Keynote Session 2:

The model externality in the Brazilian power system: a call for a new data and model governance

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Alexandre Street, Associate Professor

Electrical Eng. Department at the Pontifical Catholic University of Rio de Janeiro

Rio de Janeiro, Brazil, IAG PUC-Rio, October 31, 2024

Preliminaries

• How do we make them useful?
• Especially for the energy transition challenges

Preliminaries

• Models provide us with:
• Accuracy
• Reliability
• Efficiency in complex calculations
• Transparency
• Reproducibility
• Accountability
• Track record: “knowledge storage”

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Preliminaries

• Models are the platform through which we deliver most of the relevant elements we use in electricity markets
• Generation and reserve schedules, price signals, security, etc.
• Market incentives for innovation, the optimal use of flexibility, and supply adequacy
• All these features are addressed though the models
• The changes we want implement to provide low-cost electricity for consumers while transitioning to a sustainable low-emission system rely on model updates
• Storage opportunity cost assessment is among the most sensitive aspects
• Uncertainty modeling, policy look-ahead, and an accurate description of system characteristics are the building blocks of all opportunity-cost assessments we need to perform

Preliminaries

How to make computer models to capture all the relevant feature we want to consider?

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• We need to tell them what we want
• But it can not be done case by case…

Preliminaries

This is the goal of Operations Research, Computer Science and AI

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1. We express our goals through an objective function
2. We teach them how our world functions through learning processes and mathematical expressions (constraints and decision variables)
3. And this is converted into a code that runs and give us a solution

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• Depending on how we describe the world, steps 1-3, the solutions will be more or less realistic (useful)…

Agenda

1. What is a policy with look-ahead?
2. What is relevant to be considered?
3. Some evidences of market and operation distortions
4. Recommendations

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What is a policy with look-ahead?

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Introduction to opportunity cost assessment

How do we operate systems with large storage capacity?

• Balance between the benefit of using stored resources today or tomorrow
• Storage opportunity cost estimation (centralized or decentralized)
• In Brazil, due to relevant externalities and historical reasons, we use the centralized approach to estimate the water opportunity cost (water values)

• Inflows and all system information are forecasted

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• The optimal operation is planned based on forecasts and system characteristics

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• First-stage decision is implemented (orange star)

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How to account for opportunity costs?

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Rolling-window policy with look-ahead is one way (MPC)

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Forecast model

Planned policy

• Then, we observe actual inflows and uncertainties

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• The planning window is rolled forward

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• The operation planning with look-ahead is repeated

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• And a new first-stage decision for t+1 is now implemented (orange star)

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Rolling window policy with look-ahead

Forecast model

Planned policy

• This process is repeated every day, every month

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Rolling window policy with look-ahead

Forecast model

Planned policy

• This process is repeated every day, every month

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• Implemented and planned decisions may significantly differ

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Rolling window policy with look-ahead

The SDDP is an efficient algorithm to

translate the look-ahead cost into a cost-to-go function!

And it explicitly provides the water opportunity costs (water values)

What is the role of storage opportunity costs in the operation?

How do we compute storage opportunity costs through SDDP?

How do we compute storage opportunity costs through SDDP?

Coupling variables

From t to t+1

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How do we compute storage opportunity costs through SDDP?

How do we compute storage opportunity costs through SDDP?

How do we compute storage opportunity costs through SDDP?

How do we compute storage opportunity costs through SDDP?

It is equivalent to a fuel cost for water

What are the challenges in the estimation of opportunity costs?

System initial

state (storage)

use water

this month

Store water

for next month

Accurate state

measurements

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What is relevant to consider?

Studies with Brazilian Power System Data

• The immediate cost is generally easier to calculate (short-term models)
• Transmission constraints, Unit commitment constraints, fuel costs, hydro’s producibility

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• But
• In general, short-term models are deterministic UC problems, despite the increasingly amount of uncertainty being added with renewables
• Due to the lack of short-term uncertainty representation, short period look-ahead, and good-quality degradation models, some ISOs in US are experiencing difficulties with batteries coordination

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Representing “tomorrow” to decide today

• The cost-to-go function is much more challenging

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• Multi-period (stages) must be considered

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• Simplifications on the system representation are needed

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• Forecast for all uncertainties must be given

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• The challenge is: what would happen if we simply or forecast optimistically ?

