EMK:Multi Dimensional Water Values

Scenario Projection Modelling for Stochastic Water Valuation in EMarket

Disclaimer

Reasonable care has been taken to ensure that the information in this paper is up to date at the time of issue. Potential users of EMarket should, however, ensure that they evaluate EMarket and this paper through an appropriate evaluation process in consultation with Energy Link. The authors are also reliant on certain information external to EMarket and Energy Link, for which no liability or responsibility can be accepted.

Introduction

This technical bulletin is intended to provide users and interested parties with a detailed explanation of how EMarket’s multi-dimensional (MD) water values are calculated and applied. EMarket was designed as a market simulation model rather than as an operational model and the algorithm developed by Energy Link for use in EMarket was designed to give a high degree of accuracy at high speed for this purpose. Speed of operation is a strength of EMarket and ensures that users can turn new or modified simulations around quickly, achieving high levels of productivity.

EMarket4 replaced EMarket3 which used two-dimensional (2D) water values. A 2D water value for reservoir A is calculated with reference to time of year and to storage currently in reservoir A. MD water values in EMarket are calculated with reference to time of year, storage in reservoir A and storage in all other reservoirs (i.e. they are 3D water values). MD water values therefore take account of total storage, and recognise the fact, for example, that when storage in reservoir A is low, future market outcomes may be different depending on whether total storage is either high or low. The behaviour of MD water values relative to 2D water values is briefly explained in: Water Values and Hydro Offers.

EMarket is now set up to allow the user to switch between MD and 2D water values, ensuring backward compatibility.

The water values have also been rewritten in EMarket to make future enhancements easier to implement. For example, water values in Pukaki could be enhanced to take account of time of year, storage in Pukaki, storage in Tekapo, and all other storage (4D water values). Or water values could take account of contract position, market power, or uncertainty in demand, for example.

This document is divided into three parts. Section 3 outlines the scenario projection method and its application in EMarket. Section 4 describes the mathematic principles behind the method is a more thorough manner.

Summary

When water values have been calculated using the projection method described in this bulletin, and applied to the operation of hydro plant, they should be valid in the following sense:

Given that the scenarios modeled are considered to be representative of expected market conditions, and that the inputs used in the water value function are representative of the values considered when evaluating water value, then the marginal water value produced by this method will reflect the expected marginal value of that water.

MD water values currently use time of year, local storage, and total of all other storage to calculate and to look up water values in each major reservoir. This method is an improvement over 2D water values which made strong assumptions about how storage evolved across all reservoirs. These assumptions have been relaxed in MD water values so at each time step storage in other reservoirs can take on values other than those assumed in 2D water values. As a result, MD water values produce model outputs which are more consistent with actual market outcomes.

An important feature of the EMarket MD method is that it is able to allow for serial correlations in market scenarios, regardless of the form that such correlations might take. This avoids the need for the statistically based corrections applied in some other models. Serial correlations are not only important for individual reservoirs, but their impact on the market will also be affected by correlation of inflows between different catchments. Other statistical properties such as wind flow correlation can also be captured provided realistic sets of scenario can be generated.

Scenario Projection Modelling in Practice

This section aims to give a general overview of how scenario projection is applied to water valuation.

General Principles

The underlying meaning of water value relates to the decision to use water for generation at any given time. This decision involves comparing the immediate benefit accrued by using the water with the benefit of holding it for future use. Water value can be defined as expected future benefit that a small, or marginal, amount of extra storage would confer in this situation. Determining this value is a stochastic process because of the unpredictable elements affecting future operation, especially the variability of reservoir inflows.

The expected benefit of a marginal amount of storage is normally only easily determined in situations where reservoir storage is constrained. When the reservoir has reached its upper limit and storage cannot be reduced operationally, this marginal value is nominally zero – the extra water confers no benefit. When the reservoir reaches empty, and operational guidelines force all available water to be used, the marginal value is equal to the immediate value of using the water.

When the reservoir is unconstrained the marginal value is harder to determine. As well as requiring a good model of the stochastic elements of the market, a number of subtle assumptions need to be made about the relationship between estimated water value and hydro system operation.

The usual methods of solution for this problem all involve iteration. The reason for this iteration is a circular relationship between a chosen set of water value guidelines and the expected benefit that results from using those guidelines. In a very simple form this relationship could be summarised as:

• Water value guidelines too low → Water use and Generation Higher → Greater likelihood of shortage → Higher expected marginal benefit.
• Water value guidelines too high → Water use and Generation lower → Lower likelihood of shortage → Lower expected marginal benefit.