To improve the stability of the power system under the disturbance signal, the paper proposes an H_∞ optimal excitation control method based on sum of squares method of the single machine infinite power system. The power system is a kind of non-polynomial system, while the proposed method uses the Taylor formula of non-polynomial systems transformed into polynomial system which keeps the high order infinitely small. The methods transform the non-polynomial systems using the Talor method and keep the high order infinitely small. Under a given attenuation coefficient and taking the advantages of sum of squares in the construction of Lyapunov function and parameter optimization,the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities constraints. After applying the policy iteration technique,the method is able to design the H_∞ optimal excitation controller and enhance the reality of simulations. Experimental results prove that the method can not only effectively improve the system performance but also enhance the anti-interference ability of the system.