Gustav S. Christensen
Gustav Stroem Christensen; (1 April 1929, Laesoe, Denmark – 9 August 2007, British Columbia, Canada), was an academic mathematician and engineer. He was the second youngest of 9 children and first worked as a radio operator in the Danish merchant marine. Later he was professor of electrical engineering at the University of Alberta in Edmonton for 27 years. In 1957 he won the Engineering Institute of Canada's prize and the Henry Birks Gold Medal in Engineering. He received a B.Sc. in engineering physics from the University of Alberta, Edmonton, in 1958 and a M.A.Sc. from the University of British Columbia, Vancouver in 1960. Later he obtained a Ph.D. in 1966, also in electrical engineering, from the University of British Columbia. Christensen wrote over 140 scientific papers, co-authored four books and four chapters.[3]
Gustav Stroem Christensen | |
|---|---|
 | |
| Born | April 1, 1929 |
| Died | August 9, 2007 (aged 78) Abbotsford, British Columbia, Canada |
| Nationality | Canadian |
| Alma mater | University of Alberta, University of British Columbia |
| Known for | Electric power system studies, nonlinear systems, stability theory, and Mathematical optimization |
| Spouse(s) | |
| Children | Lynne,[2] Neil |
| Awards |
|
| Scientific career | |
| Fields | Mathematics, Electrical Engineering, Computational Intelligence |
| Institutions | University of Alberta |
| Thesis | Aspects of Nonlinear System Stability (1966) |
| Doctoral advisor | Avrom Chaim Soudack |
| Doctoral students | Mohamed E. El-Hawary, Soliman Abdel-hady Soliman |
Biography
Personal life
He was born 1 April 1929 on a farm on the tiny Danish island of Laesoe. The eighth of nine children, Gustav completed 9 years of schooling there in an ancient one-room elementary school and a brand-new junior high school. In 1945 he ventured to Copenhagen to take a radio operator apprenticeship, served with the Danish Merchant Navy for four years and on an American oil tanker for another two as a radio operator. He was fortunate to travel around the world visiting ports on five continents, including Canada, where he visited his brother and sister, who had emigrated to the prairies.
He decided to join his siblings in Canada. In 1969 he married an English immigrant, Penelope Janet Gardner,[1] in Edmonton, and they have two children, Lynne (MBA, B.Comm., CAE)[2] and Neil (B.CIS).
Academic life
After he settled in Canada, Christensen completed his entire high school diploma in six months, mainly through correspondence school in Edmonton. He enrolled in engineering physics at the University of Alberta, where he took the top engineering award, the Henry Birks Gold Medal, in 1958 along with several other scholarships. After a summer with the National Research Council[4] in Ottawa, he took his M.A. Sc. in Electrical Engineering under Frank Noakes at the University of British Columbia in 1960 and subsequently obtained practical industrial experience with the BC Energy Board and Chemcell in Edmonton. He disliked the odours associated with chemical engineering so beat a hasty retreat to the rarified atmosphere of academia at UBC. His Ph.D. thesis (1966) was on the stability of non-linear mathematical models of systems with supervisor Avrom C. Soudack.
Even before he had defended his thesis he was lured back to University of Alberta as assistant professor in July 1966 and spent 27 years teaching, researching and taking a large load of administrative responsibilities for the Department of Electrical Engineering. He taught 16 different courses but his forte was the one-on-one training of his 24 graduate students. His research was mainly concentrated on the optimum economic operation of various types of power systems, minimizing the energy lost in transmission lines while at the same time using, for example, the water available in all the hydro plants in a system to generate the maximum amount of power.[5][6][7][8] This produced the cheapest energy and the best return on investment. Gus authored over 140 scientific papers, four books and four chapters in books on his research specialties.
Society
Christensen retired as full professor to Mission, British Columbia, in 1993, took up ham radio and returned to playing bridge at which he was rather good; he patiently suffered partners who could not remember every card that had been played, as he was able to do. Gus and Penny joined the Church of Jesus Christ of Latter-Day Saints and they both served at the church's Family History Centre in Abbotsford. Gus was appreciated there for his knowledge of Danish, Swedish, Norwegian and German and his patience with newbies on the computers. In co-operation with his wife Penny, a professional genealogist, Gus wrote his autobiography, the history of his parents' 172 descendants and a volume of translations of historical articles on Laesoe, the island of his birth.
Electric power industries
Christensen was an active intervener in the National Energy Board (NEB)[9] hearings which ultimately resulted in the rejection of the huge SE2 (Sumas Energy 2) coal-fired plant, one that would have emitted unacceptable pollution into the Fraser Valley funnel. With his professional knowledge of the operation of power systems he quietly but firmly refuted the bafflegab produced by the SE2 lawyers and 'experts' and helped quash the project. We will always remember the chairman of the NEB saying, "So, Dr. Christensen, is that your entire argument?" Christensen replied in his quiet yet effective way, "No sir, I am just getting started." It brought the house down.
Final years
At the age of 75 Christensen took up an adjunct professorship in the School of Engineering Science at Simon Fraser University in Burnaby, BC, where he had an office, a computer and a grad student – but no salary. He spent one or two days there each week until he died, and he published what he considered to be his best work during this time. These papers were in the field of asymptotic stability of linear and nonlinear systems, a continuation of his Ph.D. work. He simplified the solutions to Lyapunov's widely applicable stability theorems so that they are now useful to the electric power engineers, other practical engineers and many other professionals. Another development was the solution of the least absolute value estimation problem originally posed by Laplace in 1750 by using linear programming.
Death
Gus was unlucky with his health, having his first heart attack in 1984, ten major operations in the following 19 years, as well as a number of ongoing chronic conditions for over 40 years. He was a quiet man known for his wry sense of humour and for dissolving into uncontrollable chuckles before he had got to the punch line of his legendary fund of coffee-room jokes. Everybody laughed anyway – he was such a good, honest man that one couldn't help but enjoy his company.
