Whale-Optimized Fuzzy Energy Management for Photovoltaic/Grid/Supercapacitor-Assisted Electric Vehicle Fast Charging under Weak-Grid Outages

Table 1 positions the present work relative to selected implementation-oriented studies by comparing system configuration, grid-stress representation, control/service evaluation, and the complementary focus addressed here.

The station is represented as a four-port PV/grid/EV/SC system connected through a quadruple-active-bridge/multi-active-bridge (QAB/MAB)-style isolated DC routing stage [20]. The grid interface is modeled at supervisory power-flow level. The service side has one 60 kW outlet and a two-EV queue, making charger capacity explicit while isolating routing effects. Table 2 lists the station ratings and assumptions, while Table 3 provides the complete electric-vehicle service scenario.

Table 2. Station ratings and weak-grid scenario assumptions

Table 3. Complete electric-vehicle (EV) service scenario used in the 24 h stress-day simulation

Note: Window denotes arrival–departure time. Ebat is the EV battery capacity. SOCinit→SOCtar gives the initial-to-target SOC range. Pch/PV2G, max gives the maximum charging power and maximum V2G discharge power, respectively; a PV2G, max value of 0 indicates that V2G discharge is not enabled for that EV.

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Figure 3. Binary grid-connection status with voltage, frequency and grid-support request layers for the weak-grid scenario

6.1 Baseline controllers

Two non-optimized controllers are used as same-seed baselines.

The Rule-Based controller supplies EV demand from photovoltaic generation first, then the grid, then the supercapacitor when the supercapacitor SOC is above the support threshold. Photovoltaic surplus charges the supercapacitor first; any remaining photovoltaic power is exported to the grid when the grid is connected, no grid import is active, and the quality-dependent export limit permits export. Grid-to-supercapacitor charging is allowed only during connected non-support periods with no active EV demand. Limited EV/supercapacitor grid support is allowed during connected support events subject to service, SOC, and path constraints.

The expert-fuzzy controller uses the same structure as §6.2 with engineering-selected base weights {PV→EV 0.12, Grid→EV 0.08, SC→EV 0.06, PV→SC 0.10, PV→Grid 0.08}, gains {PV→EV 1.35, Grid→EV 1.00, SC→EV 1.05, PV→SC 1.25, PV→Grid 0.85, Grid-support 1.00} and SC charge target 45%.

The expert-fuzzy parameters are not fitted to the reported WOA result. They are fixed engineering-selected weights chosen before the optimization run to express the same qualitative dispatch priorities as the rule base: photovoltaic power is preferred for electric-vehicle service when available, the grid is used for residual electric-vehicle demand when connected and permitted by the grid-quality constraints, supercapacitor support is increased during weak-grid periods, photovoltaic surplus is preferentially absorbed by the supercapacitor, and photovoltaic-to-grid export remains a deterministic residual-routing path subject to quality-dependent derating. All expert-fuzzy gains remain within the same search ranges later used by WOA, but they are not iteratively tuned. To reduce comparison bias, the three controllers are evaluated on the same nominal stress day and on identical Monte Carlo perturbation seeds. These shared nominal and stochastic cases provide a consistent basis for interpreting the baseline comparison.

6.2 Whale Optimization Algorithm-tuned fuzzy-weighted energy management system

The EMS uses a fuzzy-weighted continuous routing structure based on fuzzy-set theory [22, 23]. Membership grades for PV ratio, grid quality, EV request, SC SOC, and support request activate routing rules; the outputs are normalized into port-to-port shares using Eq. (7), then constrained by outage blocking, SOC limits, and path-capacity checks. This continuous supervisory EMS formulation is also consistent with related fuzzy EMS designs for grid-connected DC microgrids [24]. Figure 4 shows the membership functions.

Table 4 summarizes the fuzzy rule base. For reproducibility, the fuzzy EMS is implemented as a Mamdani-type inference system. At each 60 s supervisory time step, the normalized PV availability, grid-quality index, EV charging request, SC SOC, and grid-support request are evaluated through the membership functions in Figure 4 and the rules in Table 4. Rule firing strengths are computed using the minimum operator for antecedent conjunction, and the activated rule outputs are aggregated using the maximum operator. The crisp outputs are obtained using centroid defuzzification. These outputs are interpreted as continuous power-sharing tendencies rather than direct switching commands; they are normalized into the port-to-port routing shares of Eq. (7), after which outage blocking, SOC bounds, path-capacity limits, and no-simultaneous-charge/discharge constraints are enforced.

Table 4. Fuzzy-weighted routing rule base used by the supervisory energy management system (EMS)

Table 5 lists the WOA-tuned parameters. WOA is selected because its encircling and spiral-search operators support convergence and reduce premature local trapping in continuous routing-weight problems [25]. Search bounds follow station ratings: base weights [0.02, 0.50], gains [0.10, 3.00], and SC charge target [20%, 80%].

