Modeling Power System Buses Using Performance Based Earthquake Engineering Methods Vishvas Chalishazar, Chen Huo, Ian Fox, Travis Hagan, Eduardo Cotilla-Sanchez, Annette Von Jouanne, Julia Zhang, and Ted Brekken School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, Oregon 97330 Email:
[email protected]
Abstract—The Pacific Northwest region is in a constant threat of an imminent earthquake event. Numerous efforts are being made to make the electrical grid in the region more resilient to seismic activities. Performance-Based Earthquake Engineering (PBEE) is one of the approaches being used by researchers to analyze the risk associated with structures such as buildings and bridges. This research intends to introduce modeling of power systems using the PBEE method. Each bus in a oneline representation of a power system is a mini-substation with a different configuration and should be modeled as such. This paper also proposes guidelines for modeling every bus of a power system. Application of these guidelines on a 3-bus system is illustrated. An augmented model for a general power system with arbitrary number of buses is also described for adding system resiliency considerations.
I. I NTRODUCTION This work presents methods for enhancing power systems models with parameters for resiliency modeling. The practical benefit of this effort is to allow power systems engineers to integrate probabilities of power system asset (e.g., buses, generators, transmission lines, etc...) loss into power flows and reliability analysis. An earthquake in the Cascadia Subduction Zone has been labeled as the greatest natural threat posed to the state of Oregon and its inhabitants. Thus in the year 2011 Oregon legislature passed House Resolution 3 to understand the full extent of the impact that this hazard can pose to the state and devise a plan to make the state more resilient [1]. The Oregon Seismic Safety Policy Advisory commission (OSSPAC) was formed for this purpose and has been since commanding the direction of making a resilience plan [1]. Other organizations such as the Federal Emergency Management Agency (FEMA) and the Cascadia Region Earthquake Workgroup (CREW) have started working on making different plans for emergency situations. FEMA has started an initiative called Cascadia Rising under which officials of many countries, majority military commands and the three state governments of Oregon, Washington and Idaho have joined forces together to work as a team and organize an earthquake readiness excercise [2]. One of these 4 day exercises was carried out from 7th to 10th June 2016. CREW is a coalition of private and public sector companies
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Robert B. Bass Department of Electrical and Computer Engineering Portland State University Portland, Oregon 97207 Email:
[email protected]
Fig. 1. Flow chart of the PBEE method [3].
and their primary goal is to educate homeowners and private business owners about the intensity of an earthquake and help them devise a plan to reduce the impact. The researchers at the Pacific Northwest Earthquake Engineering Research (PEER) Center are using the PBEE technique to produce probabilistic predictions of the performance of structures and providing them to the owners in the form of expected monetary loss and risk involved with respect to post hazard operability [4]. They are implementing this method on six different testbeds at four different locations [4], namely, (1) Van Nuys [5], (2) UC Science Building, (3) Humboldt Bay Bridge, (4) I-880. They have also created an open source software called OpenSEES, which implements this methodology on a range of synthetic structural models (SSMs). This software also has capabilities to carry out sensitivity and reliability testing on SSMs [4]. There are other processes, such as Load and Resistance Factor Design (LRFD), used before by the structural engineers to analyze different structures like buildings and bridges. But the PBEE method offers advantages over the LRFD method because LRFD assesses only the performance on the basis of probabilistic failure of each asset [4]. II. P ERFORMANCE BASED E ARTHQUAKE E NGINEERING A PPROACH The PBEE process is a four step deductive method. The flow chart of this process is shown in Fig. 1. The facility or the asset to be analyzed and its location are defined at the beginning
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followed by the first step of this process, Hazard Analysis. In this step the frequency with which different hazards are recurring at the asset site is depicted. In the next step, which is Structural Response Analysis, the types of responses that are shown by the asset located at that specific site is calculated. The third step is the Damage Analysis where the measure of the actual physical damage to each component of the asset is calculated using damage probability distribution (e.g., lognormal distribution) [3]. The last step is the Loss Analysis in which quantities such as repair costs, loss of life and other losses to each component as well as the total system is calculated. The graphical representation of an example of this method is as shown in Fig. 2. For this example only two levels for each analytical step has been chosen for simplicity but the number of levels in each step can be more or less than two. The probability calculations are as follows: p[H|A] denotes the probability of a given Asset (A) experiencing a typical Hazard (H1 or H2); p[R|H] denotes the probability of an asset (based on its location) expressing a typical Response (R1 or R2) given a particular hazard; p[D|R] denotes the probability of the asset being in a precisely defined Damage state (D1 or D2) given the type of response; p[L|D] denotes the probability of incurring a certain amount of Loss (L1 or L2) given the damage state the asset is in. Damage states and loss states for a few power system assets are listed in Table I. All the probabilities are calculated to be fed in the equations (1), (2) and (3), which represent the sum of all probabilities at the end of each step including probabilities from all the previous steps. Equation (3) is commonly addressed as the framework equation for performance assessment and this equation describes the basic structure for the PBEE process [5]. At the end the value of equation (3) gives the total probability of each asset incurring a level of predefined loss. p[R] = p[H|A] dH (1) p[D] =
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Fig. 3. One line diagram of (A) Single Bus Single Breaker Type Configuration, (B) Ring Bus Configurations, (C) Breaker and a Half Type Configuration and (D) Double Bus Double Breaker Type Configuration.
