Stockholm Power Tech. Power systems

Stockholm Power Tech

June 18-22 1995

International Symposium on Electric Power Engineering

KTH

Royal Institute of Technology and

IEEE Power Engineering Society

Power system expansion planning

SPT PS 01-01-0051 Technical problems in relation to an entirely renewable 1 energy-based electricity supply system. A. Zahedi, Monash University,

Caulfield, Australia.

SPT PS 01-02-0130 Optimal hydropower development: New version. R. 6 Duquette, Institut de recherche d'Hydro-Quebec, S. Weyman, G. Brosseau,

Hydro-Quebec, Canada.

SPT PS 01-03-0277 A heuristic procedure to cope with multi-year 12 transmission expansion planning. S. Binato, G.C. Oliveira, CEPEL, Brazil.

SPT PS 01-04-0283 Planning of new generating capacity for Estonia using 18 MARKAL model, O. Liik, Tallinn Technical University, Estonia.

SPT PS 01-05-0413 A hybrid system based on knowledge applied to the 2 4 electrical power networks expansion planning. R.C.G. Teive, L.G.S.

Fonseca, University of Santa Catarina, Florianöpolis, Brazil.

SPT PS 01-06-0415 Expansion planning of generation systems under 3 0 uncertainties. J. Coelr.o, University of Santa Catarina, Florianöpolis, Brazil,

A.M. Leite da Silva, Federal School of Engineering at Itajuba, Brazil.

Thermal power operation planning

SPT PS 02-01-0008 An improved two stages dynamic 3 6 programming/artificial neural network solution model to the unit commitment of

thermal units. N H. Abbasy, College of Tech. Studies, Kuwait, M.K.

Elfayoumy, University of Alexandria, Egypt.

SPT PS 02-02-0075 Fast economic dispatch solution with piecewise 4 2 quadratic cost function using Lagrangian multiplier. Young-Sik Baek, Jin-Hee

Han, Kyungpook National University, Korea.

SPT PS 02-05-0484 A novel economic dispatch approach-implementation 4 8 of genetic algorithm. H.-C. Chang, P.-H. Chen, National Taiwan Inst. of

Tech. Taiwan.

SPT PS 02-06-0532 ELD calculation using quadratic programming based 5 5 on binary search. T. Kashiwagi, T. Wakabayashi, Y. Hayashi, S. Iwamoto.

Waseda University, Japan.

Short-term hydro-thermal power scheduling

SPT PS 03-01-0100 Lagrangian relaxation technique in power systems 6 1 operation planning: multipliers updating problem. S. Ruzic, Electric Power

Utility of Serbia, Yugoslavia.

SPT PS 03-02-0190 Network model of short-term optimal hydrothermal 6 7 power flow with security constraints. A. Chiva, F.J. Heredia, N. Nabona,

Universitat Politechnica de Catalunya, Spain.

SPT PS 03-03-0334 Security constrained short-term hydro-thermal 7 4 scheduling in a flexible market environment. O.B. Fosso, A. Johannesen,

Norwegian Electric Power Research Institute, Norway.

SPT PS 03-04-0335 Hydro power scheduling in Norway, before and after 8 0 deregulation, G. L. Doorman, A. Gjelsvik, A. Haugstad, Norwegian Electric

Power Research Institute, Norway.

SPT PS 03-05-0427 Short-term resource scheduling in large-scale 8 6 hydrothermal power systems: dual optimization by a modified e_ subgradient

algorithm. V.M.F. Mendes, Institutto superios de Engenharia, Portugal, L.A.F.M. Ferreira, Instituto Superior Técnico, Portugal, P. Roldao, R.

Pestana, Electricidade de Portugal, Portugal.

SPT PS 03-06-0459 A mixed rule based-linear programming method 93 applied to daily operation planning of a hydro power system. L. Söder, KTH,

Sweden.

SPT PS 03-07-0460 A mixed-integer model for daily hydro planning. O. 99 Nilsson, KTH, Sweden, D. Sjelvgren, Vattenfall AB, Sweden.

Power system planning

SPT PS 04-02-0400 Decision convergence in stochastic multireservoir 1 05 hydroelectric system optimization. P.M.S. Carvalho, L.A.F.M. Ferreira,

Instituto Superior Técnico, Portugal.

SPT PS 04-03-0478 A medium term bulk production cost model based on 110 decomposition techniques. A. Ramos, L. Munoz, Universidad Pontificia

Comillas, F. Martfnez-Corcoles, V. Martin-Corrochano, IBERDROLA, Spain.

SPT PS 04-04-0576 Relevant factors in loss of load cost evaluation in 117 power systems planning. J.C.O. Mello, A.C.G. Melo, CEPEL, A.M. Leite da

Silva, EFEI, M.V.F. Pereira, PSRI, M.Th. Schilling, UFF, Brazil.

Reliability

SPT PS 05-01-0414 Maintenance scheduling of generating units with 123 reliability constraints: a mathematical programming approach. E. Luiz da Silva,

M. Morozowski, University of Santa Catarina, Brazil.

SPT PS 05-02-0439 Incorporating reactive power into power system 128 reliability analysis. D J . Coates, P.T. Manning, National Grid Company, UK.

SPT PS 05-04-0578 Probabilistic adequacy evaluation of large scale power 132 systems-a Brazilian case. A.C.G. Melo, J.C.O. Mello, G.C. Oliveira, S.P.

Romero, CEPEL, R.N. Fontoura Filho, Eletrobras, Brazil.

SPT PS 05-05-0124 Sensitivity analysis for the availability with spares in 138 electric power systems. M.A. Metaweh, Arab Maritime Transport Academy,

Egypt.

SPT PS 05-06-0535 "Netbas reliability": Transmission system and 143 delivery point reliability assessment. A. T. Holen, O. Kvennås, J. Heggset, I.

St0len, Norwegian Institute of Technology, Norway.

Voltage stability: Dynamic aspects and protective actions

SPT PS 06-01-0024 Predicting voltage instabilities. C.A. Roa-Sepulveda, 155 Universidad de Concepcion, Chile, U.G. Knight, Imperial College of Science,

England.

SPT PS 06-02-0133 A comprehensive approach to dynamic simulation of 161 voltage collapse phenomenon. N. Dizdarevic', S. Tesnjak, Faculty of Electrical

Eng. and Comp., Zagreb, Croatia.

SPT PS 06-03-0378 On strategies for undervoltage load shedding in power 167 systems. S. Arnborg, G. Andersson, KTH, Sweden.

SPT PS 06-04-0426 Voltage oscillations with cascaded load restoration, 173 CD. Vournas, National Technical University of Athens, Greece, T. Van

Cutsem, University of Liége, Belgium.

SPT PS 06-05-0455 A strategy for prevention of voltage instability by 179 generation dispatch. T. Tran-Quoc, Laboratoire d'Electro-technique de

Grenoble, L Pierrat, Electricité de France, France.

SPT PS 06-06-0507 Dynamic voltage stability indices based on existence of 184 stable equilibrium point. Y. Zhou, K. Yasuda, R. Yokoyama, Tokyo

Metropolitan University, Japan.

Voltage stability: Modelling and analytical techniques

SPT PS 07-01-0113 Voltage collapse with a laboratory power system 191 model. N.U. Krantz, M.N. Gustafsson, J.E. Daalder, Chalmers University of

Technology, Sweden.

