In this dissertation, we present an energy supply chain model called, energy planning problem, as a basic problem for analyzing distributed energy systems. We use multi-objective optimization and risk theory to optimize and analyze this problem under different circumstances. In the first chapter, we present energy planning problem with single or multiple decisions makers in energy system. These decision makers are able to buy or sell energy in the system according to their respective risk attitudes. We consider energy price of each generator as a decision problem under risk where each decision maker chooses its energy price as a function of its generated energy. Three different functions for risk attitude are considered for each decision maker; step function, piece-wise linear function, and polynomial function. A robust, simple, and verifiable approach for understanding and measuring risk of energy storages in distributed energy systems is introduced. We also show that the relationship between risk attitude and energy price simulates the behavior of real energy retailers or energy distribution companies. The resulting efficient optimization models provide the optimal risk strategy together with optimal amount of stored energy for each storage. In the second chapter, we use multi-objective optimization to formulate this problem using three criteria of cost, environmental impact and failure rate while satisfying operational and design constraints. We analyze the relationship between total cost, environmental impact, and failure rate using additive and goal seeking utility functions. We show that energy planning problem increases the flexibility of energy system in terms of changes in demand and energy price. Computational results and complexity analysis show that problems with extensive number of entities can be solved efficiently in reasonable time.