Hierarchical Volt-VAR Optimization Framework Considering Voltage Control of Smart Electric Vehicle Charging Stations Under Uncertainty

In the IEEE 33-node test feeder, Cases2-3 and 2-4 yield higher minimum and maximum voltage magnitudes than Cases1-1 and 1-2.

“In addition, note from Table 4 that Cases2-3 and 2-4 yield higher minimum and maximum voltage magnitudes than Cases1-1 and 1-2.”

In the CCO-based VVO approach, total active power loss increases as the probability level β increases.

“Another observation from Table 3 is that the CCO approach results in an increasing active power loss as the probability level β increases.”

The CCO-based VVO approach is robust against uncertainties in terms of total active power loss and voltage deviation.

“Simulation results demonstrate the effectiveness of the proposed DO-and CCO-based VVO methods integrated with optimized Q-V curves and the robustness of the CCO-based VVO approach against uncertainties in terms of total active power loss and voltage deviation.”

In Case2-1, the upper bound of SOC is larger than in Case2-2.

“Another observation from Fig. 12 is that the upper bound of SOC in Case2-1 is larger than in Case2-2.”

In the IEEE 33-node test feeder, Case2-1 (optimized Q-V curve, no PV/EV uncertainty, DO) yields 8.1861% less total active power loss than Case1-1 (fixed Q-V curve, no PV/EV uncertainty, DO).

“Note from Table 3 that Case2-1 yields less active power loss than Case1-1; the relative reduction of the active power loss in Case2-1 to Case1-1 is 8.1861%.”

In the IEEE 33-node test feeder, the OLTC tap positions for Cases2-1 and 2-2 (-3 ≤ Tap_OLTC_t ≤ 5) fluctuate more than for Cases1-1 and 1-2 (-4 ≤ Tap_OLTC_t ≤ 8).

“We can see from the comparison of Figs. 7 and 8 that, in general, the OLTC tap positions for Cases2-1 and 2-2 (-3 ≤ T ap OLTC t ≤ 5) fluctuate more than for Cases1-1 and 1-2 (-4 ≤ T ap OLTC t ≤ 8).”

In the IEEE 33-node test feeder, the minimum and maximum voltage magnitudes for Cases2-1 and 2-2 using optimized Q-V curves are higher than those for Cases1-1 and 1-2 using fixed Q-V curves.

“From this table, we verify that the minimum and maximum voltage magnitudes for Cases2-1 and 2-2 using the optimized Q-V curves are higher than the minimum and maximum voltage magnitudes for Cases1-1 and 1-2 using the fixed Q-V curves.”

After 5:00 a.m., the SOCs gradually increase as the EVCS load and PV generation output increase.

“After 5:00 a.m., the SOCs gradually increase as the EVCS load and PV generation output increase as shown in Fig. 4.”

In Cases2-1 and 2-2, the SOC of ESS23 remains at its minimum limit during the time period [12:00 a.m., 5:00 a.m.].

“Note from this figure that the values of the SOC remain at their minimum limit during the time period [12:00 a.m., 5:00 a.m.]”

In Case2-2, an increasing probability level β results in a decreasing upper bound of the SOC.

“In addition, in Case2-2, note that an increasing probability level β results in a decreasing upper bound of the SOC because the limits of chance constraints associated with the SOC are further constricted.”

The proposed DO- and CCO-based VVO methods integrated with optimized Q-V curves are effective.

“Simulation results demonstrate the effectiveness of the proposed DO-and CCO-based VVO methods integrated with optimized Q-V curves and the robustness of the CCO-based VVO approach against uncertainties in terms of total active power loss and voltage deviation.”

In Case2-2 with β = 0.85, the smart inverters inject more reactive power into the grid than the smart inverters in Case1-2.

“Note from this figure that the smart inverters in Case2-2 inject more reactive power into the grid than the smart inverters in Case1-2.”

The computation time of the proposed approach increases as the size of the test system becomes larger (from IEEE 33-node to IEEE 69-node).