SPT PS 07-02-0217 Voltage stability of a synchronous generator feeding a 197 restorative load. G.A. Manos, CD. Vournas, National Technical University,

Athens, Greece.

SPT PS 07-03-0312 Sequential use of optimal power flow for improving 203 the static voltage stability margin. P. Mangang, University of Karlsruhe,

Germany, S.S. Ahmed, A. Petroianu, University of Cape Town, South Africa.

SPT PS 07-04-0340 Features of voltage stability of power systems and 209 common reasons of voltage collapse. N. Hatziagyriou, B. Papadias, National

Technical University, Athens, Greece.

SPT PS 07-05-0357 Distribution system modelling for voltage stability 215 studies. R. Lind, KTH, D. Karlsson, Sydkraft AB, Sweden.

SPT PS 07-06-0492 Behaviour of generator current limiters near the point 221 of voltage collapse. F.G.A. Sjögren, S.G. Johansson, J.E. Daalder, Chalmers

University of Technology, Sweden.

SPT PS 07-07-0612 Experiences of voltage collapse assessment for large 227 longitudinal power systems. S. Rios, Catholic University of Chile, Chile, P-A.

Lx>f, KTH, Sweden, S. Milic, H. Tapia, Catholic University of Chile, Chile.

I l l

Robust controllers for power systems

SPT PS 08-02-0121 Comparison of power system stabilizer design using 233 H

optimization and |i-synthesis approach. S. Chen, O.P. Malik, University of

Calgary, Alberta, Canada.

SPT PS 08-04-0344 Robust H« tuning of power system stabilizers. S.S. 238 Ahmed, L. Chen, A. Petroianu, University of Cape Town, South Africa.

SPT PS 08-05-0370 Robust supplementary damping controllers. H. 244 Othman, R. Vedam, ABB Transmission Technology Institute, Raleigh, USA,

L.Ängquist, ABB Power Systems AB, Sweden.

SPT PS 08-06-0373 Optimal design of flexible controllers in large power 250 systems using a modal performance measure. J.B. Simo, University Laval,

Quebec, I. Kamwa, Institut de recherche d'Hydro-Québec (IREQ), Canada.

SPT PS 08-07-0417 Coordinated robust controllers in power systems, 256 A.S. Bazanella, A.S. e Silva, University of Santa Catarina, Brazil, A.

Fischman, J.M. Dion, L. Dugard, Laboratoire d'Automatique de Grenoble, France.

FACTS Control of damping and stability

SPT PS 09-01-0087 Stabilization of inter-area and/or oscillatory modes in 262 large-scale power system by VIPS apparatus based on decentralized control

scheme. M. Nagata, A. Yokoyama, University of Tokyo, Y., Sekine Science Univ. of Tokyo, Japan.

SPT PS 09-03-0399 Design of TCSC controllers to damp power swings by 268 using eigenvalue analysis method. X.R. Chen, N.C. Pahalawaththa, U.D.

Annakkage, University of Auckland, C.S. Kumble, TransPower New Zealand Ltd., Wellington, New Zealand.

SPT PS 09-04-0620 Power oscillation damping with controlled active 274 loads. O. Samuelsson, G. Olsson, Lunds Tekniska Högskola, B. Eliasson,

Sydkraft AB, Sweden.

SPT PS 09-05-0627 Sensitivity analysis of FACTS control characteristics 280 with respect to network configuration and requirements. R. Caldon, A. Mari,

A. Paolucci, R. Turn, University of Padova, Italy.

Transient stability

SPT PS 10-01-0018 Neural network nonlinear classifier for on-line stability 286 evaluation. J.V. Wijayakulasooriya, W.M.N. Jinadasa, M. Sellathurai,

M.A.R.M. Fernando, P.R.P. Hoole, University of Peradeniy, Sri Lanka.

SPT PS 10-02-0172 A novel approach to transient stability simulation using 290 neural networks. N. Kandil, R.J. Marceau, X-D Do, Ecole Polytechnique de

Montreal, G. Tuong, V. Sood, Hydro-Quebec, Canada.

SPT PS 10-03-0274 Dynamic equivalents of sub-transmission networks for 296 transient stability studies. H. Nakra, R. Belhomme, C. Gagnon, Institut de

recherche d'Hydro-Quebec (IREQ), C. Thomassin, J. Gagnon, Direction Exploitature Hydro-Auebec, Canada.

SPT PS 10-04-0317 Transient stability assessment: Setting-up a direct- 302 method-based tool for expert system environment. S. Massucco, A. Morini,

University of Genova, Italy, T. Siewierski, University of Lodz, Poland.

SPT PS 10-05-0436 Power system transient stability analysis using 308 Kohonen layer. Y.M. Park, G.-W. Kim, Seoul National University, Korea,

K. Y. Lee, Pennsylvanian State University, USA.

SPT PS 10-06-0558 A hybrid system for transient stability analysis of 314 power systems using genetic algorithms and pattern recognition. K.L. Lo,

University of Strathclyde, U.K., Q. Yin, South China University of Technology, China.

SPT PS 10-07-0562 Analysis of induction machine effects in the 319 synchronous generator stability during a fault in the electrical system. C.H.

Salerno, J.R. Camacho, L.M. Neto, Universidade Federal de Uberlandia, Brazil.

Modern power system stabilisation

SPT PS 11-01-0122 Implementation of a fuzzy logic based PSS using Intel 324 8051 micro-controller. K.A. El-Metwally, Cairo University, Egypt, O.P.

Malik, University of Calgary, Canada.

SPT PS 11-02-0147 Enhancement of power system stability by fuzzy logic 329 control. P.Y. Wang, G.S. Wang, B.H. Li, Electric Power Research Institute,

China.

SPT PS 11-03-0249 A fuzzy logic self-organizing decentralized power 335 system stabilizer for a multi-machine power system. M. Ramezanian, West

Region Electric Co., A. Mahmina, University of Technology, Iran.

SPT PS 11-04-0424 An inverse neuro power system stabilizer using pole 341 shifting control technique. Y.M. Park, S.-H. Hyun, J.-H. Lee, University of

Söul, H.-J. Lee, Kwang Woon University, Korea.

SPT PS 11-05-0508 Neural network based fuzzy controller of the 346 synchronous generator. Z. Lubosny, Technical University of Gdansk, Poland.

Power system control

SPT PS 12-01-0022 Optimal placement of static var compensators in power 352 system for stability improvement. M.A. Golkar, D. Jalali, H. Berahmand-

pour, Electric Power Research Center, Iran.

SPT PS 12-02-0055 The problem of large electric power system 357 survivability. NX Voropai, Siberian Energy Institute, Russia.

SPT PS 12-03-0058 Power system stabilizer output feedback design for 363 expanding construction of multimachine system. M.A. El-Gammal, Egypt.

V

SPT PS 12-04-0127 The simplified linear model derivation of power 370 systems with static var compensators to improve system damping. C.S. Chen,

C.T. Hsu, National Sun Yat-Sen University, Taiwan.

SPT PS 12-06-0621 Damping control of SVCs in the presence of dynamic 376 loads. I. A. Hiskens, J.V. Milanovic, University of Newcastle, Australia.

SPT PS 12-07-0633 New concepts for microprocessor based voltage 380 regulators. F.P. de Mello, Consulting Engineer, Burnt Hills, USA.

