Final Project Report
Senior Design
“Statistical Analysis of Power System Faults”
May99-15
April 22,1999
Advisor:
Dr. James McCalley
Team Members:
Corey K. Proctor / ______Chris Dennison / ______
Alvina Hendradi / ______
Greg Bahl / ______
1
Table of Contents
1Abstract......
2Problem Statement......
2.1What is risk?......
2.1.1Events
2.1.2Consequences
3Objectives......
4End product description......
5Assumptions and Limitations......
6Technical Approach......
6.1Overview of the research including:......
6.1.1Description of the data......
6.1.2Description of the statistical method......
6.1.3Description of the power line......
6.2Description of the process used to determine the associated risk......
6.2.1Statistical model......
6.3Determine a recommendation for the power line......
6.4Identify areas of further study......
7Evaluation of Project Success......
8Summary of Testing......
9Recommendations for continued and/or additional work......
10Final Budgets......
10.1Budget Chart......
11Final Timeline......
12Lessons Learned......
13Group Members: Team MAY 99-15......
14Summary and Conclusions......
15Appendix......
15.1Proposed Technical Solution......
15.2Progress to Date......
15.2.1Research......
15.2.2Risk Calculation......
15.2.3Power Flow......
15.2.4MATLAB......
15.3Design Flow Chart......
16References......
Figures
Figure 1 Locations for weather data collectors......
Figure 2 System one-line......
Figure 3 Load duration curve......
Figure 4. One line diagram......
Figure 5. Design flow chart......
Tables
Table 1 Data collector tolerances......
Table 2 Included data and units......
Table 3 Location key for Iowa map......
Table 4 Weather data sites......
Table 5. Transmission line characteristics......
Equations
Equation 1 Number of outages per year......
Equation 2 Probability for transformer fault......
Equation 3 Risk equation for day and night values......
Equation 4 Probability equations......
Equation 5 Summation of risk during the day and night......
Equation 6 Total risk equation......
Equation 7 Decision rule......
Equation 8. Heat balance equation......
Equation 9. Reduction of tensile strength......
Equation 10. Risk calculation formula......
1
1Abstract
The purpose of this project is to study a power line to determine the risk of an outage. In order to make this decision two kinds of analysis will be conducted using statistical data including wind velocity, temperature, and outage probability. The first analysis to be done will be the study of the overloading risk of the current power line without any changes. The second analysis is the benefit assessment, which will analyze the cost and benefits associated with reinforcement to the given power line. These results will then be used to make an assessment of risk of the power line and compare that to an upgraded system.
2Problem Statement
A power line transports electricity for most of its life, barring outages or normal switching operations. This means that the power line is subject to all seasons, all types of weather, and all outage cases.
The effects of weather in a statistical setting have not been fully explored in the past operation of the power system. A conservative estimate has been used to determine the safe operating point of the power line. Because of deregulation in the power system industry, construction has slowed or stopped while the load is increasing and slowly approaching the lower limit of the estimate.
This project will look at weather and outage statistics to try to determine a new operating limit of a power line. It will also determine the amount of risk associated with running the power line over the current limits and study reinforcements that will reduce this risk.
2.1What is risk?
In order to understand the problems of running a power delivery system, a definition of risk is needed.
Risk is the product of an event’s probability and its resultant impact or consequence.
2.1.1Events
Load growth, weather, and/or outages are events that may cause overloading of a transmission line. Outages can be forced or scheduled. Forced outages are faults, miss-operation, or miss-coordination. The utility and the consumer plan scheduled outages. Scheduled outages have minimal impact or are financially rewarding to the consumer, allowing the utility to do scheduled maintenance or reduce loading during peak load conditions.
2.1.2Consequences
Consequences of these events affect the consumer’s ability to live and do business. Depending on the type of consumer, there could also be financial losses. There will also be a cost to the utility due to these consequences, these costs include damage to the system and loss of profits.
