my wonderful article for isarc?9 -...

ADVANCES IN SEISMIC PERFORMANCE EVALUATION OF POWER NETWORKS

Masanobu Shinozuka1,Stephanie Chang2,

T.C. Cheng3,

1, University of California, Irving2, University of Washington

3, University of Southern California

This study provides a method to evaluate performance of electric power systems before and after a major catastrophic event, such as an earthquake, an accidental or manmade disablement of system components, and more importantly incorporate the results of evaluation as an integral part of the methodology that will enhance the seismic resilience of communities. Based on our experience in the analysis of the seismic performance of the Los Angeles Department of Water and Power (LADWP) system after the Northridge earthquake, we derived a useful set of data and gained significant knowledge on the robustness of electric power network and grid during and after a catastrophic event.

Keywords: Earthquake, Power Network, Power Grid, Outages

1. INTRODUCTION

This paper presents recent advances in seismic performance analysis of electric power systems performed primarily at MCEER (Multidisciplinary Center for Earthquake Engineering Research) headquartered in Buffalo, N.Y. (Shinozuka, M., et al., 2002 and 2003, Dong, X., et al., 2002 and 2003). The advances are prominent in (1) integration of WECC (Western Electricity Coordination Council) database with EPRI’s (Electric Power Research Institute’s) IPFLOW (Interactive Power FLOW) computer code for systematic power flow analysis using LADWP’s power transmission network as an example, (2) development of fragility curves for transformers, circuit breakers and disconnect switches in a transmission network on the basis of damage information from the 1994 Northridge earthquake and enhanced fragility curves from the test results (Murota, N., 2000 and 2003), (3) estimation of the likelihood for the power availability and for the number of households without power after an earthquake, (4) development of preliminary performance criteria for power systems, (5) equipment retrofit study in order to examine the extent of the enhancements such retrofit work can produce, (6) application of a life cycle cost methodology to evaluate seismic mitigation for urban infrastructure systems in general, and power systems in particular, and (7) evaluation of effect of a disabling event within a power grid on its performance of the grid which is possibly as disastrous as the August 14, 2003 power blackout.

Throughout, the systems analysis of the LADWP’s transmission network system under actual and simulated earthquakes is performed. The analysis was based on an inventory database of the network, together with available fragility information of power equipment and Monte Carlo simulation techniques. This is a unique research work where an actual database from WECC is used in conjunction with the computer code IPFLOW (EPRI, 1998). In this analysis transmission lines are assumed to be seismically not vulnerable, which is obviously not always the case as demonstrated clearly in the 1999 Chi-Chi earthquake.

Figure 1. Transmission network and service areas of LADWP’s power system

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Figure 2. Electric power output for service areas under intact condition

2. SENARIO EARTHQUAKE

To gain a complete understanding of the seismic performance of LADWP’s power system, 47 scenario earthquakes are selected and simulated as discussed later in detail. These scenario earthquakes are associated with annual “equivalent probabilities” of occurrence so that collectively, they represent the full range of the regional seismic hazard (Chang, E.S., et al., 2000). The results of this analysis produce risk curves for households without power after an earthquake.

For urban infrastructure systems, evaluating the benefits and costs of hazard mitigation measures is complicated by several important considerations. First, electric power, water, and other infrastructure networks are spatially distributed across a wide area; hence, evaluations must account for system functionality as well as the spatial correlation of hazard (such as earthquake ground motion) across the area. Actually, this is the reason why scenario earthquakes are used here. Second, these systems have long service lives. Analyses must therefore consider how the system itself, as well as the potential impacts of its failure, might change over a period of many decades. In this respect, continual monitoring and maintenance is needed and yet easily neglected in practice. Third, infrastructure systems are vital to all sectors of the urban community. Mitigation assessments should therefore include the benefits to both the lifeline infrastructure provider and society as a whole. This paper applies a life cycle cost methodology for evaluating the effect of infrastructure mitigation techniques for seismic retrofit of an electric power system. Total life cycle costs include repair cost,

utility revenue losses and societal losses in future earthquake disasters.

