Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems

arXiv:2410.09166 · eess.SY, cs.SY · Submitted 2024-10-11 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems".

Dev: Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply.

Rosa: First, who's behind it and why it matters.

Title and authors: Rosa: Well, we’re diving into "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems" today. This paper looks at how we can better handle the messy, non-linear efficiency issues that come up when you try to balance renewable energy sources with battery storage.

Dev: I'm curious about the authors and what this title actually suggests for our control loops; it sounds like they are trying to tackle a specific kind of modeling hurdle in power system optimization.

Taro: From an autonomy angle, I think this is important because when we try to make autonomous decisions for battery dispatch, you need models that don't break down when things get unpredictable.

Rosa: Exactly, Taro, and the paper tackles this by looking at how input-convex neural networks can be used to approximate those tricky nonlinear efficiencies with a convex function.

Dev: That’s a key point; if they can make the efficiency relationship look convex through this ICNN approach, it should make it much easier for the optimization algorithms to find solutions without getting stuck in overly complicated or intractable problems.

Taro: If we think about when the world misbehaves, like sudden cloud cover affecting solar input, having a model that stays tractable during those rapid changes is essential for any autonomous system to react quickly.

Rosa: Right, and the paper specifically applies this relaxed ICNN method to two real-world scenarios: PV smoothing and revenue maximization.

Dev: PV smoothing is something we deal with daily when trying to keep the grid stable, so seeing an application there makes it much more tangible than just theoretical modeling.

Taro: And for revenue maximization, that points toward a future where battery decisions aren't just about safety or stability, but also maximizing financial return based on market conditions.

Rosa: That’s right; the paper compares their ICNN-based results against three other ERM formulations: nonlinear, linear, and mixed-integer models to show how much benefit this new method brings.

Dev: It sounds like the comparison helps establish a clear trade-off between computational tractability and modeling accuracy in these different optimization problems.

Taro: I wonder if this approach scales well when we move from smoothing a small solar farm to managing a massive distributed battery network across an entire region.

Rosa: That’s a valid question for the field, Dev, because the authors are exploring how this structure can be used to create convex programs directly from the epigraph of that convex function.

Title and authors: Dev: So they're essentially using machine learning to create a mathematical structure that fits neatly into existing optimization frameworks by relaxing those hard non-convex constraints.

Taro: That relaxation is what allows the system to remain solvable, which is crucial when you’re trying to design systems for complex power distribution networks.

Rosa: And they even look at different ways to construct these ICNNs, like quadratic polynomials or exponential functions, showing that the choice of structure matters for how accurately it captures the physical behavior.

Dev: The paper mentions that while simpler models are computationally convenient, nonlinear functions tend to capture those actual physical relationships more accurately when modeling battery efficiency.

Taro: If we look at their methodology, they are building this architecture layer by layer, which suggests a systematic way to increase the complexity of the approximation if needed.

Rosa: They model the nonlinear and non-convex behavior of efficiencies specifically by using two ICNN models for charging and discharging separately, represented as fICNN(Pc) + gICNN(Pd).

Dev: That splitting it into charging and discharging components is a clever way to ensure that the overall system still benefits from the convexity relaxation across both directions.

Taro: I’m interested in how this could translate to real-time operation; if the ICNN can approximate these efficiencies quickly, it means we might get faster decision-making times in grid control.

Rosa: That’s what we hope for, Taro; a method that provides a structured way to handle non-convexities without needing those overly burdensome high-fidelity electrochemical models or constant parameter adjustments from ECMs.

Dev: I'm thinking about the deployment aspect: if this works well in simulation, how does the latency look when we try to run this on actual hardware for real-time control?

Taro: The paper points out that data-driven models use machine learning techniques to capture these complex behaviors from large datasets, which suggests they can be trained offline and then deployed for fast inference.

Rosa: And the ICNNs are particularly suited for optimization because they are designed so the function mapping input to output is guaranteed to be convex, which is a strong mathematical property for solvers.