Gus died 9 August 2007 at the age of 78,[3] satisfied that he had completed his life's work of solving important applied mathematical problems and completing his family history. His last years were memorable. He enjoyed many trips with his family and was happy his wife, daughter and son were well provided for and focused on education and careers. Gus was a wonderful man, touched many lives and is sadly missed.
Work experience
Christensen was a professor emeritus (retired from University of Alberta – Edmonton, Alberta, Canada) since 1993.
Industrial experience
Academic experience
- Simon Fraser University, Burnaby, British Columbia – adjunct professorship – 2004 until he died.
- University of Alberta, Edmonton, Alberta – Professor – 1974 to 1993.
- University of Alberta, Edmonton, Alberta – Associate professor – 1969 to 1973.
- University of Alberta, Edmonton, Alberta – Assistant professor – 1966 to 1969.
- University of British Columbia, Vancouver, British Columbia – Lecturer – 1964 to 1965.
Administrative experience
- 1966-1974 Chairman of the Department of Electrical Engineering Admissions Committee (2 members) for graduate students.
During that period the Department received up to 500 applications a year. The work involved corresponding with all prospective students regarding course requirements and financial assistance and also circulation of individual students' files to members of the Department and return of these files to the Faculty of Graduate Studies and Research. - 1967-1974 Chairman of the Department of Electrical Engineering Pattern II Curriculum Committee.
- 1967-1974 Member of the Department of Electrical Engineering Course Allocation Committee.
- 1972-1973 Member of the Faculty of Engineering Salary and Promotions Committee.
- 1974-1975 Chairman of the Department of Electrical Engineering Academic Planning Committee.
- 1976-1978 Member of the Department of Electrical Engineering Executive Committee.
- 1979-1980 Member of the Faculty of Engineering Tenure Committee.
- 1979-1982 Member of the Department of Electrical Engineering Graduate Student Admission Committee.
- 1979-1980 Member of the Faculty of Engineering Power Selection Committee.
- 1982-1985 Member of the Department of Electrical Engineering Graduate Steering Committee.
- 1983-1986 Member of the Department of Electrical Engineering Nominating Committee.
- 1986-1989 Member of the Department of Electrical Engineering Executive Committee.
- 1989-1990 Associate Chairman for Graduate Studies, Department of Electrical Engineering.
Achievements
Education
- University of Alberta, Edmonton, Alberta, Canada | 1958 - B.Sc. Engineering Physics.
- University of British Columbia, Vancouver, British Columbia, Canada | 1960 - M.A.Sc. Electrical Engineering.
- University of British Columbia, Vancouver, British Columbia, Canada | 1966 - Ph.D. Electrical Engineering.
Undergraduate
- Engineering Institute of Canada (EIC)[13] Prize 1957
- Two University of Alberta First Class Standing Prizes
- One University of Alberta Honor Prize
- Schlumberger Undergraduate Scholarship
- Henry Birks Gold Medal in Engineering, graduated with High Distinction
Postgraduate
- Northern Electric Fellowship 1958
- National Research Council (NRC) Studentship 1959
- National Research Council (NRC) Studentship 1960
- University of British Columbia Scholarship 1964
- University of British Columbia Scholarship 1965
Civic award – British Columbia
- District of Mission: Award for achievement in mathematics, engineering and science.
May 7, 2007. Presented by Mayor James Atebe.
Scientific communities' memberships
- Senior Member, Institute of Electrical and Electronics Engineers (IEEE)
- Associate Member, Canadian Electricity Association (CEA), Canada
- Member, The Association of Professional Engineers and Geoscientists of Alberta (APEGA), Alberta
NRC and NSERC grants
| Date | Amount | Comment |
|---|---|---|
| February, 1967 | $3,200 | |
| February, 1968 | $4,200 | |
| February, 1969 | $8,000 | |
| February, 1970 | $10,000 | |
| February, 1971 | $12,000 | |
| February, 1972 | $10,700 | |
| February, 1973 | $10,000 | |
| February, 1974 | $11,000 | 3 year grant |
| February, 1975 | $11,700 | |
| February, 1976 | $11,700 | |
| February, 1977 | $11,700 | |
| February, 1978 | $14,800 | 3 year grant |
| February, 1979 | $14,800 | |
| February, 1980 | $16,300 | |
| February, 1981 | $18,300 | 3 year grant |
| February, 1982 | $21,200 | |
| February, 1983 | $21,400 | |
| February, 1984 | $26,800 | 3 year grant |
| February, 1985 | $26,800 | |
| February, 1986 | $26,800 | |
| February, 1987 | $25,800 | 3 year grant |
| February, 1988 | $25,800 | |
| February, 1989 | $25,800 | |
| February, 1990 | $24,600 | 3 year grant |
| February, 1991 | $24,600 | |
| February, 1992 | $24,600 |
Graduate students
| Name | Program | Graduation Date |
|---|---|---|
| R.K. Verman | M.Sc. | June 1968 |
| M.B. Singh | M.Sc. | August 1968 |
| R.K. Ghai | M.Eng. | December 1968 |
| R.S. Rao | Ph.D. | September 1969 |
| A.M.H. Rashed | M.Sc. | April 1970 |
| G.W. Trott | Ph.D. | June 1971 |
| B. Bussman | M.Sc. | August 1971 |
