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Application-Driven Learning:�A Closed-Loop Prediction and Optimization Approach�Applied to Dynamic Reserves and Demand Forecasting

www.puc-rio.br/lamps

Clik to go to appdrivenlearning

Speaker: Alexandre Street (LAMPS PUC-Rio, Brazil)

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Joaquim Dias Garcia (PSR, Brazil)�Tito Homem-de-Mello (UAI, Chile) �Francisco Muñoz (Generadoras de Chile)

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March 5th, 2024 - Brazopt 2024, Rio de Janeiro, RJ, Brazil

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Motivation: Energy and reserve scheduling in power systems

  • We first make a forecast
    • Demand forecast for energy scheduling
    • ISOs perform this in regular basis: daily, hourly, 5 and 5 mins,
  • Based on that a given forecast an action is planned and implemented
    • Given the demand and renewables point forecast for the next hour
    • Given the net injection deviation point forecast: reserve requirements
    • Generation and reserve schedules are scheduled
  • Given the actual demand, real time adjustments are made
    • There is a cost for the forecast error
    • If the observed demand lies within scheduled energy +/- reserves the cost is low
    • If it lies out of reserves the cost is high

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Motivation: ad hoc biasing �(“heuristic forecasts”)

  • Independent system operators knows very well the cost asymmetry and its consequence
  • 2019 Annual Report on Market Issues and Performance of the California ISO (CAISO 2020)
    • “actions include routine upward biasing of the hour-ahead and 15-minute load forecast”
  • The national system operator in Brazil uses an “heuristic forecast” to implement ad hoc load biasing to protect the system against uncertainty unaware decisions (deterministic models)
  • It is easer to change the forecast model than the scheduling model
  • There is no ISO using two-stage stochastic models for various reasons
    • Computational tractability
    • Interpretability
    • Compliance: how selects the scenarios (prices and schedules would change)
    • Difficult to make a probabilistic joint forecast in high dimension

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Motivation: Asymmetric costs

Parkour: forecasted targets are biased

 

 

Energy

loss

Serious

injuries

or death

 

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Motivation: Asymmetric costs

Weather: forecasted targets are biased

 

 

Extra�weight

Getting�wet�and cold…

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Objective

  • To present a new closed-loop framework,
  • named application-driven learning,
  • in which the best point forecasting model is defined according to a given application cost function
  • that can be represented by a two-stage linear program with uncertainty on the right-hand side.

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Literature Review: Application-Driven Learning

Using a financial training criterion rather than a prediction criterion

Neural networks (Bengio 1997)

Task-based learning (Donti et al. 2017)

Used stochastic gradient descent with automatic differentiation of QPs

Smart Predict and Optimize (Elmachtoub and Grigas 2017)

Relaxation+convexification with SGD to estimate uncertainty in objective

A bilevel framework (Morales et al. 2020)

Use bilevel optimization with KKT reformulations (Fortuny-Amat and NLP)

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Literature Review: Load Forecast/Reserve Sizing

Load, Renewables are key sources of uncertainty

    • Systems must be ready to withstand diverse conditions (Van der Meer et al. 2018)

Reserves (exogenous approach)

    • Used in practice (Ela et al. 2011)
    • More recently: Dynamic reserves (De Vos et al. 2019)

Stochastic optimization (endogenous approach)

    • Uncertainty modelling (Zheng et al. 2014)
    • Computational performance (Aravena and Papavasiliou 2020, Knueven et al. 2020)
    • Market design (Morales et al. 2014, Wang and Hobbs 2015)

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The general model: Open-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The general model: Open-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

The general model: Open-Loop

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The general model: Open-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The general model: Open-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The general model: Open-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The bilevel model: Closed-Loop

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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The bilevel model: Closed-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The bilevel model: Closed-Loop

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

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The bilevel model: Closed-Loop

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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The bilevel model: Closed-Loop

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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The bilevel model: Closed-Loop

  • Train Load Forecast and Reserve Model
  • Forecast Loads and Reserve Requirements
  • Plan the Operation
  • Re-Dispatch Resources in Real Time

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Convergence of

  •  

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Solution method: MILP

Linear models

KKT based MPEC reformulation

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Solution method:�MILP with BilevelJuMP.jl

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Solution method: Scalable Heuristic

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Solution method: Scalable Heuristic

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Solution method: Scalable Heuristic

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Solution method: Scalable Heuristic

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Solution method: Scalable Heuristic

Uncertainty Forecast

 

 

Policy Planning

 

Cost Assessment

 

 

Model Training

 

 

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Application Driven Model for Load and Reserve

 

- Load Balance

- Network Flows

- Zonal Reserve Requirement

- Reserve and Generation�

- Bounds

- Bounds

- Load Balance

- Network Flows

- Generation redispatch

Policy Planning Cost

Generation, Reserve, Shed, Spill

Real Time Cost Assessment

Generation, Reserve, load shed, gen. spillage

 

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Application Driven Model for Load and Reserve

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Case Study: Data

  • PGLib-OPF: The power grid library for benchmarking ac optimal power flow algorithms (Babaeinejadsarookolaee 2019)
  • https://github.com/power-grid-lib/pglib-opf

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  • Forecasting functions used:

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Case Study: Method Comparison

  • Single bus systems and limited number of samples
  • MILP X Heuristic

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Case Study: Method Comparison

  • One sample with 250 observations

Optimize Load AR(1)�with fixed reserve

Optimize up and down reserve

with fixed load AR(1)

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Case Study: Convergence of Objective

  • LS-Ex (red)�Least-Squares load�Exogenous reserves
  • LS-Opt (blue)�Least-Squares load�Optimized reserves
  • Opt-Ex (yellow)�Optimized load�Exogenous reserves
  • Opt-Opt (green)�Optimized load�Optimized reserves

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Case Study: Convergence of Objective

  • LS-Ex (red)�Least-Squares load�Exogenous reserves
  • LS-Opt (blue)�Least-Squares load�Optimized reserves
  • Opt-Ex (yellow)�Optimized load�Exogenous reserves
  • Opt-Opt (green)�Optimized load�Optimized reserves

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Case Study: Convergence of Objective

  • LS-Ex (red)�Least-Squares load�Exogenous reserves
  • LS-Opt (blue)�Least-Squares load�Optimized reserves
  • Opt-Ex (yellow)�Optimized load�Exogenous reserves
  • Opt-Opt (green)�Optimized load�Optimized reserves

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Case Study: Convergence of Out-of-sample Costs

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Case Study: Convergence of Out-of-sample Costs

In more detail

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Case Study: Convergence of Solution

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Case Study: Convergence of Solution

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Case Study: Large-Scale Optimization

  • Training time limit: 30 minutes
  • In sample scenarios: 600
  • Out of sample scenarios: 10.000
  • Server: 64 cores and 1024 Gb RAM @ PSRCloud

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Case Study: Large-Scale Optimization

  • Realistic system 6470-rte (from the previous Section)
  • Real hourly load data from the PJM power system - (EIA 2023)
  • Results: improvements on the LS-Ex benchmark

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Conclusions:

  • New framework described
  • Theoretical guarantees
  • Heuristic approximating the bilevel formulation
    • Works well in very large data sets
    • Can be used in practice
  • Optimal load forecasts are BIASED
  • That forecast bias depends on reserves (and should be co-optimized)
  • Method outperformed open-loop framework and ad hoc biasing
    • Provides the scientific basis for actual heuristics used to implement biased forecasts

https://arxiv.org/abs/2102.13273

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