PINNs-for-IEEE-systems

This library provides power system dynamic solvers implemented in PyTorch based on the simultaneous solution algorithm. The developed algorithms, based on Runge-Kutta integration schemes, allow the integration of Physics-Informed Neural Networks (PINNs), boosting their computation performance and unlocking a wide range of modeling and privacy opportunities. The solvers are implemented using test systems from the IEEE test system library available at ieeelib.

PINNs are integrated as a more accurate alternative to traditional Runge-Kutta schemes over larger time steps.

The motivation, methodology, and applications are discussed in the following paper under review:

Ignasi Ventura, Rahul Nellikkath, and Spyros Chatzivasileiadis. "Physics-Informed Neural Networks in Power System Dynamics: Improving Simulations' Accuracy." 2025.

Installation

To install the latest on GitHub:

pip install git+https://github.com/ignvenad/PINNs-for-IEEE-systems

Run configuration

The present implementation supports the available IEEE 9-, 14-, and 30-bus test systems. We support two types of network disturbances: load and mechanical torque. These can be implemented with the fault type, fault time, fault magnitude, and fault bus location. To include the PINN in any of the simulations, add the bus number of the dynamic component to be represented by a PINN in the pinn_models_list. In the paper, we considered a PINN for bus 2 in the 9-bus system and bus 1 in the 14- and 30-bus systems. The sim_time and sim_time_step apply the desired simulation time and time step size, respectively. Different plots can be selected in the post-processing module. The parameters of the system and dynamic components can be found in the Cases and Machine_models folders.

PINN implementation structure

As explained in the paper, the PINN integration is very modular: any component can be captured, and a simulation can include multiple components captured by a PINN. PINNs accurately capture single-component dynamics considering the interaction with the system and thus can be included in a plug-and-play fashion. We envision a library of PINNs that can improve the simulations' accuracy and speed by capturing the trained components more accurately for larger time step sizes. See the following figure.

Figures for the IEEE 30-bus System $L^{20}_{+0.08}$ simulation

Voltage evolution

Line power flows

Generated power and frequency evolution

Simulation Tables

The following tables include more detailed information on the results provided in the paper. These values are obtained by comparing the traditional and hybrid files to the true file in the simulations "Saved_sims" folder, using the check_accuracy file to compare the numerical results and calculate the accuracy improvements.

IEEE 30-Bus System ($L^{20}_{+0.08}$)

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	2.37	$\delta_{2}$	39.24	$\delta_{5}$	6.00	$\delta_{8}$	6.98	$\delta_{11}$	1.39	$\delta_{13}$	1.89
$\omega_{1}$	0.50	$\omega_{2}$	38.88	$\omega_{5}$	3.03	$\omega_{8}$	4.64	$\omega_{11}$	1.68	$\omega_{13}$	1.06
$Id_{1}$	2.16	$Iq_{1}$	18.09	$Id_{2}$	37.65	$Iq_{2}$	39.36	$Id_{5}$	7.72	$Iq_{5}$	6.00
$Id_{8}$	8.24	$Iq_{8}$	6.98	$Id_{11}$	4.47	$Iq_{11}$	1.40	$Id_{13}$	3.48	$Iq_{13}$	1.89
$Vm_{1}$	0.57	$Vm_{2}$	0.84	$Vm_{3}$	2.80	$Vm_{4}$	3.57	$Vm_{5}$	7.82	$Vm_{6}$	4.97
$Vm_{7}$	5.80	$Vm_{8}$	8.33	$Vm_{9}$	4.41	$Vm_{10}$	4.25	$Vm_{11}$	4.44	$Vm_{12}$	3.44
$Vm_{13}$	3.46	$Vm_{14}$	3.56	$Vm_{15}$	3.84	$Vm_{16}$	4.05	$Vm_{17}$	4.18	$Vm_{18}$	4.13
$Vm_{19}$	4.16	$Vm_{20}$	4.18	$Vm_{21}$	4.29	$Vm_{22}$	4.31	$Vm_{23}$	4.25	$Vm_{24}$	4.55
$Vm_{25}$	5.51	$Vm_{26}$	5.51	$Vm_{27}$	6.19	$Vm_{28}$	5.46	$Vm_{29}$	6.19	$Vm_{30}$	6.19