Dev: That guarantee of convexity is what makes it appealing; most traditional methods struggle when efficiency isn't perfectly linear or convex, leading to those computational burdens we talked about earlier.

Title and authors: Taro: If this technique can provide both feasibility and optimality outcomes across different use-cases like PV smoothing and revenue maximization, that really broadens its applicability in power system management.

Rosa: It definitely seems like the main promise is moving from models that oversimplify things to data-driven models that capture complex physics accurately while remaining computationally tractable for optimization.

Dev: So, the authors are pushing toward a formulation where we get high fidelity from data while keeping the computational load manageable enough for operational use.

Taro: The implication here is that future battery management systems could be much more sophisticated in how they react to dynamic grid conditions because they wouldn't have to rely on overly simplistic assumptions about efficiency.

Rosa: Indeed, the paper suggests this ICNN-based approach shows promise for future battery optimization with desirable feasibility and optimality outcomes across both those key use-cases.

Dev: It’s encouraging to see a data-driven approach that explicitly addresses the non-linearity in a way that respects the limits of current computational resources.

Taro: I think this work opens up avenues for developing more resilient control strategies, especially when we consider integrating many different battery assets into one system.

Rosa: So, to wrap up on "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems," the key is using ICNNs to create a convex program for ERM optimization by approximating nonlinear efficiencies with a convex function derived from data.

Dev: And the main benefit is that this allows us to apply these powerful optimization techniques to real-world problems like PV smoothing and revenue maximization without hitting those NP-hard computational walls.

Taro: This work suggests that data-driven methods can provide the necessary accuracy for modeling complex physical relationships while maintaining a structure friendly enough for practical deployment in power system management systems.

Rosa: So, we’ve seen how this ICNN formulation compares to other ERM types and what it offers in terms of solving optimization problems reliably.

Dev: It really moves the goalposts on how we can incorporate real-world efficiency data into control design, which is a big deal for our engineering work.

Taro: The future direction seems to be using these relaxed methods as a baseline for developing more adaptive and robust decision-making systems in energy grids.

Rosa: That’s what we have here with "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems." We'll keep an eye on how this data-driven approach matures into operational hardware, and then we’ll be back to explore other papers.

The paper's summary: Rosa: So, to recap, this paper is about using input-convex neural networks to create a convex program for optimizing battery energy storage systems by approximating their nonlinear efficiency with a convex function derived from data.

Dev: Exactly, and what’s really interesting here is that they are tackling the big problem of non-linear efficiency in power system optimization by making it mathematically solvable through this relaxation method.

Taro: That makes sense because when we look at real-world scenarios, like PV smoothing or maximizing revenue, the traditional models get bogged down by those tricky curves that don't fit simple linear equations.

Rosa: Right, and the paper shows how they apply this ICNN approach to two key use cases—PV smoothing and revenue maximization—and they compare their results against several other battery optimization models to show the advantage of this data-driven method.

Dev: The impact here is that we might be able to deploy more accurate, real-time control loops because the optimization problem itself becomes easier for solvers to handle, even when dealing with those complex nonlinearities.

Taro: If this holds up outside the lab—meaning it can actually run on a live grid system for extended periods—it changes how we design autonomous battery dispatch strategies in unpredictable environments where things constantly misbehave.

Rosa: I’m really excited about the idea that we can use machine learning to capture these complex physical relationships without needing those super detailed, high-fidelity electrochemical models that take forever to run.

Dev: The potential for faster loop rates is huge if the inference time from the ICNN isn't too slow; but I need to know how robust this approximation is when the operating conditions shift rapidly.

Taro: And think about what this means for autonomy; if we can reliably optimize battery use based on real-time data using these models, autonomous systems can make much smarter, more resilient decisions during grid disturbances.

Rosa: It really puts a lot of emphasis on making these AI models flexible enough to handle novel operating conditions that we haven't explicitly programmed into the traditional math.