“As expected, this table shows that the computation time increases as the size of the test system becomes larger.”

In Case2-4, in general, the number of charging EVs and their charging power increase as the probability level β increases.

“Note from Case2-4 in Fig. 13 that, in general, the number of charging EVs and their charging power increase as the probability level β increases.”

In Case2-4, the dead bands for all Q-V curves are shifted to a voltage higher than 1 p.u.

“A similar phenomenon shown in Fig. 5, in which only the PV uncertainty is considered, is observed in Fig. 14, which considers both PV and EV uncertainties; the dead bands for all Q-V curves are shifted to a voltage higher than 1 p.u.”

In the IEEE 69-node test feeder, Case2-4 yields less active power loss than Case1-4 under different β.

“Similar to the result in the IEEE 33-node test feeder, we verify from this table that Case2-4 yields less active power loss than Case 1-4 under different β.”

The piecewise Q-V curve can be embedded as linear constraints into the VVO problem at the global control stage using the approach reported in [33].

“Using the approach reported in [33], the aforementioned piecewise Q-V curve can be embedded as linear constraints into the VVO problem at the global control stage.”

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Fluctuations in DER power outputs, such as intermittent PV generation and uncertain EV charging behavior, may lead to unstable grid conditions and voltage violations owing to reverse power flow.

“However, fluctuations in the DER power outputs (e.g., intermittent PV generation output due to cloud movements and uncertain charging behavior of EV users) may lead to unstable grid conditions, thereby yielding voltage violations owing to reverse power flow [9], [10].”

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• cites [10]Not matched

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The decreasing upper bound of SOC with increasing β in Case2-2 is because the limits of chance constraints associated with the SOC are further constricted.

“because the limits of chance constraints associated with the SOC are further constricted.”

The nonlinear constraint (30) can be linearized using a binary expansion method along with auxiliary integer variables.

“However, (30) is still a nonlinear constraint because it includes the terms of the multiplication of two variables, α q i,t,3 V q i,3 and α q i,t,4 V q i,4 .To linearize the nonlinear constraint, a binary expansion method along with auxiliary integer variables, ϕ q,min i and ϕ q,max i , is used as follows [37]:”

• cites [37]Not matched

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The aforementioned optimization-based VVO methods may not conduct optimal voltage regulation when unexpected and sudden local voltage changes occur due to intermittent DER power output because OLTCs and CBs are not sufficiently fast.

“The aforementioned optimization-based VVO methods may not conduct optimal voltage regulation in situations where unexpected and sudden local voltage changes occur due to intermittent DER power output because OLTCs and CBs are not sufficiently fast to regulate voltage.”

DER inverters using the Q-V curve absorb or inject reactive power based on voltage measurements to rapidly mitigate local voltage violations.

“Using the Volt-VAR curve [29], namely the Q-V curve, which is one of the droop control curves, DER inverters absorb or inject reactive power of the DER from or to the grid based on their voltage measurements to rapidly mitigate local voltage violations.”

• cites [29]Not matched

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The reason EVCS23's smart inverter supplies reactive power without absorbing is that the ESS in EVCS23 reduces the active power consumption of EVCS23 through the discharging process, thereby increasing the capability of the reactive power support for the smart inverter of EVCS23.

“This is because the ESS in EVCS23 reduces the active power consumption of EVCS23 through the discharging process, thereby increasing the capability of the reactive power support for the smart inverter of the EVCS23.”

VVO using the optimized Q-V curve can further reduce active power loss compared to VVO using the Q-V curve with fixed parameters.

“The aforementioned observations demonstrate that VVO using the optimized Q-V curve can further reduce the active power loss compared to VVO using the Q-V curve with fixed parameters.”

The prediction error of PV generation output may result in an incorrect SOC level of the ESS in the EVCS because the PV generation output is preferentially charged to the ESS.

“The prediction error of the generation output of the PV system installed at the smart EVCS may result in an incorrect SOC level of the ESS in the EVCS because the PV generation output is preferentially charged to the ESS.”