3. DEVEROPMENT OF FRAGILITY CURVES

Failure of transmission equipment is one of the most common and significant types of damage to electric power systems due to earthquakes. In particular, transformers are crucial components in an electric power network, and yet their redundancy is not as high as other equipment due mainly to their large size and high cost. Therefore, it is very important to make a pre-event evaluation of the seismic performance of transformers on the basis of damage information obtained from the past earthquakes as well as from laboratory experiments. In this research, substantial effort was expended to acquire damage information for transmission level transformers related to the Northridge earthquake identified from one-line diagrams of the LADWP and Southern California Edison (SCE) receiving stations. The damage information is transformed into empirical fragility curves expressed in the form of two-parameter (median and log-standard deviation) lognormal distribution, as a function of peak ground acceleration (PGA) which represents the intensity of the seismic ground motion at each site. Use of PGA for this purpose is considered reasonable: The PGA value at the location of each receiving station is determined from the PGA contours (see Wald, 1998, http://quake.wr.usgs.gov/research/strongmotion/effects/shake/). In this research, the maximum likelihood method (Shinozuka M., et al. 2000) is employed to estimate the two parameters of the fragility curve resulting in c=0.45g (median) and =0.42 (log-standard deviation). With these two parameters, the fragility curve for the transformers in the transmission network has been developed and is shown in Figure 3 (in red) with the label Case 1 (Dong, X., 2002).

There exist a number of possible methods for seismic retrofit of transformers including a base-isolation technique (Murota, N., 2002 and 2003 and Saadeghvaziri M.A., et al., 2000-2001). The improvements to the seismic performance using these methods are measured by the enhancement index (Cr/C)-1 where Cr and C are the median values of fragility curves retrofitted and not-retrofitted transformers, respectively. The change in the log-standard deviation is disregarded for the reasons that their influence on the final result is secondary.

The methods of retrofit examined tend to be quite effective, and therefore in the following analysis, 50% and 100% enhancement index values are assumed to be achievable and used. The enhanced fragility curves are also plotted in Figure 3

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(blue and green for 50% and 100% enhancement, respectively) (Dong, X., 2002).

Figure 3. Fragility curves for transformers in transmission network.

4. SEISMIC PERFORMANCE OF A POWER SYSTEM

To demonstrate our method of systems analysis, LADWP’s network which is part of the WECC’s (Western Electrici ty Coordination Council’s) power transmission network (http:/ /www.wecc.biz/main.html ) is analyzed. WECC’s grid covers 14 western states in the U.S. two Canadian provinces and northern Baja California in Mexico. The analysis method to predict the seismic performance of the electrical power network is described below (Dong, X., 2002, Tanaka, S., et al., 1997) and also depicted in a flow chart (Figure 4) which emphasizes that this procedure is an iterative process: (1) Use 47 scenario earthquakes (13 Maximum

Credible and 34 User Defined, http://shino8.eng.uci.edu)

(2) For each scenario earthquake, simulate equipment damage using fragility curves with and without retrofitting

(3) Simulate damaged transmission networks

(4) Calculate power flow using IPFLOW under network failure criteria Imbalance of Power

(2)

Abnormal voltage

(3) Frequency change

IPFLOW does not check this criterion Lose of connectivity

(5) Compute reduction in average power supply (total and for each service area)

(6) Compute relative number of households without power

(7) Develop seismic risk curves (annual probability that system performance will be reduced more than a specified level due to earthquake)

(8) Examine system performance relative to performance criteria with and without rehabilitation

(9) Determine effectiveness of rehabilitation

Figure 4. Power Flow Analysis

By applying the systems analysis procedure, LADWP’s power flow analysis is performed 20 times on the network for each scenario earthquake. Each simulation result represents a unique state of network damage. Figure 5 shows the PGA distribution associated with the Northridge earthquake in LADWP’s service areas. Figure 6 shows the ratio of the average power supply of the damaged network to

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that associated with the intact network for each service area when only transformers are considered vulnerable. The average is taken over the entire sample size equal to 20. The extent to which the retrofit of transformers contributes to improvement of system performance is evident if we compare the power supply ratio under Case 1 (not enhanced), Case 2 (50% enhanced) and Case 3 (100% enhanced) in Figure 6.

Figure 5. PGA under Northridge earthquake

Figure 6. Relative average power output with

only transformers vulnerable

Aside from transformers, there is a set of transmission level equipment in the power network which is also very vulnerable to earthquakes, particularly circuit breakers and disconnect switches. Figures 7 shows the seismic performance analysis results involving these equipments, using different fragility curves for circuit breakers (Figure 8) and for disconnect switches (Figure 9). These fragility curves are empirically developed based on Northridge damage data. The results show that if transformers, circuit breakers and disconnect switches are considered vulnerable under earthquakes, the power output is significantly reduced throughout LADWP’s service areas. This result matches the actual outcome of the 1994 Northridge earthquake. It is noted that the blackout was quickly remedied in the case of Northridge earthquake, due to effective emergency network management.