| M.E. El-Hawary | Ph.D. | May 1972 |
| S. Tang | M.Sc. | June 1972 |
| D. Liang | Ph.D. | June 1974 |
| A. Steckhahn | M.Sc. | June 1975 |
| R. Nieva | Ph.D. | November 1978 |
| M. Abdelhalim | Ph.D. | April 1983 |
| S. Yoo | M.Sc. | May 1983 |
| S.A. Soliman | Ph.D. | January 1986 |
| N. Greenwood-Madsen | M.Eng. | May 1987 |
| A. Atallah | Ph.D. | August 1988 |
| A. Rouhi | M.Sc. | August 1988 |
| S. Fouda | M.Sc. | April 1989 |
| N. Liu | M.Sc. | July 1990 |
| S. Persaud | M.Sc. | July 1991 |
| K. El-Naggar | Ph.D. | July 1992 |
| J. Johal | M.Eng. | June 1993 |
Postdoctoral fellows
| Name | Period | Comment |
|---|---|---|
| I. Filanovsky | 1976-1977 | |
| A. Shamaly | 1976-1980 | |
| Y. Chen | 1980-1982 | Chinese Scholar |
| S. Rao | 1980-1983 | |
| M. Abdelhalim | 1984 | summer only |
| S.A. Soliman | 1986 | summer only |
| S.A. Soliman | 1987 | summer only |
| S.A. Soliman | 1988 | summer only |
| S.A. Soliman | 1989 | summer only |
| S.A. Soliman | 1990 | summer only |
Publications
Most of Gustav Stroem Christensen's publications still are not archived well in Google Scholar, ResearchGate, etc. The following information is based on the legacy preserved by Gus family:
Theses
| G.S. Christensen's M.Sc. and Ph.D. Theses: |
|---|
| 1- M.Sc. Thesis, Optimization of Conductor Shapes and Configurations of Conductor Bundles for High Voltage Transmission, May, 1960.[14] |
| 2- Ph.D. Thesis, Aspects of Nonlinear System Stability, August 17, 1966.[15] |
Books
| G.S. Christensen's List of Books: |
|---|
| 1- M.E. El-Hawary and G.S. Christensen, "Optimal Operation of Electric Power Systems." Academic Press, New York, pp. 280, 1979. (This was written on invitation from Richard Bellman, U.C.L.A.) |
| 2- G.S. Christensen, M.E. El-Hawary and S.A. Soliman, "Optimal Control Applications in Electric Power Systems." Plenum Press, New York, pp. 200, May 1987. |
| 3- G.S. Christensen and S.A. Soliman, "Optimal Long-Term Operation of Electric Power Systems." Plenum Press, New York, pp. 310, August 1988. |
| 4- G.S. Christensen, S.A. Soliman and R. Nieva, "Optimal Control of Distributed Nuclear Reactors." Plenum Press, New York, pp. 250, January 1990. |
Refereed chapters in books
| G.S. Christensen's List of Refereed Chapters in Books: |
|---|
| 1- M.E. El-Hawary and G.S. Christensen. "Optimal Operation of Large Scale Power Systems." In Advances in Control and Dynamic Systems (C.T. Leondes, Editor), Academic Press, New York, Vol.13, pp. 1–70, 1977. |
| 2- A. Shamaly, G.S. Christensen and M.E. El-Hawary. In "Information Linkage Between Applied Mathematics and Industry" (A.L. Schoenstadt et al. Editors), Academic Press, New York, 1980. |
| 3- G.S. Christensen and S.A. Soliman. "Optimization Techniques in Hydroelectric Systems." In Advances in Control and Dynamic Systems, (C.T. Leondes, Editor), Academic Press, New York, Vol.30, pp. 100, in press, Mar 1990. |
| 4- G.S. Christensen, S.A. Soliman and M.Y. Mohamed, "Power Systems State Estimates based on Least Absolute Value (LAV)." Advances in Control and Dynamic Systems Vol.36, 1991, pp. 1–143. |
Journal papers
| G.S. Christensen's List of Journal Papers: |
|---|
| 1- F. Noakes and G.S. Christensen, The Effect of Conductor Shapes and Arrangement on the Electric Field Intensity of High Voltage Transmission Lines. Transactions E.I.C. Vol.4, No.4, 1960. |
| 2- G.S. Christensen, Cost of Power Transmission at 345KV. A report prepared for the B. C. Power Commission, Victoria, B. C., September 1960. |
| 3- G.S. Christensen and G. J. Berg, Technical and Economical Aspects of Electrical Power Transmission from Plants in System D to Load Centres in the Fraser River Basin. A report prepared for the Fraser River Board, Victoria, B.C., December 1960. |
| 4- Report on the Columbia and Peace River Projects, British Columbia Energy Board, Victoria, B.C., 31 July 1961. (Did preparatory work in this report.) |
| 5- G.S. Christensen, A Control System for Automatic Blending of Solvents. A report prepared for Canadian Chemical Co, Edmonton, July 1962. |
| 6- G.S. Christensen, Criticism of paper entitled - Inside Hydrothermal Coordination by C.W. Watchorn, IEEE Transactions PAS, January 1967. |
| 7- G.S. Christensen, On the Convergence of Volterra Series. IEEE Transactions A.C., Vol.13, p. 736, 1968. |
| 8- R.S. Rao and G.S. Christensen, Bounded-Input Bounded-Output Stability of a Class of Nonlinear Discrete-Data Systems via Contraction Mapping. Int. Journal of Control, Vol.12, No.3, p. 449, 1970. |
| 9- R.S. Rao and G.S. Christensen, A Criterion for the Bounded-Input Bounded-Output Stability of a Discrete-Data System with a Slope-Restricted Nonlinearity. Int. Journal of Control, Vol.12, No.4, p. 637, 1970. |
| 10- R.S. Rao and G.S. Christensen, On the Convergence of a Discrete Volterra Series. IEEE Transactions A.C., Vol.15, p. 140, 1970. |
| 11- G.W. Trott and G.S. Christensen, On the Uniqueness of the Volterra Series. IEEE Transactions A.C., Vol.14, p. 759, 1970. |
| 12- G.S. Christensen and G.W. Trott, On the Inclusion of Initial Conditions in Volterra Series. Int. Journal of Control, Vol.12, No.5, p. 835, 1970. |
