The increases in renewable current sources, prosumers and decentralised control generation in centralised grids have increased the fluctuations in electricity costs, increased the bi-direction power flow problems and changed the operation and investment of the centralised grid. These new constraints have to be observed to manage the design of the market, the new management near the load and the new operators for the power system. This study proposes a stochastic framework for the centralised grid with a market-based, decentralised management and bi-directional power flow of mixed generators of electrical energy. A decentralised and bi-directional market-based management system (DBMBMS) model is developed which considers the operation costs, security and reliability of the centralised grid, the spot market price, weather changes and the fluctuations in the load. A differential evolution technique with a Monte Carlo program is used in aggregation with bi-directional power flows to find the optimal solutions, depending on the uncertainties of the centralised grid. Using a DBMBMS model, optimal load and price management are then realised, based on the decision-maker's choices. The impacts of this new management system on the reduction of the total electricity prices of the different power sources are analysed and illustrated with practical case studies.