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1. Hedging Rule for Reservoir Operation -Theory and Numerical Modeling Jiing-Yun You
Ven Te Chow Hydrosystems Laboratory
Department of Civil and Environmental Engineering
University of Illinois at Urbana-Champaign
2. This study performs an interdisciplinary research of reservoir planning and operation When I decided to come to U of I in 2003, my mother asked me, what are you going to study. I told her, water resource management.
She asked me, why are you going to study that? Everyone can do management.
So, what to do with water resource management. Management is to do things right. How about water resources management.
In the past, water resource management address the important of engineering approach like construct large scale facility to help us do something with water.
However, today, because of the increasing complexity of water resources system, engineers today cannot afford to neglect broad social issues.
So Growing anticipation of link between water management and other social interests.
We need to provide a rational framework for today's water resource management. This study try to bring new ideas from economics and operational researches.
Actually, these three field share similar conceptual framework.
While water resources focus more on the engineering approach, economics address the scarce resource allocation in social issue> and operational researches focus on the methodology sides.
So we try to do an interdisciplinary study for reservoir operation according the pricinciples from these fields. When I decided to come to U of I in 2003, my mother asked me, what are you going to study. I told her, water resource management.
She asked me, why are you going to study that? Everyone can do management.
So, what to do with water resource management. Management is to do things right. How about water resources management.
In the past, water resource management address the important of engineering approach like construct large scale facility to help us do something with water.
However, today, because of the increasing complexity of water resources system, engineers today cannot afford to neglect broad social issues.
So Growing anticipation of link between water management and other social interests.
We need to provide a rational framework for today's water resource management. This study try to bring new ideas from economics and operational researches.
Actually, these three field share similar conceptual framework.
While water resources focus more on the engineering approach, economics address the scarce resource allocation in social issue> and operational researches focus on the methodology sides.
So we try to do an interdisciplinary study for reservoir operation according the pricinciples from these fields.
3. Reservoir issues: from construction to management Reservoir contributes a significant role in the development of human civilization.
In the early and middle 20th century, human beings made a great effort in the construction of reliable dams.
Due to significant social
and environmental impacts,
today, the attention focuses
on how to operate reservoir
for effective use with existing
reservoir systems. What is reservoir. Reservoir play a important role for human civilization. In the past years, human beings concentrate on the construction of reliable dams. For example, the famous reference book, Design of small dams. Was published in 197s, it summarize the engineer technique for dam construction.
However, today, it is more and more difficult to build large dam, we need to pay attention to more efficient use of current dam system.
What is reservoir. Reservoir play a important role for human civilization.In the past years, human beings concentrate on the construction of reliable dams. For example, the famous reference book, Design of small dams. Was published in 197s, it summarize the engineer technique for dam construction.
However, today, it is more and more difficult to build large dam, we need to pay attention to more efficient use of current dam system.
4. An Overview of Reservoir Operation Rippl’s (1883) mass diagram method built the basis for contemporary reservoir planning and operation study. It was used to design most surface water supply reservoirs in the U.S.
Standard Operating Policy (SOP) based on the Rippl’s method was developed for reservoir operation under a fixed water delivery target. SOP aims to release water close to the current delivery target as much as possible, saving only surplus for future demand.
Let overview our reservoir knowledge,
I believe most of us all learn the rippl method from different textbooks.
This method was developed one century ago but shows the undeniable conventional wisdom.
Some methods extended from Rippl’s method just make it feasible for different needs. For example, Standard operating policy, (SOP)
The idea of this kind methods is to provide fixed delivery target.Let overview our reservoir knowledge,
I believe most of us all learn the rippl method from different textbooks.
This method was developed one century ago but shows the undeniable conventional wisdom.
Some methods extended from Rippl’s method just make it feasible for different needs. For example, Standard operating policy, (SOP)
The idea of this kind methods is to provide fixed delivery target.
5. A Milestone: the Harvard Water Program The Harvard Water Program (1955-1960), first interdisciplinary study, significantly advanced and popularized innovative thinking in water resource management.