IEEE 30-Bus System ($G^{1}_{-0.3}$)

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	0.74	$\delta_{2}$	39.74	$\delta_{5}$	7.96	$\delta_{8}$	21.69	$\delta_{11}$	0.64	$\delta_{13}$	0.95
$\omega_{1}$	0.38	$\omega_{2}$	39.51	$\omega_{5}$	4.31	$\omega_{8}$	14.34	$\omega_{11}$	0.59	$\omega_{13}$	0.67
$Id_{1}$	0.62	$Iq_{1}$	35.43	$Id_{2}$	38.01	$Iq_{2}$	39.46	$Id_{5}$	6.80	$Iq_{5}$	8.02
$Id_{8}$	4.72	$Iq_{8}$	21.78	$Id_{11}$	3.75	$Iq_{11}$	0.74	$Id_{13}$	2.83	$Iq_{13}$	0.95
$Vm_{1}$	0.46	$Vm_{2}$	0.68	$Vm_{3}$	2.20	$Vm_{4}$	2.67	$Vm_{5}$	6.89	$Vm_{6}$	3.47
$Vm_{7}$	4.02	$Vm_{8}$	4.89	$Vm_{9}$	3.36	$Vm_{10}$	3.28	$Vm_{11}$	3.55	$Vm_{12}$	2.85
$Vm_{13}$	2.81	$Vm_{14}$	2.89	$Vm_{15}$	3.01	$Vm_{16}$	3.07	$Vm_{17}$	3.21	$Vm_{18}$	3.10
$Vm_{19}$	3.17	$Vm_{20}$	3.19	$Vm_{21}$	3.28	$Vm_{22}$	3.29	$Vm_{23}$	3.14	$Vm_{24}$	3.34
$Vm_{25}$	3.86	$Vm_{26}$	3.86	$Vm_{27}$	4.13	$Vm_{28}$	3.67	$Vm_{29}$	4.13	$Vm_{30}$	4.13

IEEE 30-Bus System ($L^{12}_{-0.11}$)

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	3.55	$\delta_{2}$	34.44	$\delta_{5}$	11.30	$\delta_{8}$	12.89	$\delta_{11}$	0.08	$\delta_{13}$	0.17
$\omega_{1}$	1.26	$\omega_{2}$	33.32	$\omega_{5}$	6.87	$\omega_{8}$	9.57	$\omega_{11}$	0.15	$\omega_{13}$	0.05
$Id_{1}$	3.26	$Iq_{1}$	29.51	$Id_{2}$	33.30	$Iq_{2}$	34.00	$Id_{5}$	8.03	$Iq_{5}$	11.30
$Id_{8}$	7.63	$Iq_{8}$	12.89	$Id_{11}$	4.99	$Iq_{11}$	0.06	$Id_{13}$	3.56	$Iq_{13}$	0.19
$Vm_{1}$	0.93	$Vm_{2}$	1.30	$Vm_{3}$	3.42	$Vm_{4}$	4.07	$Vm_{5}$	7.97	$Vm_{6}$	5.42
$Vm_{7}$	6.42	$Vm_{8}$	7.57	$Vm_{9}$	5.14	$Vm_{10}$	4.76	$Vm_{11}$	5.07	$Vm_{12}$	3.68
$Vm_{13}$	3.62	$Vm_{14}$	3.91	$Vm_{15}$	4.57	$Vm_{16}$	4.57	$Vm_{17}$	4.89	$Vm_{18}$	4.61
$Vm_{19}$	4.86	$Vm_{20}$	4.91	$Vm_{21}$	4.91	$Vm_{22}$	4.96	$Vm_{23}$	4.60	$Vm_{24}$	5.24
$Vm_{25}$	6.00	$Vm_{26}$	6.00	$Vm_{27}$	6.36	$Vm_{28}$	5.69	$Vm_{29}$	6.36	$Vm_{30}$	6.36