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III. G UIDELINES FOR ASSIGNING BUS CONFIGURATIONS In this research general rules of thumb that can be used when modeling buses in a power system are proposed. In doing so the fundamental correlation between buses in a synthetic
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model and their analogous assets at a real facility has also been explored. These rules for applying different configurations are based on the number of feeders connected on a bus as well as the criticality of the bus. In these rules both generators and loads at any bus are considered as an individual feeder. There are four types of bus configurations that are most
A. Single Bus Single Breaker Type configuration In the SBSB type configuration each feeder is connected to the bus through a series of a normally closed switch (NCs), a circuit breaker (52s) and another normally closed switch as seen in Fig. 3(A). This design has no flexibility and offers the least reliability as well. All the assets under risk for a bus modeled as this type of configuration and 2 feeders connected to it are as follows: 2 circuit breakers, 4 switches, 8 internal transmission cables and 1 bus bar. Each of these assets can be clearly seen in side view image of a substation with this configuration as shown in Fig. 4(A). B. Ring Bus Configuration In this type of configuration each circuit breaker is shared between its two neighbouring feeders protected by two normally closed switches on both sides as seen in the one line diagram in Fig. 3(B). This configuration is a very common choice for high voltage applications. This design is also flexible and offers a basic level of reliability with least number of circuit breakers. All the assets under risk for a ring type bus with 3 feeders are as follows: 3 circuit breakers, 6 switches, 12 internal transmission cables and 3 bus bars. These assets can be observed in side view image in Fig. 4(B). C. Breaker and a Half Type Configuration Fig. 4. Sideview images of (A) Single Bus Single Breaker Type Configuration, (B) Ring Bus Configurations, (C) Breaker and a Half Type Configuration and (D) Double Bus Double Breaker Type Configuration [7].
commonly used at a real facility [6]. They are listed here in the order of least expensive to the most expensive. (1) Single Bus Single Breaker (SBSB) type: Known as the simplest and cheapest type of configuration [6]. Rule: Single Bus Single Breaker configuration is considered for the buses with only two feeders connected to it. (2) Ring type: This configuration provides higher operational flexibility and reliability compared with the previous one [6]. Rule: Ring type configuration is applied when there are three or four feeders on the bus and the bus does not have critical components (e.g., generators, H.V. transformers etc.) attached to it. (3) Breaker-and-a-half type . This type of configuration provides even higher flexibility and reliability comparing with previous two [6]. Rule: If there are more than four feeders on the bus, Breaker-and-a-half type configuration is considered. (4) Double Bus Double Breaker (DBDB) type: This type of configuration provides the most reliability and operational flexibility when compared to all the other configurations [6]. Rule: Overall, if there is a generator connected on the bus, no matter how many feeders, the bus is considered as a Double Bus Double Breaker type configuration. In a more generic case this configuration is assumed for all critical buses of the system.
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Three circuit breakers are shared between two feeders in this type of configuration as seen in Fig. 3(C). Thus the name breaker and a half type. This configuration is a cheaper option than the DBDB configuration and offers high flexibilty as well as high reliability. The assets involved in this configuration with 4 feeders are: 6 circuit breakers, 12 switches, 24 internal transmission cables and 2 bus bars. Fig. 4(C) shows the side view of a part of the substation with this type of configuration. D. Double Bus Double Breaker Type Configuration Each feeder in this type of configuration connects to two seperate bus bars through a series of two normally closed switches and one circuit breaker on each side as seen in the one line diagram of this configuration in Fig. 3(D). This adds redundancy and thus no interruption is experienced in service to any circuit due to bus fault. This type of configuration is very flexible and has the highest reliability when compared to all the other configurations. But it is only used for critical buses such as a generator bus because it is also very expensive. All the assets, that are physically under risk of damage due to seismic activities, for a bus modeled as this configuration and with 3 feeders connected to the bus are as follows: 6 circuit breakers, 12 switches, 24 internal transmission cables and 2 bus bars. Each of these assets can be clearly seen in side view image of a substation with this configuration as shown in Fig. 4(D). Note that the feeder towers are considered one with the external transmission line corresponding to that feeder and are thus not considered as a seperate asset.