3Objectives
Develop a report that will outline the following items
- Overview of the research including:
-Description of the data
-Description of the statistical method
-Description of the power line
- Description of the process used to determine the associated risk
- Determine a recommendation for the power line
- Identify areas of further study
4End product description
Our project is a risk assessment of an actual transmission line. This risk assessment took in account real statistical weather data, a transmission line in a real power system. The client for this project will take full ownership of this report and all information that is obtain from this project.
(Including a summary of capabilities and ownership)
5Assumptions and Limitations
Concerning some line characteristics data, due to the limitation of source, the data needed for the Matlab Program input cannot be an exact and accurate values. For example, the value for the absorption coefficient of the conductor. Since this value is not available for our conductor, the coefficient was approximated by doing a sensitivity test (seeing how a small percentage of increasing the value may affect the risk). This test was described in the Technical Approach section.
6Technical Approach
(Including descriptions of possible alternatives considered and reasons for selection.)
6.1Overview of the research including:
6.1.1Description of the data
6.1.1.1Weather
Weather is considered one of the largest influences on a power line. It influences the temperature of the conductor by environmental factors that include wind speed, wind direction, temperature, and the amount of solar radiation. One of the purposes for this project was to determine what was available for weather data and how can it be used to further this study past a worse case scenario.
The challenge was to find real and meaningful data that could be used in the current MATLAB code as described in SECTION ---- . In order for the data to be meaningful it has to account for the following:
- Describe a location close or exactly at the power line.
- Describe a location that closely resembles the power line corridor. This condition will exclude most National Weather Service Sites because of their location at an airport. This is a very different environment compared to the protected corridor of the power line. The airport sensors are in a wide open field while a normal power line corridor is usually protected.
- Take measurements at a reasonable rate and at the same time. Preferably as many times as can be recorded.
- Have reasonable accuracy at the low end of operation. This is especially important when measuring low wind speeds. Again NWS weather stations are not up this task because of stall speeds around 4-5 ft/sec. The apparatus is tuned to the high end, because of the importance of safety and not pure collection (Seppa, Teppani O.).
This list presents a challenge because it limits one of the largest collectors of wind data: The National Weather Service! In order to get reasonable data an outside source was required. The High Plains Climate Center was found to have digital records for weather stations throughout the Midwest. The HPCC collects data from its own set of data recorders spread throughout the state. The location and data acquired fit the most requirements.
The HPCC source was able to provide data from sites along highways and interstate roadways. This location can be assumed to be close to the power line corridor conditions. Each weather site takes readings every hour and this data is then stored in a digital format. The following tolerances from the HPCC web page show the accuracy of the data (HPCC weather page).
Table 1 Data collector tolerances
Sensor / Variable / Instal. Ht. / AccuracyThermistor / Air Temperature / 1.5m / 0.25 C
Thermistor / Soil Temperature / -10cm / 0.25 C
Si Cell Pyrometer / Radiation-Global / 2m / 2%
Cup Anemometer / Wind Speed / 3m / 5% (0.5m/s-1.64ft/s start up)
Wind Vain / Wind Direction / 3m / 2
Coated Circuit / Relative Humidity / 1.5m / 5%
Tipping Bucket / Precipitation / 0.5m to 1m / 5%
Originally obtaining free data was considered, but due to the lack of quality (only able to get monthly averages) this data was purchased. The amount of data was limited to stations in Iowa and only for a ten-year period. The ten-year period was used to ensure a good statistical setting. After ten years this data was not available at most stations. In the future more station data from outside of Iowa could be purchased to gain a better understanding of the weather.
The data obtained from the HPCC was more then what is currently used in the MATLAB code and further study could be used to determine the usefulness of the extra data. The data received includes:
Table 2 Included data and units
Month / NADay / NA
Year / NA
Hour / 1:00-24:00
Air Temperature / F
Ground Temperature / F
Relative Humidity / %
Wind Speed / MPH
Wind Magnitude / MPH
Wind Direction /
Vector Sd. /
Radiation Flux / Kcal m-2
Precipitation / in
Currently the only data used in the statistical setting was the data for wind speed and air temperature.
Figure 1 shows the state of Iowa and the location of the weather collectors in the state. Table 3 gives the latitude and longitude of each station.