| 13- G.W. Trott and G.S. Christensen, A Larger Region of Convergence for the Volterra Series. Int. Journal of Control, Vol.14, p. 377, 1971. |
| 14- A.M.H. Rashed and G.S. Christensen, Response of Nonlinear Sampled Data Systems with Non-Zero Initial Conditions and Response for In-Between Sampling via Volterra Series. IEEE Transactions A.C., Vol.16, p. 269, 1971. |
| 15- B. Bussman and G.S. Christensen, A Comparison Theorem for Stability Investigations. IEEE Transactions A.C., Vol 17, p. 138, 1972. |
| 16- M.E. El-Hawary and G.S. Christensen, Functional Optimization of Common Flow Hydro-Thermal Systems. IEEE Transactions P.A.S., Vol.91, p. 1833, 1972. |
| 17- M.E. El-Hawary and G.S. Christensen, Optimum Scheduling of Power Systems Using Functional Analysis. IEEE Transactions A.C., Vol.17, p. 518, 1972. |
| 18- M.E. El-Hawary and G.S. Christensen, Application of Functional Analysis to Optimization of Electric Power Systems. Int. Journal of Control, Vol.16, No.6, p. 1063, 1972. |
| 19- M.E. El-Hawary and G.S. Christensen, Hydro-Thermal Load Flow Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.12, No.6, p. 576, 1973. |
| 20- M.E. El-Hawary and G.S. Christensen, Extensions to Functional Optimization of Common-Flow Hydro-Thermal Systems. IEEE Transactions P.A.S., Vol.92, p. 356, 1973. |
| 21- D.F. Liang and G.S. Christensen, Comments on "Estimation in Linear Delayed Discrete-Time Systems with Correlated State and Measurement Noises". IEEE Transactions A.C., Vol 20, pp. 176–177, 1975. |
| 22- D.F. Liang and G.S. Christensen, New Filtering and Smoothing Algorithms for Discrete Nonlinear Systems with Time Delays. Int. Journal of Control, Vol.21, No.1, pp. 105–111, 1975. |
| 23- D.F. Liang and G.S. Christensen, Exact and Approximate State Estimation for Nonlinear Dynamic Systems. Automatica, Vol.11, pp. 603–612, 1975. |
| 24- G.S. Christensen and M.E. El-Hawary, Optimal Operation of Multi-Chain Hydro-Thermal Power Systems. Canadian Electrical Engineering Journal, Vol.1, No.2, pp. 52–62, 1976. |
| 25- D.F. Liang and G.S. Christensen, New Filtering and Smoothing Algorithms for Discrete Nonlinear Delayed Systems with Coloured Noise. Int. Journal of Control, Vol.25, pp. 821–825, 1977. |
| 26- D.F. Liang and G.S. Christensen, Estimation Algorithms for Discrete Nonlinear Systems and Observations with Multiple Time Delays. Int. Journal of Control, Vol.23, p. 613, 1976. |
| 27- R. Nieva, G.S. Christensen and M.E. El-Hawary, Suboptimal Control of a Nuclear Reactor Using Functional Analysis. Int. Journal of Control, Vol.26, pp. 145–156, 1977. |
| 28- R. Nieva and G.S. Christensen, Reduction of Reactor Systems. Nuclear Science and Engineering, Vol.64, pp. 791–795, 1977. |
| 29- D.F. Liang and G.S. Christensen, Estimation of Discrete Non-Linear Time-Delayed Systems and Measurements with Correlated and Colored Noise Processes. Int. Journal of Control, Vol.28, pp. 1–10. 1978. |
| 30- A. Shamaly, G.S. Christensen and M.E. El-Hawary, A Transformation for Necessary Optimality Conditions for Systems with Polynomial Nonlinearities. IEEE Transactions A.C., Vol.24, No.6, p. 983, 1979. |
| 31- R. Nieva and G.S. Christensen, Optimal Control of Distributed Nuclear Reactors Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.34, No.3, 1981. |
| 32- M.E. El-Hawary and G.S. Christensen, Optimal Active-Reactive Hydro-Thermal Schedules Using Functional Analysis. Optimal Control Applications and Methods, Vol.1, pp. 239–249, 1980. |
| 33- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Optimal Control of a Large Turbo-Alternator. Journal of Optimization Theory and Applications, Vol.34, No.1, pp. 83–97, 1981. |
| 34- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Solution of Ill-Conditioned Optimality Conditions for Control of Turbo-Alternators. Optimal Control Applications and Methods, Vol.2, pp. 81–87, 1981. |
| 35- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Realistic Feedback Control of Turbo-Generators. Journal of Optimization Theory and Applications, Vol.35, No.2, pp. 251–259, 1981. |
| 36- R. Nieva, G.S. Christensen and M.E. El-Hawary, Optimum Load Scheduling of Nuclear-Hydro-Thermal Power Systems. Journal of Optimization Theory and Applications, Vol.35, No.2, 1981. |
| 37- R. Nieva and G.S. Christensen, Symmetry Reduction of Linear Distributed Parameter Systems. Int. Journal of Control, Vol.36, No.1, pp. 143–153, 1982. |
| 38- A. Shamaly, G.S. Christensen and Y. Chen, Optimal Control of Two Interconnected Turbogenerators. Journal of Optimization Theory and Applications, Vol.40, No.2, 1983. |
| 39- Y. Chen, G.S. Christensen and A. Shamaly, Realistic Feedback Control of Two Interconnected Turbogenerators. Journal of Optimization Theory and Applications, Vol.42, No.1, 1984. |
| 40- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Optimal Load Frequency Control with Governor Backlash. Journal of Optimization Theory and Applications, Vol.45, 1985. |
| 41- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Decentralized Optimum Load Frequency Control of Interconnected Power Systems. Journal of Optimization Theory and Applications, Vol.45, 1985 |
