4.1. Hybrid-Hydrogen Energy System Application and Results
Among the eleven REDZs discussed in
Section 2.1.1, six REDZs (presented by green in
Figure 2) were chosen for the application and their respective wind data were obtained from WASA wind masts, as shown in
Table 2.
The latest 10 min wind speed data observed at anemometer height of 60 m for 2021 from wind masts are acquired and converted to 1 h average wind speed data by (
1) with monthly and annual mean speed in (
4) presented by
Figure 7.
In
Figure 7, Overberg has the highest annual mean speed, thus an expected high energy potential. Furthermore, Stormberg has the lowest annual speed, so the least energy production is expected. The wind speed frequency distribution of wind speed data using PDF in (
2), with scale and shape parameters in (
3) is obtained, as shown in
Figure 8,
Figure 9 and
Figure 10 for all the six REDZs.
In
Figure 8,
Figure 9 and
Figure 10, the occurrence frequency of different wind speeds for each wind REDZs is presented. Overberg, Komsberg and Springbok show the occurrence of high wind speeds, which is in agreement with the high annual mean speed in
Figure 7 compared to Cookhouse, Stormberg and Beaufort West. Using the wind speed characteristics, the monthly energy density in (
8) is determined in
Figure 11.
In
Figure 11, the highest energy density is noticed in Overberg, Komsberg and Springbok, and the lowest energy density in Cookhouse, Stormberg and Beaufort West, which is in accordance with their respective annual mean speeds in
Figure 7.
Table 3 concludes that Overberg has the highest energy potential, and Beaufort West has the lowest energy potential of all wind REDZs as expected from their wind speed characteristics. For accuracy in energy assessment, the annual energy production of the REDZs is obtained using wind speed frequency characteristics in conjunction with an appropriate wind turbine model for the respective wind REDZs. Therefore, the optimal wind turbine variables, cut-in speed,
, rated speed,
, cut-out speed,
, rotor diameter,
, and the hub height,
, are required.
A scope of wind turbine models from Nordex (N), DeWind (D), Vestas (V) and Gamesa (G) manufactures are shown in
Table 4 to give an idea of the wind turbine variable ranges [
21,
22,
26,
39].
In cases where
in
Table 4 is different from the anemometer height, the wind speed at
,
, is calculated using (
10) and (
11) at anemometer heights of 62 m and 60 m, as discussed in
Section 2.1.4. The calculated surface roughness coefficient,
s (
11) for each wind REDZ, is given in
Table 5 with expected values as discussed in [
12].
The appropriate wind turbine model for each wind REDZ is selected by application of the optimization problem definition and procedure in
Section 3 to ensure an optimal H-HES model in the next section.
4.2. Optimization Application and Results
To implement the optimization procedure shown in
Figure 6, the Pymoo framework, which offers NSGA-II, is utilized. Pymoo is chosen because it enables visualization of lower and upper-dimensional data, and can implement performance indicators to evaluate the quality of solutions from NSGA-II [
33]. In addition, Pymoo provides a variety of multi-criteria decision-making tools that can be implemented after the NSGA-II has converged to a Pareto front to select the best solution in
Figure 6.
The Pymoo framework only considers pure minimization of optimization problems. Therefore, objective functions to be maximized are multiplied by
to be minimized [
33]. In addition, all constraint functions should be formulated as less than or equal to (⩽) zero. From (
24), the design variables required to solve the objective and constraint functions are the variables on which the H-HES model depends. The chosen design variables include wind turbine variables (listed in
Table 4) and H-HES model efficiencies: rotor (
), gearbox (
), generator (
), EMS (
) and rectifier (
) and electrolyzer (
) presented as:
where the lower and upper bounds in (
23) of each design variable are listed in
Table 6.
in (
27) is calculated by Eskom tariff structure as discussed in
Section 2.5. The Eskom tariff structure selected for
based on Urban, Megaflex and non-local authority tariff charges, because the PEM electrolyzer in
Figure 1 is connected directly to the substation, has a notified maximum demand greater than 1 MW and is within the Eskom supply area, respectively [
38].
