides valuable information about the performance and vulnerability of the network. However, there are multiple ways to represent a given network as a graph. Electric power transmission and distribution networks have a topological structure that is straightforward to represent and analyze as a graph. However, simple graph models neglect the comprehensive connections between components that result from Ohms and Kirchhoffs laws. This paper describes the structure of the three North American electric power interconnections, from the perspective of both topological and electrical connectivity. We compare the simple topology of these networks with that of random, preferential-attachment, and small-world networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these topological forms may be misleading as models of power systems. To study the electrical connectivity of power systems, we propose a new method for representing electrical structure using electrical distances rather than geographic connections. Comparisons of these two representations of the North American power networks reveal notable differences between the electrical and topological structures of electric power networks.

The Topological and Electrical Structure of Power Grids

Numerous recent papers have found important relationships between network structure and risks within networks. These results indicate that network structure can dramatically affect the relative effectiveness of risk identification and mitigation methods. With this in mind this paper provides a comparative analysis of the topological and electrical structure of the IEEE 300 bus and the Eastern United States power grids. Specifically we compare the topology of these grids with that of random [1], preferential-attachment [2] and small-world [3] networks of equivalent sizes and find that power grids differ substantially from these abstract models in degree distribution, clustering, diameter and assortativity, and thus conclude that these abstract models do not provide substantial utility for modeling power grids. To better represent the topological properties of power grids we introduce a new graph generating algorithm, the minimum distance graph, that produces networks with properties that more nearly match those of known power grids. While these topological comparisons are useful, they do not account for the physical laws that govern flows in electricity networks. To elucidate the electrical structure of power grids, we propose a new method for representing electrical structure as a weighted graph. This analogous representation is based on electrical distance rather than topological connections. A comparison of these two representations of the test power grids reveals dramatic differences between the electrical and topological structure of electrical power systems.

Multi-Attribute Partitioning of Power Networks Based on Electrical Distance

Identifying coherent sub-graphs in networks is important in many applications. In power systems, large systems are divided into areas and zones to aid in planning and control applications. But not every partitioning is equally good for all applications; different applications have different goals, or attributes, against which solutions should be evaluated. This paper presents a hybrid method that combines a conventional graph partitioning algorithm with an evolutionary algorithm to partition a power network to optimize a multi-attribute objective function based on electrical distances, cluster sizes, the number of clusters, and cluster connectedness. Results for the IEEE RTS-96 show that clusters produced by this method can be used to identify buses with dynamically coherent voltage angles, without the need for dynamic simulation. Application of the method to the IEEE 118-bus and a 2383-bus case indicates that when a network is well partitioned into zones, intra-zone transactions have less impact on power flows outside of the zone; i.e., good partitioning reduces loop flows. This property is particularly useful for power system applications where ensuring deliverability is important, such as transmission planning or determination of synchronous reserve zones.

Transmission Switching in the RTS-96 Test System

Strategically removing transmission lines from service through “optimal transmission switching” (OTS) has been shown to produce significant system cost savings. Here, we analyze the results of OTS on the RTS-96 network to identify network characteristics that may help identify solution sets and reduce computational complexity. Our initial analysis suggests that the majority of the cost savings from OTS arises from switching a limited number of branches. This finding suggests that the speed of the OTS algorithm, which has been implemented as a mixed-integer program, could be improved by limiting switching operations to a smaller number of pre-screened branches.

Defining power network zones from measures of electrical distance

This paper describes new methods for dividing a power network into zones, such that buses are electrically close to other buses within zones. Defining zones based on electrical distance rather than asset ownership or historical affiliation has the potential to improve the utility of planning procedures, such as Load Deliverability Assessment, that are based on zone boundaries. The paper describes a set of metrics for the quality of a given zoning outcome and outlines methods that use these measures to produce improved zonal boundaries. Preliminary results from an exploratory study of the US Mid-Atlantic (PJM Interconnection) power grid illustrate the feasibility of the proposed approach.

