pennpoint is correct. Space is the major disadvantage. There is also a threshold of cost. I am most familiar with chilled water storage. For those systems, the cost of the tank must be weighed with the equivalent cost of chillers needed to meet peak loads. If your peak load integrates into an equivalent of about 10,000 ton-hours or more, then a tank may be economical. As peak loads increase, so do the advantages.
It is commonly thought that thermal storage does not save energy, only costs - by virtue of the fact that it saves the demand during peak loads. Conventional wisdom suggests that you have only "time-shifted" the load, since chillers and power usage are needed to charge the tank the night before.
However, charging the thermal storage system can be made on your terms - not the load's So, an operator can pick the ideal point of maximum efficiency from a particualr chiller's capacity/power usage profile, and use that point exclusively to charge the thermal storage.
That will actually result in saved energy, not just saved demand.
Space is No.1, but i'd add: Ability of the building operations to operate and maintain the additional equipment and controls, and with Ice systems - glycol toxicity concerns.
If "dual tariff" refers to energy demand charges (KW), besides just simple usage charges (KWH), then yes. Technically, the advantage of thermal storage is that it time-shifts the demand energy requirements to a time period where demand is very low (night time).
The savings can be significant. Most electrical rate structures use demand thresholds that lock-in for an entire billing period. For instance, if your power demands on a hot afternoon exceed your demand contract threshold, then your charges are assessed at a higher level for the entire month, not just that single day - regardless of whether you ever exceed that level again.
These days, most places in the United States have commercial/industrial rate structures that may be considered a "triple tariff" as you have termed it: Real Time Pricing (RTP). That is because RTP is often a third level of rate structure, in addition to demand and usage charges. With an RTP rate structure, utility rates are published on a real-time basis by the hour - similar to stock values in a stock exchange. With that type of billing, RTP prices are extremely high during the peak demand periods. These higher rates are justified in return for the gamble that the rest of the rate structure - off peak - is very low.
The result is an extreme incentive to time-shift the demand to more tolerable periods (night). In those cases, savings can be so great that co-generation becomes attractive. The savings (and investment) can dwarf the dividends reaped by thermal storage, and can actually negate the justification for thermal storage, since you would be generating your own power in any case, regardless of the time schedule.
