EMRG list 1993-1994 Annual Report - Management - University of Canterbury - New Zealand

Energy Modelling Research Group (EMRG)

1993-1994 Annual Report

Introduction

The Energy Modelling Research Group has been in operation since April 1993. It has been made possible by the generous support of Trans Power (NZ) Ltd. and the Electricity Corporation of New Zealand (ECNZ). Initial funding was provided for 12 months from that date, funding for PhD scholarships was subsequently extended for a further 3 months. This report covers the 15 month period to June 1994. At the beginning we had 3 PhD students.

Currently the group includes 3 staff members, 6 doctoral students and 3 research assistants. A wide range of topics is being investigated including short-term and long term models, strategic and tactical problems, as well as relevant theoretical developments. Grant Read is the EMRG research team leader with John George and Bruce Lamar from the Department of Management. John takes administrative responsibility for the group. Other people from inside and outside the university, as well as several visitors to the Department, have added considerably to the groups efforts.

As a research group, a significant measure of performance is the documents produced by the group. We have listed as part of our research report nearly 50 documents either completed or currently in progress. By the time we report in 1995 we hope that three theses will have been completed and that many of the papers will have been accepted for publication in scholarly journals.

The remainder of this report describes our research activities for 1993/1994 including both those projects funded from the scholarship money provided jointly by ECNZ and Trans Power, and those which have been undertaken under contract.

Research Areas

Mid-Term Reservoir Management

The main thrust of this work has been Yang Miao's thesis research on improved Dual Dynamic Programming (DDP) techniques. A summary of the basic ideas was presented to an ECNZ workshop in late 1993 [1]. Recent progress has been good, and Miao is expected to complete her thesis [6] by the end of 1994.

The impact of correlation on the release decision has been tested, and found to be significant. Experimental tests also indicate that the marginal water values produced by simulation differ from those produced directly by the optimisation model because of approximations used in the interpolation when implementing the DDP algorithm in the model. Several new linear interpolation schemes have been developed which improve the accuracy of the DDP algorithm, without significantly increasing computational effort. On the other hand, it turns out that improving the accuracy of the DDP can lead to worse results in practice because the effect of a poor approximation is to roughly model the impact of correlation. A report on these effects has been provided to ECNZ [4]. A model incorporating the improved interpolation scheme has been developed, and tests indicate that about 4.3% of the total cost of production, or more than $9m per year, can be saved by explicitly modelling inflow correlation. According to our tests, this compares with cost reductions of approximately 3.6% of total cost, or $7.6m per year, from the heuristic currently built into RESOP.

As a check on this work, Alister McGregor has been working on a DDP model of a linear production/inventory system in which the random elements are represented by a discrete Markov chain. Two effects are being investigated, the improvement in accuracy of solution gained by modelling the effect, and the increased computational effort required to do so. Savings of between 0% and 5% have been achieved in runs to date, which correlates well with the results being achieved by Miao's model. This work has been reported in [2], [3], and [5].

References

  1. E. G. Read and M. Yang, A Dual Dynamic Programming Approach to Reservoir Scheduling. In Proceedings of the First ECNZ Optimal Generation Scheduling Workshop, Wellington, December 1993 (Reprinted from the Proceedings of the 26th ORSNZ Conference, 1990, p. 21-25).
  2. A. D. Macgregor, Stochastic Dual Dynamic Programming with Lagged Variables. Working Paper, Department of Management, University of Canterbury, 1994.
  3. A. D. Macgregor, A Markov Chain Approximation to an AR(1) Process. Working Paper, Department of Management, University of Canterbury, 1993.
  4. M. Yang and E. G. Read, Accuracy of the DDP Algorithm. Report to ECNZ, 1994.
  5. E. G. Read, J. A. George and A. D. McGregor, Dual Dynamic Programming with Lagged Variables. In Proceedings of the 30th ORSNZ Conference, August 1994, p. 148-153.
  6. M. Yang, DDP for Reservoir Management with Correlation. Ph.D. Thesis, Department of Management, University of Canterbury (in preparation).

Market Simulation

Tristram Scott has been working with Grant Read in this area, assisted during the early part of 1993 by Chris Wallace. This work builds on, and complements, our work on reservoir management, since it uses a Dual Dynamic Programming model to optimise reservoir management with gaming. This is embedded in a modelling system designed to analyse the effects of various conditions on the efficiency of a wholesale electricity market, with special attention to the New Zealand system.

