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| Copyright 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. |  |
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Fostering Intuitive Minds for Power System Design |
| July/August 2003 | |
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| Thomas J. Overbye | ||
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Key to providing the students with intuitive insight into the operation of such a power system is the use of a user-friendly, highly interactive graphical user interface (GUI) coupled with a robust power system analysis package. With the GUI students could easily make changes to the system and then immediately see the impacts of their changes reflected on the one-line. The use of animated power flow arrows also helped to convey how power flows from the generators through the transmission network to the loads. Also, tabular displays of many different quantities such as bus voltages and loads, generator outputs, and line flows could be used to supplement the one-line values.
To better replicate actual system operation, in which power system operators and engineers work to insure that there are no violations in either the base case or for a set of statistically likely contingencies, the design project required the students to perform a full contingency analysis solution. If done manually this would have required the students to sequentially open each of the 57 individual lines and transformers, solve the power flow, check for violations, and then reclose the device. While performing such a procedure manually once or twice might have some pedagogical benefit, it would rapidly become tedious during a design process. Rather, the students were encouraged to use the built-in contingency analysis functionality, as shown in Figure 2. With a click of a button the full contingency analysis set was run (in about a second), with the results displayed based upon the severity of the violations. The case was designed so it had a total of seven initial violations caused by three different contingencies with all the violations in the western (left) portion of the system. Of the seven, six were transmission line overloads and one was a low bus voltage (defined as being less than 0.90 per unit).
To make the project assessable to students with only a background in power flow, but not necessarily in economic dispatch or optimal power flow (OPF), for the initial project the real power outputs of all the generators were assumed to be fixed, with any change in losses picked up by the system slack bus (bus SLACK345 shown in the upper right-hand portion of the one-line). This simplification is relaxed in the more advanced project described in the later part of this article.
To make the student design project manageable yet still interesting, the choices were limited to adding a new 138/69-kV transformer and associated bus work and building new transmission lines on some of the eight right-of-ways identified using the yellow lines in Figure 3. Cost information was provided for two different-sized transformers (101 MVA and 187 MVA), and three different types of line conductors for potential 69-kV lines (Partridge, Lark, and Rook conductor types), and three for the potential 138-kV line (Lark, Rook, and Condor types). The assumed costs for each of the right-of-ways are shown in Table 1.
The students were then responsible for determining the parameters for the new lines using the conductor type, an instructor-provided transmission tower configuration, and the right-of-way length. Providing the students with only the conductor type and tower configuration requires that they derive the model parameters, providing a nice reinforcement of transmission-line modeling concepts. For this article a symmetric tower configuration was assumed with 5-ft conductor spacing. In addition to minimizing construction costs, the project also required consideration of the savings associated with any decrease in system losses over the next five years, again with the simplifying assumption that the load stays fixed over the entire time period
Since this project was designed to require at least two new system devices, the number of design possibilities is relatively high. For example, if one just considers combinations of two new transmission lines with each having three possible conductor types, the number of possibilities is equal to 168. While the software environment allowed students to easily add new lines and transformers, nevertheless, students who blindly attempted all possibilities had to do a good amount of analysis.
Hence, one of the project goals was to have the students realize that an understanding of the "why" behind the system violations could help to guide them in limiting the number of design possibilities they needed to consider. For example, referring to Figure 3, the system parameters were specifically chosen so a contingent outage of the TIM69 to HISKY69 line would cause an overload on the UIUC69 to PETE69 line, which is now radially feeding the PETE69 and HISKY69 substations. Since the supply into these two substations is radial during the contingency, the only way to eliminate the line violation is to construct a new line using one of the three available right-of-ways that join to one of the affected substations.
If the project objective was limited to just removing the contingent violations, then a good solution approach would be to order all the double-line combinations that contained one of the above three right-of-ways based upon their construction costs. Then, starting with the least expensive (AMANS-PETE and AMANS-HALE using Partridge conductors), contingency analysis should be perfomed on each one until a combination was found that eliminated all the violations. For this project list, it would only require a single entry since the AMANS-PETE/AMANS-HALE combination satisfies this constraint.
However, the project also required consideration of the impact the new transmission would have on system losses over the next five years. The importance of the losses of course depends upon the assumed cost of replacement power. Here, a value of US$50/MWh was used, resulting in a five-year savings of US$2.19 million per MW decrease in these losses. This completely changed the problem, requiring the student to perform a more detailed analysis. Starting with premodification losses of 12.21 MW, Table 2 presents the new losses resulting from various combinations of new lines, with the three columns containing possible line additions required to remove the TIM69-HISKY69 contingency violation. Note that several of the double-line additions did not correct all the violations, but most did.
If the conductor type were restricted to Partridge (i.e., the least expensive), the optimal design would now require adding a 69-kV line from AMANS-PETE and a second from AMANS-UIUC. This combination would have construction costs of US$1,018,000 but losses savings of US$1,226,400, resulting in a net savings of US$208,400 over the five-year period! When the other two conductor types are considered, the optimal solution actually is to build the line from AMANS-UIUC using the more expensive but less lossy Rook conductor and to use Partridge with the AMANS-PETE line. This change slightly increases the construction costs but decreases the losses to 11.48 MW for a net five-year savings of US$409,700.