Modelling and compultation of power system stability

SPT PS 13-01-0097 Hopf limit cycles estimation in power systems. J. 386 Barquin, T. Gomez, F.L. Pagola, Universidad Pontificia Comillas, Spain.

SPT PS 13-02-0149 Representation of control devices in the calculation of 392 transients in power systems. V.A. Stroev, Y. V. Sharov, V.S. Asambaev,

Moscow Power Engineering Institute, Russian Federation.

SPT PS 13-03-0225 The effect of automatic voltage regulation on the 398 bifurcation evolution in power systems. CD. Voumas, National Technical

University, Greece, M.A. Pai, P.W. Sauer, University of Illinois, USA.

SPT PS 13-04-0462 On the practical experience with two numerical 404 algorithms for frequency estimation. V.V. Terzija, M.B. Djuric, University of

Belgrade, Yugoslavia.

SPT PS 13-05-0476 Assessment of dynamic stability of large-scale power 410 system by Rayleigh's quotient. N. Kakimoto, Kyoto University, K. Sugano,

Kansai Electric Power Co, Japan.

SPT PS 13-06-0626 Calculation of oscillatory stability margins in the space 416 of power system controlled parameters. Y.V. Makarov, V.A. Maslennikov,

D.J. Hill, Sydney University, Australia.

SPT PS 13-07-0674 Synchronous machine transient stability analysis 4 23 considering pre-fault voltage unstable operating points. R.B. Prada, J.E.O.

Pessanha, Federal University of Maranhäo, Brazil.

Nonlinear adaptive control of power systems

SPT PS 14-01-0026 Variable structure control for multimachine systems 429 using neural networks. J. Shi, L.J. Cao, Nanyang Technological University,

Singapore.

SPT PS 14-02-0386 Nonlinear decentralized control for multimachine 435 power system transient stability enhancement. Y. Wang, G. Guo, Nanyang

Technological University, Singapore,, D.J. Hill, Sydney University, Australia, L. Gao, Tsinghua University, China.

SPT PS 14-03-0395 Combined conventional-adaptive power system 441 stabilizer. J. Ritonja, D. Dolinar, B. Grcar, University of Maribor, Slovenia.

SPT PS 14-04-0432 Stabilization for multi-machine power system by 447

adaptive control of FACTS apparatuses. Y. Uriu, N. Aoyagi, F. Koyanagi,

Power flow computational techniques

SPT PS 15-01-0144 Partial matrix alterations. W. Schreiner, B. Kulicke, 452 Technical University of Berlin, Germany.

SPT PS 15-02-0150 The algorithms for alleviating line overloads using 4 5 8 pseudo-inverse method. V.A. Stroev, I.S. Rokotian, M.M.M. El-Shahat,

Moscow Power Engineering Institute, Russian Federation.

SPT PS 15-03-0517 A parallel version of Gauss-Seidel algorithm for 462 power flow analysis: providing numerical support for on-line decision support

systems. E.V. Skibenko, J.R. McDonald, University of Strathclyde, U.K.

SPT PS 15-04-0457 Modelling of constraints in linear programming based 468 optimal power flow. M. Olofsson, G. Andersson, L. Söder, KTH, Sweden.

SPT PS 15-05-0173 Elimination of load buses in power flow solutions: 47 3 application to the network of Bahrain. J. Talaq, F. Al-Basri, University of

Bahrain, Bahrain.

SPT PS 15-07-0623 A technique for exploring the power flow solution 47 8 space boundary. I. A. Hiskens, R.J. Davy, University of Newcastle,

Australia.

Power flow control

SPT PS 16-01-0223 Optimal power flow in FACTS using genetic 484 algorithms.L.L. Lai, J.T. Ma, City University, United Kingdom.

SPT PS 16-02-0520 Analysis of the effects of application of PST and SC 490 on the performance of the UCPTE system in the Balkans. T.M. Papazoglou,

TEI, Iraklion, Crete, D.P. Popovic, S. Mijailovic, NTI, Belgrade, Serbia.

SPT PS 16-03-0418 Simulating switching of transmission lines in Power 494 systems. J.G. Rolim, L.J.B. Machado.University of Santa Catarina, Brazil,

M.R. Irving, Brunei University, UK.

SPT PS 16-04-0416 Power flow solutions with intermediate control 500 adjustments. R. Salgado, A.D.R. Medeiros, University of Santa Catarina,

Brazil.

SPT PS 16-05

0295 Use of UPFC for optimal power flow control. M. 506 Noroozian, L. Ängquist, ABB Power Systems, M. Ghandhari, G. Andersson,

KTH, Sweden.

SPT PS 16-06-0208 Comparative study on steady-state performances of 512 various power flow controllers. J. Matsuki, K. Ikeda, M. Abe, Kyoto

University, Japan.

New analytical techniques for power system analysis

SPT PS 17-01-0447 Recursively parallel method of solution of power 5 1 8 system matrices. J. Bialek, University of Durham, D. J. Grey, University of

Sunderland, England.

VII

SPT PS 17-02-0438 Some generalizations for z-transform methods in 524 power systems: s-z mapping functions, generator model and discretization. L.

Isworo, D. Sutanto, University of New South Wales, Australia.

SPT PS 17-03-0237 A statistical approach to the identification of electrical 530 regions in power systems. L. Wehenkel. University of Liége, Belgium.

SPT PS 17-05-0057 The utilization of eigenvalues and eigenvectors and the 536 reliability of their calculation in power systems; A case study. A.M.A.

Hamdan, Jordan University of Science & Techn., Jordan.

SPT PS 17-06-0557 The problem of weak places in electric power systems. 542 A.Z. Gamm, I.I. Golub, Siberian Energy Institute of Russian Academy of

Sciences, Irkutsk, Russia.

SPT PS 17-07-0647 Approximate partitioned sparse inverse method via 547 MIF ordering for power network solutions. H.A. Shayanfar, H. Yousefizadeh,

Iran University of Science & Technology, Iran.

Software and analysis tools for power systems

SPT PS 18-01-0351 The small signal stability analysis of large power 552 systems by means of improved simultaneous iteration method. F. Ishikawa, M.

Kitagawa, Chugoku Electric Power Co., H. Sasaki, N. Yorino, H. Okimura, Hiroshima University, Japan.

SPT PS 18-04-0486 An efficient method for evaluation of post-dynamic 558 quasi-stationary states during the island operation of power system parts. D.P.

Popovic, S.V. Mijailovic, Nikola Technical Institute, Jugoslavia.

Load forecasting

SPT PS 19-01-0062 Short- term load forecasting using 564 unsupervised/supervised cascaded artificial neural networks. Serpil Tin, Ismet

Erkmen, Middle East Technical University, Turkey.

SPT PS 19-02-0128 Design of load survey system to identify customer 570 load patterns. C.S. Chen, J.C. Hwang, National Sun Yat-Sen University,

Taiwan.

SPT PS 19-03-0165 A sense of security for mid-term load forecasting 576 using neural net. B. Kermanshahi, M. Zhao, R. Yokoyama, Tokyo

Metropolitan University, M. Asari, Central Res. Inst. of Electric Power Industry, Japan.

SPT PS 19-04-0267 An accurate software model for off-line assessment of 582 a digital relay. P.G. McLaren,E.N. Dirks, R.P. Jayasinghe, I. Fernando,

University of Manitoba, G.W. Swift, Z. Zhang, Vansco Electronics Ltd., Canada.

