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I also find it takes EMS to do ice storage controls well. Use an EMS sensor on the tank charge fraction for the problem you describe.
It also helps for controls to set up the plant topology differently. I put the detailed ice tank on its own loop and connect it to the main chilled water loop using a heat exchanger on the chilled water supply outlet branch. This way the chillers can run on cooling load based operation scheme while the ice tank can run on component setpoint based operation scheme (which it requires). The EMS can control flow to the ice tank by manipulating temperature setpoints on the heat exchanger using its dual setpoint cooling control. These setpoints are separate from the main chilled water loop setpoint controlling the chiller. This allows for more complex modes where the chiller is both charging the tank and cooling the building at the same time or where the building loads are being met with both the (smaller) chiller and ice tank discharge. For ice charging mode it helps to add a plant load profile object in parallel with the cooling coils and use it to call for flow (flow only, no load) on the demand side when you need to get the chillers running to charge the tank.