The PV-to-SC surplus-charging gain is fixed at 1.25 throughout the energy management process and is therefore not included in the WOA search vector as an optimization variable. This fixed setting ensures that the PV-to-SC surplus-charging gain remains constant during the WOA-based optimization procedure. In addition, PV-to-Grid export is handled as a deterministic residual-routing rule after the EV charging and SC charging priorities have been satisfied, rather than being represented or adjusted as a WOA-tuned fuzzy weight. Accordingly, the PV-to-Grid export process follows the predefined priority-based energy-routing logic and does not introduce an additional decision variable into the WOA optimization framework.

Figure 5 shows how PV ratio and grid quality shape the main EV-supply shares under high EV demand. Figure 6 summarizes WOA tuning. Thirty agents represent eight-dimensional fuzzy output vectors. Each candidate is evaluated through a 24 h EMS simulation, then updated by encircling, random-search or spiral operators for 100 iterations [25]. The best vector is used in the final WOA-tuned simulation.

Figure 5. Fuzzy routing surfaces for photovoltaic (PV)-to-EV, grid-to-EV, and supercapacitor (SC)-to-EV shares under high electric-vehicle (EV) requests

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Figure 6. Flowchart of the Whale Optimization Algorithm (WOA) tuning procedure for the proposed fuzzy management system (EMS)

The service-priority tuning objective is given in Eq. (11).

$\begin{gathered}J=4.00 \overline{\mathrm{E}}_{\text {unserved}}+5.50(1-S R)+ \\ 0.45 \overline{\mathrm{E}}_G+0.35 \overline{\mathrm{E}}_{\text {curt}}-0.25 R_{\text {weak}}-0.002 \\ \min \left(E_{V 2 G}, 30\right)+0.60 P_{S C, \text { low}}+0.60 P_{S C, \text { high}}+10.00 \\ N_{\text {viol}}+0.20 P_{\text {hal}}\end{gathered}$          (11)

where, $J$ is the WOA objective function, $\overline{\mathrm{E}}_{\text {unserved}}$ is the normalized unserved EV energy, $S R$ is the service-completion ratio, $\overline{\mathrm{E}}_G$ is the normalized grid-import energy, $\overline{\mathrm{E}}_{\text {curt}}$ is the normalized residual photovoltaic curtailment, $R_{\text {weak}}$ is the normalized weak-grid support reward, $E_{V 2 G}$ is the vehicle-togrid support energy, $P_{S C, \text {low}}$ and $P_{S C, \text {high}}$ are the supercapacitor SOC-bound penalties, $N_{\text {viol}}$ is the number of failed routing or feasibility checks, and $P_{\text {bal}}$ is the normalized power-balance residual.

Table 6 gives the objective weights and normalizations. Service completion and unserved energy dominate; grid import, residual PV curtailment after conditional export, weak-grid support, V2G, SOC penalties, feasibility penalties, and residual terms are secondary.

Energy terms are normalized as in Table 6; N_viol counts failed routing checks. Figure 7 shows the best-so-far WOA objective.

After adding the conditional photovoltaic-to-grid export path, the WOA tuning was rerun using the same settings: 30 search agents, 100 iterations, and random seed 2026. The revised best objective value was 5.5562. The selected controller was then evaluated under the nominal stress day and the same Monte Carlo perturbation framework. Photovoltaic-to-grid export is handled as a deterministic residual-routing rule after electric-vehicle charging and supercapacitor charging priorities, so it does not override the service-priority objective.

Table 6. Objective-function weights used for Whale Optimization Algorithm (WOA) tuning

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Figure 7. Best-so-far Whale Optimization Algorithm (WOA) objective value for the selected fuzzy controller

Table 7 reports the main numerical results for the nominal WOA-tuned run.

The WOA-tuned EMS completes 8/10 electric-vehicle targets versus 7/10 for both baselines (+14.3%). Table 8 gives the exact controller-comparison values and units, while Figure 8 presents a normalized dimensionless comparison to avoid plotting mixed physical units on one axis.

Photovoltaic export is treated as a residual energy-accounting path rather than the primary optimization target. Therefore, higher exported energy or lower residual curtailment does not necessarily indicate better EMS performance. The proposed WOA-tuned controller prioritizes electric-vehicle service completion, unserved-energy reduction, and feasibility under weak-grid constraints.

Table 7. Nominal Whale Optimization Algorithm (WOA)-tuned energy management system (EMS) results

Table 8. Controller comparison under the nominal stress day

The WOA-tuned EMS is not intended to maximize every individual energy-accounting metric. Its tuning objective is service-priority based, giving dominant weight to electric-vehicle target completion and unserved-energy reduction, while photovoltaic export and residual curtailment are treated as secondary terms. Therefore, the rule-based controller can show higher photovoltaic export and lower residual curtailment in the nominal day, whereas the WOA-tuned controller gives the best primary service result by completing 8/10 electric-vehicle targets with all feasibility checks satisfied.