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Representing “tomorrow” to decide today

• The cost-to-go function would be distorted downwards

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• The water values would decrease

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• The new optimum would use more water today

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• Storage for tomorrow would decrease

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• Today we have lower costs, but tomorrow we would be in trouble

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What would happen if we simplify constraints or forecast optimistically ?

• The cost-to-go function would exhibit almost zero water values

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• We would reduce our storage up to levels that an exogenous action will be needed to prevent high deficit costs…

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If we push this simplifications to the limit…

Short-term opportunity costs

• Is the marginal cost the cost of the most expensive generating unit?

Slide 29

Short-term opportunity costs

• We just discussed the water opportunity cost of water calculation
• How much tomorrow’s consumers would be willing to pay for today’s consumers to keep the water stored for them
• But we have many others
• How much should consumers be willing to pay for an incremental ramping capacity?

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Maximum ramping capacity = 25 MWh/h

Slide 30

Maximum ramping capacity = 25+1 MWh/h

Short-term opportunity costs

• We just discussed the water opportunity cost of water calculation
• How much tomorrow’s consumers would be willing to pay for today’s consumers to keep the water stored for them
• But we have many others
• How much should consumers be willing to pay for an incremental ramping capacity?

Slide 31

Short-term opportunity costs

• How this opportunity cost affects the system operational marginal cost (OMgC) and the spot price?
• How much should a consumer pay for an additional demand at t=15h?
• The negative OMgC means that it is cheaper to consume more but flatter
• Incentives for batteries and demand shift! The flexibility resources that solve the problem!

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+100 $/MWh of marginal immediate cost increase

- 200 $/MWh of ROC

= -100 $/MWh of OMgC

Short-term opportunity costs

• The system OMgC should reflect all opportunity costs regarding the load supply
• Networks capacity, KVL, ramping capacity, min up and down times, individual reservoirs, and environmental constraints will play a role in the OMgC
• OMgC and spot prices may not be the cost of the most expensive unit

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Some questions:

• How do short-term opportunity costs affect the dispatch?

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• Should water be stored differently to account for these opportunity costs in the future?
• Water values change?
• See [Valor Economico] and Prof. Street’s Energy Economics [slides] for more

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• We have further examples with network KVL
• See Prof. Street’s Energy Economics [slides] for more ->

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Empirical evidence of transmission simplifications bias potential distortions

Studies with Brazilian Power System Data

Impact of simplified network model in Brazil

Implementation model

(Generally, very accurate)

Model used to make the decision at stage t

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Planning model

(Generally simplified)

Model used to assess the cost-to-go function

First-stage model

Implementation

Planning

model

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Implementation model

(Generally, very accurate)

Model used to make the decision at stage t

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Planning model

(Generally simplified)

Model used to assess the cost-to-go function

Impact of simplified network model in Brazil

Impact of simplified network model in Brazil

First-stage model

Implementation

Planning

model

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Implementation model

(Generally, very accurate)

Model used to make the decision at stage t

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Planning model

(Generally simplified)

Model used to assess the cost-to-go function

Impact of simplified network model in Brazil

First-stage model

Implementation

Planning

model

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Implementation model

(Generally, very accurate)

Model used to make the decision at stage t

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Planning model

(Generally simplified)

Model used to assess the cost-to-go function

Impact of simplified network model in Brazil

First-stage model

Implementation

Planning

model

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Implementation model

(Generally, very accurate)

Model used to make the decision at stage t

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Planning model

(Generally simplified)

Model used to assess the cost-to-go function

Impact of simplified network model in Brazil

First-stage model

Implementation

Planning

model

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Empirical evidence of inflow forecast bias potential distortions

Studies with Brazilian Power System Data

Empirical evidence of biased inflow forecasts in the SE

http://www.lamps.ind.puc-rio.br/en/publicacao/parp/

Empirical evidence of biased inflow forecasts in the NE

http://www.lamps.ind.puc-rio.br/en/publicacao/parp/

http://www.lamps.ind.puc-rio.br/en/publicacao/parp/

Empirical evidence of biased inflow forecasts in the NE

http://www.lamps.ind.puc-rio.br/en/publicacao/parp/

Empirical evidence of biased inflow forecasts in the NE

Empirical evidence of biased look-ahead

10 years of planned vs implemented storage levels in Brazil

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• Planned storage is systematically higher than the implemented

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• Does an optimistic inflow forecast imply in optimistically biased opportunity costs (water values) and reduced implemented storage levels?