Dev: I’m curious about the practical limitations; while they relax the non-convexity, there are still constraints on how large or complex these ICNN approximations can become before they start losing accuracy in a dynamic environment.

Taro: So, this isn't just a theoretical exercise; it’s providing a structured framework for building more adaptable and reliable control systems that can actually cope with the messy reality of renewable energy integration.

Rosa: That’s the big picture; moving toward optimization methods that are both data-driven for accuracy and convex enough to be computationally tractable for real-time deployment.

Dev: We need to keep watching how they handle those edge cases where the ICNN might fail to capture a sudden, sharp change in efficiency—that’s where we'll find the failure modes.

Taro: And that focus on robustness is exactly what makes this work relevant for autonomous systems operating in power grids under stress.

Rosa: So, as we look ahead, it seems like the next big step will be testing these ICNN formulations in longer-term simulations to see how they perform when facing prolonged periods of grid instability.

The paper's improvements: Rosa: So, moving on from the core findings, the paper suggests several ways to improve this ICNN approach for real-world application in power systems.

Dev: What kind of improvements are we talking about? Are they just tweaks to the model structure or something bigger regarding how we deploy it in a control environment?

Taro: I think one big suggestion is using the Big-M formulation, which helps handle those non-convex situations by transforming the problem into a Mixed-Integer Programming framework, though that does increase computational cost.

Rosa: Right, and another point they make is comparing predicted versus actual trajectories across different models so operators can assess the feasibility gap and decide which model is best for their specific real-time needs.

Dev: That comparison tool sounds very useful for determining when to trust a fast but less accurate approximation versus a slower but more precise one during critical operations.

Taro: It also implies that by training these ICNNs on extensive datasets, the AI system can develop more robust operational predictions for battery performance without needing constant manual parameter tuning from engineers.

Rosa: That brings up the point about flexibility; the ICNN approach allows us to capture those complex physical relationships—like how a battery actually loses efficiency—using data without needing those high-fidelity electrochemical models that are incredibly demanding on computing power.

Dev: If we can achieve that kind of accuracy with a more tractable model, it could mean significantly lower latency in our control loops, which is a major concern for me regarding loop rates and failure modes.

Taro: For autonomy, this means the system can adapt better to unforeseen circumstances because its underlying model isn't rigidly tied to one specific physical assumption about efficiency.

Rosa: It really seems like the authors are pushing for a methodology where we get a balance: high accuracy derived from data and a mathematical structure that’s manageable for deployment in actual hardware.

Dev: I'm still focused on the latency; if this relaxation method introduces too much overhead during inference, it won't matter how accurate the physics-based approximation is.

Taro: Ultimately, these improvements suggest a future where battery management systems are not just reactive but truly predictive in their decision-making capabilities under fluctuating grid conditions.

Rosa: It’s a big step toward creating more resilient control strategies that can handle the real volatility of renewable energy sources effectively.

Dev: We need to see how they address the actual operational constraints when scaling up these models from small test cases to massive, multi-battery systems in a live environment.

Conclusion: Rosa: So we’ve covered how this paper uses ICNNs to build convex programs for battery optimization by approximating nonlinear efficiencies, and now we’re wrapping up the main points and implications of "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems."

Dev: It really boils down to using data-driven models to handle those tricky efficiency curves in a way that makes the optimization solvable without needing overly complicated math.

Taro: I think it means we can build smarter, more adaptive autonomous systems for energy storage because they won't be limited by rigid, pre-programmed assumptions about how batteries behave when things get chaotic.

Rosa: Exactly; this work opens up avenues for developing control strategies that are both accurate from a physical standpoint and computationally feasible for real-time deployment in the field.

Dev: I’m still thinking about the latency aspect; if the approximation introduces too much overhead, it won't matter how good the physics-based result is when we’re trying to manage grid stability in milliseconds.