TABLE I D EFINED DAMAGE S TATES AND L OSS S TATES FOR E ACH A SSET Assets
Defined Damage States
Defined Loss States
D1 - No Damage D2 - Damaged, Inoperative
L1 - 0% Loss of injected power in the bus L2 - 25% Loss of injected power in the bus L3 - 50% Loss of injected power in the bus L4 - 75% Loss of injected power in the bus L5 - 100% Loss of injected power in the bus L1 - 0% Loss of injected power in the bus L2 - 25% Loss of injected power in the bus L3 - 50% Loss of injected power in the bus L4 - 75% Loss of injected power in the bus L5 - 100% Loss of injected power in the bus L1 - 0% Loss of injected power in the bus L2 - 25% Loss of injected power in the bus L3 - 50% Loss of injected power in the bus L4 - 75% Loss of injected power in the bus L5 - 100% Loss of injected power in the bus L1 - 0% Loss of injected power in the bus L2 - 25% Loss of injected power in the bus L3 - 50% Loss of injected power in the bus L4 - 75% Loss of injected power in the bus L5 - 100% Loss of injected power in the bus L1 - 0% Loss of peak load L2 - 25% Loss of peak load L3 - 50% Loss of peak load L4 - 75% Loss of peak load L5 - 100% Loss of peak load L1 - 0% Loss of generation capacity L2 - 25% Loss of generation capacity L3 - 50% Loss of generation capacity L4 - 75% Loss of generation capacity L5 - 100% Loss of generation capacity
Circuit Breakers
D1 - No Damage D2 - Damaged, Inoperative Switches
D1 - No Damage D2 - Damaged, Inoperative Bus Bars
D1 - No Damage D2 - Damaged, Inoperative Internal and External Transmission Cables
D1 - No Damage D2 - Damaged, Inoperative Load
Generators
D1 - No Damage D2 - Damaged, Inoperative. Pipes and nozzles damaged D3 - Damaged, Inoperative. Drive shaft misalignment D4 - Damaged, Inoperative. Minor electrical damage D5 - Damaged, Inoperative. Exhaust line disconnected at expansion bellows
IV. 3- BUS S YNTHETIC E LECTRICAL M ODEL (SEM) A SSETS In this research the PBEE process is implemented on a 3-bus SEM . A one line diagram of this model is shown in Fig. 5. For the purposes of this research it has been assumed that there is only one hazard level; earthquake, and three different response levels with different ranges of Peak Ground Acceleration (PGA). The three different response levels and their ranges are defined as follows: R1 (green region) - [P GA < 0.1g], R2 (yellow region) - [0.1g < P GA < 0.3g] and R3 (red region) - [P GA > 0.3g]. Different levels of damage states and loss states are assumed according to each individual asset. In this 3-bus system there are 3 buses out of which bus 1 and bus 2 are generator buses and bus 3 is a load bus as seen in Fig. 5. It is crucial to make the SEM similar to a real world testbed. To understand and analyze the different types of assets that exist in a real world testbed and the way they are represented in a one line diagram of an SEM it is considered that each bus in the system is an individual mini-substation. There are many different types of configurations for modeling each bus, as discussed in section III, keeping in mind the importance of a bus and the number of feeders connected to that bus. For this research the buses in the 3-bus SEM is modeled using two of these configurations: (1) Ring Bus Configuration (Bus no. 3) and (2) Double-Bus-Double-Breaker Type Configuration (Bus no. 1 and 2). Thus according to the rules laid down in section III, the 3-bus system is comprised of 44 assets in bus no. 1, 44 assets in bus no. 2, 24 assets in bus no. 3, 2 generators, 1 load and 3 external transmission lines connecting the 3 buses. This adds up to a total of 118 assets in a simple 3-bus
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Fig. 5. One line diagram of the 3-bus synthetic model. Based on the rules above, bus 1 and bus 2 are modeled as DBDB Configuration and bus 3 is modeled as Ring Bus Configurations.
SEM. After section III, where all the different types of bus configurations and the assets involved in each configuration have been catagorized, the authors define damage states and loss states for all those assets as described in Table I. The damage states for generators are taken from the fragility database provided by FEMA P-58 [8]. V. AUGMENTED MODEL FOR ADDING RESILIENCY TO A 3- BUS SYSTEM USING PBEE The augmented model for resiliency of a power system with N number of buses is shown in Table II. For this model, all
TABLE II AUGMENTED M ODEL FOR R ESILIENCY U SING PBEE M ETHOD . Bus ID
Asset ID
p[Hi |Aq ], i = 1, . . . , w
p[Rj |Hi ], j = 1, . . . , x
p[Dk |Rj ], k = 1, . . . , y
p[Ll |Dk ], l = 1, . . . , z
1 . . . . . . . . . N
A1 . . .
α11 . . . α1i . . . α1w . . .