| 42- M.E. El-Hawary, R.S. Rao and G.S. Christensen, Optimal Hydro-Thermal Load Flow. Optimal Control Applications and Methods, Vol.7, pp. 18, 1986. |
| 43- S.A. Soliman, G.S. Christensen and M. A. Abdelhalim, Optimal Operation of Multireservoir Power Systems Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.49, No.3, pp. 449–461, 1986. |
| 44- G.S. Christensen and S.A. Soliman, Long-Term Optimal Operation of a Parallel Multireservoir Power System Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.50, No.3, pp. 383–395, 1986. |
| 45- S.A. Soliman and G.S. Christensen, Modelling and Optimization of Series Reservoirs for Long-Term Regulation with Variable Head Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.50, No.3, pp. 463–477, 1986. |
| 46- S.A. Soliman and G.S. Christensen, Optimization of the Production of Hydroelectric Power Systems with a Variable Head. Journal of Optimization Theory and Applications, Vol.58, pp. 301–317. 1988. |
| 47- S.A. Soliman and G.S. Christensen, Optimization of Reservoirs in Series on a River with a Nonlinear Storage Curve for Long-Term Regulation. Journal of Optimization Theory and Applications, Vol.58, pp. 109–126, 1988. |
| 48- G.S. Christensen and S.A. Soliman, New Analytical Approach for Long-Term Optimal Operation of a Parallel Multireservoir Power System Based on Functional Analysis. Canadian Electrical Engineering Journal, Vol.11, No.3, pp. 118–127, 1986. |
| 49- G.S. Christensen and S.A. Soliman, Optimal Long-Term Operation of a Multireservoir Power System for Critical Water Conditions Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.53, No.3, pp. 377–393, 1987. |
| 50- G.S. Christensen and S.A. Soliman, Modelling and Optimization of Parallel Reservoirs Having Nonlinear Storage Curves Under Critical Water Conditions for Long-Term Regulation Using Functional Analysis. Journal of Optimization Theory and Applications, Vol.55, No.3, pp. 359–376, 1987. |
| 51- G.S. Christensen and S.A. Soliman, On the Application of Functional Analysis to the Optimization of the Production of Hydroelectric Power. IEEE Transactions P.W.R.S.-2-No.4, pp. 841–847, 1987. |
| 52- S.A. Soliman and G.S. Christensen, Long-Term Optimal Operation of Series-Parallel Reservoirs for Critical Period with Specified Monthly Generation. Canadian Electrical Engineering Journal Vol.12, pp. 116–122, 1987. |
| 53- S.A. Soliman and G.S. Christensen, Application of Functional Analysis to Optimization of a Variable Head Multireservoir Power System for Long-Term Regulation. Water Resources Research, Vol.22, No.6, pp. 852–858, 1986. |
| 54- S.A. Soliman and G.S. Christensen, A New Approach for Optimizing Hydropower System Operation with a Quadratic Model. Lecture Notes in Control and Information Sciences, Vol.95 Oberwolfach, pp. 273–286, 1986. |
| 55- S.A. Soliman and G.S. Christensen, A Minimum Norm Approach to Optimization of Production of Multireservoir Power Systems with Specified Monthly Generation. Journal of Optimization Theory and Applications, Vol.58, pp. 501–524, 1988. |
| 56- S.A. Soliman and G.S. Christensen, Optimization of Hydropower Systems Operation with a Quadratic Model. Automatica, Vol.24, p. 249-256, 1988. |
| 57- G.S. Christensen and S.A. Soliman, Optimal Discrete Long-Term Operation of Nuclear-Hydrothermal Power Systems. Journal of Optimization Theory and Applications, Vol.62, No.2, pp. 239–254. 1989. |
| 58- S.A. Soliman, G.S. Christensen and A.H. Rouhi, A New Technique for Curve Fitting Based on Minimum Absolute Deviations. Computational Statistics and Data Analysis, Vol.6, pp. 341–351. 1989. |
| 59- S.A. Soliman and G.S. Christensen, Parameter Estimation in Linear Static Systems Based on LAV Estimation. Journal of Optimization Theory and Applications, Vol.61, No.2, pp. 281–294. 1989. |
| 60- G.S. Christensen and S.A. Soliman, A New Technique for Linear Static State Estimation Based on LAV Approximations. Journal of Optimization Theory and Applications, Vol.61, No.1, pp. 123–136. 1989. |
| 61- G.S. Christensen and S.A. Soliman, Long-Term Optimal Operation of Series-Parallel Reservoirs for Critical Period with Specified Monthly Generation and Average Monthly Storage. Journal of Optimization Theory and Applications, Vol.63, No.3. 1989. |
| 62- G.S. Christensen, S.A. Soliman and A.H. Rouhi, A New Technique for Unconstrained and Constrained Linear LAV Parameter Estimation. Canadian Electrical Engineering Journal, Vol.14, pp. 14–30. 1989. |
| 63- S.A. Soliman, S.E.A. Emam and G.S. Christensen, A New Algorithm for Parameter Estimation of Synchronous Machine from Frequency Test Based on LAV Approximation. Canadian Electrical and Computer Engineering Journal, Vol.14, No.3, pp. 98–102. 1989. |
| 64- S.A. Soliman, S.E.A. Emam and G.S. Christensen, Optimization on Site and Control Setting of Shunt Capacitors on Distribution Feeders. Journal of Optimization Theory and Control, Vol.65, No.2. May1990. |
| 65- S.A. Soliman, S.E.A. Emam and G.S. Christensen, A New Approach for the Identification of Power System Economic Dispatch Parameters. Journal of Optimization Theory and Applications, Vol.65, No.1. April 1990. |