Figure 1 Locations for weather data collectors
Table 3 Location key for Iowa map
Data was ordered from the following sites because ten years worth of data was available, Table 4.
Table 4 Weather data sites
CrawfordsvilleCastana
Chariton
Gilbert
Gilmore
Nashua
Sutherland
6.1.1.2Power-flow data
A single contingency analysis has been completed. A firm understanding of the local power system was required to minimize the number of contingencies to only contingencies that affect the transmission line.
The utility has provided us with the power flow case for the transmission network. They have also given us specific information about the transmission facilities, loads, and approximate costs for the particular reinforcements. To solve the power flow for the different cases and contingencies, IPFLOW developed by EPRI was used. These power flows solutions gave currents for the four cases.
The four cases are types of reinforcements. The first is no change and is called the "base case". The second is "re-building" the transmission line. The third is called "add new transmission line". The final case is adding "micro-generation" at the location of the load.
Each case was analyzed for current conditions, five, ten, fifteen, and twenty years of load growth for only the substation. The client has provided an estimate about 3.5 percent load per year growth for the load in question. This portion of the project has given us the currents flowing down the transmission line under different contingencies. These currents will be used to directly determine the risk. Higher current lead to a higher risk.
To re-conductor the two sections with conductor that improves the current carrying capacity of the transmission line, the structure would have to be either modify structurally or rebuild. Due to time limitations and project goals we have decide that rebuilding is the only choice that we will have time to explore.
The client's planning department suggested, under increased loading, ACSR 1431 kcmil wire for the replacement conductor. This wire would increase the current carrying capacity to 1272 amperes.
Adding a new transmission line was considered to reduce the loading of the south section under a single contingency. This line will be in parallel with the north line but come for substation 1's bus 1.
Adding a combustion turbine generator was considered to reduce the load.
6.1.1.3Matlab inputs
Deterministic Data:
- Diameter
As obtained from the conductor description table, the equivalent diameter of the conductor used, which is 636.0 AWG-kcmil with AAC type, is 1.090 inches.
- emissivity coefficient
Obtained from the web, assuming the conductor material is Aluminum Alloy A3003, oxidized with temperature above 900 F, the emissivity coefficient is 0.40.
- absorption coefficient
By doing a sensitivity test due to unavailability of sources, the value cannot be determined accurately. The default value of the software is 0.5 .
Coefficient / Mean PDT / Deviation PDT / Probability / Risk0.5 / 61.4691 / 15.3185 / 0.022398 / 0.011034
0.6 / 61.6269 / 15.2749 / 0.022369 / 0.010986
0.7 / 61.7835 / 15.2315 / 0.02234 / 0.010937
0.4 / 61.3099 / 15.3626 / 0.022425 / 0.01108
For 10 % changes of the coefficient:
The PDT mean value will change by = 0.25%
The probability will change by = 0.13%
The risk will change by = 0.435%
Impacts’ Data:
- Safety margin of sag = 37.3871 inches
This is an IEEE standard.
- Sag increasing rate
The default value suggests 0.6 inches/Celsius. By doing a sensitivity test, apparently changes made in Impact’s Data column will not change other output except the risk.
Rate / Mean PDT / Deviation PDT / Probability / Risk0.7 / 61.4691 / 15.3185 / 0.022398 / 0.011034
1.7 / 61.4691 / 15.3185 / 0.022398 / 0.039949
1.9 / 61.4691 / 15.3185 / 0.022398 / 0.068864
2 / 61.4691 / 15.3185 / 0.022398 / 0.083322
The risk starts to change if the rate reaches 1.7 in/C. Below that value there is no changes whatsoever. Apparently the change rate is somewhat varies. For example the risk of 1.8 rate is the same as the risk when the rate is 1.7. Therefore it cannot be determined. However, just for a suggestion, if the sag increasing rate falls between 0 to 1.7 in/C, than the risk will not be affected by the value. According to Hua Wan’s report on page 19 “The example consists of a 1000 ft. “Drake” conductor 795 kcmil 26/7 ACSR, and for every 1C temperature increase, the sag of the line increases by 0.6 in.”. Assuming that the sag increasing rate does not vary too much among the conductors, then a number between 0 to 1.7 is a valid input for the value of the sag increasing rate.
