## 7 Optimization Techniques for Demand-Side Resources in Active Distribution Networks
### Classical/Deterministic Optimization Methods
\begin{table}
\begin{tabular}{p{42.7 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Authors** & **Type** & **Implementation** & **Resources** & **Limitations** \\ \hline
[138] & Fuzzy logic adaptive prediction control (Heuristic) & Tune the input parameter on a cost function from the diesel generator and fuel cell to optimally regulate frequency in the microgrid. & Standalone microgrid that is made up of fuel cells, diesel generator, wind turbine battery storage, and loads (Simulation-based). & The high number of input variables affects model formulation, leading to more computational power \\ \hline
[139] & Stochastic recording horizon control & Minimize uncertainties from renewable energy sources by employing simplified Z-Bus with sequential linear programming to linearize horizon control & Grid-field microgrid with solar PV, wind turbines, and loads (Simulation-based). & Slow in handling fast transient systems. \\ \hline
[140] & Enhanced model predictive control (Heuristic) & Minimize consumption from the grid, improve battery lifespan, and increase renewable sources’ participation in catering for the load. & Grid-field with microgrid PV, Battery ban, and loads (Simulation-based). & Accuracy of models is a challenge. \\ \hline
[141] & Adaptive predictive control (Heuristic) & Minimize frequency fluctuations in the existence of disturbances and mitigate oscillations caused by external disturbances on tie line variation. & Grid-field microgrid with a diesel generator, flywheel, battery storage, fuel cell, wind turbines, hydrogen electrolyzer, and loads (Simulation-based). & The model becomes complex when handling a large number of controls. \\ \hline \end{tabular}
\end{table} 
Table 5: _Cont._Principles and Different Methods Used in Classical Optimization  
Classical optimization methods operate on the assumption that the objective function and constraints are deterministic and known with certainty. The core principle is to identify the optimal solution by systematically searching through the feasible solution space. Key elements of these methods include mathematical modeling, objective function formulation, decision variables, and constraints. The foundation of classical optimization methods lies in mathematical modeling. It is crucial to know how optimization problems related to DSRs are represented mathematically. It represents the formulation of objective functions, identification of decision variables, and incorporation of constraints. An accurate mathematical representation is critical for developing optimization models that reflect the unique characteristics of DSRs. Linear programming is particularly well-suited for optimizing DSRs in active distribution networks where objectives and constraints are linear [142]. LP models can be used to minimize operational costs, such as energy procurement costs or grid infrastructure investments, while adhering to constraints related to capacity, voltage limits, and DSR availability. LP provides valuable insights into cost minimization and resource allocation. The integration of discrete decisions into DSR optimization is addressed by mixed-integer linear programming [143]. MILP models are beneficial for problems that involve both continuous and discrete decision variables, which are common in DSR management [144]. Examples include determining optimal load-shedding strategies during demand response events or selecting the best time to charge electric vehicles (EVs). Deterministic optimization methods are instrumental in load scheduling for DSRs. Classical techniques, such as linear programming and mixed-integer programming, are used to optimize the timing and magnitude of electricity consumption for various DSRs, including industrial processes, HVAC systems, and residential loads. These methods ensure efficient energy utilization while meeting operational and economic objectives. Classical optimization methods are employed in demand response (DR) programs, where the goal is to optimize DSR participation to balance supply and demand [145].