Simulation technique
The use of simulations on high-speed computers. (Maass and Hufschmidt, 1959; Hufschmidt 1962)
Synthetic hydrologic records. (Fiering 1964, 1967)
Optimization technique
Dorfman first demonstrated the application of Linear Programming model to reservoir operation.
a group of professors with different backgrounds at Harvard University began an interdisciplinary study to improve the planning and design of water resource systems. This is the famous Harvard water program. The Harvard water program benefit the whole community with a lot of innovation thinking. It established the fundamental of two mainstreams: simulation and optimization techniques.
( Several professor first introduce the framework of using the high speed computers with synthetic inflow series to simulate the performance fo water system. It is still wide accepted today. Of course, the computer is no more fast now)
In other side, the optimization technique, Dorfman ,the famous economist who devote a lot to mathimatical programming and optimal control theory, demonstrate the application of linear programming to ROa group of professors with different backgrounds at Harvard University began an interdisciplinary study to improve the planning and design of water resource systems. This is the famous Harvard water program. The Harvard water program benefit the whole community with a lot of innovation thinking.It established the fundamental of two mainstreams: simulation and optimization techniques.
( Several professor first introduce the framework of using the high speed computers with synthetic inflow series to simulate the performance fo water system. It is still wide accepted today. Of course, the computer is no more fast now)
In other side, the optimization technique, Dorfman ,the famous economist who devote a lot to mathimatical programming and optimal control theory, demonstrate the application of linear programming to RO
6. Limitation of optimization technique in reservoir operation Once the objective function and constraints have been determined, the solution of the model depends on algorithms.
A continuing gap between theoretical development and real-world implementation exists. Operators rarely rely fully on formal optimization for their operating decisions, although the models provide some guidance.
For reservoir operation optimization problem, we first need to decide the objective function, the constraint, after that, the problem lead to algorithm: how to solve the optimization problem. Most researches in optimization technique develop different algorithms. For example, LP, NLP, DP, and GA, ..Yeh’s classical paper in 1985 provides a comprehensive review of the optimization technique. However, he and the later reviewers, also mentioned the continuous gap between theoretical development and real world implement. There are several reasons, one is the solution of optimizaon model is hardly to interpreted and understood. Another reason is, Operators do not like to be told…What they should do
For reservoir operation optimization problem, we first need to decide the objective function, the constraint, after that, the problem lead to algorithm: how to solve the optimization problem. Most researches in optimization technique develop different algorithms. For example, LP, NLP, DP, and GA, ..Yeh’s classical paper in 1985 provides a comprehensive review of the optimization technique.However, he and the later reviewers, also mentioned the continuous gap between theoretical development and real world implement. There are several reasons, one is the solution of optimizaon model is hardly to interpreted and understood. Another reason is, Operators do not like to be told…What they should do
7. Limitation of simulation technique in reservoir operation Simulation technique used as Decision-Support System is well-accepted.
Model is driven by a pre-determined set of operating rules to answer what-if questions.
Reservoir operating rules specify operating procedures to determine reservoir release and storage during simulation.
The goal of simulation model is to represent the real world as much as possible. Although it is sometimes controversial in detail. It always well-accepted and used as a DSS for operators. Simulation model is driven by a pre-determined operating rules to answer what if questions. Operating rules guide us when reservoir need to release and when it need to store water.
The goal of simulation model is to represent the real world as much as possible. Although it is sometimes controversial in detail. It always well-accepted and used as a DSS for operators. Simulation model is driven by a pre-determined operating rules to answer what if questions. Operating rules guide us when reservoir need to release and when it need to store water.
8. We need optimal operating rules to balance current and future demands Reservoir operating rules for water supply commonly seek to meet water demand with the greatest reliability rather than vulnerability. (SOP, LDR)
However, because of increasing water stress, those operating rules ignoring future demand may cause considerable shortage and economic loss.
