Error analysis in electric power system available transfer capability computation
Introduction
This paper revises and expands the two conference papers referenced in Refs. 12, 13. It summarizes recent results on the approximations of available transfer capability (ATC) computations and the analytical treatment of errors.
There has been interest in quantifying the transmission transfer capabilities of power systems for many years. When systems were isolated and largely radial, these capabilities were fairly easy to determine and consisted mainly of a combination of thermal ratings and voltage drop limitations. In most cases, these two limitations were easily combined into a single power limitation (either MW, MVA, or SIL). As such, ATC for a given transmission line at a given time could be interpreted as the difference between the power limitation and the existing power flow. The North American Electric Reliability Council (NERC) has been careful to distinguish the word `capacity' from the word `capability'. Capacity is normally a specific device rating (i.e., thermal), whereas capability refers to a limitation which is highly dependent on system conditions. Another interpretation is that capacity refers to the ability of a system to serve native load and engage in transfers while capability is solely the ability to engage in transfers.
As isolated systems became interconnected for economic and reliability reasons, looped networks introduced technical issues with the definition and calculation of ATC. In addition, the differences between contract path and actual power-flow path introduced additional complexity to the quantification of ATC. System stability became an important constraint for some areas of the interconnected network and this required the consideration of a third limiting phenomena. The introduction of St. Clair curves were one of the first attempts to include thermal, voltage, and stability constraints into a single transmission line loading limitation [17]. These results were later verified and extended from a more theoretical basis in Ref. [5]. This `single rating' concept is extremely valuable from a computational point of view. Linear load flow and linear programming solutions made transmission transfer capability determination relatively fast and easy 10, 9, 18, 6, 11. They focused on both the `Simultaneous Interchange Capability (SIC)' and the `Non-Simultaneous Interchange Capability (NSIC)'. Many extensions to this work have appeared including economic dispatch and nonlinear considerations such as VAR limits and transient stability constraints 1, 8, 14, 15, 16.
Section snippets
Documentation and definitions
In May 1995, NERC revised its earlier reference documents on transfer capability to provide additional clarifications and examples [19]. This 1995 document recommends two NERC transfer capability measures: `First Contingency Incremental Transfer Capability (FCITC)' and `First Contingency Total Transfer Capability (FCTTC)'. The FCITC was defined to be the amount of electric power, incremental above normal base power transfers, that can be transferred over the interconnected transmission systems
Dealing with the technical challenges
A possible scenario for the computation of TTC proceeds as follows.
(a) Definition of a base case. This may be a current or forecasted condition, existing or planned configuration and must specify what is meant by areas. An `area' may include one or more generators. If it is one generator, the increase or decrease of power out is easily specified. If it is more than one generator, the appropriate unit allocation (dispatch) must be specified both for the increase and decrease in outputs.
(b)
An example
A three-area system was used to explore the various options for computing TRM. Each area consists of a single bus with generation and load as shown in Fig. 2. Each area is connected by a single line. The areas were numbered 1, 2 and 3. The base case data for the system are as follows.
Base power is 100 MVA.
Bus 1 was the swing bus with 1500 MW load
Bus 2 had 600 MW generation and 600 MW load
Bus 3 had 800 MW generation and 800 MW load
Bus 1 had a voltage set point of 1.00 pu
Bus 2 had a voltage set
Summary and conclusions
The computation of TTC and TRM presents a major challenge for power system engineers. While the NERC definitions and methods for determination provide considerable guidance for these calculations, there are still many major issues associated with their practical implementation. One of the main issues is related to the question of what to study. The concept of Available Transfer Capability requires the determination of what is available from a particular condition. If the exact condition were
Acknowledgements
The authors thank Ian Dobson, Hsiao-Dong Chiang, Ray Klump and David Takach for comments provided in the preparation of this paper. This work was supported in part by funds from National Science Foundation Grant NSF EEC 96-15792, the University of Illinois Power Affiliates Program, the Grainger endowments to the University of Illinois, Power Engineering Research Center (PSERC) subcontracts from Cornell University, and The Fulbright Scholarship Board.
Peter W. Sauer obtained his Bachelor of Science degree in Electrical Engineering from the University of Missouri at Rolla in 1969, the Master of Science and PhD degrees in Electrical Engineering from Purdue University in 1974 and 1977, respectively. From 1969 to 1973, he was the electrical engineer on a design assistance team for the Tactical Air Command at Langley Air Force Base, Virginia, working on design and construction of airfield lighting and electrical distribution systems. He has been
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Peter W. Sauer obtained his Bachelor of Science degree in Electrical Engineering from the University of Missouri at Rolla in 1969, the Master of Science and PhD degrees in Electrical Engineering from Purdue University in 1974 and 1977, respectively. From 1969 to 1973, he was the electrical engineer on a design assistance team for the Tactical Air Command at Langley Air Force Base, Virginia, working on design and construction of airfield lighting and electrical distribution systems. He has been on the faculty at Illinois since 1977 where he teaches courses and directs research on power systems and electric machines. His main interests are in modeling and simulation of power system dynamics with applications to steady-state and transient stability analysis. From August 1991 to August 1992 he served as the Program Director for Power Systems in the Electrical and Communication Systems Division of the National Science Foundation in Washington DC. He is the Chairman of the IEEE Power Engineering Society (PES) Working Group on Dynamic Security Assessment, and Chairman of the IEEE Central Illinois Chapter of PES. He is a registered Professional Engineer in Virginia and Illinois and a Fellow of the IEEE.
Santiago Grijalva was born in Quito, Ecuador in November 1970. He received the Engineer Degree from the National Polytechnic University—Ecuador in 1994, and the MS Diploma from the Army Polytechnic University—Ecuador in 1997, in Electrical Engineering and Information Systems, respectively. Since 1995 he worked as EMS Engineer and then as Head of the Software Department in the Ecuadorian National Center of Energy Control, on maintenance and development of real-time SCADA-EMS systems. By means of a Fulbright Fellowship, he is currently a Graduate Student and a Research Assistant at the University of Illinois at Urbana-Champaign. His interests are concentrated in power system control and operation, real-time power applications, and information systems.