Taro: And that resilience is what matters for autonomy; if a system can intelligently adjust its battery discharge based on real-time efficiency predictions from this AI model, it handles unexpected events much better than current methods.

Rosa: It really seems like the future involves integrating these types of data-driven models into control loops so they can make those kinds of intelligent adjustments autonomously.

Dev: We need to keep pushing the authors on how this performs when we scale it up to manage a huge number of batteries, because that’s where I see the biggest failure modes creeping in.

Taro: Scaling up is definitely the next frontier; if this works for a single battery setup, we need to know if it holds up across an entire distribution network.

Rosa: Overall, this paper shows a promising path toward creating more flexible and accurate AI models for power system management that respect the constraints of actual hardware.

Dev: It’s encouraging to see a structured way to tackle non-convexity using ICNNs, provided we can manage the computational cost associated with those deep network approximations.

Taro: So, this suggests a real shift toward more robust decision-making in energy management as we move into more complex, dynamic power grids.

Rosa: Indeed; "Towards Input-Convex Neural Network Modeling for Battery Optimization in Power Systems" offers a solid foundation for that next phase of development.

Department of Electrical and Biomedical Engineering, University of Vermont

eess.SY, cs.SY

Submitted: 2024-10-11

Updated: 2026-09-28

DOI: 10.23919/ACC63710.2025.11108102

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 75/100

The gist: Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply.

Key concepts

Input-Convex Neural Network (ICNN): A type of neural network used to approximate nonlinear efficiency relationships by forcing the function mapping input to output to be convex. This mathematical property makes the resulting optimization problem much easier for solvers to handle compared to traditional non-convex models.
PV Smoothing: A real-world application discussed where ICNNs are used. It relates to keeping the power grid stable by managing sudden changes in renewable energy input, such as cloud cover affecting solar generation, using battery storage.
Optimization Frameworks (ERM): The episode focuses on applying the ICNN method to Energy Resource Management (ERM) formulations. This involves comparing the new ICNN approach against traditional nonlinear, linear, and mixed-integer models to show its benefits in finding solutions.
Computational Tractability: The ability of a model to be solved within reasonable time limits for real-time applications. The ICNN approach aims to achieve high accuracy while maintaining a structure that is computationally manageable for deployment in operational systems.

Terminology

Accuracy — 15× in this paper · explained in 1 episode
Fidelity — 7× in this paper · explained in 2 episodes
Activation Function — 6× in this paper · explained in 1 episode
Energy Reservoir Model — 6× in this paper
Objective Function — 5× in this paper · explained in 2 episodes
Computational Tractability — 4× in this paper · explained in 2 episodes
Failure Modes — 3× in this paper · explained in 3 episodes
Adam — 2× in this paper · explained in 2 episodes
Adaptability — 1× in this paper · explained in 1 episode
Core — 1× in this paper · explained in 2 episodes
IEEE Conference on Decision and Control — 1× in this paper
Robustness — 1× in this paper · explained in 5 episodes

Summary

Battery energy storage systems (BESS) play an increasingly vital role in integrating renewable generation into power grids due to their ability to dynamically balance supply. Grid-tied batteries typically employ power converters, where part-load efficiencies vary non-linearly. While this non-linearity can be modeled with high accuracy, it poses challenges for optimization, particularly in ensuring computational tractability. In this paper, we consider a non-linear BESS formulation based on the Energy Reservoir Model (ERM). A data-driven approach is introduced with the input-convex neural network (ICNN) to approximate the nonlinear efficiency with a convex function. The epigraph of the convex function is used to engender a convex program for battery ERM optimization. This relaxed ICNN method is applied to two battery optimization use-cases: PV smoothing and revenue maximization, and it is compared with three other ERM formulations (nonlinear, linear, and mixed-integer). Specifically, ICNN-based methods appear to be promising for future battery optimization with desirable feasibility and optimality outcomes across both use-cases.

