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A set of differential equations describing the dynamics of the transmission system and connected machines, including the voltage regulators and governors, is formed. The terms of these equations are divided into two groups, the linear terms and the nonlinear terms. The solution of the set of equations as a function of time can then be expressed as a function of the exponential of the matrix formed by the linear terms and an integral. The advantages and disadvantages of this method of approach for solving the transient stability problem on a digital computer are discussed.