A significant period of time has been spent refining, improving, and generalising these models. Chris contributed to this process by checking and debugging the models and creating various programs to automatically display solution results. He gathered data approximating the NZ system for likely breakup scenarios, and conducted runs to investigate the sensitivity of different input parameters. The main experiments have been documented, together with the graphical output produced. Results to date indicate that the model is performing effectively, and confirm the crucial role of contracting, and of backup contracting between generators, in determining market outcomes. In particular, we have confirmed the hypothesis that if the contracts are set in an appropriate way, market results will be very close to perfect competition results. We are now ready to perform a more comprehensive series of experiments, should that be desired.

Tristram expects to complete experimental work for his thesis [11] by the end of 1994. The current state of this work is summarised in [9]. Preliminary results have been presented to an ORSNZ conference [7], and an ECNZ workshop [8]. The work has been discussed with Newbery and Green during a visit by Tristram and Grant to Cambridge in 1993, and has recently attracted interest from Australia. It will be presented to the international CEPSI conference, here in Christchurch, later this year [10].

References

  1. T. J. Scott and E. G. Read, Optimising Reservoir Management in a Deregulated Electricity Market. In Proceedings of the 29th ORSNZ Conference, August 1993, p. 92-99.
  2. E. G. Read and T. J. Scott, A Medium-term Simulation Model of Reservoir Management in a Deregulated Market. In Proceedings of the First ECNZ Optimal Generation Scheduling Workshop, Wellington, December 1993.
  3. T. J. Scott, Simulating a Competitive Wholesale Electricity Market, EMRG Internal report, Department of Management, University of Canterbury, 1994.
  4. E. G. Read and T. J. Scott, Hydro-generator Gaming in a Deregulated Electricity Market,CEPSI 10, Christchurch, New Zealand, September 1994.
  5. T. J. Scott, Medium-term Simulation for a Competitive Electricity Market. Ph.D. Thesis, Department of Management, University of Canterbury (in preparation).

Nodal Pricing

Early work on this topic included involvement by Brendan Ring and Grant Read in the testing and development of Trans Power's Nodal Pricing Model. The model was later adapted to include spinning reserve constraints, using results from our earlier work by Brendan and Bruce Lamar on GARSP (see Section 2.4). Also, a variety of tests were performed by Glenn Drayton and Brendan Ring, as described in [14].

More recently, Brendan has concentrated on developing his thesis [23] on the theory and practice of spot pricing in the electricity sector. In the course of this work we have produced a working paper which compares Hogan's ex post pricing approach with the solution achieved with the Wolfe Dual [17]. This work verifies the derivation employed by Hogan and demonstrates that the choice of pricing model objective function is arbitrary, as long as complementary slackness conditions are satisfied.

Brendan has largely finalised a theory for pricing of reserve generating capacity. This work has been reported in research reports for Trans Power ([15],[16]) and in papers presented to the ORSNZ ([12],[21]) and ECNZ ([13]). A working paper on pricing for sub-optimal dispatches has also been written [18]. This is an important area of research as the ex post pricing model approach will often have to be applied to dispatches which are not in fact optimal. We are now attempting to combine this work, along with work on pricing for inter-temporal constraints and integer cost structures, into a single unified pricing theory.

An initial thesis draft has been produced, and should be completed by August. In June 1994 Brendan visited Bill Hogan at Harvard University and Shmuel Oren at Berkeley University. He presented papers on competitive electricity markets to the Canadian Economics Association in Calgary [19], and a paper on pricing for stochastic contingencies at The Institute of Management Science meeting in Anchorage [20]. Grant and Brendan are currently working on a paper requested for a book on transmission pricing for Kluwer Academic Press [22].