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Empirical evidence of biased look-ahead

10 years of planned vs implemented thermoelectric generation in Brazil

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• Planned thermoelectric generation is systematically lower than the implemented

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Empirical evidence of biased look-ahead

10 years of planned vs implemented spot prices in Brazil

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• Forecasted spot prices are systematically lower than the implemented
• Do optimistic inflow forecasts affect spot prices levels and volatility, market incentives, attractiveness, and hedging costs?

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Preliminary controlled experiments on the effect of unbiased forecasts

Brazilian Power System Data

Jump to conclusions

Controlled experiment

Simulate the rolling window implementation policy with

• Currrent (official) forecast model (control group): PAR-p-a forecast
• Heuristically unbiased process (treatment): PAR-p-a forecast / (1+bias factor)

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Controlled experiment

Simulate the rolling window implementation policy with

• Currrent (official) forecast model (control group): PAR-p-a forecast
• Heuristically unbiased process (treatment): PAR-p-a forecast / (1+bias factor)

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PAR-p-a forecast / (1+bias factor)

Preliminary controlled experiment

Simulate the rolling window implementation policy with

• The implementation model should be as close as possible to the model used in practice
• Preliminary results using the planning model as the implementation model
• In practice this disregards the compound impact of other well-known simplifications:
• Reservoir aggregation
• Transmission constraints (treated before)
• Intra-day constraints (UC, ramps, etc) and uncertainties
• Anticipative decisions: hazard-decision information structure used in planning
• So, results should be worse than the reported here
• The complete study is part of Arthur Brigatto’s PhD thesis

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Controlled experiment

10 years backtest: planning with biased inflow forecasts

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Controlled experiment

10 years backtest: planning with unbiased inflow forecasts

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10 years backtest comparison:

operating with biased (control) vs unbiased planning look-ahead

Controlled experiment

Backtest experiment indicates relevant differences in crises periods

Controlled experiment

Federal Court of Accounts determines

New governance for data and models

A call for new data and model governance

Conclusions and

Recommendations

Conclusions

1. Addressing renewable integration sustainably requires the characterization of storage opportunity costs
2. To capture the most relevant opportunity costs and sustainably utilize system’s resources
• We need to consider short-term uncertainties and constraints
• Both play a relevant role in the water values
• The optimistic bias has, in general, the same effects:
• Reduced reservoir levels,
• Increased supply risk
• Distorted spot price signals
3. In Brazil:
• A systematic bias on inflow forecasts is observed (in the last 10 years)
• Relevant evidence that inflow forecast bias and transmission simplifications led to lower reservoir levels
• Relevant evidence that transmission simplifications induce higher costs and marginal cost distortions

Recommendation

To capture the opportunity costs and sustainably utilize system’s resources

1. We need a new model and data governance
• For both short- and long-term models
• Processes to incrementally incorporate the missing pieces of the reality that are “causing” new opportunity costs
• out-of-the-market decisions (pós-DESSEM) into the model (DESSEM, DECOMP, NEWAVE, and into the expansion models)
• Network, wind curtailment, hydro UC, reserve allocation, and demand response need to be integrated
• Processes to incrementally integrate data, methods, and standards across ONS, CCEE, and EPE
2. New monitoring procedures (Academy and international experts should be formally involved)
• Input and output data adherence
• Forecast bias and accuracy for multiple steps ahead should be monitored
• Adherence of planned decisions (from the look-ahead) should be statistically monitored
• Benchmarking the models with the state-of-the-art methods and off-the-shelf software
• Systematic studies to monitor new opportunity costs to be considered

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Recommendation: sent to CONCEPE

1. Funding for Academic Training for EPE, ONS, and CCEE Professionals
• The energy transition will be driven by people using mathematical/computational models and shaped by regulation.
• Without top-tier professionals in these institutions, we will rely on “suboptimal” models, regulation, and, consequently, miss the opportunities to maximize Brazil’s natural and intellectual resources.
2. Creation of Industry-wide Academic and Sectorial Project Pools:
• Allow companies to allocate up to 10% of their R&D quotas to an "academic training pool for EPE/CCEE/ONS" and another 10% to a "sectoral project pool for EPE/CCEE/ONS."
• These pools could support closer academic collaborations, promote the recommended new governance and monitoring processes
• And reduce the lobby industry influence, promoting a more scientifically grounded sector, less prone to external pressures

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Research on the topic

supporting possible improvement pathways

• ERROR type I or II

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• The application cost should be observed

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If the error or simplification is inevitable?

