Voltage Collapse in Power Systems: Loss of steady state?
Given the Jacobian, what do you know  about the total system energy trajectory?

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I am seeking to understand the Jacobian uses in a system model.

With the energy heading toward zero (assumed), then there no longer is energy being supplied to the system, or an enormous dampener has appeared (possibly a SHORT circuit or an OPEN circuit). Are these thoughts accurate?

If a finite dampener has suddenly been inserted, then the circulating energy will be dampened, and current and voltage amplitudes will be altered, until the new dampener losses are accommodated and a new steady state vector is reached.

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From what I've read, the power organizations seek to avoid total voltage collapse, and various industrial users are designated as "discretionary". Thus these users will the FIRST energy consumers to be SHED, to be DROPPED, to be DIS_CONNECTED from the grid.

In dropping certain users, the residual energy in the various rotating masses will be adequate to serve the remaining loads. 

Realize you have energy producer rotating masses, and energy consuming rotating masses (motors), thus the enormous mass ( many thousands of horsepower, with spinning armatures) of motors may assist in stabilizing the grid.

In load shedding, the grid is forced to react to energy transients.

This is exactly what an adaptive_communication link does, with echo cancellation or using high-pass filters to reverse the losses of low-pass wiring and PCB_dissipative copper surfaces and insulation loss tangents.

Thus we can examine how the grid system becomes adaptive, with pre-selected loads_to_be_shed, with a time constant of seconds.

I was out driving yesterday, and spotted 7 new towers on the horizon. These new structures have the height and aspect ratio of the exhaust_cleansing systems attached to the exhausts of natural_gas_powered jet_turbine power generators.

These new natural_gas generators have replaced the previous dual oil-fired boilers/turbines/generators of that square kilometer power station.

Key point is the reaction time of a jet_turbine natural_gas rotating mass, under computer control. Compared to the huge thermal mass of boiler/water.

The natural_gas system NEED NOT CHANGE ANYTHING ROTATIONAL. There is no inertia to alter.

A 0.5 second change in the natural_gas throttle is the only adaptation to a huge and sudden demand upon the grid.

Thus natural_gas power plants, and fields of solar panels with their DC_AC converters needing only 1/2 power cycle to synchronize to the grid, have a wonderful potential in stabilizing our power grids.