## 4 Optimization Techniques
### Optimization Techniques Regarding Power Flow  
The operation of a microgrid is studied and enhanced using modern algorithms to achieve the optimal power flow, with the main aim to reduce losses and minimize the cost. The complex power in each node of a power system has a real active part and an imaginary reactive part, and the voltage magnitude and angles on these nodes are adjusted to meet the desired results. A large number of DC equipment and converters with more complex power characteristics and modern control algorithms add to the difficulty in the modeling of power flow. It is the need of the hour to develop the steady-state model for new devices such as DC transformers, PET (power electronic transformer), and distributed generators. The latest research in this field has been summarized below. In [26], the authors focus on the maximization of renewable energy usage and the minimization of the operational cost of a hybrid AC-DC microgrid. It stresses the need for load coordination of the source network and uses an improved memetic algorithm (IMA) which gives shorter running time and excelled results compared to the basic memetic algorithm. In [27], the authors apply a multi-objective particle swarm optimization technique which achieves a good configuration and sizing of the proposed system of PV, wind, battery, and fuel cell for remote areas. It employs supervisory control and fuzzy logic control with input and output membership functions for battery charging and discharging. In [28], the authors propose new equipment, a power electronic transformer (PET), and a decentralized model for optimum power flow to attain the autonomous operation with the help of voltage source converter power injection control and kriging model. It decomposes the optimal power flow problem of hybrid microgrid using the analytic target cascading (ATC). It shows that the Kriging model of PET with ATC gives better fitting accuracy to loss characteristic functions, has low communication requirements, and can solve decentralized and centralized power flow problems on a large scale. In [29], the authors employ fuzzy logic to meet the load demand, monitor battery charging and discharging, and optimize the cost of operation considering the high penetration of renewable energy resources in the hybrid grid. In [30], the authors propose the fuzzy logic system for cost and emission optimization using optimal droop control values. It compares the particle swarm optimization algorithm (PSO) and multi-objective genetic algorithm (GA) and finds that later gives results in close proximity comparatively. In [31], the authors deal with the increase in interaction between electrical and thermal energy with the help of an energy hub embedded in a hybrid microgrid. A two-stage stochastic problem based on optimization is formulated by using a sample average approximation mechanism. The decomposition technique (Bender) is used to solve multiple cases generated by this mechanism. In this technique, the cost of the grid is minimized. By using the heating and cooling systems, the operational efficiency of the energy hub can be increased. In [32], the authors introduce a novel dynamic power routing (DPR) technique for the operation of islanded AC-DC hybrid microgrid. This work can be summarized as introducing a novel DPR technique, integrating it with a controller supervisory, which uses a generic algorithm to minimize load-shedding. The results demonstrate the enhancement of system reliability. In [33], the authors target the increase in steady-state stability by optimum power flow (OPF) by using the Interior Point (IP) method. The presented AC/DC optimal power flow (OPF) can be used to discover the challenges (technical and economic) associated with a hybrid microgrid. It results in the optimization of droop parameters of energy resources and interlinking of the converters to maximize system load-ability. In [34], the authors propose the optimal operation under the spot price method to ensure the economic benefit of the hybrid microgrid.