Is there a way to model a complex electric rate for thermal energy storage in OpenStudio or EnergyPlus?

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David Goldwasser's answer indicates how to get the Tariff integrated into EnergyPlus.

As far as a UtilityCost:Tariff in EnergyPlus that can do mid-peak over weekend hours, in the UtilityCost:Tariff reference a schedule name in the Time of Use Period Schedule Name field that defines those hours using the number 4 as the value for those hours. Then for the UtilityCost:Charge:Simple reference the midPeakEnergy variable as the source variable. You might want to take a look at the "Example F Seaonal Time of Use Energy " from the documentation to understand how it works.

For the monthly customer charge, in the UtilityCost:Tariff object, put the cost in the Monthly Charge or Variable Name field.

OpenStudio uses EnergyPlus measures to add tariffs to a model, so you can add any tariff structure that EnergyPlus supports. There is a Tariff Selection Generic Measure on BCL that lets you add any IDF files to a "resources" folder to use as tariffs. It includes a number of example tariff structures that may serve as a starting point for you.

Additionally here is a link to the UtilityCost:Tariff documentation for EnergyPlus.