EPS Example Notebook

This notebook shows how fmdtools can be used for static propagation models. Static propagation models are meant to represent events occurring within a time-step (as opposed to over several timesteps). The electric power system used as an examples replicates a previous power system case study implemented in IBFM, and also showcases some basic fault propagation and visualization.

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The “"Fault Model Design tools - fmdtools version 2"” software is licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0. 

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from fmdtools_examples.electric_power_system.model_main import EPS
import fmdtools.sim.propagate as propagate

This script provides some example I/O for using static models, using the EPS system implemented in eps.py as an example.

A graphical representaiton of this system is shown below:

mdl= EPS()
mg = mdl.as_modelgraph()
fig, ax = mg.draw()

As with dynamic models, in static models we use fp.run_one_fault to see the effects of single faults. All setup is performed in the Model class definition

result, mdlhist = propagate.one_fault(mdl, 'ee_to_me', 'toohigh_torque', to_return=["graph"])

In this case, however, the output in mdlhists will be a single-dimensional dictionary (not something we can plot very well)

fig, ax = mdlhist.plot_line(*mdlhist.nominal.keys())

C:\Users\dhulse\Documents\GitHub\fmdtools\src\fmdtools\analyze\common.py:547: UserWarning: Attempting to set identical low and high xlims makes transformation singular; automatically expanding.
  ax.set_xlim(*xlim)

As a result, it’s better to look at the results graph for a visualization of what went wrong. In this case resgraph better represents the fault propagation of the system than in a dynamic model, since there is only one time-step to represent (rather than a set)

graph = result.get_faulty().tend.graph
graph.set_edge_labels(title='')
fig, ax = graph.draw(figsize=(14,10))

We can run the set of single-fault scenarios on this model using fmdtools.sim.propagate.single_faults. For single-fault scenarios, one does not need to use a SampleApproach, since all faults are injected at a single time-step.

mdl= EPS(track='all')
results, mdlhists = propagate.single_faults(mdl, staged=True)

SCENARIOS COMPLETE: 100%|██████████| 35/35 [00:00<00:00, 75.36it/s]

Using analyze.tabulate.result_summary_fmea, one can see the degradation effects of this fault on the flows:

from fmdtools.analyze.tabulate import result_summary_fmea

tab = result_summary_fmea(results, mdlhists, *mdl.fxns, *mdl.flows)
tab.sort_values("expected_cost")