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Figure 7. Relative average power output with transformers, circuit breakers and disconnect switches vulnerable

Figure 8. Fragility Curve of Circuit Breakers

Figure 9. Fragility Curve of Disconnect Switch5. RISK CURVES OF LADWP’S

POWER SYSTEM

The locations of LADWP’s and SCE’s receiving stations relative to faults in and around the Los Angeles area indicates that many are near active faults and have a high possibility of suffering from damage due to an earthquake. In evaluating the risk and costs associated with potential future earthquakes, the performance of the power system in 47 (deterministic) earthquake scenarios was evaluated. These scenarios were developed by Chang et al (2000), applying a loss estimation software tool, EPEDAT, which was used to generate regional ground motion patterns for a given earthquake epicenter, magnitude, and depth (USC-EPEDAT, 1999). The 47 events included 13 maximum credible earthquakes on various faults in the Los Angeles region and 34 other events of magnitude 6.0 or higher. Based on these analyses, together with their hazard-consistent probabilities, seismic risk of LADWP's power system due to earthquake-induced performance degradation is developed in terms of a risk curve in Figure 10 for Case 1 (no enhancement) and for Case 2 and 3 (enhancement index 50% and 100%, respectively).

Figure 10. Risk curves of LADWP's power system

The percentage of households with and without power supply are computed as follows:

where:m = service areas number (1,2,…,M)

M=21 in this examplen = simulation number (1,2,…,N)

N=20 in this exampleRd(m,n) = power output ratio in service area m under n-th simulationHshld(m)= total households in service area m

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The risk curve in this study plots the expected annual probability that the system will suffer from a power supply reduction more than a specified rate, as a function of that rate. Each data point in the figure represents one of the scenario events. The risk curve is useful for economic impact analysis of the Los Angeles area as well as cost and benefit analysis to determine the effectiveness of enhancement technologies (see the curves with solid triangles and squares) (Dong, X., 2002). Of equal importance is the use of the risk curve in relation to the development of the performance criteria and their verification as described in the section that follows.

6. SYSTEM PERFORMANCE CRITERIA

The performance criteria for power systems listed in Tables 1 and 2 demonstrate a possible format in which the criteria can be given. Table 1 lists criteria to be satisfied in pre-event assessment, and Table 2 those in post-event emergency response. These tables also include performance criteria for water and acute care hospital systems. In combination, they conceptually establish the degree of community resilience in terms of robustness, rapidity and reliability. Specific values (in percentages for robustness, rapidity in restoration and reliability) are examples to better understand the concept. The performance criterion for power systems shown in Table 1 is represented by a point double-circled in Figure 11 (enlarged version of Figure 10) where the robustness corresponds to the annual probability that 80% or more households will have power immediately after any earthquake is equal to 0.99. The risk curve for Case 1 (without rehabilitation) does not satisfy this criterion, but the risk curves for Case 2 and Case 3 (with rehabilitation) do satisfy it. These criteria can also be used to judge the effectiveness of rehabilitation as carried out in this study. Data collection and modeling for rapidity in restoration are much more difficult to pursue (Shinozuka M., et al., 2002). Further research is needed to develop analytical models based on past experience so that performance criteria, such as those shown in Table 2, become meaningful in practice.

Table 1. System Performance Criterion I for Pre-event Assessment and Rehabilitation

Robustness and Resourcefulness Reliability

Power A majority (at least 80%) of households will have continued power supply after

With a high level of

reliability (at least 99%

earthquake per year)

Water

A majority (at least 80%) of households will have continued water supply after earthquake



per year)

Hospital

A majority (at least 95%) of injured or otherwise traumatized individuals will be accommodated in acute care hospitals for medical care



per year)

Table 2. System Performance Criterion II for Post-Event Response and Recovery

Robustness and Resourcefulness Reliability

Power

A majority (at least 95%) of households will have power supply as rapidly as possible within a short period of time (3 days)


reliability (at least 90% of earthquake

events)

Water

A majority (at least 95%) of households will have water supply as rapidly as possible within a short period of time (3 days)



events)

Hospital

All the injured and traumatized individuals will be accommodated in acute care hospitals as rapidly as possible within a short period of time (1 days)



events)

Figure 11. Annual probability of exceedance for households without power (enlarged view)