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Parkour: forecasted targets are biased

Energy

loss

Serious

injuries

or death

Weather: forecasted targets are biased

• ERROR type I or II

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• The application cost should be observed

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• Operators implement pessimistic forecast: CAISO and ONS

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If the error or simplification is inevitable?

• ERROR type I or II

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• The application cost should be observed

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• Operators implement pessimistic forecast: CAISO and ONS

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If the error or simplification is inevitable?

• Train Load Forecast and Reserve Model

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• Forecast Loads and Reserve Requirements

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• Plan the Operation

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• Re-Dispatch Resources in Real Time

If the error or simplification is inevitable?

• Realistic system 6470-rte (from the previous Section)
• Real hourly load data from the PJM power system - (EIA 2023)
• Results: improvements on the least-squares load forecast and exogenous reserve requirements benchmark

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Incorporating n-K criterion in SDDP

2011: robust optimization IS the n-K security criterion

(First transactions power systems paper on robust models for power systems operation)

With no transmission constraints, binary uncertainty set becomes polyhedral

• Robust optimization: optimize for the nominal but ensure the system is functional under all (critical) scenarios

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Incorporating n-K criterion in SDDP

2014: n-K in transmission constrained system -> optimal endogenous reserves

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

• Column and Constraint Generation discovers the umbrella-set of outage scenarios that covers all other cases

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Incorporating n-K criterion in SDDP

2014: Endogenous reserves for n-K via Column and Constraint Generation

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

Feasible space projection

in the pre-contingency variables

x

y

• Few critical (max-violation-selected) scenarios support the optimal decision

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Incorporating n-K criterion in SDDP

2014: Endogenous reserves for n-K via Column and Constraint Generation

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

Feasible space projection

in the pre-contingency variables

x

y

• Few critical (max-violation-selected) scenarios support the optimal decision

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Incorporating n-K criterion in SDDP

2014: Endogenous reserves for n-K via Column and Constraint Generation

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

Feasible space projection

in the pre-contingency variables

x

y

• Solve the problem with no scenarios

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Incorporating n-K criterion in SDDP

2014: Endogenous reserves for n-K via Column and Constraint Generation

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

Feasible space projection

in the pre-contingency variables

x

y

• Find the worst-case violation and include it and solve it again

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Incorporating n-K criterion in SDDP

2014: Endogenous reserves for n-K via Column and Constraint Generation

• CCG is a cutting planes with polyhedral cuts
• Stronger albeit heavier than Benders cuts
• Works well in medium sized networks

Feasible space projection

in the pre-contingency variables

x

y

• Repeat until no violation is found
• This is optimal and ensures complete coverage

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Incorporating n-K criterion in SDDP

2017: n-K in SDDP via Distributed CCG

Incorporating n-K criterion in SDDP

Solve the first problem and find the umbrella set of constraints

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scenario 1

scenario 1

scenario 1

Incorporating n-K criterion in SDDP

Second problem is initialized with previously found constraints

scenario 1

scenario 1

scenario 1

Incorporating n-K criterion in SDDP

New violated constraints are added if any

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scenario 1

scenario 1

scenario 1

Incorporating n-K criterion in SDDP

We turn off CCG for a while the search if no violation is found in a complete forward iteration

scenario 1

scenario 1

scenario 1

Impact of simplified network model

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• Simplifications in network constraints
• Planning: NFA, DC, DC-LL, SOCP, SDP �Implementation: AC
• Results indicate that DC with losses (DCLL) is the model with the best tradeoff between computational time and cost/distortions
• Lowest implementation cost, lowest inconsistency gap, highest reservoir levels, second lowest marginal cost profile

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Optimistic bias vs optimality

• The best point forecast for a deterministic scheduling is pessimistically biased

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Application-Driven Learning:

A Closed-Loop Prediction and Optimization Approach

Applied to Dynamic Reserves and Demand Forecasts

To appear in