SPT PS 19-05-0605 A comparative study of static parameter estimation 588 algorithms in short-term load forecasting. S.A. Soliman, A.M. Al-Kandari,

College of Technological Studies Kuwait, S. Persaud, K. El-Naggar,

University of Alberta, Canada.

SPT PS 19-06-0651 Artificial neural network based models for short-and 595 long-term load forecasting in the power system. J. Malko, Technical University

of Wroclaw, H. Mikolajeczak, W. Skorupski, Inst. of Power Systems Automation, Poland.

Power quality and harmonics

SPT PS 20-01-0107 Digital determination of power system frequency in 601 the presence of harmonics. T. Lobos, J. Rezmer, Technical University of"

Wroclaw, Poland.

SPT PS 20-02-0167 Assessment of voltage quality in electric energy 607 systems. D. Blume, TEAM, E. Handschin, University of Dortmund, J.

Schlabbach, Fachhochschule Bielefeld, Germany.

SPT PS 20-03-0231 Simulation of power system disturbances for testing of 612 digital systems. C. A. Russell, K. E. Russell, LADWP, J. Balachandra,

CSUS, USA.

SPT PS 20-04-0359 Power measurement uncertainties in a non-sinusoidal 617 power system. S. Svensson, Swedish National Testing and Research Institute,

Sweden.

Security assessment

SPT PS 21-01-0042 Estimating transient stability transfer limits for normal 623 contingencies. R.J. Marceau, École Polytechnique de Montreal, Canada.

SPT PS 21-02-0043 Application of neural networks in transient stability 629 security assessment. M. Eslamy, A.M. Ranjbar, Electric Power Research

Center, Iran.

SPT PS 21-03-0450 Fuzzy steady state security assessment. M.A. Matos, 635 J.A. Pecas Lopes, INESC Inst. de Engenharia de Sistemas e Comp., Portugal,

N.D. Hatziargyriou, Electric Power Systems Lab., Greece.

SPT PS 21-04-0451 Derivation of classification structures for fast 641 evaluation of dynamic security assessment in power systems using genetic

algorithms. J.A.P. Lopes, J.V. Ranito, J. Neto, INESC Inst. de Engenharia de Sistemas e Comp., Portugal, N. Hatziargyriou, National Techn. University of Athens, Greece.

SPT PS 21-05-0463 Economical security enhancement. E. Amthauer, 647 Laufenburg, I. Nordanlycke, Intercompro AG, Zurich, Switzerland.

SPT PS 21-06-0556 Localization concepts applied to cyclic security 651 analysis. H. Le Kim, N. Hadjsaid, J.-C. Sabonnadiére, Laboratoire

d'Electrotechnique de Grenoble, France.

Reactive power planning and voltage control

IX

SPT PS 22-01-0068 Application of an interior point optimisation method 656 for determining the reactive margin from voltage collapse in reactive power

planning. CJ. Parker, Electricity Transmission Authority of New South Wales, I.F. Morrison, D. Sutanto, University of New South Wales, Australia.

SPT PS 22-02-0073 Optimal reactive power dispatch using evolutionary 662 programming. J.T. Ma, L.L.Lai, City University, United Kingdom.

SPT PS 22-03-0181 A fuzzy expert system for low-cost security- 668 constrained reactive dispatch. K.R.W. Bell, A.R. Daniels, R.W. Dunn,

University of Bath, UK.

SPT PS 22-04-0182 Security enhancement aspects in the reactive-voltage 674 control. A. Berizzi, Technical University of Milano, P. Bresesti, CESI SpA, P.

Marannino, M. Montagna, University of Pavia, S. Corsi, G. Piccini, ENEL SpA, Italy.

SPT PS 22-05-0338 A multi-level automatic voltage control system for the 680 Spanish transmission network: Situation and simulation results. J.L.

Fernandez, J.L. Sancha, A. Cortés, J.T. Abarca, Red Electrica de Espana, S.A., Spain.

SPT PS 22-06-0405 Coordinated control of cascaded tap changers in a 686 radial distribution network. M. Larsson, Lunds Tekniska Högskola, D.

Karlsson, Sydkraft AB, Sweden

Wheeling and pricing

SPT PS 23-02-0287 Wheeling costs: an economic analysis illustrated by 692 short term and long term simulation. Y. Smeers, F. Jonard, Université

Catholique de Louvain, Belgium, P. Bruel, P.B. Heilbronn, Electricité de France, France.

SPT PS 23-03-0236 Network effects in a competitive electricity industry: 698 Non linear and linear nodal auction models. N. Pamudji, R. J. Kaye, H.R.

Outhred. University of New South Wales, Australia.

SPT PS 23-04-0354 Penalty factor calculations for marginal pricing of 704 transmission systems in a hydroelectrical system. R. Palma, H.

Rudnick,Catholic University of Chile, Chile, H. Rudnick.H. Lira, National Energy Commission, Chile.

SPT PS 23-05-0377 Area price based multi-area economic dispatch with 710 transmission losses and constraints. J. Wernérus, L. Söder. KTH, Sweden.

SPT PS 23-06-0549 Allocation of transmission fixed charges: An economic 716 interpretation. J. W. Marangon, Lima Escola Federal de Engenharia de

Istajuba, Brazil.

Analysis and control of distribution systems

SPT PS 24-01-0483 An efficient approach for reconfiguration problem in 722 distribution systems, H.-C. Chang, C.-C. Kuo, National Taiwan Inst of

Technology, Taipei, Taiwan.

728

SPT PS 24-03-0021 A new method for load flow study in radial 733 distribution systems. M.A. Golkar, K.N. Toosi, University of Technology,

Tehran, Iran.

SPT PS 24-04-0148 Distribution feeder reactive power compensation by 738 shunt capacitor. M.Y. Cho, National Kaohsiung Inst of Techn., C.S. Chen,

National Sun Yat-Sen University, Kaohsioung, Taiwan.

SPT PS 24-05-0152 A neural network for modeling and forecasting MV- 744 feeder loads. M. Kärenlampi, P. Järventausta, P. Verho, Tampere University

of Technology, J. Partanen, Lappeenranta University of Technology, Finland

SPT PS 24-06-0662 The probabilistic approach to the analysis of power 750 distribution systems. J. Nazarko, W. Zalewski, Bialystok Technical

University, Poland, G. Cross, University of Ulster, Ireland.

SPT PS 24-08-0420 Application of decision support systems to power 756 distribution system planning. M. El-hami, Iran University of Science and

Technology, Tehran, Iran.

Optimisation of distribution systems

SPT PS 25-01-0034 Optimal allocation of sectionalizers in radial 761 distribution networks. G. Levitin, Sh. Mazal-Tov, D. Elmakis, Israel Electric

Corporation Ltd., Israel.

SPT PS 25-02-0106 A new approach on optimal capacitor allocation and 766 sizing in radial networks. H. Berahmandpour, Electric Power Research Center,

Iran.

SPT PS 25-03-0060 Load influence on minimum loss reconfiguration of 771 automated distribution networks. A. Augugliaro, L. Dusonchet, S. Mangione,

University of Palermo, Italy.

SPT PS 25-04-0125 Loss calculation integrated process in distribution 777 systems. J. Bacelar, Companhia de Eletricidade do Estado da Bahia-Coelba,

Brazil.