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7. SYSTEM RESTORATION

It was demonstrated that the restoration for utility power systems tend to be rapid compared with that for water, gas and transportation systems. Figure 10 shows the empirical restoration curves for the LADWP system after the Northridge earthquake. The curve plots the percentage of instruments with restored power as a function of elapsed time. To reproduce and simulate the curve, seismic damage sustained by transformers, circuit breakers and disconnect switch have the same probability function as assumed in Figure 11 for the repair/restoration. The curve for example indicates that a damaged transformer can be replaced or repaired within a half day with a probability of 25%. This is merely an assumption on which we initiate and gain numerical insight for the restoration simulation. In reality, a transformer probably cannot be replaced or repaired in such rapidity unless the degree of damage is light. We follow the fragility simulation and power flow analysis as outlined in Figure 4 and add an extra layer of Monte Carlo simulation where damaged components are restored in accordance with the restoration probability function assumed in Figure 12. Resulting simulation for restoration is represented by four points in Figure 13 which underestimate the speed of restoration. We note that power system restoration procedure caries out repair or replacement of damaged components in the order reflecting the priority established for the purpose of accelerating the entire network restoration. If such a procedure was taken into consideration, the simulation performed here might have more closely agreed with the empirical curve.

Figure 12. Restoration probability for transformers, circuit breakers and disconnect switches

Figure 13. LADWP’s power system customers restored versus time

8. EVALUATING MITIGATION OF LADWP’S POWER WYWTEM

The evaluation of seismic mitigation for urban infrastructure systems is carried out by applying the life cycle cost method, particularly to LADWP’s power system used in this study. The word “mitigation” here is used in a much broader sense than “rehabilitation.” The latter refers to specific seismic retrofit of systems and their components, as described below. In contrast to more traditional benefit-cost analysis, the life cycle cost framework readily and transparently accommodates costs that may change over time. For infrastructure systems, this is advantageous for addressing such issues as infrastructure deterioration and urban growth. Moreover, the framework developed here emphasizes costs that would be imposed on the community, as well as the lifeline agency, in the event of infrastructure failure in a disaster. The framework therefore allows a comprehensive assessment of mitigation benefits. Details of the methodology, along with an application to the Portland, Oregon, water delivery system, can be found in Chang (forthcoming). In this approach, the options of “mitigation” and “no mitigation” are compared in terms of their total life cycle costs. These include repair costs, utility revenue losses, and societal losses in future earthquake disasters. These costs are evaluated for a period of N years, with expected annual costs discounted to their present value. For the mitigation case, life cycle costs also include the cost of the retrofit itself.

In this paper, the case study examines mitigation of high voltage transformers using base isolation. Hence, “mitigation” is synonymous to “retrofit by base-isolation” here. The impact of the mitigation on network performance was assessed by using the results from power flow analysis of LADWP’s power system. The total life cycle costs, C, can be expressed as follows:

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where Cs is the cost of the seismic mitigation (retrofitted) measure (assumed to take place in the initial year of analysis), Cr,t is expected annual earthquake repair costs in year t, Cv,t is expected annual earthquake revenue loss to the utility in year t, Ce is expected annual direct economic loss to the community in year t, and y is a discount rate (assumed to be a real rate of 3 percent). The total timeframe of analysis is 50 years. All costs are evaluated in constant dollars, not of inflation. Cr,t, Cv,t, and Ce,t are each probabilistically aggregated over the 10 or 20 simulations of the 47 earthquake scenarios, as described above.

In the analysis, the mitigated case was represented by a weighted average of the results from the “as-is,” “50% performance enhancement,” and “100% performance enhancement” analyses. The respective weights are 0.08, 0.12, and 0.80. These weights were based on the confidence levels associated with each performance level in the base isolation testing.

The mitigation case consists of base isolating 109 transformers. Although actual data on the mitigation cost was not available, based on our research and consultation with LADWP, a rough estimate of $60,000 per transformer was used for this analysis. Seismic mitigation cost Cs is therefore $6.54 million.

Table 3 summarizes the four cost components for the mitigated and unmitigated cases. Mitigation leads to considerable reductions in expected repair costs and revenue loss in future earthquakes. Total discounted costs to the utility agency are reduced from $1.67 million to $0.21 million. However, these savings do not outweigh the cost of mitigation. If societal impacts are disregarded, total life cycle costs with mitigation ($6.75 million) are four times as large as costs in the do-nothing case ($1.67 million), and mitigation does not appear advisable.

