# Design and Development of a Management System for Energy Microgrids Using Linear Programming
## 2 Materials and Methods
### Literature Review  
The UC has usually been formulated as a non-convex and nonlinear combinatorial optimization problem by some authors. However, in some cases, the UC strategy can be applied to models like the one described by [15], where a lineal cost function is considered and only management constraints are taken into account. This research adopts a linear definition of the cost function based on the amount of energy produced by each of the generation technologies. Optimal power flow and UC has been also divided by [13] into two more specific problems: static and dynamic economic dispatch. The first one is a typical mode of power system planning and operation, which only studies the optimization scheme of a single time section rather than the connection between each time period. When modeling the static economic dispatch of the microgrid system, the objective function is usually to minimize the overall operating cost of the microgrid. Most of the constraints only consider the active power limits of the generating units in the microgrid and the power balance constraints within it, while ignoring the characteristics of battery storage units such as useful life, loading and unloading ramps, among other. On the other hand, dynamic economic dispatch is defined in [16] as one that considers the relationships between the values of the optimization variables in subsequent periods; for example, the battery level in a defined period affects the battery charge level in future periods depending on the state of charge or discharge that is defined through optimization. The dynamic economic dispatch model of the microgrid takes into account factors such as the ramp restriction of the controllable sources and the operation restriction [17] of the energy storage units, etc., which is closer to the power system. The addition of energy storage units not only makes the microgrid more closely connected in time, but also makes the operation more economical and reliable. In [18], it is shown that dynamic economic scheduling with energy storage units can save about 37% of the operating cost compared to static economic scheduling without an energy storage unit. One example of the implementation of a UC strategy to manage microgrids is presented in [15]. This research proposed a optimization model for planning an appropriate stand-alone, renewable-based electricity system for off-grid communities in Colombia. It used implicit stochastic optimization to make decisions regarding the sizing of renewable energy sources to meet energy demand during an average day. This research also considers the use of a unitary battery system for each zone in such a way that the energy generated from renewable sources during a certain period of time can be used later. This work concludes that the use of renewable energies must be adaptive according to the conditions associated with the environmental variables. In addition, the combination of these technologies provides a solution that is significantly cheaper for the community than typical diesel platforms because it is not necessary to buy or transport fuel. Another important study related to power microgrid management is [19]. In this study, a multi-objective economic-emission dispatch problem of combined heat and power is developed. In their model, multiple energy sources are also considered: renewable and non-renewable, but its objective function involves unit operating costs, emission level, emission tax, and the cost of power purchase from the main external grid. Their case is also important since it is possible to study the chance of managing microgrids in non-isolated areas, whose access to energy from the main grid is partial and, therefore, energy from it can be accessed to fully or partially satisfy the demand in certain periods of time. An important approach to mention is the one developed in [20], where the microgrid is approached from the basic consumer unit.