Electrostatically confined quantum dots in semiconductors hold the promise to achieve high scalability and reliability levels for practical implementation of solid-state qubits where the electrochemical potentials of each quantum dot can be independently controlled by the gate voltages.In this paper, the current and charge stability diagram of two-well potentials arising from electrostatically defined double quantum dot (DQD) are analytically realized. We propose to apply the Generalized Hubbard model to find the Hamiltonian of the system. The proposed analysis takes the tunnel coupling between the dots, Coulomb interaction, and Zeeman energy arising from an external magnetic field into account. Using quantum master equations to predict the probability of the final states in a DQD system, we study the tunneling current through two quantum dots coupled in series with two conducting leads, and therefore, the charge stability diagram is theoretically investigated. The impact of the tunnel coupling and Zeeman energy on the charge stability diagram is deeply discussed. The validity of the presented analysis is confirmed by experimental data as well as the classical capacitance model.