The design and operation of energy systems, specifically those driven by chemical processes such as gasification and coal combustion have long been associated with theoretical modelling studies done within chemical engineering. However, with the rising need to face challenges brought upon by a warming climate and increased emissions from fossil fuel sources, there is significant interest in being able to design and operate systems that can harness the power of renewable energy sources while also providing economic benefits derived from operating them in a flexible manner. Mathematical modelling of such systems will therefore need to borrow concepts from chemical process engineering as well as power systems engineering and energy economics. The project currently being undertaken involves the mathematical modeling and optimization of a polygeneration-based energy system. Existing research in the area of modeling and optimization of systems behaving as a polygeneration plant, have primarily included the use of coal or biomass gasification to obtain syngas. With this key unit operation as the foundation, the energy systems have been designed in a manner in which they depend on the syngas produced to drive both the production of power as well as value added chemicals and liquid fuels. In this project, the key difference in the design is the inclusion of renewable energy sources, specifically intermittent sources of renewable energy such as wind and solar power. Additionally, aside from the syngas derived from gasification unit, power derived from other established pathways are also included, namely natural gas combined cycle process as well direct coal combustion processes. The main contribution from this project would be to look closely into the behavior of these energy pathways and investigate how and to what extent the energy system can be made more flexible while also taking into account that we seek to maximize profitability from the perspective of the operator. The flexibility of the polygeneration optimization framework can be obtained by reformulating it into a stochastic optimization problem. By doing so, the uncertainty and intermittency of renewable energy sources, domestic electrical and chemicals demand can be accounted for and accordingly, operational and design decisions can enhance the flexibility of the system based on intermittence/uncertain data assumptions. The integration of these intermittent sources into polygeneration mathematical framework requires some electrical engineering (i.e. power system mathematical modelling) background. The resultant polygeneration system is expected to act as a smart tool with which the interactions between chemical process plants and power plants (i.e. either renewable or conventional) can be harmonized to obtain optimal temporal decisions (when to produce power or chemicals or when to store power) and strategic decisions (e.g. what chemical plant should we design and what would their capacity be). This project represents an intersection where process engineering and power systems concepts meet to better design and operate flexible polygeneration systems as we look to transition to future energy systems.