References

  1. B. J. Ring, E. G. Read, and G. R. Drayton, Optimal Pricing for Reserve Electricity Generation Capacity. In Proceedings of the 29th Annual ORSNZ Conference, August 1993, p. 84-91.
  2. B. J. Ring, and E. G. Read, Nodal Pricing and Extensions to the Theory. In Proceedings of the First ECNZ Optimal Generation Scheduling Workshop, Wellington, 1993.
  3. B. J. Ring, G. R. Drayton and E. G. Read, Transmission System Pricing Model: Record of Experimental Tests. EMRG Report to Trans Power, 1993.
  4. E. G. Read, B. J. Ring and G. R. Drayton, Pricing for Reserve Capacity Part 1: Single, Deterministic Contingencies. EMRG Report to Trans Power, 1993.
  5. E. G. Read, B. J. Ring and G. R. Drayton, Pricing for Reserve Capacity Part 2: Multiple Probabilistic Contingencies. EMRG Report to Trans Power, Department of Management, University of Canterbury, 1993.
  6. B. J. Ring, B. W. Lamar and E. G. Read, A Review of the Ex Post Pricing Methodology. Working Paper, Department of Management, University of Canterbury, February 1994.
  7. B. J. Ring, B. W. Lamar and E. G. Read, Determining Ex Post Prices for a Sub-Optimal Power System Dispatch. Working Paper, Department of Management, University of Canterbury, March 1994.
  8. E. G. Read and B. J. Ring, Short Run Pricing in Competitive Electricity Markets. In Proceedings Canadian Economics Association, June 1994.
  9. E. G. Read and B. J. Ring, Pricing for Reserve Capacity in a Competitive Electricity Market. Presented to TIMS XXXII, Anchorage, June 1994.
  10. E. G. Read and B. J. Ring, Pricing for Reserve Electricity Generation Capacity to Meet Stochastic Contingencies. In Proceedings of the 30th ORSNZ Conference, August 1994, p. 154-159.
  11. E. G. Read and B. J. Ring, Electricity Transmission: Pricing and Access Issues in New Zealand. Invited contribution to R Siddiqi and M Einhorn (editors), EPRI volume on transmission pricing and access (in preparation).
  12. B. J. Ring, Short Term Pricing in Decentralised Power Systems. Ph.D. Thesis, Department of Management, University of Canterbury (in preparation).

Optimisation of Reserve

The Generation and Reserve Scheduling Program (GARSP) is a research model used to incorporate spinning reserve requirements in a short term generation schedule. Previous work on this model was based on an heuristic approach. Bruce Lamar worked with Glenn Drayton to develop a sequential linear approximation method to solve the GARSP model. This project was presented to the ORSNZ Conference in the previous year and resulted in conference proceedings papers ([12],[24],[25]) and an article submitted to a journal [26]. In future, Bruce and Glenn are planning to submit a further paper on the application of successive linear approximation to the problem.

Work in this area has influenced developments in other areas, providing the stimulus to include reserve constraints in Brendan Ring's pricing work, and reserve response optimisation in our treatment of hydro and thermal unit optimisation. Integration of these aspects into the more general context of hydro/thermal coordination is a central theme of Glenn Drayton's Ph.D. research.

References

  1. G. R. Drayton, Generation and Reserve Scheduling Program: A Modelling Procedure for Single-period Hydro-thermal Scheduling and Contingency Planning. In Proceedings of the First Annual ECNZ Optimal Generation Workshop, December 1993.
  2. B. W. Lamar, G. R. Drayton, E. G. Read and A. J. Turner, Non-linear Optimisation of Spinning Reserve in an Electrical Power Network. In Proceedings of the TIMS/ORSA Joint National Meeting, April 24-27, 1994.
  3. A. J. Turner, B. W. Lamar and G. R. Drayton, Spinning Reserve and Frequency Management in the New Zealand Power System. Submitted for publication in IEEE Transactions on Power Systems.

Optimisation of Hydro/Thermal Coordination

Glenn Drayton is concentrating on short-term hydro-thermal coordination for his Ph.D. research [28]. He is currently conducting a literature review in this area [27] and has developed a simplified model of the North Island system called OASIS. This will be used to examine the merits of various models currently being proposed as methods for hydro sub-groups to bid to the coordinator, and will examine the impact of spinning reserve on the co-ordination mechanism. This work is expected to bring together elements of all of the research streams identified above, and to interface with the work on market pricing and generator gaming.

References

  1. G. R. Drayton, A Review of Hydro-thermal Coordination. EMRG Discussion Draft, Department of Management, University of Canterbury, 1993.
  2. G. R. Drayton, Hydro-thermal Coordination in a Competitive Electricity Market. Ph.D. Research Proposal, Department of Management, University of Canterbury, May 1993.

Optimisation of River Chains

Following on from initial work on identifying the optimisation needs of the hydro groups, and a literature search on the topic, a comprehensive formulation and discussion of short-term Hydro River Chain Optimisation [29] was completed by Grant Read, Bruce Lamar, Glenn Drayton and Gavin Bell. This document was supplemented with more detailed reports on the modelling of particular river chains and with a draft generic data map for river chain scheduling models [30]specifying the relationships between all the data elements required in the model and how they may be derived from group data.