Table 3. Life Cycle Cost Results(2000$ millions)

However, if direct economic losses are considered, mitigation appears very cost-effective. Direct economic losses are on the order of 50 times as large as the utility’s repair and revenue losses combined. If they are included in the analysis, total life cycle costs without mitigation ($97.19 million) are 5.7 times as large as costs with mitigation. Mitigation could reduce discounted, expected direct economic loss by some $85 million. Base isolation of the transformers appears highly cost-effective.

Table 4 presents the results if it is assumed that population and economic activity remain constant over the 50-year period (i.e., no urban growth or productivity increase). The basic finding – that mitigation is cost-effective if societal impacts are considered, but not if they are excluded – is unchanged. In this case, direct economic losses are on the order of 30 times as large as repair and revenue losses combined (Chang, E.S., et al., 2003).

Table 4. Life Cycle Cost Results without Urban Growth

(2000$ millions)

9. EVALUATION OF EFFECT ONA DISABLING EVENT OF THE

PERFORMANCE OF LARGE UTILITY SYSTEMS AND

POWER GRIDS

A general methodology is also developed in this study to analyze the behavior of large electric utility networks or grids under a catastrophic event, such as a severe earthquake or an intentional disablement of system components. In this respect, we are working on the outages just experienced in Midwest and northeastern part of this nation and southern Canada on August 14, 2003 in order to analyze and simulate what happened not only to the power grid, but also to transportation, water supply, and other infrastructure systems and associated socio-

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Unmitigated Case

Mitigated Case

Mitigation Cost $0.00 $6.54 Repair Cost (discounted) $0.39 $0.07

Revenue Loss (discounted) $1.28 $0.14

Direct Economic Loss (discounted) $95.52 $10.45

Total Life Cycle Costs $97.19 $17.19

Total Life Cycle Costs without Direct Economic Loss

$1.67 $6.75

Unmitigated Case

Mitigated Case

Mitigation Cost $0.00 $6.54 Repair Cost (discounted) $0.39 $0.07

Revenue Loss (discounted) $0.89 $0.09

Direct Economic Loss (discounted) $39.38 $4.29

Total Life Cycle Costs $40.66 $11.00 Total Life Cycle Costs

without Direct Economic Loss

$1.28 $6.70

economic disturbance. Initially, the research was motivated by an accident in August 1996, in which a tree came into contact with a high-voltage aerial power line at a location in the State of Oregon, disabling its transmission capability. The result was a wide-spread blackout in several states and cities, including part of Los Angeles. We were able to simulate the outage in Los Angeles under the Oregon scenario, making use of grid inventory data and an electric power flow simulation code. This type of accidents often creates a chain of events such as power imbalance and abnormal voltage leading to blackout. The research became more seriously significant after the tragic September 11 event from homeland security point of view and has just added another layer of relevance since the August 14, 2003 power outage. This is because disablement can be man-made, accidental or malicious, and cause a devastatingly negative impact on socio-economic welfare of the directly affected regions immediately and of the nation in the long run.

10. CONCLUSION/FUTURE RESEARCH

This study integrated many of the technologies developed by the authors over the years, including GIS inventory data of the LADWP’s electric transmission systems, multiple scenario earthquakes representing the Los Angeles area seismic hazard, fragility characteristics of system components with and without seismic retrofit, systems analysis using WECC’s database and EPRI’s IPFLOW computer code, life-cycle cost estimation methods, and preliminary versions of performance criteria definitions and their verification procedures. This integration leads to the capability to evaluate the performance of both power and water systems and the consequences of system interruptions caused by earthquakes. Additional study will be undertaken to further establish performance criteria that can be quantitatively mapped into the response space, in technological, economic, organizational, and social dimensions. Future study will also include the development of probabilistic procedures to estimate the reliability of the seismic resilience of the community. Also, integration with other critical systems such as emergency response organizations, medical care systems (a regionally designated network of acute care hospitals) and highway transportation systems will be carried out to evaluate the community resilience. Finally, the application of SCADA in the inverse analysis of power system performance is of significant future interest. This is to improve the time it takes to achieve restoration of system function degraded by the earthquake, which is the rapidity aspect of the resilience criteria. An added dimension to our

future research is to provide recommendation to prevent, protect and quickly restore the power network and grid from the outage due to natural, technological and malicious causes.

Acknowledgments

This work was done under National Science Foundation Grant EEC9701471 through Multidisciplinary Center for Earthquake Engineering Research and also supported by National Science Foundation Grant CMS-0112665. The authors acknowledge technical support provided by Mr. R. Tognazzini and Mr. J. Mochizuki of LADWP and Dr. X. Jin, University of Southern California and Dr. X.J. Dong, University of California, Irvine.

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