IEEE 9-Bus System - 100% step bus 8

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	6.26	$\delta_{2}$	19.26	$\delta_{3}$	40.34	$\omega_{1}$	4.82	$\omega_{2}$	14.10	$\omega_{3}$	39.87
$Id_{1}$	24.63	$Iq_{1}$	6.16	$Id_{2}$	18.05	$Iq_{2}$	22.83	$Id_{3}$	40.20	$Iq_{3}$	40.41
$Vm_{1}$	26.37	$Vm_{2}$	12.20	$Vm_{3}$	13.44	$Vm_{4}$	13.29	$Vm_{5}$	11.29	$Vm_{6}$	10.10

IEEE 14-Bus System - 100% step bus 14

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	5.68	$\delta_{2}$	44.38	$\delta_{3}$	2.31	$\delta_{6}$	1.76	$\delta_{8}$	1.42	$\omega_{1}$	0.66
$\omega_{2}$	40.52	$\omega_{3}$	0.08	$\omega_{6}$	0.86	$\omega_{8}$	1.03	$Id_{1}$	5.19	$Iq_{1}$	40.06
$Id_{2}$	41.49	$Iq_{2}$	43.68	$Id_{3}$	7.21	$Iq_{3}$	2.31	$Id_{6}$	6.16	$Iq_{6}$	1.76
$Id_{8}$	1.22	$Iq_{8}$	1.42	$Vm_{1}$	0.12	$Vm_{2}$	0.34	$Vm_{3}$	7.19	$Vm_{4}$	1.84
$Vm_{5}$	1.89	$Vm_{6}$	6.29	$Vm_{7}$	1.02	$Vm_{8}$	1.14	$Vm_{9}$	0.69	$Vm_{10}$	0.80

IEEE 30-Bus System - 100% step bus 30

Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)	Variable	Value (%)
$\delta_{1}$	10.16	$\delta_{2}$	52.32	$\delta_{5}$	1.74	$\delta_{8}$	3.61	$\delta_{11}$	1.54	$\delta_{13}$	2.89
$\omega_{1}$	2.20	$\omega_{2}$	45.60	$\omega_{5}$	1.68	$\omega_{8}$	2.55	$\omega_{11}$	0.08	$\omega_{13}$	2.30
$Id_{1}$	9.50	$Iq_{1}$	29.38	$Id_{2}$	51.29	$Iq_{2}$	51.82	$Id_{5}$	7.06	$Iq_{5}$	1.74
$Id_{8}$	13.61	$Iq_{8}$	3.62	$Id_{11}$	9.98	$Iq_{11}$	1.54	$Id_{13}$	7.53	$Iq_{13}$	2.89
$Vm_{1}$	1.36	$Vm_{2}$	2.51	$Vm_{3}$	5.19	$Vm_{4}$	6.75	$Vm_{5}$	7.05	$Vm_{6}$	10.74
$Vm_{7}$	12.81	$Vm_{8}$	13.57	$Vm_{9}$	9.69	$Vm_{10}$	9.33	$Vm_{11}$	9.83	$Vm_{12}$	7.66
$Vm_{13}$	7.62	$Vm_{14}$	7.69	$Vm_{15}$	8.27	$Vm_{16}$	8.59	$Vm_{17}$	8.99	$Vm_{18}$	8.79
$Vm_{19}$	8.91	$Vm_{20}$	8.97	$Vm_{21}$	9.44	$Vm_{22}$	9.48	$Vm_{23}$	9.13	$Vm_{24}$	10.12
$Vm_{25}$	11.87	$Vm_{26}$	11.87	$Vm_{27}$	12.79	$Vm_{28}$	12.17	$Vm_{29}$	12.79	$Vm_{30}$	12.79