Problem
The solar-array power system lockups in the battery-discharge mode when there is sufficient energy to charge the battery.
The problem occurs in a Direct Energy Transfer (DET) system consisting of a solar array directly powering the system voltage bus. System voltage regulation is provided by a shunt regulator working against the solar-array impedance. A battery provides power when there is insufficient energy from the solar array and a battery charger charges the battery when the solar-array output exceeds that required by the load.
Lockup can occur during a dark-to-light transition of the solar-array power source. In space systems, this can occur during initial deployment at launch or each time there is an orbital transition from eclipse to sunlight. It can also occur on the transition back to solar-array power if a transient increase in load requires transient energy from the battery.
D
Figure 1: DET System I-V Characteristics
Figure 1 shows the state-plane of the system where I is the current in the inductance of the cable from the solar array (approximates the solar-array current) and V is the voltage across the bus capacitance (approximates bus voltage). Superimposed on the I-V state-plane are the input characteristic of a switching-mode power supply (red) and the output characteristic of a solar-array (blue). (Notice other discussions in this hypertext sometimes plot similar characteristics in the V-I plane instead of the I-V plane as shown here.)
A family of system trajectories can be plotted on this plane for practical values of system inductor current and capacitor voltage. The trajectories and isoclines are not plotted here, but are in the references. What these trajectories show is that point B is an unstable operating point on a separatrix that passes between operating points A and B (dotted black line). Point A is stable and a node (real) or a focus (complex), but not a desired operating point since it is on the turn-on resistive part of the load line before the switching-mode power supply load begins operation. The stability of point C, which is the voltage the system goes to if the regulating shunt regulator fails open, depends on the values of L and C. For practical values of L and C it is usually stable. The normal end-of-life full-load operating point, point R, is usually selected to be the peak power point, near the inflection point of the solar-array characteristic. This point is unstable but is stabilized by the shunt regulator which regulates to a voltage near the point R voltage.
Also not plotted in Figure 1 are the composite load lines in the various operating modes -- battery charging, shunt regulation, etc, and plots of the solar-array characteristics at various illumination levels.
If these were added to Figure 1, then the trajectories from sun to eclipse and eclipse to sun could be plotted along these load lines. When this is done (see references), there is no latchup possible on the sun to eclipse trajectories. However, when the battery is powering the load, the operating point is on the left-side of the separatrix (dotted black line through point B) and under some conditions can not get back to the desired right-side of the separatrix. This presents a controllability problem and results in latchup. The load continues to be partially powered by the battery, even if there is sufficient energy from the solar-array to power the load and charge the battery.
The discharge is usually small in tightly regulated bus systems but can be very large in semi-regulated bus systems.
Relevance
This problem illustrates the complexity of problems that occur in powering a constant power load with a current limited source. It also illustrates a controllability problem, that is, the system getting into a state that it can not get out of without outside help. The problem illustrated is a real problem for direct-energy-transfer power systems consisting of a solar-array power source and battery, a constant power load, a shunt power bus regulator, and a battery charger. This configuration is often used in space power systems orbiting the earth.
Solvability
Determine the stable operating points and how to move from an undesired stable operating point to the desired stable operating point. The pragmatic solution to the real latchup problem (getting the system to unlatch) is to reduce the load (load shedding) or increase the output of the solar array by pointing it more directly at the sun.
Solution
The problem and its solutions are described in a 1989 IECEC paper "Large-Signal Analysis of Spacecraft Power Systems" by Seong J. Kim, Jae R. Lee, and Bo H. Cho. Helpful to understanding the analysis is an earlier 1987 PESC paper by the same authors with the same title.
In this hypertext, see also: Latchup of Constant-Power Load With Current-Limited Source
Personal Anecdote
I ran across this when I thought I might get involved in Direct Energy Transfer Systems. I never did get involved, but I thought it was a good example of a problem occurring with powering a switching-mode power supply from a current-limit source as well as being a controllability problem. You can get into a lot of controllability problems (getting into modes that you can't get out of except by turning off the system or taking some other drastic action) with switching-mode power supplies. I hope to eventually discuss these types of controllability problem on this website.
On the Web
So far I have not found any related material on the Web.
References
Abstracts of papers related to Solar-Array Power System Battery Lockup