SPT PS 25-05-0191 A method for loss minimization in unbalanced 783 distribution networks. V. Borozan, D. Rajicic', R. Ackovski, University "Sv.

Kiril i Metodij", Macedonia.

SPT PS 25-06-0316 Optimal reconfiguration of distribution networks for a 789 diversity of regulatory frameworks. G. Carrillo-Caicedo, I. J. Perez-Arriaga,

Universidad Pontificia Comillas, Spain.

Reliability and outage costs in distribution systems

SPT PS 26-01-0007 Monte Carlo simulation in distribution network 795 analysis. A. Dimitrovski, R. Ackovski, University "S. Kiril i Metodij",

Skopje, Macedonia.

SPT PS 26-02-0207 Reliability assessment of power distribution systems 801 considering the effects of supply restoration procedures. E.N. Dialynas, D.G.

Michos, National Technical University, Athens, Greece.

XI

SPT PS 26-04-0493 Reliability evaluation in open ring distribution 807 systems. M. Abedi, F. Rameshkhah, D. Jalali, Electric Power Research

Center, Tehran, Iran.

SPT PS 26-05-0412 Evaluation of outage costs in distribution systems. 813 M.G. Da Silva, UFMA, Brazil, R.N. Allan, UMIST, Manchester, U.K.

Planning of distribution systems

SPT PS 27-01-0542 Development of medium voltage network structures in 820 the rural field. E.Romanello, EDF, France

SPT PS 27-03-0449 Fuzzy modelling of independent producers for 826 multicriteria electric distribution planning. M. T. Ponce de Leäo, M.A. Matos,

INESC Inst. de Engenharia de Sistemas e Comp., Portugal.

SPT PS 27-04-0454 A general methodology for distribution planning under 832 uncertainty, including genetic algorithms and fuzzy models in a multi-criteria

environment. V. Miranda, L.M. Proenca, INESC Inst. de Engenharia de Sistemas e Comp., Portugal

SPT PS 27-05-0345 Distribution planning with energy storage. Z.A. 838

Styczynski, University of Stuttgart, Germany.

Technical Problems in Relation to an Entirely Renewable Energy-Based Electricity Supply System

A. Zahedi MIEEE CEng. MIEE Alternative Energy Research Group

Department of Electrical and Computer Systems Engineering Monash University, Caulfield Australia

Abstract-The objectives of (his contribution to the conference is to discuss the technical problems in relation to connection of renewable energy to utility distribution network and to introduce a technique which has been developed for solving the power fluctuation problem which is a result of this connection. The generation of electricity from wind energy and solar energy has been considered world wide, particularly in the United States and Europe.

The integration of wind power and solar power with the utility network create some technical problems. Electric pov.\T generated from wind generator for example is a function of wind velocity which varies stochastically. The variation of wind velocity causes the rotor speed, the terminal voltage, the frequency of generator and the output power to vary. This paper describes integrated renewable energy and energy storage system (IREES), which delivers power from intermittent renewable source to interconnected network at a constant rate. The IREES system is a totally renewable energy based electricity- supply system. It finds many applications, as it can be used as a large scale power supply being connected to national distribution network as well as small scale power supply for remote areas.

I. INTRODUCTION

Energy supply and energy usage are the largest sources of pollution which cause negative impacts on the environment, however, the magnitude of the impacts can vary widely depending on location, scale of application and the technology- used. Environmental consideration experienced in recent years have led to encouragement of generating electricity using renewable sources such as solar and wind.

Paper SPT PS 01- 01- 0051 accepted for presentation at the IEEE/KTH Stockholm Power Tech Conference, Stockholm, Sweden, June 18-22,1995

Connection of wind and solar energy to interconnected network causes negative effects on quality of supply and reliability of system. The effects of wind energy on the dynamic behaviour of a network includes worsening the voltage and frequency quality, increasing demand on control deuce of wind turbine and increasing load on control system of network. The power fluctuation is the result of changes in wind speed in different times. In order to reduce these negative effects there arc conventional methods such as using rotation-variable generating system, increasing the short circuit power at the junction of wind turbine and the network. This paper develops a technique which involves integration of generation and storage system for constant power supply.

II. POWER FLUCTUATION COMPENSATION The major technical problem in relation to grid connection of wind energy and solar energy is power fluctuation which is undesirable and also unavoidable.

Power fluctuations can be improved by integration of energy storage deuces located next to the wind turbine and network. Storage devices arc used to improve the quality of supply and to guarantee the system reliability.

While the battery storage systems are used as long term storage, SMES systems are more appropriate for short term storage. A hybrid storage system offers a combination of both short term and long term storage.

To investigate the performance of the wind turbine and the storage system and to also predict the performance of the entire system an accurate mathematical model has been developed and simulated in computer. In the developed model, the location of the storage device has been chosen to be next to generation plant, however, the location of storage device is not restricted to this place and it can be at any place in the system.

HL THE METHOD USED TO SOLVE THE POWER FLOW PROBLEM

Power flow in transmission networks is calculated using linear mathematical model for transmission line, transformer and shunt or series reactance, but non-linear electrical descriptions for generation and load at the

buses. The non-linear electrical specifications result in non-linear forms of KirclihofTs laws for power flow, so called power flow problem. There are two main sources of non-linearity. First, the power demand on the transmission network from distribution connections is closely modelled by constant real and reactive power. A second reason is that generating plants normally operate at a regulated voltage level and fixed real power injection. The voltage phase angles between generators on the system are not known. The conventional methods of solving power flow problems such as Gauss - Scidel did not help to solve the power flow problem of investigation of this type. Therefore an exact

mathematical model has to be developed and special technique needs to be used to solve the pouer flow problem of this integrated system and also to investigate the performance of the entire system.

Power equation:

k

Solar Array

DC/AC

ZJI

I'tility Distribution Network 415 V 1 VI

Z32 Z21

- G D -

Wind Turbine

Input Dili Output Data

System Controller

S2

Energy Storage Device

Constant Power

Figure 1 The single phase equivalent circuit of TREES under investigation The power equations are rearranged to make the

unknown quantities as subject, and a mathematical technique is developed to achieve the results. If the injected power into the distribution network, fcr example, is to be maintained constant, then calculations are restricted to a fix and constant value of power .The proposed scheme of Fig. 1 has been simulated in computer. It is tried to keep the power injected to the utility grid at a constant level. The developed mathematical model and computer program is able to

IV. VOLTAGE CONTROL

Traditionally voltage magnitude of a high voltage distribution network is mai Gained at almost constant value by using an on-load tap changer transformer associated with an automatic voltage control relay which has been shown in Fig. 2. The function of the automatic voltage control relay is to ensure voltage levels are kept within the acceptable limits. To achieve

Wind Generator

I'fility Distribution Network Constant Voltage

<£>

\ T

CT

Automatic voltage control

Figure 2 Conventional voltage control system

V. FREQUENCY CONTROL

Variation of frequency at the generator terminals as a result of wind speed variation has negative effects on the quality of frequency. To overcome this problem an asynchronous link is used to rectify the variable frequency at the generator terminals, which has been shown in Fig.

3. AC power is converted into DC power and this power is transferred to the utility grid through a line commutatcd inverter.