Computationally efficient optimal Transmission Switching: Solution space reduction

Recent studies have shown that the dynamic removal of transmission lines from operation (“Transmission Switching”) can reduce the costs associated with power system operation. Smart Grid technologies introduce flexibility into the transmission network topology and enable state dependent co-optimization of generation and network topology. The optimal transmission topology problem has been posed in previous research on small test systems. However, the problem complexity and large system size makes optimal transmission switching (OTS) intractable on real power systems. We analyze the optimal transmission switching results of prior work on the RTS-96 network and find that most of the economic benefits arise from switching a small number of lines. We decompose the results to determine the marginal savings contribution of each optimally switched line. Our marginal analysis leads to the development of an off-line screening method, based on network sensitivities, for identifying candidate switchable lines. When compared to OTS on the RTS-96 network, our screening tool generates near optimal solutions in a fraction of the time.

Correcting Optimal Transmission Switching for AC Power Flows

Optimal Transmission Switching (OTS) has demonstrated significant savings potential on test systems when formulated in a linearized DC power flow framework. OTS solutions generated from DC models, however, are not guaranteed to produce a feasible AC dispatch. Additionally, whether AC-feasible OTS solutions will generate cost savings similar to those suggested in the DC model is not guaranteed. We present a method to correct OTS solutions obtained in the DC model to ensure feasible AC power flow solutions. When applied to the RTS-96 benchmark network, the method achieves results that are both AC feasible and generate significant system cost reductions - in some cases larger than the cost reductions suggested by the DC OTS.

Implications of Model Structure and Detail for Utility Planning: Scenario Case Studies Using the Resource Planning Model

NOTICE This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or any agency thereof. formerly) deserves our special gratitude for his thought leadership and insights at the inception of the Resource Planning Model. Any remaining errors or omissions are the sole responsibility of the authors. Abstract Capacity expansion models are computational tools designed to find the least cost option for planning a system under a variety of policy, business, and operational constraints. In this report, we analyze the impacts of model configuration and detail on resource selection decisions of capacity expansion models. Our analysis focuses on the importance of model configurations— particularly those related to capacity credit, dispatch modeling, and transmission modeling—to the construction of scenario futures. Our analysis is primarily directed toward advanced tools used for utility planning and those impacts that are most relevant to decisions about future renewable capacity deployment. To serve this purpose, we develop and employ the National Renewable Energy Laboratorys Resource Planning Model to conduct a case study analysis that explores 11 capacity expansion model configuration scenarios for the Western Interconnection through 2030. While the analysis results cover the entire Western Interconnection, the model and research examine in greater detail a region within the interconnection that consists of two balancing areas—the Public Service Company of Colorado and the Western Area Power Administration Colorado/Missouri—that serve load primarily in and around the state of Colorado. We examine how model investment decisions change under different model configurations and assumptions related to renewable capacity credit, the inclusion or exclusion of operating reserves, dispatch period sampling, transmission power flow modeling, renewable spur line costs, and the ability of a planning region to import and export power. For all modeled scenarios, we …

Using Network Metrics to Achieve Computationally Efficient Optimal Transmission Switching

Recent studies have shown that dynamic removal of transmission lines from operation (“Transmission Switching”) can reduce costs associated with power system operation. Smart Grid systems introduce flexibility into the transmission network topology and enable co-optimization of generation and network topology. The optimal transmission switching (OTS) problem has been posed in on small test systems, but problem complexity and large system sizes make OTS intractable. Our previous work suggests that most economic benefits of OTS arise through switching a small number of lines, so pre-screening has the potential to produce good solutions in less time. We explore the use of topological and electrical graph metrics to increase solution speed via solution space reduction. We find that screening based on line outage distribution factors outperforms other methods. When compared to un-screened OTS on the RTS-96 and IEEE 118-Bus networks, the sensitivity-based screen generates near optimal solutions in a fraction of the time.

Time Domain Partitioning of Electricity Production Cost Simulations

Production cost models are often used for planning by simulating power system operations over long time horizons. The simulation of a day-ahead energy market can take several weeks to compute. Tractability improvements are often made through model simplifications, such as: reductions in transmission modeling detail, relaxation of commitment variable integrality, reductions in cost modeling detail, etc. One common simplification is to partition the simulation horizon so that weekly or monthly horizons can be simulated in parallel. However, horizon partitions are often executed with overlap periods of arbitrary and sometimes zero length. We calculate the time domain persistence of historical unit commitment decisions to inform time domain partitioning of production cost models. The results are implemented using PLEXOS production cost modeling software in an HPC environment to improve the computation time of simulations while maintaining solution integrity.