## 5 Optimization
### Unit Commitment Problem  
One of the key objectives of a smart grid architecture is dispatching energy from all the available sources in order to meet the electric load. In other terms, there is a problem of coordination between energy demand and generation. This problem has been formalized under the name of Unit Commitment. Figure 13: Electricity price, grid capacity and charging power chart [48]. Unit commitment (UC), also known as pre-dispatch, is the problem of scheduling the production of energy by generation units of a power system. The objective is to minimize total production costs, while observing several operating constraints. Thus, UC is a complex mathematical problem, based on both integer and continuous variables. In order to solve this problem, an optimized algorithm is needed, because complete enumeration of all the possible solutions would require excessive computation time. For this survey's purposes, we analysed two possible solutions, which involve different approaches for solving the Unit Commitment Problem. [PERSON] _et al_. [PERSON] _et al_. (2010) propose a solution based on Adaptive Dynamic Programming (ADP). _\"ADP is able to optimize the system over time under conditions of noise and uncertainty. If optimal operation samples are used to train the networks, ADP can learn how to commit the generators and follow the operators customs. When load is changed, it can change the operation according to the load changing\" [PERSON] _et al_. (2010). The solution presented by the authors focuses on a specific family of ADP: the Heuristics Dynamic Programming (HDP). _\"The implementation is divided into **action network**, **critic network** and **model network**. The function of **action network** is to determine the feasibility region of operation of the power systems and to detect the emergency state with corresponding violations under different contingencies. The function of **critic network** is for post-optimization process, evaluation and assessment of control options during contingencies. And the function of **model network** is to read power system parameters and obtain distribution function for state estimation of measurement errors inherent in data, ascertain and improve accuracy of data. The aim of all these kinds of methods is to approximate the cost-to-go function which is relative to the output of critic network\" [PERSON] _et al_. (2010). After training, the HDP gives the generation plan. Figure 14 shows the load curve and the generation schedule of a three-generators system. X1, X2, X3 and [X1], [X2], [X3] represent the actual and expected output of the three generators respectively. Another approach for the UC problem is presented by [PERSON] _et al_. [PERSON] _et al_. (2010), where the authors introduce a solution using Genetic Algorithms (GAs). The application of the GAs to the UC problem included encoding each solution with a simple binary alphabet. At first, a number of initial binary-coded solutions (_genotypes_) are produced randomly to form  
Figure 14: Load curve of a 3-generators system and the corresponding HDP generation plan [PERSON] _et al_. (2010). the initial population. Then, a fitness value is given to each solution, calculated as a sum of penalties for violating certain problem constraints. Afterwards, a new offspring genotype (new solution) is produced by means of the two basic genetic operators: _crossover_ (combining different solutions by mixing their binary codes) and _mutation_ (modifying randomly chosen bits of the offspring genotypes. The above procedure is repeated until a new set of genotypes is produced, which is considered as the new generation of solutions. The new generation totally replaces the parents. By also implementing some adjustments to the fitness calculation, the GA technique has proven to converge in the order of hundreds of generations, as can be seen from Figure 15.  
[PERSON] _et al_. [51] provide another view of the Unit Commitment problem.