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# Definition of co-energy

## Definition of co-energy

(OP)
Related to my previous post - Can anyone tell me the meaning of the term co-energy, with respect to a magnetic system?
It vaguely rings a bell from my school physics many years ago, but I couldn't find a definition anywhere on the web. Even Wikipedia doesn't have an opinion, which is a first!
What I really want to know is the energy stored in my electromechanical actuator when current is flowing. I am modelling it in MagNet. Magnet gives 2 energy results - Magnetic energy and co-energy. These change when I simulate current flowing in the coil. They change by almost, but not exactly, the same amount. I suspect the difference is an artifact of the modelling, and actually they should change by the same amount.
Chris
Replies continue below

### RE: Definition of co-energy

If it's a linear system, energy is equal to coenergy.

Coenergy is defined as a convenience for computing force with current held constant.

F = -dW/dx with flux linkages held constant.
F = +dW'/dx with currents held constant

where W is energy and W' is coenergy.

W' = Sum(Lamdbak * Ik) - W

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### RE: Definition of co-energy

F = -dW/dx (with lambda held constant) seems like an obvious result from conservation of energy.

If you have a linear system, we have the surprising result:

F = + dW/dx (with currents held constant).  Seems to violate conservation of energy at first glance.

But there is electrical input energy to consider

P = dWe/dt = i * v = i * dLambda/dt
dWe = i dLambda

If you hold current constant while changing x which changes L, then lambda  must change (since lambda = L*i).  That means energy is input from the elctrical system.  The amount of energy input from the electrical system is exactly twice the energy output to the mechanical system in a linear electromagnetic system.

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