Hedging rules are needed under water stress conditions. (i.e., water availability is below water demand) However, the common operating rules aslways seek to meet a fixed water demand with greatest reliability. For example, SOP and LDR
But, due to the increasing water stress, we do really need to consider an raitonal opearting rule which can account the shortage and nonlinear economic loss under water stress risk
It is Hedging rules.However, the common operating rules aslways seek to meet a fixed water demand with greatest reliability. For example, SOP and LDR
But, due to the increasing water stress, we do really need to consider an raitonal opearting rule which can account the shortage and nonlinear economic loss under water stress risk
It is Hedging rules.
9. What is Hedging Rule? It accepts a certain deficit in current demand so as to decrease the probability of a more severe water or energy shortage. (Bower et al., 1962)
Providing only portion of the target release even more volume could be provided. (Klemes, 1977; Stedinger, 1978; Loucks et al. 1981; Hashimoto et al., 1982)
Previous studies lack a theoretical basis, which leave some fundamental questions for the implementation of hedging rules.
It accepts a certain deficit in current demand so as to decrease the probability of a more severe water or energy shortage (Bower et al., 1962) This concept was also proposed by Prof Bower during the Harvard water program. However, he did not provide more detail about hedign rule. Following researchers use numerial model to expereiment hedign rule and give it a better interpretation. They think, Providing only portion of the target release even more volume could be provided.
However, It accepts a certain deficit in current demand so as to decrease the probability of a more severe water or energy shortage (Bower et al., 1962)
It accepts a certain deficit in current demand so as to decrease the probability of a more severe water or energy shortage (Bower et al., 1962) This concept was also proposed by Prof Bower during the Harvard water program. However, he did not provide more detail about hedign rule. Following researchers use numerial model to expereiment hedign rule and give it a better interpretation. They think, Providing only portion of the target release even more volume could be provided.
However, It accepts a certain deficit in current demand so as to decrease the probability of a more severe water or energy shortage (Bower et al., 1962)
10. These questions includes: When How much and How long to
This is my thesis framework, we interprets hedging rule as the dynamic decision making in reservoir operation and try to answer these questions for hedging.
First, we develop the analytical and numerical model to discuss the mechanism of hedging rules. And we introduce the horizon theory and do some numerical experiment of different inflow time series. These model are used to discuss factor of reservoir and hydrological characteristics such as uncertainty. These questions includes: When How much and How long to
This is my thesis framework, we interprets hedging rule as the dynamic decision making in reservoir operation and try to answer these questions for hedging.
First, we develop the analytical and numerical model to discuss the mechanism of hedging rules. And we introduce the horizon theory and do some numerical experiment of different inflow time series. These model are used to discuss factor of reservoir and hydrological characteristics such as uncertainty.
11. Research Outline The analytical analysis of hedging rules
The explicit stochastic numerical analysis of hedging rules
Theoretical analysis of horizon for reservoir operation
Explore the impact of hydrological uncertainty to horizons
Case study
We are going to develop the analytical analysis of hedging., and a explicit stochastic numerical analysis. Also we introduce the theory horizon to water resource system. And do explore the impact of hydrological uncertainty to decision.
We are going to develop the analytical analysis of hedging., and a explicit stochastic numerical analysis.Also we introduce the theory horizon to water resource system. And do explore the impact of hydrological uncertainty to decision.
12. Draper and Lund (2003) first provided an analytical framework for hedging rules Draper and Lund first provide the analytical framework for hedging rules
They derive the optimal solution for a two period model according to the first order condition . In economics, that’s understood as the marginal principle. Which means we will have the maximum benefit while the marginal value of current delivery equals marginal benefit of carryover storageDraper and Lund first provide the analytical framework for hedging rules
They derive the optimal solution for a two period model according to the first order condition . In economics, that’s understood as the marginal principle. Which means we will have the maximum benefit while the marginal value of current delivery equals marginal benefit of carryover storage
13. This study extend Draper and Lund’s model with considering explicit future inflow “Storage plus anticipated inflow is probably a better candidate for rational signal” - Shih and ReVelle (1996)
Extension of the model: account the second-period inflow (If) in total water availability (Atotal) However, their study does not consider the explicit future inflow, but the anticipate inflow play a significant role in hedging decision. So, our model separately account for the term of inflow in the formulation.However, their study does not consider the explicit future inflow, but the anticipate inflow play a significant role in hedging decision. So, our model separately account for the term of inflow in the formulation.