| 66- G.S. Christensen and S.A. Soliman, Optimal Filtering for Continuous Linear Dynamic Systems Based on WLAV Approximations. Automatica, Vol.26, No.2, pp. 399–400. 1990. |
| 67- G.S. Christensen and S.A. Soliman, Optimal Filtering of Linear, Discrete Dynamic Systems Based on WLAV Approximations. Automatica, Vol.26, No.2, pp. 389–395. 1990. |
| 68- G.S. Christensen, S.A. Soliman and A. Rouhi, Discussion of "An example showing that a new technique for LAV estimation breaks down in certain cases". Computational Statistics and Data Analysis, Vol.9, pp. 203–213. 1990. |
| 69- G.S. Christensen, S.A. Soliman and A. Atallah, Optimal Scheduling of Multichain Hydro Power Systems, Long Term Study. Canadian Journal of Electrical and Computer Engineering, Vol.14, No.4, pp. 152–156.1989. |
| 70- G.S. Christensen, S.A. Soliman and A.H. Rouhi, An Observability Algorithm for Sequential Measurement Processing in Power System State Estimation. Electric Machines and Power Systems, Vol.17, pp. 203–219. 1989. |
| 71- S.A. Soliman and G.S. Christensen, A New Algorithm for Optimal Parameter Estimation. Journal of Optimization Theory and Applications, Vol.66, No.3. September 1990. |
| 72- S.A. Soliman, G.S. Christensen and S.S. Fouda, On the Application of the Least Absolute Value (LAV) Parameter Estimation Algorithm to Distance Relaying. Electric Power Systems Research, Vol.19, pp. 23–35. 1990. |
| 73- S.A. Soliman, G.S. Christensen, D.H. Kelly and N. Liu, An Algorithm for Frequency Relaying Based on Least Absolute Value Approximations. Electric Power Systems Research, Vol.19, pp. 73–84. 1990. |
| 74- S.A. Soliman, G.S. Christensen and D.H. Kelly, A State Estimation Algorithm for Power Systems Harmonics Identification and Measurements. Electric Power Systems Research, Vol.19, No.2, pp. 195–206. 1990. |
| 75- S.A. Soliman, S.E.A Emam and G.S. Christensen, Application of Optimization to the Size and Control Settings of Shunt Capacitors on Distribution Feeders. Electric Machines and Power Systems, Vol.18, pp. 41–51, 1990. |
| 76- S.A. Soliman, S.E.A. Emam and G.S. Christensen, Optimal Coefficients Estimation of Non-Monotonically Increasing Incremental Cost Curves. Electric Power Systems Research, Accepted September 10, 1990. Manuscript pages: 20. |
| 77- G.S. Christensen and S.A. Soliman, Least Absolute Value Estimation of the Generalized Operational Impedances of Solid-Rotor Synchronous Machines from SSFR Test Data. Electric Power Systems Research, Accepted September 7, 1990. Manuscript pages:24. |
| 78- S.A. Soliman, G.S. Christensen and A.H. Rouhi, A New Algorithm for Nonlinear L1-Norm Minimization with Nonlinear Equality Constraints. Computational Statistics and Data Analysis, Vol.11, pp. 1–13. 1990. |
| 79- G.S. Christensen, S.A. Soliman and A. M. Atallah, Efficient Load Following Schedule with Application to the B.P.A. Hydro-Electric System. International Journal of Electrical Power and Energy Systems, Vol.13, Feb. 1991, pp. 45–50. |
| 80- G.S. Christensen, S.A. Soliman and A.M. Atallah, Optimal Long-Term Operation of the B.P.A. Hydro-Electric Power System. International Journal of Computer Systems Science and Engineering, Accepted Vol.13, No.1 Feb. 1991 pp. 38–42. |
| 81- S.A. Soliman and G.S. Christensen, Estimating of Steady State Voltage and Frequency of Power Systems from Digitized Bus Voltage Samples. Electric Machines and Power Systems, Vol.19 1991, pp. 555–576. |
| 82- S.A. Soliman and G.S. Christensen, Power Systems Digital Voltmeters with Low Sensitivity to Frequency Change. Electric Machines and Power Systems Journal, accepted July 5, 1991, Man. 20. |
| 83- G.S. Christensen, S.A. Soliman, D.H. Kelly and K.M. El-Naggar. Identification and Measurements of Power System Harmonics Using Disacrete Fourier Transform (DFT). Electric Machines and Power Systems, accepted July 5, 1991, Man. 29. |
| 84- S.A. Soliman and G.S. Christensen, Digital Analysis of Power Systems Dynamic Oscillation Using a Curve Fitting Technique. Electric Machines and Power Systems, Vol.20 1992 pp. 309–320. |
| 85- S.A. Soliman and G.S. Christensen, Modelling of Induction Motors from Standstill Frequency Response Tests and a Parameter Estimation Algorithm. Electric Machines and Power Systems, Vol.20, 1992 pp. 123–126. |
| 86- S.A. Soliman, G.S. Christensen and A.H. Rouhi, Power System State Estimation with Equality Constraints. Electric Machines and Power Systems, Vol.20 1992, pp. 183–202. |
| 87- S.A. Soliman, G.S. Christensen, D.H. Kelly and K.M. El-Naggar, Least Absolute Value based linear Programming Algorithm for Measurement of Power System Frequency from a distorted Bus Voltage Signal. Electric Machines and Power Systems, Vol.20 1992, pp. 549–568. |
| 88- S.A. Soliman, G.S. Christensen, D.H. Kelly and K.M. El-Naggar, Dynamic Tracking of the Steady State Power System Voltage Magnitude and Frequency using Linear Kalman Filter: a Variable Frequency Model. Electric Machines and Power Systems, Vol.20, 1992 pp. 593–611. |