The paper discusses various BESS models classified into four main categories: i) Energy Reservoir Models (ERMs), ii) Charge Reservoir Models (CRMs) or Equivalent Circuit Models (ECMs), iii) Electrochemical-based models, and iv) Datadriven models. The ERM treats the battery and inverter as an energy reservoir focusing on the dynamic relationship between SoC and charging and discharging power without explicitly considering internal electrochemical dynamics. While ECMs use passive electrical components such as resistors and capacitors to model the battery, they require frequent parameter adjustments due to variability in operating conditions. Electrochemical-based models are highorder representations of internal physical processes (e.g., PDEs, SDEs) that place significant burdens on computing and require high-fidelity battery (cell) data. Data-driven models utilize machine learning techniques to accurately predict the battery’s nonlinear behavior by training on extensive datasets. In power systems, the ERM is often employed to model the combined battery and inverter system performance to drive the SoC trajectories based on controlled charging and discharging inputs (powers), while accounting for energy losses due to inverter efficiencies. In many cases, the ERM is engineered to assume no losses or constant efficiency, leading to model mismatches. Incorporating these nonlinear efficiency relations in the ERM introduces non-convexity in power system optimization. This issue is addressed by different relaxation methods in the literature, such as a piecewise linear efficiency model for unit commitment problems and a dynamic programming method for revenue maximization, but these methods can lead to significant computational burdens as the problem scale increases.

To address these challenges, data-driven approaches leverage machine learning techniques to capture complex, nonlinear behaviors from large datasets. Input-convex neural networks (ICNNs) are designed so that the function mapping input to output is convex. This makes them particularly suitable for optimization applications and allows them to directly learn from data without requiring predefined functional forms. The mathematical definition of an N-layer ICNN architecture is given by:

zi = gi(Wizi-1 + Dix + bi), f(x; θ) = zN, (3)

where the function f is guaranteed to be a convex function in x, provided that all W2:N are non-negative and all activation functions gi are convex and non-decreasing. The paper models the nonlinear and non-convex behavior of efficiencies of BESS using ICNNs, specifically by approximating the nonlinear portion by the sum fICNN(Pc) + gICNN(Pd), representing two ICNN models for charging and discharging, respectively.

The methodology presented involves four battery optimization problem formulations: (i) Full NLP formulation, (ii) Constantefficiency linear formulation, (iii) Relaxed ICNN formulation, and (iv) Big-M ICNN formulation.

Improvements for AI systems

Based on the provided research paper, here are specific improvements for AI systems and what those improved systems can achieve:

The proposed ICNN-based BESS formulation (specifically the relaxed version) can be integrated into real-time power system control loops, enabling dynamic optimization of battery dispatch decisions (charging/discharging rates) that accurately account for non-linear inverter efficiencies.
The improved AI system can perform high-fidelity, short-term forecasting and smoothing of intermittent renewable energy sources like solar PV by minimizing fluctuations in net PV power output, leading to more stable grid integration and reduced reliance on backup generation.
The ICNN model allows for the optimization of Battery Energy Storage Systems (BESS) in complex economic scenarios (e.g., revenue maximization), enabling the system to determine optimal charging/discharging schedules that maximize profit while respecting grid constraints, leading to higher financial returns compared to simpler linear models.
The Big-M ICNN formulation provides a structured way to handle non-convexities, allowing AI systems to solve larger optimization problems (like those with more time steps or more batteries) by transforming the problem into a Mixed-Integer Programming (MIP) framework, though this comes with increased computational cost.
The system can be developed to provide robust operational predictions for BESS performance by comparing predicted vs. actual trajectories across different models, allowing operators to assess the feasibility gap and choose the model that best balances computational burden and accuracy for real-time applications.
The ICNN approach enables the development of data-driven models that capture complex, non-linear physical relationships (like battery efficiency curves) without requiring explicit, high-fidelity electrochemical models or extensive parameter tuning, increasing the flexibility and adaptability of the AI system to novel operating conditions.

Abstract

Sources

Adam: A Method for Stochastic Optimization