Pushing the Boundaries of SCDDP for Reservoir Management -or musings from my theoretical garden shed Presented to EPOC Winter Workshop 2016 by Rosie Read 7/09/2016

Disclaimer Disclaimer 7 September 2016 The information in this presentation was prepared by Rosemary Read in her personal capacity whilst undertaking her academic research and does not represent the opinions and/or ideas of her employer Meridian Energy Limited. The presentation was prepared with due care and attention. However, the information is supplied in summary form and is therefore not necessarily complete, and no representation is made as to the accuracy, completeness or reliability of the information. Neither Rosemary Read, or Meridian Energy Limited nor any of its directors, employees, shareholders nor any other person shall have liability whatsoever to any person for any loss (including, without limitation, arising from any fault or negligence) arising from this presentation or any information supplied in connection with it.   This presentation may contain opinions or forward-looking statements and projections. These reflect Rosemary’s current expectations, based on what she thinks are reasonable assumptions and do not represent the views of her employer Meridian Energy Limited. Neither Rosemary nor Meridian gives any warranty or representation as to any of the opinions expressed in this presentation or Meridian’s future financial performance or any future matter. Except as required by law or NZX or ASX listing rules, Meridian is not obliged to update this presentation after its release, even if things change materially. This presentation does not constitute financial advice. Further, this presentation is not and should not be construed as an offer to sell or a solicitation of an offer to buy Meridian Energy securities and may not be relied upon in connection with any purchase of Meridian Energy securities.

SCDDP in New Zealand Stochastic Constructive Dual Dynamic Programming (SCDDP) Implementations of SCDDP in New Zealand include SPECTRA, DUBLIN and LPCon These SCDDP models have been used for valuation of water, to advise dispatch, new build, retirement and investment decisions across the industry for over 30 years Early models including SPECTRA and DUBLIN are based on a simplified two reservoir model of the New Zealand system. These focus almost entirely on the tradeoff between water and the gas, coal and oil plants in the system. LPCon is a more recent incarnation developed by Grant Telfar for Meridian. This is specifically developed for the New Zealand system of today with increasing levels of base-load intermittent generation, and price driven demand response An early representation of the New Zealand system – recreated from an OHP

SCDDP vs SDDP Both use some representation of opportunity cost as the basis for valuing water SCDDP has been only used for smaller numbers of reservoirs so far, and constructs the entire dual (pricing) decision surface. It currently is used to give an indepth view for significant reservoirs while treating less significant reservoirs as run-of-river. SDDP has been used for higher reservoir numbers and focuses on subsets of the solution space to provide an approximation of the dual (pricing) decision surface. It currently gives a higher level view, but gives that view for all reservoirs. Key focus is arguably primal release solutions Many SCDDP implementations run in a matter of minutes rather than hours. The key release values are precomputed so the mathematics becomes a simple addition of matrices SCDDP gives complete solutions for a sample of reservoirs. SDDP uses sampling to express approximate solutions for a larger set of reservoirs. The core focus of my research is to allow SCDDP to be enhanced to solve larger number of reservoirs simultaneously using the cornerwise algorithm.

Hydro-Thermal Scheduling Theory What is the value of water used for generation? The value of water is the value of what that water replaces in fulfilling the energy needs of the nation. $90 SRMC Peaker % of Time National Energy Requirement (MW) $0.50 SRMC Baseload $40 SRMC Midmerit 5500 3000 5000 4500 AUFLS? Scarcity Pricing? $???

Hydro-Thermal Scheduling Theory What is the value of water used for generation? The value of water is the value of what that water replaces in fulfilling the energy needs of the nation.

Cornerwise SCDDP Traditionally SCDDP has constructed the solution space based on guidelines which enumerate the reservoir in terms of key guidelines, and calculate prices associated with these. This means there are a lot of points over which the solution must be found The conceptual basis is firmly based in geometric shapes, so if you try to expand beyond to higher reservoirs it gives you a whopping headache. The cornerwise algorithm is based on the idea that the solution only significantly changes when the hydro releases displace thermal generation in filling the load duration curve. This occurs at significant price points, so by identifying these and their associated quantities the solution space can be constructed. This means there are fewer points over which the solution must be found Conceptually it is easier to extend beyond two reservoirs. Higher reservoir numbers seem to be feasible but mind-bending But stochasticity adds further complications.

