Residential consumers have electrical and thermal loads. Therefore they can be utilized hybrid thermal and electrical energy systems to procure their required energy. In the proposed system, in order to supply residential loads, a hybrid energy system (HES) is proposed which consists of photovoltaic/solid oxide fuel cell/thermal and electrical storages/boiler. Also, the uncertain parameters such as thermal and electrical loads, electricity market price, and solar irradiation are considered in the stochastic formulation. Uncertain parameters can be led to financial risks in the system operation. In order to measure imposed risks, in this paper, a novel risk management method called downside risk constraints method is used to model the financial risks imposed from the uncertain parameters. According to obtained results, the operator of the hybrid energy systemby utilization of the downside risk constraints method has obtained a strategy that is scenario independent. In other words, the downside risk constraints method by minimizing the imposed risks introduced a zero-risk strategy which operation cost would not increase by changing the scenario. Results are shown that system operators by paying 1.3% more expected cost ($ 40.22 instead of $ 39.69), can make its operation independent of the scenario. Also, riskbased operational strategies of the proposed hybrid energy system are reported in the results as graphical results. The proposed risk-measurement operation problem of the designed hybrid energy system is formulated as a mixed-integer linear programming (MILP) model and modeled by GAMS software using CPLEX solver. (C) 2020 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.