	degraded	faulty	rate	cost	expected_cost
nominal	[]	[]	1.0	0.0	0.0
eps_fxns_ee_to_he_open_circuit_t0p0	['ee_to_he', 'ee_h', 'he']	['ee_to_he']	0.0	550.0	2.409
eps_fxns_supply_ee_open_circuit_t0p0	['supply_ee', 'ee_2', 'ee_3', 'ee_m', 'ee_o', ...	['supply_ee']	0.0	1450.0	3.1755
eps_fxns_ee_to_he_high_heat_t0p0	['supply_ee', 'store_ee', 'ee_to_he', 'ee_2', ...	['supply_ee', 'store_ee', 'ee_to_he']	0.0	2500.0	10.95
eps_fxns_ee_to_oe_optical_resist_t0p0	['ee_to_oe', 'ee_o', 'oe', 'he', 'waste_he_o']	['ee_to_oe']	0.0	520.0	11.388
eps_fxns_supply_ee_short_t0p0	['supply_ee', 'store_ee', 'distribute_ee', 'ee...	['supply_ee', 'store_ee', 'distribute_ee']	0.0	5150.0	22.557
eps_fxns_ee_to_he_low_heat_t0p0	['ee_to_he', 'he']	['ee_to_he']	0.000002	550.0	48.18
eps_fxns_ee_to_oe_burnt_out_t0p0	['ee_to_oe', 'ee_o', 'oe', 'he', 'waste_he_o']	['ee_to_oe']	0.000002	550.0	48.18
eps_fxns_import_signal_no_signal_t0p0	['import_signal', 'ee_2', 'ee_3', 'ee_m', 'ee_...	['import_signal']	0.000001	2000.0	87.6
eps_fxns_ee_to_he_toohigh_heat_t0p0	['store_ee', 'distribute_ee', 'ee_to_he', 'ee_...	['store_ee', 'distribute_ee', 'ee_to_he']	0.0	5100.0	111.69
eps_fxns_supply_ee_adverse_resist_t0p0	['supply_ee', 'ee_2', 'ee_3', 'ee_m', 'ee_o', ...	['supply_ee']	0.000002	1650.0	144.54
eps_fxns_export_waste_ho_ineffective_sink_t0p0	['export_waste_ho', 'he', 'waste_he_o']	['export_waste_ho']	0.000005	1000.0	219.0
eps_fxns_export_waste_ho_hot_sink_t0p0	['export_waste_ho', 'he', 'waste_he_o']	['export_waste_ho']	0.00001	500.0	219.0
eps_fxns_export_waste_h1_ineffective_sink_t0p0	['export_waste_h1', 'he', 'waste_he_1']	['export_waste_h1']	0.000005	1000.0	219.0
eps_fxns_export_waste_h1_hot_sink_t0p0	['export_waste_h1', 'he', 'waste_he_1']	['export_waste_h1']	0.00001	500.0	219.0
eps_fxns_export_waste_hm_hot_sink_t0p0	['export_waste_hm', 'he', 'waste_he_m']	['export_waste_hm']	0.00001	500.0	219.0
eps_fxns_export_waste_hm_ineffective_sink_t0p0	['export_waste_hm', 'he', 'waste_he_m']	['export_waste_hm']	0.000005	1000.0	219.0
eps_fxns_export_he_hot_sink_t0p0	['export_he', 'he']	['export_he']	0.00001	600.0	262.8
eps_fxns_import_ee_low_v_t0p0	['import_ee', 'ee_1', 'ee_2', 'ee_3', 'ee_m', ...	['import_ee']	0.00001	700.0	306.6
eps_fxns_export_he_ineffective_sink_t0p0	['export_he', 'he']	['export_he']	0.000005	1500.0	328.5
eps_fxns_supply_ee_major_overload_t0p0	['supply_ee', 'store_ee', 'ee_2', 'he', 'waste...	['supply_ee', 'store_ee']	0.000003	2600.0	341.64
eps_fxns_store_ee_low_storage_t0p0	['store_ee']	['store_ee']	0.000005	2000.0	438.0
eps_fxns_import_ee_high_v_t0p0	['import_ee', 'supply_ee', 'store_ee', 'ee_1',...	['import_ee', 'supply_ee', 'store_ee']	0.000005	2300.0	503.7
eps_fxns_import_ee_no_v_t0p0	['import_ee', 'ee_1', 'ee_2', 'ee_3', 'ee_m', ...	['import_ee']	0.00001	1550.0	678.9
eps_fxns_store_ee_no_storage_t0p0	['store_ee', 'ee_3', 'ee_m', 'ee_o', 'ee_h', '...	['store_ee']	0.000005	3250.0	711.75
eps_fxns_import_signal_partial_signal_t0p0	['import_signal', 'ee_2', 'ee_3', 'ee_m', 'ee_...	['import_signal']	0.00001	2000.0	876.0
eps_fxns_distribute_ee_adverse_resist_t0p0	['distribute_ee', 'ee_2', 'ee_3', 'ee_m', 'ee_...	['distribute_ee']	0.00001	2750.0	1204.5
eps_fxns_ee_to_me_open_circuit_t0p0	['ee_to_me', 'ee_m', 'me', 'he', 'waste_he_m']	['ee_to_me']	0.00005	650.0	1423.5
eps_fxns_distribute_ee_poor_alloc_t0p0	['distribute_ee', 'ee_2', 'ee_3', 'ee_m', 'ee_...	['distribute_ee']	0.00002	1750.0	1533.0
eps_fxns_ee_to_me_high_torque_t0p0	['ee_to_me', 'ee_m', 'me', 'he', 'waste_he_m']	['ee_to_me']	0.0001	450.0	1971.0
eps_fxns_supply_ee_minor_overload_t0p0	['supply_ee', 'store_ee', 'distribute_ee', 'ee...	['supply_ee', 'store_ee', 'distribute_ee']	0.00001	5150.0	2255.7
eps_fxns_distribute_ee_open_circuit_t0p0	['distribute_ee', 'ee_2', 'ee_3', 'ee_m', 'ee_...	['distribute_ee']	0.00003	2750.0	3613.5
eps_fxns_distribute_ee_short_t0p0	['store_ee', 'distribute_ee', 'ee_3', 'ee_m', ...	['store_ee', 'distribute_ee']	0.00002	4750.0	4161.0
eps_fxns_ee_to_me_short_t0p0	['store_ee', 'distribute_ee', 'ee_to_me', 'ee_...	['store_ee', 'distribute_ee', 'ee_to_me']	0.00005	4950.0	10840.5
eps_fxns_ee_to_me_toohigh_torque_t0p0	['store_ee', 'distribute_ee', 'ee_to_me', 'ee_...	['store_ee', 'distribute_ee', 'ee_to_me']	0.00005	5050.0	11059.5
eps_fxns_ee_to_me_low_torque_t0p0	['store_ee', 'distribute_ee', 'ee_to_me', 'ee_...	['store_ee', 'distribute_ee', 'ee_to_me']	0.0001	4950.0	21681.0