A potential problem with many classroom assignments is excessive collaboration, to the point of copying, by some students. In order to minimize this, each student was given a slightly different variant of this design project with the assignments differentiated by the assumed symmetrical conductor spacing. The spacings ranged from 4.25 ft to 14.5 ft in 0.25-foot intervals, resulting in a maximum variation of the line reactance values between students of approximately 25%. The line resistance values, of course, remained unchanged. This change in the modeled line reactances did slightly alter the system losses and for the high reactance models did result in several additional line combinations not being able to remove all the violations. But it did not change the optimal design.
Overall, about 30% of the students correctly identified the optimal design including the correct conductor choice. Another 45% of the students correctly identified the two new lines but chose to build both using either all Rook or all Partridge conductors (with the students split evenly between the two). About 12% of the students choose to build the near optimal AMANS-UIUC and HANA-PETE lines with one student mentioning this choice might be more politically palatable to the residents living close to the AMANS substation since it avoided building two new lines at a single substation. All of the student designs satisfied the contingency constraints with only one choosing the least-expensive construction cost alternative. The students were told the project would require approximately 15 hours to complete, but most reported it took them considerably less time.
A large number of the students immediately dismissed the new MORO-HANA 138-kV line because of its high initial costs. With losses priced at US$50/MWh this line was not an optimal solution, but it was actually much closer to being optimal than most realized. Using the Condor conductor for a new MORO-HANA 138-kV line, coupled with a new AMANS-PETE 69-kV line, would result in new losses of 10.76 MW. With losses priced at US$50/MWh this design has a net cost of US$27,000 over the five-year period. But if the assumed cost of losses were increased to US$64/MWh or higher, then this design actually becomes optimal. This analysis can be helpful in pointing out to the students that high initial cost designs may actually be the best over the long-term. The analysis also presents a second option for problem variants--different students could work the same design using different assumed costs for losses.
The goal of the SCOPF is to obtain an "optimal" dispatch of the system generation (and possibly other controls) subject to the requirement that the solution not have any violations in either the base case or in any of the contingencies. Once the SCOPF has been solved, the marginal cost of supplying electricity to each bus in the system (i.e., LMPs) can be computed. While the definition of "optimal" may vary, a common SCOPF objective function is to minimize the total system operating cost subject to the aforementioned constraints. The extension of this design to include the SCOPF is facilitated by the project software including an integrated SCOPF algorithm.
The use of the SCOPF does not completely eliminate the need to perform system design since, regardless of the generator outputs, the line from UIUC69-PETE69 is still overloaded during the TIM69-HISKY69 line outage contingency. Without at least some new transmission the only way to remove this overload would be to perform load shedding. Still, the SCOPF could lessen the need for system transmission upgrades since some of the contingent violations could now be managed by optimally redispatching the generation.
For example, by using the SCOPF all the design case contingent violations can now be eliminated through the addition of a single 69-kV line from AMANS to PETE; that is, the lowest "construction cost" design. But a consequence of this design is it requires a generation redispatch away from the economic dispatch solution. This redispatch causes the bus LMPs to vary with high prices in the western portion of the system, and low prices elsewhere. Figure 4 shows a contour of the bus LMPs, with the values ranging from a low of US$23/MWh to a high of US$43/MWh. The total modeled operating cost with this design is US$16,125/hr. If the second line proposed above is built, from AMANS-UIUC, the operating cost drops to US$16,027/hr while the bus LMPs equalize at US$26/MWh.
The inclusion of the SCOPF results in a more difficult but also more realistic design process. It also opens the door for an effective classroom discussion of the issues associated with restructured power market design and operation. For example, in an LMP-based market, in which generators are paid based upon the LMP at their bus, one of the goals of high LMPs is to send a signal to generation companies of where to site new generation. In the case of Figure 4, the best locations for new generation, at least from an LMP viewpoint, would be at the HISKY and PETE substations. New generation at either of these sites would help to mitigate the overloads in the area. But the overloads could also be eliminated through the addition of a new transmission line, eliminating the high LMPs in the process. What is the right balance between new generation and new transmission is ultimately a market and societal decision, but it is certainly a good topic for classroom discussion.
A final extension of the design project could be to move from considering just a single-load snapshot to a load-variation profile. The inclusion of this load variation would help to emphasize to the students that power system engineers need to consider a wide variety of different operating conditions. While one could perform such analysis manually by looking at a set of load snapshots, it would be much more convenient to have the software manually change the load, performing contingency analysis or the SCOPF at each load level. Figure 5 shows an implementation in the design project software to automatically vary the load, in this case over the course of 24 hours. During this time period the load varied between 470 and 900 MW, while the bus LMPs ranged from US$18/MWh to US$66/MWh. The solution time for this 24-hour study was about 20 seconds, low enough to continue to allow interactive design.
Design should be an essential aspect of a power system education. The appropriate level of detail for a design project depends, of course, upon the level of the students and the time available within the course. This case study article has presented a design case that would be appropriate for higher-level undergraduates and has also shown how it could be extended for use in introductory graduate-level courses.
J. Bastian, J. Zhu, V. Banunarayanan, and R. Mukerji, "Forecasting energy prices in a competitive market," IEEE Computer Applicat. Power Mag., vol. 12, no. 3, pp. 40-45, July 1999.
T.J. Overbye, D.A. Wiegmann, and R.J. Thomas, "Visualization of power systems," PSERC Report 02-36 (Online). Available: www.pserc.wisc.edu