β111 . . . β1ij . . . β1wx . . .
γ111 . . . γ1jk . . . γ1xy . . .
δ111 . . . δ1kl . . . δ1yz . . .
Aq . . . Am
αq1 . . . αqi . . . αqw . . . αm1 . . . αmi . . . αmw
βq11 . . . βqij . . . βqwx . . . βm11 . . . βmij . . . βmwx
γq11 . . . γqjk . . . γqxy . . . γm11 . . . γmjk . . . γmxy
δq11 . . . δqkl . . . δqyz . . . δm11 . . . δmkl . . . δmyz
the defined quantities are as follows : • [Aq , q = 1 . . . m] - Asset IDs for a total of m assets • w - Total number of hazards • x - number of responses • y - number of damage states • z - number of loss states • [αqi , i = 1 . . . w] - probability of asset Aq facing hazard Hi • [βqij , j = 1 . . . x] - probability of asset Aq expressing response Rj facing hazard Hi • [γqjk , k = 1 . . . y] - probability of asset Aq being in damage state Dk expressing response Rj • [δqkl , l = 1 . . . z] - probability of asset Aq being in loss state Ll being in damage state Dk • [w+(w∗x)+(x∗y)+(y∗z)] - Total number of probability columns in the augmented model • [2 + [w + (w ∗ x) + (x ∗ y) + (y ∗ z)]] - Total number of columns in the augmented model • m - Total number of rows in the model (one for each asset) The branch probabilities shown in Fig. 2 between Asset to Hazard relates to αqi for all q and i; similarly the probabilities between Hazard to Response relates to βqij for all q, i and j; and between Response to Damage relates to γqjk for all q, j and k; and between Damage to Loss relates to δqkl for all q, k and l. For the 3-bus system (N = 3) discussed at the beginning of this section earthquake is defined as the only hazard so w = 1; Three responses have been considered so x = 3; Different number of damage states for different assets are considered and listed in Table I so y = 2 or y = 5; Five loss states for each asset are assumed so z = 5. For this model it is assumed that there are m = 118 assets and thus there will be 118 total rows in the augmented model. The total number of columns in the augmented model will be 46. Using all these probabilities the framework equation for performance assessment can be calculated and the predicted quantification of the risk attached with any individual asset can be assessed. VI. C ONCLUSION In this research a way to model the buses of a synthetic power system is demonstrated such that they very closely represent a real world facility. As a general rule it is considered that all the generator buses are double bus double breaker type configuration and all the non critical buses with three to six
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feeders are ring type configuration. A way to apply the PBEE method on a power system with N buses is also described in this paper. The augmented model for resiliency for the same power system is shown. An example of a 3-bus system for modeling the buses, such that it very closely represents the real world facility are discussed. The definitions for Response levels, Damage states and Loss states to implement the PBEE method on the same 3-bus system are also discussed for all the different types of assets considering earthquake as the only hazard. To accurately calculate the probabilities for each asset numerous factors, specific to the location of each asset, should be considered. Some of the major factors are soil strength, soil liquefaction point and standards used for the installation of a particular asset. Initial efforts to calculate these factors for some critical substations in the Pacific Northwest region have already begun. This approach to modeling the power system has not been implemented before and adds an interesting perspective to system resiliency modeling. ACKNOWLEDGMENT The authors gratefully acknowledge the input from Dr. Armin Stuedlein and Central Lincoln PUD. The authors are also grateful to the Oregon Talent Council for funding this project. R EFERENCES [1] ”The Oregon Resilience Plan,” tech. rep., Oregon Seismic Safety Policy Advisory Commission (OSSPAC), Feb. 2013 [2] ”Cascadia Subduction Zone (CSZ) Pacific Northwest Catastrophic Earthquake and Tsunami Functional Exercise.” [Online], Accessed 7 Nov 2016, Available: http://tinyurl.com/gnof9oc [3] Porter, Keith. ”Beginners Guide to Fragility, Vulnerability, and Risk.” Encyclopedia of Earthquake Engineering (2015): 235-260. [4] Porter, Keith A. ”An overview of PEERs performance-based earthquake engineering methodology.” Proceedings of Ninth International Conference on Applications of Statistics and Probability in Civil Engineering. 2003. [5] H. Krawinkler, ”Van Nuys Hotel Building Testbed Report: Exercising Seismic Performance Assessment,” PEER 2005/11. [6] Blackburn, J. Lewis, and Thomas J. Domin. Protective relaying: principles and applications, CRC press, 2015. [7] D. Nack, “Reliability of substation configuration,” 2005. [Online], Available: http://tinyurl.com/zetmvsp [8] ”Guidelines for Seismic Performance Assessment of Buildings,” 2012. [Online], Accessed 7 Nov 2016, Available: http://tinyurl.com/pu8fpum
