State-of-the-art electrical energy storage (EES) systems are mainly homogeneous, i.e., they consist of a single type of EES elements. None of the existing EES elements is capable of simultaneously fulfilling all the desired features of an ideal EES system, e.g., high charge/discharge efficiency, high energy density, low cost per unit capacity, long cycle life. A novel technology, i.e., a hybrid EES system that employs heterogeneous EES elements organized in a hierarchy of storage banks and linked by appropriate charge transfer interconnects, has shown great promise in overcoming the aforesaid limitations of conventional EES systems. However, the widespread adoption/deployment of hybrid EES systems is hampered by lack of a hybrid EES system simulator. This paper thus presents SIMES, a powerful and scalable simulator for hybrid EES systems, which provides fast and accurate system simulations, while accounting for key characteristics of various EES elements, power converters, charge transfer interconnect schemes, etc. Experimental results on two different applications (one targeting load shifting for households, the other related to battery rate capacity effect minimization in portable electronic devices) demonstrate the value and usefulness of SIMES for designing energy-aware facilities and products.