Integrated energy systems can increase the use of volatile renewable energy generation while reducing operation cost in the electric power system. The benefits result from shifting energy between energy infrastructures and using the network storage capability of district heating and gas systems. But the more strongly the different energy systems are linked the more complex their operation becomes. To ensure a secure and reliable system operation while using the full potential of integrated energy systems the interactions and the network storage effects of the district heating and gas system must be analyzed. Existing power flow calculation methods of integrated energy systems, however, neglect the network storage effects which result from the dynamic behavior of the district heating and gas system. The dynamic behavior is only investigated if the different energy systems are solved separately. As existing methods do not directly represent the interactions and effects of the dynamic behavior in an integrated energy system, the effect of any unit's power change on the power flows in the integrated energy system can only be determined by a complete power flow calculation, leading to a high computational cost. To reduce the computational cost this thesis derives sensitivity factors estimating the effect of a power change on the system state of an integrated energy system. To derive the sensitivity factors a joined quasi-steady-state power flow calculation method for integrated energy systems is developed extending existing steady-state approaches. For this, the system state of the electric power system, district heating system, and gas system is determined simultaneously, directly representing their interactions. To include the dynamic behavior a gradient method is proposed, which allows temperature and calorific value changes to be tracked in a coupled power flow calculation. The gradient method can accurately depict the dynamic behavior in the joined quasi-steady-state power flow calculation method even with simulation time increments of up to 60 min. Hence, compared to existing methods larger simulation time increments can be chosen to reach the same accuracy, leading to a reduced computation time. The sensitivity factors are on average ten times faster in estimating a new system state after a unit's power change compared to a power flow calculation. Besides the high computational efficiency, they can provide good estimates considering the complexity of the interactions and the dynamic behavior in an integrated energy system. As the joined quasi-steady-state power flow calculation method is based on the steady-state analysis existing use cases can be easily extended to consider the full potential of integrated energy systems. Therefore, the thesis provides system operators with a method to accurately analyze the full potential of Integrated energy systems.