The mentality for a greener future with zero emissions is not a blurry thought far away from reality anymore. It is a driver that push people to re-think again the way the resources from the Earth are being used. This paper aims to study a possible transition before it is possible to utilize 100% green energy. Co-optimization systems are proposed in order to add flexibility, in this case, to the power system and therefore, introduce as much as possible green energy to societies. To be more specific, a co-optimization model where the natural gas is used in the gasfired power plants to produce the extra energy needed to meet demand is developed. At the same time, minimizing the total system costs of both systems. Besides, this master thesis also proposes a co-optimization between power and natural gas systems under the uncertainty deriving from renewable energy sources. To do so, the application of chance-constrained programming is a crucial factor. As a result, by assuming known the probability distribution of the total wind power mismatch in the recourse stage, it is possible to quantify the optimal scheduled power to dispatch in the first stage, minimizing the overall system costs and obtaining the maximum wind penetration as possible. Lastly, several factors are modified to understand, which are the main drivers that affect the most to chance constraints - optimal power flow. The risk level chosen for this new approach and the consequences of varying it is also shown to understand how significant the degree of risk is applied to the chance constraints and how it can affect both variables and total system costs.