In the course of that work, we examined, with Ian Coope of the Mathematics Department, the form of the revenue function when head effects and variable prices over multiple time periods are taken into account. Some rules to determine when such functions are convex have been developed [31]. We also considered several options for solving the generic river chain scheduling model as a network [32]. Work on one of those approaches is now proceeding, as discussed in Section 2.8.

More recent work has concentrated on the problem of developing river chain scheduling models that account for, or include, the individual generating units in the modelling framework. A scoping report is currently being finalised [33] but, with the assistance of Professor Rick Rosenthal, we have also developed an experimental integer programming model [34], using GAMS. We plan to present this at a TIMS/ORSA conference next year. We have begun discussing experiences and options in this area with Dr Andy Philpott and his team at Auckland University.

References

  1. E. G. Read, B. W. Lamar, G. R. Drayton and G. J. Bell, River Chain Optimisation. EMRG Contract Report (to ECNZ) EMRG-CR-94-08, Department of Management, University of Canterbury, 1994.
  2. G. J. Bell and E. G. Read, River Chain Optimisation: Model Implementation. EMRG Contract Report (to ECNZ) EMRG-CR-94-07, Department of Management, University of Canterbury, 1994.
  3. B. W. Lamar, G. R. Drayton and I. C. Coope, Complexity of Head Effects. EMRG Working Paper, Department of Management, University of Canterbury (in preparation).
  4. G. J. Bell and B. W. Lamar, Alternative Formulation Options. EMRG Discussion Draft, Department of Management, University of Canterbury, 1994.
  5. J. A. George, B. W. Lamar and E. G. Read, Integer Programming and Network Optimisation Options for River Chain Optimisation. EMRG Report to ECNZ (in preparation).
  6. J. A. George, E. G. Read and R. E. Rosenthal, Hydro Unit Commitment Using Integer Programming. EMRG Working Paper Department of Management, University of Canterbury (in preparation).

Optimisation of Thermal Units

Grant Read and Gavin Bell have developed a trial dynamic programming model to schedule a thermal station in a price decomposition "framework" [35]. More recently, Andrew Kerr has developed an Integer Programming model [36], using GAMS, for the same purpose. We have assessed the relative value of these two approaches [37] is currently in progress. In the course of that research, a paper [38] outlining the economics of thermal station operation has been prepared, in order to foster discussion on the issues.

References

  1. E. G. Read and G. J. Bell, Optimal Scheduling of Thermal Stations: A Dynamic Programming Model. EMRG Contract Report (to ECNZ) EMRG-CR-94-02, Department of Management, University of Canterbury, 1994.
  2. E. G. Read and A. L. Kerr, Optimal Scheduling of Thermal Stations: An Integer Programming Model. EMRG Contract Report (to ECNZ) EMRG-CR-94-04, Department of Management, University of Canterbury, 1994.
  3. A. L. Kerr and E. G. Read, Optimal Thermal Unit Commitment Dispatch Scheduling. EMRG Contract Report (to ECNZ) EMRG-CR-94-03, Department of Management, University of Canterbury, 1994.
  4. E. G. Read and A. L. Kerr, Thermal Station Operation: An Economic Perspective. EMRG Contract Report (to ECNZ) EMRG-CR-94-06, Department of Management, University of Canterbury, 1994.

Non-convex Network Optimisation

In some cases, formulations of the short-term scheduling problem require the use of discrete variables. For instance, committing or turning off individual generators is a binary ("Yes/No") decision. These discrete variables make the formulation non-convex, meaning that the problem is much harder to solve optimally. Yet, to be useful, short-term scheduling formulations must be able to be solved very efficiently. One promising approach that provides a realistic representation of the problem while, at the same time, being computationally tractable is the use of non-convex network optimisation methods.

In a recent paper [39] Bruce Lamar showed how a procedure referred to as "capacity improvement" can significantly reduce both computational time and data storage requirements for non-convex network problems. In addition, Bruce showed that networks with costs that are neither concave nor convex could be converted into concave cost networks [40]. This means that problems involving start-up costs as well as generation efficiencies can be incorporated within the non-convex network framework.

Currently, Chris Wallace is conducting a review of computational tests comparing the capacity improvement procedure with other methods described in the literature. In addition, Gavin Bell is studying non-convex network optimisation techniques for his Ph.D. [41]. Gavin is looking at theoretical approaches for solving general integer programming problems using non-convex network optimisation techniques as well as applying these methods to problems in the energy sector, such as the unit commitment problem. Bruce has presented his ideas at MIT [42] and will be presenting preliminary results at the upcoming Mathematical Programming Symposium in Ann Arbor [43].

