This paper presents dynamic budget-balanced integration mechanisms for LQG power networks based on mechanism design theory in economics. The LQG power network model, which is motivated by an average system frequency model, consists of generators and consumers, called agents, and one public commission, called the utility. Each agent, who has a type with his preference, exercises private control to minimize the costs according to a personal cost functional, while the utility decides prices to minimize the costs according to a public cost functional and manages information transmission. In this problem setting, we propose dynamic budget-balanced integration mechanisms that integrate the strategic determination of private controls by rational agents into the optimal public controls with real-time pricing and monetary transfer costs. Two dynamic integration mechanisms, which together achieve all of social welfare maximization, Bayesian incentive compatibility, and budget balance, are proposed based on the cost functional and the Hamiltonian. The effectiveness of the proposed mechanisms are assessed through simulations.