14. Interior solution for the model is derived base on economic incentives With the general form of utility function, a delivery ratio is defined to represent the interior solution according to marginal utility principle. We still follow the some first order conditon, however, without giving a specific from of utility, we can not derive the exact amount of water we need to delivery or hedging, so, we define the delivery ratio which follow the same marginal utility principle.We still follow the some first order conditon, however, without giving a specific from of utility, we can not derive the exact amount of water we need to delivery or hedging, so, we define the delivery ratio which follow the same marginal utility principle.
15. Curve of interior solution for two period model The delivery ratio represent the relationship of optimal release and water availability. This curve only demonstrates the economic inccenetives.
The delivery ratio represent the relationship of optimal release and water availability. This curve only demonstrates the economic inccenetives.
20. Slower. (SWA-EWA) important, directly means some rule for opertaion. Ask a question to when to start and when to end.Slower. (SWA-EWA) important, directly means some rule for opertaion. Ask a question to when to start and when to end.
21. Range of Hedging Rule according to water availability With the information on current water availability and future inflow, we may evaluate the range for applying the hedging rule.
The range declines with the increase of future inflow level.
Unit of water availability in the vertical axis?Unit of water availability in the vertical axis?
23. Don’t mention equlibrum. (Solution) If we do nto consedier the unceraitny. If we consider the uncertaion. It will be B.. The delivery will lower, It mean we will save water for the future. The same way for the second one.Don’t mention equlibrum. (Solution) If we do nto consedier the unceraitny. If we consider the uncertaion. It will be B.. The delivery will lower, It mean we will save water for the future. The same way for the second one.
24. Numerical Model The model explicitly incorporates hedging rules derived from the theoretical analysis with stochastic simulation processes for reservoir operations.
The findings from the theoretical analysis will be verified through a numerical example and detailed numerical results will be provided under a specific form of the utility function and of the inflow prediction.
25. Two-period multi-state Markov model A explicit stochastic multi-state Markov process model
The transition probability is derived from the property of Markov chain and the explicit hedging rules. State/ Storage…. Continuous variable by multi-state. Discretized.State/ Storage….Continuous variable by multi-state.Discretized.
26. Numerical Model Assumptions The distribution of inflows between time periods is defined as independent identically distribution (IID).
Derive the probability for steady state - long term behavior not affected by initial state
The steady state is also known as equilibrium condition, implying that the long term behavior of a reservoir responding to inflow uncertainty will be steady. There are several assumptions to develop the numerical model. 1. I.I.D. 2. Steady state to represent the long term behavior of resrvoir perofrmaion.There are several assumptions to develop the numerical model.1. I.I.D.2. Steady state to represent the long term behavior of resrvoir perofrmaion.
27. The improvement of expected utility by hedging compared to SOP
At a certain demand level, hedging rules results in lower water supply reliability but higher utility compared to SOP; and the difference depends on reservoir capacity.
The is the result of numerical model, we can find, hedging rule increase the utility compared to SOP. And with the inceasing of resevoir capcity, the imporvement is more signficant. The incerase speed will slow when the resevoir is large enough. The is the result of numerical model, we can find, hedging rule increase the utility compared to SOP. And with the inceasing of resevoir capcity, the imporvement is more signficant. The incerase speed will slow when the resevoir is large enough.