- Conductor Tensile Loading
Suggested default value from the program is 60%.
Loading / Mean PDT / Deviation PDT / Probability / Risk70 % / 61.4691 / 15.3185 / 0.022398 / 0.011242
61% / 61.4691 / 15.3185 / 0.022398 / 0.011055
59% / 61.4691 / 15.3185 / 0.022398 / 0.011012
The effect of 9% increase of the tensile loading resulted 1.69% increase of risk.
Since this is proven to give a very small change of the risk, then the conductor tensile loading can be assumed to be around 60%.
- Loss of strength in fully annealing condition = 56%
(Obtained from IEEE Transactions on Power Delivery, Vol.11, No. 1, January 1996,”Effect of Elevated Temperature Operation on the Tensile Strength of Overhead Conductors”.)
- Parameter of Strength Reduction Curve
According to the default value:
A / 14.8B / 140
C / -7500
D / 7.5
Rr / 86
Rr = the percentage reduction in cross-sectional area during wire drawing.
This data is obtained from the IEEE Transactions on Power Delivery, Vol.11, No. 1, January 1996,”Effect of Elevated Temperature Operation on the Tensile Strength of Overhead Conductors”. Below is the complete table:
Metal / R (%) / T (C) / t(h) / A’ / B’ (K) / C’ (K) / D’ / -C’/A’Aluminum / 86.0 / 80-200 / 0.1-700 / 14.8 / 140 / 7500 / 7.5 / 507
92.1 / 80-200 / 0.1-250 / 11.4 / 110 / 6000 / 7.5 / 526
84.8 / 75-150 / 50-550 / 10.3 / 170 / 5800 / 7.5 / 563
91.3 / 50-150 / 48-2160 / 8.98 / 130 / 5000 / 7.5 / 557
The reason why the first row is chosen for the parameter values is because it has the widest range of temperature and time. Similarly for this project, the same values are chosen.
6.1.2Description of the statistical method
6.1.3Description of the power line
The particular transmission facilities are double circuit and where build in different years. The north and 43 % south section were built or rebuilt in 1993. These portions were rebuilt because of a new load and galloping problems near the south substation. The remaining 57 % of the south section is the original transmission line and is believed to have been built about 1974, when substation 2 was built.
The load is currently fed from two substations. Substation 1 that feed the north line, it comes from a split bus. Bus 1 is feed by the 161/69 kV transformer and feed bus 1, which feeds bus 2. Bus 2 in turn feeds the north line. Substation 2 feeds the south line. A 161/69 kV transformer feeds this substation's 2 69 kV bus.
Figure 2 System one-line
6.2Description of the process used to determine the associated risk
6.2.1Statistical model
A statistical model was developed to understand the effects of weather on a power system. The statistical model was developed to describe the effects of weather during two different times. The mean and standard deviation was found for wind speed and temperature for night (20:00 to 8:00) and day times (8:00 to 20:00). The method used to get the mean and standard deviation can be found in section XXX. The mean and standard deviation where then inputted into the MATLAB program as probabilistic data.
Our client supplied a model of the power system. The model of the power system gave important information on the safety and liability of the power line. The model was tested using the EPRI IPFLOW software. The current described by the software was then inputted in to the MATLAB code and the program output a Risk value.
In order to understand the statistical nature of the system a model or a system of equations was developed to explain the problem. This model was developed with a few very important assumptions. Without these assumptions the problem and the amount of uncertainty would quickly grow and become unmanageable. The following list will detail the assumptions made.
Assumptions:
- Wind and weather are statistically independent. This assumption needs further study, but due to the nature of the MATLAB code it could not be changed in time. The code is currently undergoing changes to reflect the statistical dependence.
- N-1 situation for outages (only one bus or line out per study).
- Outages in N-1 conditions only to two busses from the critical load.
This assumption could be made from simulation of the power line in IPFLOW showed that outages of further busses did not have an effect on the studied line.
- Assumed load duration curve.
The load duration curve was not available, so from empirical data the curve is as follows.