• AssumptionRests on an assumption: PV generation output is preferentially charged to the ESS in the EVCS.

The nonlinear constraint for reactive power capability of EVCS can be linearized using the polygon-based realization method.

“In contrast to the linear constraint (20) of the reactive power capacity for the PV system, (23) defines a nonlinear constraint with two quadratic decision variables.The nonlinear constraint can be linearized using the polygon-based realization method [36] as follows.”

• cites [36]Not matched

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Centralized VVO integrated with smart inverter-based local voltage control allows smart inverters to rapidly inject or absorb reactive power using local droop control to mitigate local voltage violations.

“Furthermore, the centralized VVO is integrated with smart inverter-based local voltage control for smart inverters to rapidly inject or absorb the reactive power of DERs by using their local droop control function to mitigate local voltage violations [13].”

• cites [13]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The optimized Q-V curves with higher dead bands than the fixed Q-V curves enable the smart inverters to further supply reactive power to the grid to maintain a stable grid operation.

“This demonstrates that the optimized Q-V curves with higher dead bands than the fixed Q-V curves enable the smart inverters to further supply reactive power to the grid to maintain a stable grid operation.”

A more restricted charging capability of the ESS owing to a higher β leads to an increase in the active power loss.

“As shown in the results shown in Table 3, a more restricted charging capability of the ESS owing to a higher β leads to an increase in the active power loss.”

The increase in number of charging EVs and charging power with increasing β is due to the fact that an increasing β leads to a larger number of realizations for the EV driving patterns, thereby providing the EVCS with the capability of flexible adaptation to the EV charging demand.

“This phenomenon is due to the fact that an increasing β leads to a larger number of realizations for the EV driving patterns, thereby providing the EVCS with the capability of flexible adaptation to the EV charging demand.”

The robustness of the CCO-based VVO problem against uncertainties in PV generation outputs and driving patterns of EV users was verified with varying probability levels of chance constraints.

“Furthermore, the robustness of the CCO-based VVO problem against uncertainties in PV generation outputs and driving patterns of EV users was verified with varying probability levels of chance constraints.”

A higher charging power from the EVCS owing to a higher β yields a greater active power loss.

“A higher charging power from the EVCS owing to a higher β yields a greater active power loss, which is verified in Cases2-3 and 2-4 in Table 3.”

The optimized Q-V curves under PV uncertainty and/or EV uncertainty can successfully reduce the total active power loss at the expense of increasing voltage magnitudes.

“Based on the aforementioned observations, we conclude that the optimized Q-V curves under PV uncertainty and/or EV uncertainty can successfully reduce the total active power loss at the expense of increasing voltage magnitudes.”

The simulation results show that, compared to the VVO framework with fixed Q-V curves, the proposed framework based on the optimized Q-V curves can successfully reduce the total active power loss and voltage deviation.

“The simulation results show that, compared to the VVO framework with fixed Q-V curves, the proposed framework based on the optimized Q-V curves can successfully reduce the total active power loss and voltage deviation.”

This study proposes a hierarchical framework to conduct the VVO process that involves global and local voltage controls of smart EVCSs integrated with PV systems and ESSs.

“This study proposes a hierarchical framework to conduct the VVO process that involves global and local voltage controls of smart EVCSs integrated with PV systems and ESSs.”

To incorporate the uncertainties in PV generation outputs and driving patterns of EV users into the proposed framework, the DO-based VVO problem at the global control stage was reformulated into the CCO-based VVO problem with probability constraints.

“To incorporate the uncertainties in PV generation outputs and driving patterns of EV users into the proposed framework, the DO-based VVO problem at the global control stage was reformulated into the CCO-based VVO problem with probability constraints.”

At the local control stage, the Q-V curves optimized at the global control stage are exploited by the smart inverters to rapidly mitigate local voltage violations owing to intermittent PV generation output.

“At the local control stage, the Q-V curves optimized at the global control stage are exploited by the smart inverters to rapidly mitigate local voltage violations owing to intermittent PV generation output.”