28. Change of utility (in percentage) from SOP to Hedging Rule under inflow uncertainty Utility improvement increases when uncertainty is larger. This figure shows the impact of unceratiny. We can find, utileiiy imporvement iscreases when the uncertainy and reservoir capacity is larger This figure shows the impact of unceratiny. We can find, utileiiy imporvement iscreases when the uncertainy and reservoir capacity is larger
29. Summary of Numerical Results The scope of hedging characterized by the difference between SWA and EWA depends on the prediction of future inflow and current water availability.
In general, hedging tends to reduce vulnerability and is particularly useful for mitigating economic loss of water supply during severe drought periods.
The performance of hedging is complex with different levels of reservoir capacity and water stress, and an effective hedging policy is found with a certain range of reservoir capacity.
30. The analytical and numerical study of hedging rules is limited to two-period model. These two period model is mainly suitable for analyzing over-year hedging.
For intra-year operations, we need extend to multi-period model with short-period intervals for particular reservoir operation purposes. These concerns are relevant to the choice of the period interval and the period horizon for reservoir operation decisions.
31. Managers and planners are responsible to make imminent decision for coming periods.
The decision depends on subsequent future events which have diminishing impact to the initial decision.
Forecasts of inflow further into the future are expensive and/or less reliable.
32. For optimal dynamic reservoir operation, the decisions in some initial periods are not affected by future data beyond a certain period; this period is known as “forecast horizon (FH) ” and the number of the initial periods is known as the “decision horizon.(DH)”
33. The philosophy to determine the forecast horizon Changing current policy within decision horizon will cause loss due to the conservation and have future gain. When the future gain after a certain period is smaller than the loss, it is worthless to change the decision. These periods after the certain period are out of forecast horizon.
36. How do hydrologic characteristics influence the forecast horizon?
37. Experiment the forecast horizon for three type time series
38. Experiment the forecast horizon for three type time series
39. Experiment the forecast horizon for three type time series
40. The influence of water shortage level and reservoir capacity When inflow is high enough, the reservoir operation problem becomes static. This explains why SOP, which is understood as a static optimization policy, is always suitable for a condition without much pressure of water stress.
41. The influence of water shortage level and reservoir capacity Around the slight water stress condition, the forecast horizon is longest while the severe water stress have relative short forecast horizon.
A larger reservoir capacity always can have a longer forecast horizon than a smaller one.
Around the normal conditon, the forcast horizon is longest.Around the normal conditon, the forcast horizon is longest.
42. Findings from Periodic Time Series Model The period of seasonality does not have significant impact. The low frequency of extreme events just very slightly shortens the forecast horizon.
The amplitude of inflow, which represents the deterministic intensity of extreme events, has an evident influence to the length of forecast horizon.
The randomness reduces the forecast horizon when water stress is mild; but it increases the forecast horizon when the inflow is very high or low.
43. Findings from Random Walk Time Series Model Apply the random walk time series model to discover the effect of propagation of uncertainty.
Higher speed of uncertainty propagation causes shorter forecast horizon, this is because less certain future reduces the incentive for longer-period plan.
44. Summery (Analytical /numerical model of hedging rules) A theoretical model including explicit future and two-period multi-state Markov numerical model is extended to incorporate the optimal hedging rules derived from the theoretical analysis.
The theoretical analysis provides an updated basis for further studies, it also can be used to enhance the numerical reservoir modeling with a specific utility function.
The two-period analytical and numerical model for hedging rules proved or re-confirmed some intuitive knowledge on reservoir operation. Additionally, the model explore some knowledge has not been addressed in details in pervious studies.
45. Summery (Decision and forecast horizons ) This study introduces and modifies operational research theory on decision and forecast horizons and suggest a general stopping rule for detecting decision and forecast horizons for reservoir operation.
Moreover, the stopping rule applies to different type of inflow time series to evaluate the impact of hydrological uncertainty to reservoir operation decision making.
46. This study needs a more precise interpretation of information reliability to discuss its impact on hedging operating policy. I am still searching for appropriate stochastic theory to represent reliability of stochastic forecast.
47. Thank you Questions and Comments ?