SCDDP basics What is the value of stored water for generation? The value of water is the value of what that water replaces in fulfilling the energy needs of the nation. Demand Surface for Storage (DSS) Demand Surface for Storage and Release (DSS’) Demand Surface for Release (DSR) Marginal Water Value

SCDDP basics Storage limits applied Inflow adjusted Demand Surface for Storage

Stochastic Inflows

Impact of uncertainty Uncertainty in inflows can reduce or increase the value stored water has for the system. If the amount you stored + inflows is more than you need to then you can lose value due to: Storage Constraints: Spill Release Constraints: Lower value use If the amount you stored + inflows is less than you need to then you can run into issues due to: System Constraints: Shortage situation Value: Water may have already been used for a lower value use

Stochastic Inflows and Truncation - Timing When stochastic inflows are applied then, at some point the Demand Surface for Storage must be resolved into some Expected Demand Surface for Storage based on the probability of each inflow sequence. So for stochastic inflows a second decision arises: Do we apply the storage limits to the Expected Demand Surface for Storage, or to each possible Demand Surface for Storage before resolving them into the Expected Demand Surface for Storage?

Stochastic Inflows In Reverse

Expected Inflows

Truncating Cornerwise SCDDP The cornerwise algorithm is based on identifying significant price points, and their associated quantities to construct the solution space. Applying reservoir limits is based on identifying significant quantity points, and their associated prices to limit the solution space to feasible reservoir storage values. With stochastic inflows, these two become incompatible. Linear interpolation in the quantity space to find implied price. Either introduces: Approximation at the limit A new key point A set of primal key points alongside the set of dual key points Simple additive properties are reduced.

Truncating Cornerwise SCDDP – 2 reservoir For a two reservoir problem then you don’t just have to truncate 2 dimensional space for this reservoir, you have to truncate the 3 dimensional space. This means: Approximation at the limit (a larger space) A new key set of points for each reservoir limit A large set of key primal points for each reservoir limit. For each reservoir we need to establish the points at which the other reservoir solution space changes and create a truncated price/quantity point for each of those key points. Not too bad in the deterministic view. Increasingly difficult in the stochastic. For storages where the reservoir limit intersects where reservoirs have the same marginal water value, this requires adding points.

Cornerwise SCDDP For a three reservoir problem then you have to truncate a four dimensional space and store a 3 dimensional surface for each reservoir for when each other reservoir is at its storage limit. Each surface must cover all possible storage spaces for the other two reservoirs when this reservoir is at its limit. ???

A new way forward? Reservoir 1 Reservoir 2 Reservoir 3 Using points on either side of the critical point as a representation of the extrema to explicitly allow the easy re-creation of the relationship between the surface of 1 reservoir and the other reservoirs. One of the ways to think of this would be as informed slice sampling of a multivariate space with known discontinuities. But that’s probably a discussion better left for over coffee. Reservoir 3

Where to from here? - Technical Test storage truncation first vs inflow first impact with current NZ data. Establish base-line deterministic 3 reservoir algorithm with a truncation algorithm that could be adapted to higher reservoir numbers. Evaluate discrete vs continuous representations of stochasticity for 2 reservoir algorithm Develop 3 reservoir implementation with stochasticity.

Hydro-Thermal Scheduling for the Future What has changed? Some generation types are becoming scarce: Thermal retirements How is scarcity valued in a given time period? How is long term security of supply valued? Some new technologies are becoming significant: Demand response Intermittent generation Electric Vehicles, batteries? Distributed Generation? How do we price these in? % of Time National Energy Requirement (MW) $0.50 SRMC Baseload 5500 3000 5000 4500 AUFLS? Scarcity Pricing? Peaking? $???

Hydro-Thermal Scheduling for the Future What has changed? Flexibility is being lost from the system: Tightening reserves market – Does the water value need to take into account the opportunity cost and future value of the alternative use of TWD to provide reserves? Thermal retirements imply running reservoirs harder – but reservoirs also have environmental constraints Changing incentives: North Island load growth Shareholder value Cost recovery is more complex then SRMC alone Are both long term national benefit signals and short term national benefit signals allowed equal air time? % of Time National Energy Requirement (MW) $50 Baseload 5500 3000 5000 4500 AUFLS? Scarcity Pricing? Peaking? $???

Where to from here? - Philosophical What is the definition of good reservoir management in a post thermal world? What is the opportunity cost in a post thermal world? How do we value short term shortages? How do we value security of supply buffers absent of thermal generation? When is the tipping point where shortage is influencing the water value too significantly? How do we best represent intermittent generation when filling the Load Duration Curve? How do we best represent the potential value of reserves? Where do investment incentives come from in a renewables and shortage dominated market? How would a reservoir trade off against a household battery? Do we need to explicitly price distributed generation? Can hydro + batteries really offset the gap in the North Island demand/supply balance? What about climate change?