Using
Figure 4, the transmission zones of the six wind REDZs in
Table 2 and shown
Figure 2 (in green) are concluded as >600 km and ≤900 km: Cookhouse, Stormberg and Beaufort West and >900 km: Overberg, Komsberg and Springbok. The transmission zones are listed in
Table 7 including the assumed voltage level of the PEM electrolyzer.
In addition,
Table 7 gives active energy costs for TOU periods and demand seasons in
Figure 5. The objective functions
and
in (
27) are constrained by the nominal power or energy of the PEM electrolyzer. The PEM electrolyzer chosen for application is the H-TEC SYSTEMS because it offers mobility and reliability and can be scaled up for large-scale plants [
40]. In
Table 8, 2 MW H-TEC PEM electrolyzer specifications are listed. The electrolyzer’s nominal power is the load,
, on which a load factor of
is used. To give flexibility for NSGA-II to obtain the optimal solution, a constraint output range of
–
MW is applied to get the nominal power of the electrolyzer.
Since the energy required by the electrolyzer (i.e., nominal energy,
) is known.
for green H
production assuming only the G-ES (shown in
Figure 1) used is calculated using (
18), with respect to the tariff charges for respective transmission zones in
Table 7 of the REDZs, and given in
Table 9.
From
Table 9, it can be concluded that the tariff charge increases with the transmission zone distance, as discussed in
Section 2.5. With the design variables, objective and constraint functions are defined, NSGA-II is initialized with the operating parameters in
Table 10 to carry out the optimization procedure in
Figure 6.
The number of generations in
Table 10 is used for the convergence in optimization procedure shown in
Figure 6 to obtain the scaled Pareto front solutions of objective functions,
in
Figure 12. The execution time that NSGA-II takes to obtain solutions during the optimization process illustrated in
Figure 6 is fast due to simple analytical equations used to model the H-HES in
Section 2. Therefore, large population sizes and the number of generations can be adopted for improved accuracy.
The best solution selection is conducted only after the search for solution sets ends, thus NSGA-II has converged to a Pareto front. With the Pareto front (presented in
Figure 12) known, the best solution is selected using multi-criteria decision-making techniques. However, before implementing the chosen technique, normalization of the objective functions is necessary due to different scales, as indicated by their different upper and lower bounds. Therefore, normalization ensures both objective functions equally dominate any distance evaluation in the objective space during the decision-making process [
33].
After normalization, the compromise programming multi-criteria decision-making technique available in Pymoo is adopted due to its flexibility, as it employs any type of decomposition function. The augmented scalarization decomposition function is applied with an equal weight of both objective functions, resulting in the best solution (presented by X in
Figure 12) for each wind REDZ.
The actual best solution of
passed to the H-HES model by interface model (as shown in
Figure 6) for each REDZ is given in
Table 11.
It can be concluded that an optimal H-HES ensures cost savings when optimal design variables are utilized, as noted in
Table 9 and
Table 11. The cost of electricity in
Table 9 is reduced by up to
with the optimal H-HES model as given in
Table 11 at maximum efficiency. Furthermore, from the optimal solutions of
and
in
Table 11, the optimal design variables in (
26) for each wind REDZ are given in
Table 12.
For application purposes, the appropriate wind turbine model selected for all the wind REDZs is Nordex (N43) in
Table 4, guided by the optimal variables in
Table 12. Furthermore, using the PEM electrolyzer efficiency,
, in
Table 8 and the optimal
,
,
,
and
efficiencies in
Table 12, the recalculated
and
is given in
Table 13.
In
Table 13, the calculated
using appropriate wind turbine and optimal efficiencies is in close agreement with the best solutions from NSGA-II in
Table 11. The calculated efficiency is slightly lower than the optimal efficiency, which is influenced by the efficiency (
) of the chosen PEM electrolyzer. It can be concluded that the optimal design variables have a great influence on the choice of wind turbine for each REDZ, hence an optimal H-HES model is successfully developed.