J

Wind Generator

©-H3D- X

I'fility Distribution Network DC / / AC

Constant Frequency

Figure 3 Frequency control system

By combining these power, voltage and frequency control units in series, electricity at a fairly constant rate of power, voltage and frequency will be flowing into the network. Figure 4 shows a possible combination of these three units.

R S

Frequency Control

Power Control

Voltage Control

enewaWe V d U t y

•""•« Network

Figure 4 Three control units

VI. LARGE SCALE OF IREES

Due to the cyclical human life, utility loads appear to be cyclical. During day time most factories arc in operation, therefor the electricity demand is very high During night time most people arc sleeping, then the electric load is very low usually only half of the peak load amount. To meet this large gap between peak load and light load, utilities must idle many generation plants during the light load period while operating all generation plants during peak load period no matter how expensive they arc. This low utilisation factor of generation plants and uneconomical operation encourages utilities to use energy storage devices such as pumped storage plants, compressed air energy storage plants, the battery energy storage system (BES) and the superconducting magnetic energy storage system (SMES) etc. Among these, pumped storage is already commercialised and is the most widely used device.

Battery energy storage is one of the most promising devices that may succeed pumped storage as the next generation storage device.

Renewable energy and energy storage device can be combined to make a large scale integrated system for more reliable and efficient supply system. Most of the renewable energy sources are of an intermittent nature.

Therefore it would be appropriate to use intermittent sources of energy in conjunction with non-intermittent sources such as hydro and biomass. If this power supply combination is used to supply an interconnected grid, more effective use could be made of the most prospective renewable energy and storage facility. On days when there is not enough solar or wind energy available, the biomass and hydro power plants would be used. The most cost effective solution for using the back-up generating plants would be to use one generating plant for continuous operation and one generating plant for operation during peak periods. Three possible options have been shown in Fig. 5. To ensure that the reliability of electricity supply is not adversely affected, it would be necessary that the collective power output of both hydro and biomass power plants plus storage facilities are

sufficient to meet the peak load on the electricity grid.

Storage systems are to store the surplus of energy generated in the system. For this purpose either electrochemical batteries or existing hydro dams can be used as the storage facilities. The storage facilities must also have sufficient generation capacity to serve for variations in supply from intermittent energy sources.

The existing hydro dams can be upgraded for use as pumped storage facilities. Such systems can represent a comparatively low cost storage option. An alternative option would be to rely on solar energy using hydrogen as a storage medium.

Electrochemical Batterio

O

Intermittent Energy

Biomu.is

Hydro

Storage

Network

Elisting Hydro Dams for Energy Storage Intermittent

Energy

Storage

Illomass

Network

Intermittent Energy

El ertri tin- Network

Electrohser

0

Transportation

Figure 5 Combination of renewable energy and energy storage facility (large scale)

By using this arrangement,(solar-Hydrogen), it would be

fuel cell. In off peak periods the excess electrical energy is to produce hydrogen which can be used in a variety of forms. It can be used as fuel in vehicles for transportation purposes, it can be burnt in a combustion chamber to generate thermal, mechanical and electrical energy, it can be used in fuel cells to generate electricity. Unlike conventional power generation technologies, fuel cells are not restricted by theoretical limits on efficiency that apply to heat engines. This means that provided internal cell losses are minimised, fuel cells will be significantly more efficient than conventional power stations.

VII. SMALL SCALE OF IREES FOR RAPS (Remote Areas Power Supply)

For many years, people who arc remote from the National Grid have diesel generators which supply electricity for their use. These generators arc auto- start/auto-stop and their size arc at least four times larger than the average load requirement and they have to run for a long period of time under light load which causes relatively high maintenance and fuel costs. It is not possible to include renewable sources in such systems. If a batter,' is added to this system, the battery is used during periods of light load and the generator is used during periods of heavy loads. Using a batter)1 has this advantage that the diesel generator running time is reduced and power is available 24 hours a day. Another advantage of this system is that renewable sources of energy namely solar or wind, can be easily added to this system. Fig. 6. PLC controls the power flow between the inverter, generator and the battery to optimise the operation time and the loading of the diesel as well as to maximise batten' life.

Battery

is

• •

; ' • -

ft Wind Generator

I)

E DC/AC

System Controller

SoUr Array

HeselAItemstor

^* " -^

( ^

Consum er lends

Figure 6 A simplified renewable energy based electricity

VIIL CONCLUSION

Our future energy needs will be supplied by a combination of many different sources, ranging from small wind and water wheels that provide pow-jr for a single home to central power stations that provide power in very- large scales fed into the national grid. Computer control systems will integrate the performance of all these systems to make sure that as much power as possible comes from environmentally friendlier sources. As alternative sources become more widely available, small scale systems meeting local needs may start to replace current large scale central power stations. Grid connection of intermittent energy causes negative effects on supply quality, voltage, frequency and reliability of the system. Integrating renewable energy- and suitable energy storage device can help to improve the quality of power, voltage and frequency. The IREES system described in this paper offers advantages such as combining different types of sources of energy to produce power from mostly available and environmentally safer one. The IREES system finds so many applications as it can be used as a large scale power supply being connected to national grid as well as small scale power supply for remote areas.

Findings and results arising from this research project will be of practical value for both power suppliers and people as energy consumers as this system not only conserves energy but also helps preserving the environment.

IX. REFERENCES

1. IEEE Power Engineering Review June 1991, January 1992.

2. IEE Review, April 1992

3. BMFT-Publications. Bundesminesterium fuer Forschung und Technologic Bonn, Germany

CADDET, IE A, OECD 1991-1992 Publications

4. DPIE-Publications Energy Division of Commonwealth Department of Primary Industry and Energy, Canberra

5. Zahedi A. "Environmentally Acceptable Power Generation, Power People Environment", in proceeding of CEPSI Conference 1992 Hong Kong.

6. Lov. FM "Final Year Industrial Project. Monash University", 1993

7. Mark Stevens "renewable Electricity for Australia"

commonwealth of Australia 1992

8. Ian Walker "Energy and the Environment" DPIE.

1992

9. Peter Bullock "Energy from Municipal Solid Waste"

DPIE. 1994

10. World Energy Council Publications

11. Zahedi, A. "Conversion of stand-by-generator facilities to combined heat and power unit", in ' proceeding of IEEE/I AS'94. Orange County/USA 12.Zahedi, A. "Waste disposal and energy recover)"

1994 Submission to the standing committee on Environment, Recreation and the Arts , Australian Senate in Canberra

13.Tsung-Ying Lee, Nanming Chen, "Optimal Capacity of the Battery Energy Storage System in a Power System" IEEE Power Engineering Review, 93 WM 198-2 EC. T-EC December 1993

14. Zahedi. A. "Energy, People, Environment Integrated Renewable Energy and Energy Storage System ", in proceeding of 1994 IEEE International Conference on Systems Man Cybernetic. Texas/USA

15. Zahedi, A. "Investigaion of Feasibility of Establishing Waste to Energy Facilities in Australia", in proceeding of 1994 IEEE International Conference on Systems Man Cybernetic, Texas/USA

16. Salman S K et al "Effects of wind power generators on the voltage control of utility distribution networks"

Renewable Energy Conference Publication No. 385, IEE 1993

Optimal Hydropower Development: New Version

Robin Duquette, Student Member IEEE Steven Weyman Institut de recherche d'Hydro-Quebec Hydro-Québec

1800 montée Ste-Julie 800 de Maisonneuve est, 19

floor Varennes (Quebec), Canada J3X 1S1 Montreal (Quebec), Canada H2L 4M8

Gilles Brosseau

Hydro-Québec

800 de Maisonneuve est, 20™ floor Montreal (Quebec), Canada H2L 4M8

Abstract—Currently, the mathematical model associated to the optimal hydropower development at Hydro-Québec manages the reservoirs with only one scenario of natural inflows — the problem is solved deterministically; must meet a firm demand of energy without resorting to other means of production; and minimizes only the investment cost. In this paper, a new mathe- matical model based on Robust Optimization that considers the stochasticity of natural inflows, the existing system and neigh- boring utilities, and some environmental constraints is presented.