Figure 8. Normalized controller comparison under the nominal stress day

Each metric is normalized by the maximum value among the compared controllers to avoid mixing physical units on a common axis. Numerical values and units are reported in Table 8. For cost-type metrics such as unserved energy and residual photovoltaic curtailment, lower normalized values indicate better performance.

WOA records lower V2G energy because the objective prioritizes EV target completion. It preserves EV energy for service while still delivering 3.03 kWh of V2G support.

V2G operation is deliberately constrained to avoid overstating the available support. Only the EVs marked as V2G-capable in Table 3 may discharge, and discharge is allowed only when the grid is connected, a support request is active and no higher-priority charging demand is waiting. The supervisory model also enforces a 60% owner-reserve SOC, a 30 kW EV discharge limit and a 30 kW grid-support cap. Battery-degradation cost is not modeled; therefore, the V2G results should be interpreted as limited emergency support from eligible parked EVs rather than a full market-participation assessment.

Table 9 lists the main routed energy paths. The photovoltaic-energy accounting closes as follows: the stress-day available photovoltaic energy is 1006.36 kWh, of which 171.76 kWh is routed from photovoltaic generation to electric-vehicle charging, 32.39 kWh is routed from photovoltaic generation to supercapacitor charging and 288.00 kWh is exported to the grid under the conditional export rule. The remaining 514.21 kWh is residual photovoltaic curtailment after electric-vehicle charging, supercapacitor absorption and grid export. This residual is caused by the single active outlet, finite supercapacitor absorption, outage periods, weak-grid export blocking, and the grid-interface export limit.

Table 9. Daily port-to-port routed energy and peak path power

Figure 9 compares the initial, departure, and target SOC of each EV, clearly identifying the two underserved vehicles.

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Figure 9. Electric-vehicle (EV) service completion by initial state of charge (SOC), departure SOC and target SOC

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Figure 10. Supercapacitor (SC) state of charge (SOC) trajectory under Whale Optimization Algorithm (WOA)-tuned operation

Figure 10 shows the SC SOC trajectory. Total SC discharge is 44.95 kWh (39.33 kWh to EV and 5.62 kWh to grid support; Table 9), including 23.57 kWh during weak-grid intervals. SOC remains within 23.14–95.00%. The two underserved EVs arrive late in the evening during overlapping outage and high-demand intervals.

Table 14. Supercapacitor sensitivity under quality-derated photovoltaic-to-grid export

A 50 kWh supercapacitor sensitivity case was added to determine whether residual photovoltaic curtailment is mainly storage-limited or constrained by the combined charger/export bottleneck. The 30 kWh supercapacitor remains the main base configuration, while the 50 kWh case is used only as an engineering sensitivity. The 50 kWh case reduces unserved energy from 104.92 kWh to 97.14 kWh and residual photovoltaic curtailment from 514.21 kWh to 508.21 kWh, indicating that additional local buffering helps but the remaining curtailment is still dominated by the single-outlet and grid-interface bottleneck.

A seasonal photovoltaic sensitivity was also performed to determine whether the high residual curtailment is only a summer sizing artifact or whether the station remains stressed under low winter irradiation. The same WOA-tuned controller was used without winter retuning. As shown in Table 15, the January case reduces residual photovoltaic curtailment from 514.21 to 56.76 kWh because the available photovoltaic energy falls from 1006.36 to 442.80 kWh. However, the lower photovoltaic availability increases grid-to-electric-vehicle energy from 59.83 to 71.50 kWh and slightly increases unserved energy from 104.92 to 107.25 kWh, while the number of completed electric-vehicle targets remains 8/10. January is selected as the explicit representative month because it has the lowest monthly photovoltaic production in the PVGIS benchmark, while the interpretation is extended cautiously to the broader low-production period that includes January, February, November, and December. This confirms that the 150 kWp array is not reduced solely to improve summer curtailment; its rating supports service resilience during low-photovoltaic months and outage-constrained operation. The January representative sensitivity confirms that the 150 kWp photovoltaic rating should not be downsized solely to reduce summer residual curtailment. Although only January is explicitly simulated, it represents the low-photovoltaic production period that includes January, February, November, and December. Although the January case reduces residual photovoltaic curtailment because available solar energy is much lower, it also increases grid-to-electric-vehicle energy and slightly increases unserved energy under the same outage and demand conditions. Therefore, the selected photovoltaic rating is interpreted as a seasonal sizing trade-off between low-irradiance service resilience and summer surplus management.

Table 15. Seasonal photovoltaic (PV) sensitivity under summer and January availability