**5. Result discussion**

The projected QOGWO has been used to find the solution of a hydrothermal test system. It has been simulated using MATLAB software. As HTS is a real time problem so, it is necessary that each run of the program should reach close to optimum solution. 20 independent runs are executed to get the optimum solutions for all the algorithms considered here.

#### **5.1 Test system-1**

Here the test system-1 is similar to that in [1] but the supplementary data for VPL effect and PDZ of turbines are taken from [2]. Then the fuel cost of the corresponding thermal unit with VPL is given in (22)

$$\begin{aligned} \text{FC(PT}\_{i,j}) &= \sum\_{i=1}^{N\*} \sum\_{j=1}^{Z} \mathbf{0.002PT}\_{i,j}^{2} + \mathbf{19.2PT}\_{i,j} + \mathbf{5000} \\ &+ |\mathbf{700} \times \sin\left(\mathbf{0.085} \times \left(PT\_{i,\quad\text{min}} - PT\_{i,j}\right)\right)| \end{aligned} \tag{22}$$

The respective minimum and maximum thermal generations correspond to 500 and 2500 MW. The water loss in the spillway and the energy loss in catering the load from the hydro plant are ignored. The respective lowest and highest hydro generation correspond to 0 and 500 MW.

Three cases of the test system-1 such as Case 1 (HTS problem considering quadratic cost function only), Case 2 (with PDZ) and Case 3 (with VPL and PDZ) are under study. The several controlling parameters like *a*, *A*, *C*, size of the pack and maximum iteration number have been tried in this algorithm. The values of *a*, *A*, *C* are varied as per Eqs. (13) and (14), the size of the pack is 30 and the maximum iterations took is 500.

#### *5.1.1 Case 1: (HTS problems considering quadratic cost function only)*

This is the simplest case where the PDZ of the hydro units and the VPL effect of the steam power plant are neglected. The convergence characteristic in **Figure 3** gives an idea about the working of projected QOGWO approach. From **Figure 3** it is clear that the fuel cost is reduced in 50 numbers of iterations. The considered QOGWO approach takes the computation time of 340.452 s to get the optimal HTS. To validate the proposed QOGWO method, its simulation outcomes are compared in terms of best, average and worst fuel cost over 20 independent runs with the results of other approaches as shown in **Table 1**. The optimal results found by the projected algorithm

**Figure 3.** *Convergence features of QOGWO in case-1 of the test system.*


#### **Table 1.**

*Comparison of optimal costs for the test system (case 1) after 20 independent runs.*

are contrasted with other referred results shown in **Table 1**. It is clear that the QOGWO founded superior result than the above-mentioned accessible techniques. Though SOS has taken less time with a smaller number of iterations and population size, it gives the minimum cost but its minimum is higher than that by GWO and QOGWO.

#### *5.1.2 Case 2: (with PDZ)*

The PDZs of reservoirs of hydro power units have taken into account to ensure the viability of the projected method. This case has not been dealt with by many researchers but it is an important case for operation. The results of the proposed method QOGWO are compared in terms of best, average and worst fuel cost over 20 independent runs with the results of other approaches as shown in **Table 2**. It is observed that the QOGWO decreased the minimum, average and worst costs at less execution time than those obtained by the other existing techniques when population size and iterations are similar. The cost convergence feature of QOGWO algorithm is revealed in **Figure 4**.

### *5.1.3 Case 3: (with VPL and PDZ)*

Now the VPL of thermal power units and PDZ of hydro power units are included to confirm the robustness of the projected algorithm. The best rates of hydro


#### **Table 2.**

*Comparison of optimal costs in case-2 for the test system (case 2) after 20 independent runs.*

**Figure 4.**

*Convergence features of QOGWO in case-2 of the test system.*

*Dynamic Economic Load Dispatch of Hydrothermal System DOI: http://dx.doi.org/10.5772/intechopen.108052*

**Figure 5(a).** *Convergence features of QOGWO in Case-3 of the test system.*

**Figure 5(b).** *Hourly hydro power generation obtained by QOGWO in Case-3 of the system.*

discharges in slots got by the projected QOGWO are shown in **Table 3**. The convergence plot attained by QOGWO is illustrated in **Figure 5(a)**, respectively. In this case, the hourly hydropower generations found by the QOGWO method are given in **Figure 5(b)**.