Keywords—Hydropower Development, Nonlinear Optimiza- tion, Robust Optimization

I. INTRODUCTION

T TYDROPOWER development at Hydro-Québec X X consists first in selecting the sites on a valley where reservoirs, hydroelectric power plants and pos- sibly derivations have to be built to meet a firm de- mand of energy; and then in determining the size of each reservoir, power plant and derivation. This problem can be expressed as a nonlinear programming

Paper SPT PS 01- 02- 0130 accepted for presentation at the IEEE/KTH Stockholm Power Tech Conference, Stockholm, Sweden, June 18-22,1995

problem with both integer and continuous variables;

integer variables give the selection of reservoirs, plants and derivations to be built while continuous variables represent dam heights, capacities of the power plants, etc. The problem is nonlinear mainly because the construction cost functions are nonlinear and because power plant generation is a nonseparable function of both the water head and the water flowing through the turbines. Furthermore when we fix the integer variables (i.e., when the selection is made), the re- maining problem is nonconvex.

This problem is currently solved at Hydro-Québec by a program called Minerve [1]. Minerve is an im- proved version of Athena [2] program. The latter has allowed Hydro-Québec to save around 50 mil- lion $ CAN (approximatively 36 million $ US) on one project only. These two programs have been imple- mented at Hydro-Quebec.

The current mathematical model in Athena and Minerve of hydropower development is characterized as follows: the reservoirs are managed with only one scenario of natural inflows — normally, the most pes- simistic one is considered; a firm demand of energy must be met without resorting to other means of pro- duction; and only the investment cost for a giving energy demand is minimizing. Moreover, the scenari- o's horizon is about 600 periods — the life duration of hydroelectric installations is about 50 years and the

the existing system and neighboring utilities, and to also minimize the negative impact on some important environmental issues. Formally introducing only one of these items to the current model represents a diffi- cult task. First, solving a nonlinear stochastic prob- lem formally is very difficult by itself. Second, it is not clear how the new project should interact with the existing system since there is no direct cost associated to the operation of this system — 96% of the Hydro- Quebec's energy is produced by hydropower plants.

Last, most of the important environmental issues are qualitative rather than quantitative (e.g., unpleasant consequences to local populations).

However such improvements to the model are im- portant if we want to solve realistically the problem associated to hydropower development. But because data are generally approximated in the case of natural inflows and energy demand, the resulting model must remain intuitive, i.e., if we have an intuition on data, we must have an intuition on the solution.

In this paper we describe a way to introduce such improvements into the model without increasing too much its complexity and while maintaining its intu- itive nature. More precisely, we show in the following section how we can use a method called Robust Op- timization to deal with the stochasticity of natural inflows. In section III, market structures are intro- duced which allow to relate the development problem to the operation of the existing system and to ex- change with neighboring utilities. In the following section we show how we can capture some impor- tant environmental issues through the flooded area and through the river flows. Finally, we end the pa- per by concluding and giving potential impacts of a competitive electricity market on hydropower devel- opment at Hydro-Quebec. This new structure can change considerably the problem by introducing new uncertainties into the model.

II. STOCHASTIC OPTIMIZATION

The goal here is to find a development scheme that is optimal on the average for all possible scenarios of natural inflows, i.e., for any scenarios, we can produce the amount of energy needed to meet the electricity demand at a minimal cost. We will define later what it meant by meeting the demand. One way to achieve this goal is to use stochastic programming in a con- ventional manner where the space of natural inflows

is represented by a discrete domain and we build from this domain a stochastic decision tree. The problem with this approach is the size of the decision tree will be so large that it will not be practically solvable.

Another way will be to define a set of scenarios that will capture as close as possible the reality of natural inflows where each of them will have a weight repre- senting its likelihood — the sum of all weights equals 1. Thus, the problem is now to find a development scheme that it is close to the optimal regardless of which scenario occurs. We will not describe in this paper the approach for determining such scenarios because it can be the subject of a paper by itself.

Nevertheless, it is sufficient to know that the number of such scenarios lies generally around 10 and each of them has a horizon of 84 periods.

The problem stated previously can be solved by a method called Robust Optimization [3]. We will de- pict partially this method by showing how it applies to our problem.

A. Current Model

The approach to solve the optimal hydropower de- velopment as described in [1] can be summarized as follows:

1. The first step consists of retaining all potential combinations of sites (i.e., combinations of reser- voirs, hydroelectric power plants and derivations) which have a strong probability of satisfying the electricity demand. For instance, we can a priori discard a combination if the maximal installed ca- pacity is not sufficient to satisfy the peak demand.

This step is necessary because for some problems the number of combinations can be as large as

124416.

2. The next step is to solve for each combination of sites retained at the preceding step, the following problem:

min Cost(x) + s.t. G ( x ) < 0

cDk —

(1) +Tk H?

Si.o = $\.,\v\

<Pk XLj m Qj.kHj.k + Dk - Ek =

In fact, with the help of some tricks, we

(1) for a small poition of combinations retained in the first step.

Here is a short description of (1):

• The function Cost(x) represents the construction cost (M$) and it is nonlinear and not necessarily convex.

• Dk and Ek denote respectively the deficit in pe- riod k (GWh) and the excess energy produced in period k (GWh); c and r are the coefficients associated to Dk and Ek (M$/GWh).

• The first set of constraints (i.e., G(x) < 0) rep- resents the sizing constraints (e.^., nonoverlap- ping of the installations, drawdown range, etc.), some operation constraints and bounds on vari- ables — G(x) is a blend of linear and nonlinear functions.

• The second set of constraints represents the wa- ter balance equations (see figure 1) where for period k, S^k is the reservoir content (hmJ), R^k is the spillage for reservoir i (m³/s), Qj,k is the plant discharge (m3/s) and cutk is the nat- ural inflow (m3/s) — T^ is a conversion factor.

• The third set of constraints imposes for each reservoir that the initial content must be equal to the final content — the electricity has to be produced only from natural inflows.

• Finally, the last set of constraints corresponds to the production of firm energy, i.e., the pro- duction of energy plus the deficit Dk (i.e., the demand that cannot be satisfied) minus the ex- cess of energy Ek must equal the firm demand of energy dy. (GWh). Dk is introduced to ensure that we have a feasible solution for all prob- lems. But since we must meet a firm demand of energy, the cost c associated to each unit of Dk is very high (in theory, we should say that c = co). Furthermore, because we build exclu- sively to meet the demand of energy, the income from the excess of energy sold is negligible. In other words, r is very small.

