## 2 Demand-Side Management Classifications and Their Roles in Cost Minimization
### Role of DERs in Cost Minimization  
DERs play an important role in cost minimization. In the literature, various articles are available where the benefits of DERs in terms of cost minimization have been explored. We have summarized all the DSM schemes where the authors used DERs as a cost minimization source in Table 8. The authors in [64], minimized the generation cost by developing a control algorithm known as the \"Lyapunov-based cost minimization algorithm\". The authors considered that each consumer has their own DER, storage devices, and an essential and flexible load. Furthermore, the consumers have coordinating control entity for the minimization of the generation cost. Another cost minimization technique was suggested by the author in [79], in which the consumers' costs are minimized by the use of DERs. The authors divided the consumers' load into two different parts, i.e., essential and flexible loads. Moreover, through the use of DERs, the authors employed the Lyapunov optimization solution in order to fill the gap between consumption and production. Similarly, the authors in [69; 79; 79; 166; 167; 168; 169] suggested distributed generation with the concept of the virtual power player (VPP) to manage the DERs. Moreover, the authors in [167] provided the concept of generation cost minimization using VPP. The authors in [95], analyzed a modified particle swarm optimization technique to integrate the DERs into the main grid and to minimize the cost of the VPP that manages the DERs. With this technique, the cost of VPP is minimized by using the mixed-integer non-linear optimization technique. The generation cost and the energy taken from the main grid are both minimized by efficiently applying the proposed schedule according to the demand response. The consumer demand is managed in three different steps where these steps are named \(Red_{A}\), \(Red_{B}\), and \(Red_{C}\). The main objective of the authors was to minimize the generation cost of electricity. The mathematical formulation of [95] is given by (5). \[\begin{array}{ll}\min&C=\sum_{t=1}^{T}\Bigg{(}\sum_{DG=1}^{N_{DG}}\Big{(}C_{A( DC,t)}X_{DG(DG,t)}+C_{B(DG,t)}P_{DG(DG,t)}+C_{C(DG,t)}P_{DG(DG,t)}^{2} \tag{5}\] \[+C_{EAP(DG,t)}P_{EAP(DG,t)}\Big{)}+\sum_{SP=1}^{N_{SP}}\Big{(}C_{ SP(SP,t)}P_{SP(SP,t)}\Big{)}+\sum_{L=1}^{N_{L}}\Big{(}C_{RED\_A(L,t)}\] \[P_{RED\_A(L,t)}+C_{RED\_B(L,t)}P_{RED\_B(L,t)}+C_{RED\_C(L,t)}P_ {RED\_C(L,t)}+P_{NSD(L,t)}\] \[C_{NSD(L,t)}\Big{)}+\sum_{S=1}^{N_{s}}\Big{(}C_{Dch(S,t)}P_{Dch( S,t)}-C_{Ch(S,t)}P_{Ch(S,t)}\Big{)}\Bigg{)}\]  
where \(C_{A(DG,t)},C_{B(DG,t)}\), and \(C_{C(DG,t)}\) represent the fixed, linear, and quadratic costs coefficient of the generator units in time \(t\), respectively, while \(C_{Ch(S,t)}\) and \(C_{Dch(S,t)}\) is the charging and discharging costs of battery \(S\) in time \(t\), respectively. The minimization problem is formulated in three different steps where each step has an associated operating cost which is represented by \(C_{RED\_A(L,t)},C_{RED\_B(L,t)}\) and \(C_{RED\_C(L,t)}\) to schedule load \(L\) in time \(t\). The cost coefficient for the excess available power at diesel generator (DG) is represented by \(C_{EAP(DC,t)}\). The cost for the non-supplied or surplus power is expressed by \(C_{NSD(L,t)}\). While \(P_{DG(DG,t)},P_{Ch(S,t)}\), and \(P_{Dch(S,t)}\) represent the active power of DG and the active charging and discharging power loads of storage \(S\). \(P_{RED\_A(L,t)},P_{RED\_B(L,t)}\), and \(P_{RED\_C(L,t)}\) are the amounts of power reduction by steps \(Red_{A}\), \(Red_{B}\), and \(Red_{C}\), for load \(L\). Furthermore, the excess generated power by DG and resupplied demand for load \(L\) is represented by \(P_{EAP(DG,t)}\) and \(P_{NSD(L,t)}\). \(P_{SP(SP,t)}\) is amount of active power acquired from the supplier at time \(t\). \(N_{L}\), \(N_{s}\), and \(N_{SP}\) are the load, number of storage devices and number of external suppliers, respectively. The authors in [84] used another DSM scheme with the objective to flatten the demand curve.