References

  1. B. W. Lamar, An Improved Branch and Bound Algorithm for Minimum Concave Cost Network Flow Problems. Journal of Global Optimisation, 3, 1994, p. 261-287.
  2. B. W. Lamar, A Method for Solving Network Flow Problems with General Linear Arc Costs. In D-Z Du and P.M. Pardaos (editors), Network Optimisation Problems, World Scientific, 1993, p. 147-167.
  3. G. J. Bell, Non-convex Network Models and Applications to Energy Modelling. Ph.D. Proposal, Department of Management, University of Canterbury, 1994.
  4. B. W. Lamar, Non-convex Network Optimisation. Presented to Operations Research Center, Massachusetts Institute of Technology, Cambridge MA., May 1994.
  5. B. W. Lamar, Non-convex Network Optimisation: Algorithms and Software. Presented at the 15th International Mathematical Programming Symposium, Ann Arbor MI., August 1994.

Scenario Development

Olly McCahon is working towards a Ph.D. [45] on scenario development under the supervision of John George and Grant Read. His first six months were spent reviewing the literature and deciding on a research topic. The objective is to investigate how insights derived from optimisation theory, and from the application of optimisation techniques, can be applied to scenario analysis. The aim is to integrate the process of scenario building with the search for robust strategies. In this context, a robust strategy is one which enables an organisation to respond effectively to future events. The strategy must be chosen and the first decisions implemented while these future events are at best uncertain, and often unknown.

He has built a stochastic optimisation model of a strategic investment problem. The model is to be used to investigate ways in which stochastic optimisation can be used to develop scenarios. Olly is also investigating the whole range of possible types of scenarios faced within a strategic decision situation. These will be studied to see how amenable the different scenario types are to manipulation with an Operations Research framework.

References

  1. O. C. McCahon, The Generation of Scenarios for use in Strategic Optimisation. Ph.D. Proposal, Department of Management, University of Canterbury, 1993.

People

Academic Staff

  • E. Grant Read
    Grant is the EMRG team leader. He is a Senior Lecturer in Management Science in the Department of Management and a private consultant. He is an expert in many areas of energy modelling in the electricity sector. Grant has provided supervision and expertise in almost every EMRG project.
  • John A. George
    John is a Senior Lecturer in Management Science and Head of the Department of Management. His speciality areas are Mathematical Programming models and Heuristic methods. In 1993-94 his involvement has been in Integer Programming modelling, DDP, and he is now responsible for the administration of EMRG.
  • Bruce W. Lamar
    Bruce is a Senior Lecturer in Management Science in the Department of Management. He specialises in Network Optimisation and Mathematical Programming. During this year Bruce has been involved in many of the projects and, in particular, the development of new methods for solving non-convex networks.

Doctoral Students

  • Gavin J. Bell
    Gavin began working for EMRG as a research assistant upon the completion of his honours degree last year. He has recently enrolled for a PhD specialising in Non-convex Networks.
  • Glenn R. Drayton
    Glen was originally employed as a research assistant for EMRG. He is now enrolled as a PhD student. His work studies the coordination of hydro and thermal stations in the developing de-centralised electricity market. He has been involved in several areas of work in electrical dispatch optimisation.
  • Olly C. McCahon
    Prior to this year Olly was an Assistant Lecturer in the Department of Management. He is now a full time PhD student. His area of interest is in Scenario Generation and Optimisation.
  • Yang Miao
    Miao is in the final stages of her PhD. Her research uses a Dual Dynamic Programming approach to produce better reservoir release rules.
  • Brendan J. Ring
    Brendan is completing his PhD thesis on Nodal Pricing this year. He recently travelled to North America to present his work in several places.
  • Tristram J. Scott
    Tristram plans to complete his thesis at the end of the year. He has continued his work on models for market simulation.

Research Assistants

  • Andrew L. Kerr
    Andrew is an honours graduate in Management Science who has recently joined the group. He is working on unit scheduling models for thermal stations.
  • Alister D. Macgregor
    Alister completed an MSc thesis on Stochastic DDP applied to the production/inventory model in 1991. He joined the EMRG staff in late 1993 to further his work by applying it to the case of correlated demand.
  • Chris A. Wallace
    Chris is an honours graduate in Management Science. He has been involved in the assessment of software, the market simulation project, and the development of Non-convex Network methods.