In summary, (l) is a nonlinear and nonconvex model, and therefore, one cannot guaranteed to find a global optimum with usual optimization methods. Moreover, there are no advantages to

Fig. 1. Water balance equations for reservoir i and power plant j .

B. Robust Optimization Model

We recall that the main deficiency of (1) is that the development scheme is only determined from one inflows' scenario. To handle to this problem, we define a set of scenarios such that the development scheme will be optimal on the average.

Let S be the set of all scenarios indices and i,s = Cost(x) + Xke? fc Dk,s - T Ek,s] for all s € S. Now, the objective function becomes a random variable tak- ing the value £,s with probability ps {J^^sVs = !)•

We define the robust optimization model as follows:

min • £

p

£ s.t. G'(x)<0

Si,k,s = S i

ps

- £

, p

.£,

. )

— TkQj,k,s Si,0 = Si,o,s =

The first term in the objective function

ses

corresponds to what is normally defined in stochastic optimization: it represents the mean value of the ob- jective function. The second term called robustness term distinguishes the robust optimization from con-

the variance. The constant A is used to parameterize the tradeoff between risk and expected outcome.

C. Nonanticipativity Constraints

The reason to consider the stochasticity of natural inflows is to not anticipate the future. We can go further in that direction in model (2) by requiring each pair of scenarios that are identical up to step t, to share the corresponding variables. As an illustration, assume that for si and S2 we have for k = 1 , . . . , t, Qi,k,si = ai,ic,s2' Thus, we have to add the following constraints in model (2) for k = 1 , . . . , t

Si,k,si = Si,k,S2 *, Qj.k.sj = Qj,k,S2

•M.k.S) ~ *M,k,S2 i '-'k.S) = LJk,S2

where j is the power plant associated to reservoir i, to be nonanticipative.

As the reader has probably already noticed, it is not necessary to include the previous constraints within model (2) because they are equivalent to variables substitution. Hence, nonanticipativity constraints have also the property of reducing the size of the prob- lem since we cannot exploit any particular structure.

D. Remarks

The robust optimization model as formulated in section II-B is not very helpful if the constants c and T associated respectively to variables D^.s and EkiSl

take the values described in section II-A. Because the development scheme will be mainly function of the most pessimistic scenario even if its likelihood is neg- ligible. Consequently, we must redefine the notion of deficit and excess of energy. Moreover, representing the risk by the variance does not make any sense ei- ther in that context because the objective function will not be "symmetric" around its mean. We de- scribe in the next section a market structure that cor- rects this problem. Nevertheless, model (2) gives the bases for a robust optimization model.

One concern about (2) can be its size. We recall that in [1], the development scheme is determined from one scenario with a horizon of 600 periods. We believe that we can capture almost all the "reality"

of natural inflows with 7 scenarios of 120 periods or 10 scenarios of 84 periods. Therefore, (2) will not get much larger than (1). On the other hand, if we want a more precise solution by considering more scenarios,

it is possible to involve parallel computing for solving (2). But it will require to write an entirely new solver to exploit the special matrix structure inherent to (2)

— presently, we use MINOS 5.3 to solve (l).

III. EXCHANGES

We describe in this section an approach that takes the existing system into account within our problem.

Next, we show how a similar approach can be ap- plied to neighboring utilities. Finally, we give the new mathematical formulation of the optimal hydropower development.

A. Existing System

We recall that 96% of Hydro-Quebec's energy is pro- duced by hydropower plants and so there is no direct cost associated to this production. Therefore, it is not sufficient to incorporate the existing system into the model because it is far more expensive to produce energy from the new project than from the existing system — the model will force the existing system to produce its full potential before starting to build and produce from the new project. Anyway, even if it is sufficient, the resulting problem would be so large that it will not be practically solvable.

What we need to know in fact is how much electric- ity the new project can take from the existing system to absorb its deficits, and how much electricity it can provide from its surplus. With this information in hand, we can create a market structure that will em- ulate the possible exchanges, i.e., the existing system will have the opportunity to sell (or to buy) a certain amount of energy at each period to the new project.

Now, the difficulty is to create a market structure that will reflect all potential exchanges.

From now on, we make the assumption that the new project must meet as much as possible a firm de- mand of energy and we allow exceptionally the project to rely on the existing system for a small portion of that demand. For instance, in the robust optimization model, we can allow the project to rely on the existing system only for the most pessimistic scenarios.

The idea here is to find for each period of the con- sidered horizon, the amount of energy that the exist- ing system can provide without any risk to the new project; the amount of energy that it can provide with

a small risk; and so forth1. In this manner, we can set up an increasing sequence of prices where the base price will be at least close to the marginal costs asso- ciated to any development schemes based on average scenarios — the marginal costs can be found by solv- ing (l) for each average scenario. The last remark is important because resorting to other means of pro- duction is exceptional.

To summarize, the resulting selling market will be a set of convex functions C£ss that will replace the coef- ficient c defined in section II-A — if s is an optimistic scenario, then Ckss can simply be the constant c.

To define a purchase market we use the opposite strategy. The result will be a set of concave functions R"s that will replace the coefficient r — in pessimistic scenarios, Rkss will take simply the value r. Moreover, the functions Rkss must take into account that it is not the goal of the new project to sell energy to the existing system. In other words, we do not build to sell electricity to the existing system.

B. Neighboring Utilities

Neighboring utilities can play two roles in the hy- dropower development problem:

1. they can act as selling/buying markets, or 2. they can help to establish the economical poten-

tial of the new project.

The first role is quite clear and relatively easy to define. The market structure will be a set of convex functions Ck" and concave functions R££ as described previously.

The second role can be useful if a priori we do not know exactly how much electricity we can produce economically from the new project. In that case, neighboring utilities can be virtual and we do not re- quire that prices have a strong relation with marginal costs mentioned earlier. We can see this virtual mar- ket as a kind of sensitivity analysis around the firm demand of energy.

C. New Mathematical Model

Now, with the market structure defined in the pre- ceding sections, we are able to define an accurate ro-

by a set of functions Ck,s. And similarly, we define the functions Rk,^s. So, let

Y^S = Cost(x)

and the new robust optimization model becomes

s p , 7 , + A £ , ps (y, - Zs< Ps'Ts' )2

s.'t. G'(x) < 0 Si.k.s = Si,k_ii S

Si,o = Si,o,s = Si^^s = Sy

ik.s - Dk,s ^ dfciS

Sk.s ^ £k,s S Ck.s

The last two sets of constraints can be used to impose some restrictions on the energy sold/bought on the various markets.

IV. ENVIRONMENTAL ISSUES

At Hydro-Quebec, many important environmental issues related to hydropower development (e.g., mer- cury concentration, spawning of fish, unpleasant con- sequences to local populations, etc.) can be consid- ered within a model like (3). For example, take the unpleasant consequences to local populations. If we want to minimize those unpleasant consequences, we have to express the unpleasantness by a convex func- tion. Normally, the unpleasantness is function of the flooded area2 and it increases with the latter. Then, it is conceivable to have a function as shown in figure 2 to represent the unpleasantness. Since the flooded area can be a function of the dam heights, it suffices to include a function into the objective function to consider, maybe partially, the unpleasantness.

We know that is not a trivial task to create a func- tion like in figure 2, but we believe that it is a less tedious task than considering those issues only after- ward. Furthermore, considering those aspects in this way does not increase too much the complexity of the problem.