| 89- S.A. Soliman, G.S. Christensen and K.M. El-Naggar, A Digital Measurement of Earth Fault Loop-Impedance Using a Parameter Estimation Algorithm. Electric Machines and Power Systems, Vol.20 1992, pp. 613–621. |
| 90- S.A. Soliman, G.S. Christensen and K.M. El-Naggar, A new Approximate Least Absolute Value based Dynamic Filtering Algorithm for on-line Power System Frequency. Electric Machines and Power Systems, Vol.20 1992, pp. 569–592. |
| 91- G.S. Christensen and S.A. Soliman, Optimization Techniques in Hydro-Electric Systems. Zentralblatt fuer Mathematik, Accepted Jan. 10, 1992, Man. 1. |
| 92- G.S. Christensen, Mehrdad Saif, and S.A. Soliman. A New Algorithm for Finding the Optimal Solution of the Least Absolute Value Estimation Problem. Canadian Journal of Electrical and Computer Engineering, Vol. 32, No. 1, pp. 5–8, Winter 2007. |
| 93- G.S. Christensen and Mehrdad Saif. The Asymptotic Stability of Nonlinear Autonomous Systems. Canadian Journal of Electrical and Computer Engineering, Vol. 32, No. 1, pp. 35–43, Winter 2007. |
Conference papers
| G.S. Christensen's List of Conference Papers: |
|---|
| 1- R.S. Rao and G.S. Christensen, Contraction Mapping Applied to Stability Analysis of a Class of Nonlinear Discrete-Data Systems. Asilomar Conference, California. October 1968. |
| 2- M.E. El-Hawary and G.S. Christensen, Optimization of Hydro-Thermal Generation Schedules via Functional Analysis. Proc. Second South- Eastern Symposium on System Theory, University of Florida. March 1970. |
| 3- M.E. El-Hawary and G.S. Christensen, Functional Optimization of Electric Power Systems with Variable Head Hydro Plants. Proc. Third South-Eastern Symposium on Systems Theory, Atlanta, Georgia. April 1971. |
| 4- G.S. Christensen and M.E. El-Hawary, Functional Optimization of Hydro-Thermal Systems with Trapezoidal Reservoirs and Variable Efficiency. Conference Paper IEEE Summer Power Meeting. July 1973. |
| 5- D.F. Liang and G.S. Christensen, Exact and Approximate Linear and Nonlinear Fixed-Interval, Fixed-Point and Fixed-Lag Smoothing with Measurement Involving Correlated Noise. Proc. Fourth Symposium on Nonlinear Estimation and its Application, San Diego, Calif. September 1973. |
| 6- D.F. Liang and G.S. Christensen, Exact and Approximate Nonlinear Filters Involving Additive Noise, Correlated Noise or Noise-Free Processes. Proc. Canadian National Conference on Control, New Brunswick. September 1973. |
| 7- D.F. Liang and G.S. Christensen, The Application of Matrix Minimum Principle to Nonlinear Estimation Problems Involving Additive Noise, Correlated Noise and Noise-Free Processes. NRC Technical Conference on Control Systems, Edmonton, Alberta. March 1974. |
| 8- M.E. El-Hawary and G.S. Christensen, A Minimum Norm Approach to Optimal Load Flow in Hydro-Thermal Power Systems. Proc. International Electrical, Electronics Conference, Toronto, Ontario. September 1975. |
| 9- M.E. El-Hawary and G.S. Christensen, Optimum Operation of a Large Scale Power System. Proc. Optimization Days, Montreal, Quebec. May 1976. |
| 10- M.E. El-Hawary and G.S. Christensen, Optimum Operation of Power Systems, with Realistic Hydro Representation. Proc. Optimization Days, Montreal, Quebec. May 1977. |
| 11- M.E. El-Hawary and G.S. Christensen, Optimal Active-Reactive Dispatch in Power Systems. Proc. IFAC-MVTS Symposium, Fredericton, New Brunswick. July 1977. |
| 12- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Functional Optimization of Systems with Polynomial Nonlinearities. Proc. 20th Midwest Symposium on Circuits and Systems, Lubbock, Texas. August 1977. |
| 13- M.E. El-Hawary and G.S. Christensen, Realistic Optimal Load Flow in Hydrothermal Electric Power Systems. Proc. IEEE Conference, Toronto, Ontario. September 1977. |
| 14- M.E. El-Hawary and G.S. Christensen, Economic Dispatch of General Hydro-Thermal Electric Power Systems. Proc. DEA Toronto, Ontario. March 1978 |
| 15- R. Nieva, G.S. Christensen and M.E. El-Hawary, Functional Optimization of Nuclear-Hydro-Thermal Systems. Proc CEA, Toronto, Ontario. 1978 |
| 16- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Application of the Ricatti Equation to Finding Initial Values in Ill-Conditioned Systems. Proc. Linear Systems Conference, Naval Postgraduate School, Monterey, Calif. February 1979. |
| 17- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Optimal Control of Turbo-Generator by Functional Analysis. Proc. Optimization Days, Montreal, Quebec. May 1979. |
| 18- A. Shamaly, G.S. Christensen and M.E. El-Hawary, A Functional Analysis Approach to Feedback Control of Turbo-Alternators. Proc. IEEE International Symposium on Circuits and Systems, Houston, Texas. May 1980. |
| 19- A. Shamaly, G.S. Christensen and M.E. El-Hawary, Realistic Feedback Control of Turbo-Alternators Using Functional Analysis. Proc. Third International Symposium on Large Engineering Systems, St. John's, Newfoundland. July 1980. |
| 20- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Optimal Tie-Line Control via the Maximum Principle. Proc. Optimization Days, Montreal, Quebec. May 1981. |
