IEEE GESS 2024

Federated Learning-based Resilient Control of Shipboard Power System

Anway Bose
anway.bose@temple.edu

Temple University

Joseph Amato
joseph.amato@navy.mil

Naval Surface Warfare Center

Li Bai
lbai@temple.edu

Temple University

November 4, 2024

Problem Formulation

Contents:

  • Problem Formulation

  • Federated XGBoost for Generator Load Prediction

  • Results

  • Convergence

  • Conclusion

Problem Formulation

Navy Shipboard Powersystem

Centralized Method

Centralized Load Dispatch

Centralized Method

Centralized Load Dispatch

Centralized Method

Centralized Load Dispatch

Centralized Method

Optimization Problem

  • Objective \(\text{arg} \min_{g_1,..,g_P} \ \frac{1}{2}\left \lVert \sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \right \rVert^2\)

  • constraint \(\sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \geq 0\)

Centralized Method

Optimization Problem

  • Objective \(\text{arg} \min_{g_1,..,g_P} \ \frac{1}{2}\left \lVert \sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \right \rVert^2\)

  • constraint \(\sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \geq 0\)

Gradient

  • Lagrangian \(\mathcal{L} = \frac{1}{2} \left\lVert \sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \right\rVert^2 - \lambda \left(\sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) + s\right)\)

  • gradient \(\nabla \mathcal{L} \lvert_{g_i(t)} = \left \lVert \sum_{i=1}^P g_i(t) - \sum_{j=1}^K z_j(t) \right \rVert - \lambda = 0\)

  • estimate \[\Rightarrow \hat{g_i}(t) = \lambda + \color{red}{\sum_{j=1}^K z_j(t)} - \color{red}{\sum_{p=1, p \neq i}^P g_p(t)}\]

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Centralized Method Vulnerabilities

Centralized Load Dispatch Vulnerabilities

Federated XGBoost for Generator Load Prediction

Contents:

  • Problem Formulation

  • Federated XGBoost for Generator Load Prediction

  • Results

  • Convergence

  • Conclusion

Federated XGBoost

3 step federated learning approach

  • Short-term Zonal Load Forecast Model

  • Total Zonal Load Demand Model

  • Generator Specific Load Model

Federated Learning

Short-term Zonal Load Forecast Model

short-term Zonal Load Forecast Model

  • xgboost objective \(\text{obj}_j^{(m)} = \sum_{t=1}^T \left(z_j(t) - \left(\hat{z}_j(t)^{(m-1)} + f_m(t)\right)\right)^2 + \sum_{i=1}^m \Omega(f_i)\)

short-term Zonal Load Forecast Model

Total Zonal Load Demand Model

Total Zonal Load Demand Model

  • xgboost objective \(\text{obj}^{(m)} = \sum_{t=1}^T \left(\sum_{j=1}^K z_j(t) - \left(\sum_{j=1}^K\hat{z}_j(t)^{(m-1)} + f_m(t)\right)\right)^2 + \sum_{i=1}^m \Omega(f_i)\)

Total Zonal Load Demand Model

Generator Specific Load Model

Generator Specific Load Model

  • xgboost objective \(\text{obj}_i^{(m)} = \sum_{t=1}^T \left(g_t(t) - \left(\hat{g_i}(t)^{(m-1)} + f_m(t)\right)\right)^2 + \sum_{j=1}^m \Omega(f_j)\)

Generator Specific Load Model

Results

Contents:

  • Problem Formulation

  • Federated XGBoost for Generator Load Prediction

  • Results

  • Convergence

  • Conclusion

Error injection simulation

  • Generator 2S Generator 2S Prediction

Error injection simulation

  • Generator 3S Generator 3S Prediction

Error injection simulation

  • Generator 5S Generator 5S Prediction

Convergence

Contents:

  • Problem Formulation

  • Federated XGBoost for Generator Load Prediction

  • Results

  • Convergence

  • Conclusion

Convergence Analysis

Convergence Analysis

  • xgboost objective \(\text{obj}^{(m)} = \sum_{j=1}^K\text{obj}_j^{(m)} + \sum_{i=1}^P\text{obj}_i^{(m)}\)

\(z_j(t) - \hat{z_j}(t) \rightarrow 0\)

\(\sum_j z_j(t) - \sum_j \hat{z_j}(t) \rightarrow 0\)

\(g_i(t) - \hat{g_i}(t) \rightarrow 0\)

Convergence Simulation (Generator 2S)

2S prediction round 2

Convergence Simulation (Generator 3S)

3S prediction round 2

Convergence Simulation (Generator 5S)

3S prediction round 2

Conclusion

Contents:

  • Problem Formulation

  • Federated XGBoost for Generator Load Prediction

  • Results

  • Convergence

  • Conclusion

Conclusion and Future Work

Conclusion

  • introduced a robust federated strategy for resilient control of distributed Synchronous generators

  • theoretically proved the convergence of our approach

  • performed experiments with the injection of various errors into the historical data of the zonal loads and have shown how resilient the system is to random injection of errors

Conclusion and Future Work

Conclusion

  • introduced a robust federated strategy for resilient control of distributed Synchronous generators

  • theoretically proved the convergence of our approach

  • performed experiments with the injection of various errors into the historical data of the zonal loads and have shown how resilient the system is to random injection of errors

Future Work

  • plan to include fuel cost in our objective function to find the optimal low-cost distribution of generator loads and demonstrate its resiliency in the face of communication disruptions

  • The aggregation server function can also be duplicated at each generator to provide redundancy to the system

  • federated learning method will also be compared to different regression approaches such as Gaussian Process Regression and combination of GPR and XGBoost on zonal and generator side modeling

THANK YOU

Anway Bose (anway.bose@temple.edu)

Joseph Amato (joseph.amato@navy.mil)

Dr. Li Bai (li.bai@temple.edu)

Computer Fusion Laboratory