| 21- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Optimal Tie-Line Control via Functional Analysis. Proc. Optimization Days, Montreal, Quebec. May 1981. |
| 22- S. Yoo, G.S. Christensen and A. Shamaly, Numerical Solution of Optimal Feedback Control of a Turbo-Generator. Proc. Optimization Days, Montreal, Quebec. May 1981. |
| 23- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Nonlinear Load Frequency Control of Interconnected Power Systems. Proc. Optimization Days, Montreal, Quebec. 1983. |
| 24- R.S. Rao, G.S. Christensen and M.E. El-Hawary, Optimal Load Flow of Variable Head Hydro-Thermal Systems. Proc. IEEE Conference and Exposition, Toronto, Ontario. 1983. |
| 25- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Optimum Decentralized Load Frequency Control of Multi-Area Interconnected Power Systems. Proc. International Symposium on Circuits and Systems, Montreal, Quebec. 1984. |
| 26- N. Greenwood-Madsen, G.S. Christensen and M.E. El-Hawary, Load Flow of Variable Head Hydro-Thermal Systems. Proc. IASTED Conference, Montreal, Quebec. June 1985. |
| 27- S.A. Soliman and G.S. Christensen, Discrete Stochastic Optimal Long-Term Scheduling of Hydro-Thermal Power Systems. Proc. 14th IASTED Conference, Vancouver, B.C. June 1986. |
| 28- S.A. Soliman and G.S. Christensen, Discrete Stochastic Long-Term Scheduling of Series Reservoirs. Proc. 14th IASTED Conference, Vancouver, B.C. June 1986. |
| 29- G.S. Christensen, S.A. Soliman and A.M. Atallah, Optimal Operation of Hydro-Power System General Configuration. Proc. North American Power Symposium, Edmonton, Alberta. October 1987. |
| 30- R.S. Rao, G.S. Christensen and M.E. El-Hawary, Optimal Load Flow of Variable Head Hydro-Thermal Systems. IEEE Conference and Exposition, Toronto, Ontario. 1983. |
| 31- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Nonlinear Load Frequency Control of Interconnected Power Systems. Proc. Optimization Days, Montreal, Quebec. 1983. |
| 32- M. Abdelhalim, G.S. Christensen and D.H. Kelly, Optimum Decentralized Load Frequency Control of Multi-Area Interconnected Power Systems. Proc. International Symposium on Circuits and Systems, Montreal, Quebec. 1984. |
| 33- N. Greenwood-Madsen, G.S. Christensen and M.E. El-Hawary, Load Flow of Variable Head Hydro-Thermal Systems. Proc. IASTED Conference, Montreal, Quebec. June 1985. |
| 34- S.A. Soliman and G.S. Christensen, Discrete Stochastic Long-Term Scheduling of Series Reservoirs. Proc. 14th IASTED Conference, Vancouver, BC. June 1986. |
| 35- S.A. Soliman and G.S. Christensen, Discrete Stochastic Optimal Long-Term Scheduling of Hydro-Thermal Power Systems. Proc. 14th IASTED Conference, Vancouver, BC. June 1986. |
| 36- G.S. Christensen, S.A. Soliman and A.M. Atallah, Optimal Operation of Hydro-Power System General Configuration. Proc. North America Power Symposium, Edmonton, Alberta. October 1987. |
| 37- A. Atallah and G.S. Christensen, Efficient Load Following Scheduling for Large-Scale Hydro-Systems. Proc. Canadian Conference on Electrical and Computer Engineering, Vancouver, BC, pp. 480–483. November 1988. |
| 38- A. Atallah and G.S. Christensen, Optimal Long-Term Operations of Large-Scale Hydro Systems. Proc. Third Water Resources Operations Management Workshop, Fort Collins, Colorado. June 1988. |
| 39- S.A. Soliman, G.S. Christensen and S. Fouda, Performance Evaluation of Digital Filters Used for Distance Relaying. Proceedings 33rd Midwest Systems Conference, Calgary, Alberta, August 1990. |
References
- Penelope Christensen's page on Genealogical Studies Website
- https://ca.linkedin.com/in/lynnechristensen Lynne V. Christensen's page
- The Abbotsford News' Obituaries: Dr. Gustav S. CHRISTENSEN
- http://www.nrc-cnrc.gc.ca/eng/ National Research Council Canada
- El-Hawary, Mohamed E.; Christensen, G. S. (1979). Optimal Economic Operation of Electric Power Systems. New York: Academic Press. ISBN 9780080956527.
- Christensen, G. S.; El-Hawary, Mohamed E.; Soliman, S. A. (1987). Applications of Optimal Control in Electric Power Systems. ISBN 978-0-306-42517-2.
- Christensen, G. S.; Soliman, S. A. (1988). Optimal Long-Term Operation of Electric Power Systems. New York: Plenum Press.
- Christensen, G. S.; Soliman, S. A.; Nieva, R. (1988). Optimal Control of Distributed Nuclear Reactors. New York: Plenum Press.
- https://www.neb-one.gc.ca/index-eng.html National Energy Board Canada
- https://www.memorybc.ca/british-columbia-energy-board MemoryBC: British Columbia Energy Board
- http://search.bcarchives.gov.bc.ca/british-columbia-energy-board BC Archives: British Columbia Energy Board
- http://www.bclaws.ca/civix/document/id/oic/arc_oic/0784_1960 An old report of British Columbia Energy Board
- http://www.eic-ici.ca/ Engineering Institute of Canada (EIC)
- Christensen, Gustav Strom (1960). Optimization of Conductor Shapes and Configuration of Conductor Bundles for High Voltage Transmission (M.Sc.). University of British Columbia.
- Christensen, Gustav Strom (1966). Aspects of nonlinear system stability (Ph.D.). University of British Columbia.
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