Analyzing and Mitigating the Impacts of Integrating Fast-Charging Stations on the Power Quality in Electric Power Distribution Systems

Abstract

The research presented in this paper focuses on the impacts of fast-charging stations on three power quality phenomena, namely voltage magnitude variations, voltage unbalance, and voltage fluctuation. The Markov Chain Monte Carlo is proposed to estimate the energy requirements of each fast-charging station when it is utilized to charge electric vehicles, considering their sto-chastic parameters such as battery capacities, state-of-charge levels at time of arrivals, and time of arrivals at charging stations. Two charging methods are implemented in this work: charging with an estimated output power and charging with an actual output power. The results reveal that the impact of fast-charging stations on voltage fluctuation by either of these charging methods can lead to light flickers. When the estimated output power is utilized, the light flicker is higher compared to when the actual output power is utilized; the proposed mitigation method is to integrate distribution static compensators, which can effectively eliminate the light flickers, whether the output power of the fast-charging station is estimated or actual. Not only will the system’s power quality be improved by installing distribution static compensators, but also the electricity consumers will not be annoyed by the light flicker, even when the rated power of the fast-charging stations is increased; this can positively lead to a reduction in charging time and an increase in customer satisfaction with electric vehicles, lending them to be more widely adopted.

1. Introduction

1.1. Background

A fast-charging station (FCS) is utilized to charge specific types of loads, which are electric vehicles (EVs). Although these EVs are represented in the electric system as constant, real, and reactive power loads, they may require different amounts of energy for each charge. The amount of energy is determined by many variables, such as the rated power of the FCS, charging time, battery state-of-charge (SOC), and battery capacity. As a consequence, the required energy used by the FCS on the electric distribution network is continuously varied, as a function of the parameters mentioned above. The AC power systems change to regulate variations in these types of loads. In accordance with the load changes, the response of the power system results in voltage variations [1]. The voltage variations can be characterized by their magnitude as undervoltage, overvoltage, and/or voltage fluctuation and light flickers.

1.2. Previous Work

Electric vehicles battery packs can be charged with either an on-board or off-board charger. The former method uses low charging power [2], while the latter method uses high charging power [3]. From the FSC point of view, transportation systems and electric power systems are influenced by both the driving behavior and charging behavior of electric vehicles [4]. Different parameters, as shown in Figure 1, may be utilized to model these two patterns, leading to shape the FCS demand profile, which, in turn, may adversely affect several power quality phenomena mentioned above. These parameters include the arrival time at the FCS, the battery capacities of EVs, their daily distance traveled, and the output power of the FCS.

In [5], an off-grid photovoltaic system has been proposed, aiming to supply the daily energy required for recharging a fully EV but with low rated power. The work in [6] uses FCSs rated at 50 kW to highlight their impact on the distribution system when different penetration levels of EVs are utilized. The findings show that voltage deviation will increase as the penetration level of EVs is increased. Moreover, the work in [7,8,9] investigates the effect of EV charging stations on the voltage deviation. However, these studies do not consider the voltage unbalance or voltage fluctuation and light flicker. The work in [10] aims to analyze the power quality issues of FCS. However, voltage fluctuation was not considered by the study. The work in [11] proposed a distributed control strategy to evaluate the impact of integration large-scale EV fleets on grid congestion. Although the results show that the proposed control method is able to minimize the aggregated charging cost and battery degradation, grid voltage quality has not been investigated by the proposed approach. In [12], a fast-charging DC has been proposed. The proposed model of the fast charger operates near to the unity power factor and, thus, minimizes the harmonics of the line current. Besides, the control mechanism is effective in stabilizing the DC bus voltage. The impact of the fast charger on voltage fluctuation and light flicker, however, has not been evaluated. The work in [13] does not take into consideration the daily traveling distance by EVs. The authors in [14,15,16,17] only consider EVs with small battery capacities. The study in [18] assumes a fixed SOC of all EVs, equal to 25% of their capacity. Previous works address the output power of the FCS using two approaches. The first approach assumes that the output power of FCS is constant, does not change over time, and always equals the rated power of the FCS. This method is utilized by [6,19,20,21], where the used rated powers are 50 kW, 50 kW, 120 kW, and 350 kW, respectively. This method is proposed when it is difficult to obtain a real FCS profile. The second approach involves changing the output power of the FCS over time, depending on the change of EV SOC. The profile is usually extracted from a fast charger fact sheet as in [22] or obtained experimentally as in [15].

1.3. Research Gaps

The aim of the work in this paper is to fill the research gaps in the previous works, which can be summarized as follows:

• None of the reported works have quantified the impact of FCS on the voltage quality such as voltage variation, voltage unbalance, and voltage fluctuation and light flicker, to mitigate that impact.
• Most of the relevant works assume the output power of the FCS is constant without justification and do not consider the power variation over time when the EV SOC is increased.
• Most of the previous works have quantified the impact of the FCS on an hourly basis. Vehicles with small battery capacities that take a couple of minutes to recharge may not be considered, which indicates that the impact may not be quantified properly.

1.4. Contribution

The aim of the conducted research in this paper is to quantify and mitigate the im-pact of FCSs on the voltage quality in the distribution systems. The list of key contributions are as follows:

• Development and modification of the test system to encompass fast-charging stations, commercial loads, and residential houses. Different scenarios were applied to quantify and mitigate the impact of the FCSs.
• Proposal of a probabilistic models for two methods of charging: when the power pro-file of FCS is estimated and when the power profile of FCS is real.
• Two voltage magnitude variations, namely undervoltage and overvoltage, as well as voltage unbalance and voltage fluctuation, are analyzed to quantify the impact of fast-charging stations.
• Introducing and comparing different mitigation technologies and selecting the best mitigation devices based on defined criteria, to improve the voltage quality.

2. Power Quality Problems of Integrating FCS

2.1. Voltage Magnitude Variations

Voltage magnitude variation is identified as a decrease or increase in the square root of the arithmetic mean of the squares of the instantaneous voltage values, over a specific period of time and a specific bandwidth. The variation is called undervoltage or overvoltage when the root mean square (rms) deviates, by a specified value assigned by the relevant PQ standards, from the nominal voltage, which is commonly defined to be close to the system’s voltage class. The American National Standard (ANSI C84.1) [23] is adopted in this study to analyze the voltage variation.

2.2. Voltage Unbalance

Voltage unbalance (VU) occurs in a polyphase system when either are not equal in their magnitudes or are not equal in their angles, for each consecutive line voltages [19]. The polyphase electric systems should be designed and operated to maintain the maximum VU to 3%, as clearly specified in ANSI. The VU can be calculated as a ratio between the maximum deviation of the phase voltages from their average divided by their average.

2.3. Voltage Fluctuation and Light Flicker

Voltage may fluctuate because of load variations. When the fluctuation occurs in the system voltage, it may lead to light intensity fluctuations. The variations in light (e.g., light flicker) can be characterized by the change in the amplitude and its frequency of occurrence [24]. This may cause irritation to the eye, causing what’s known as photosensitive epilepsy [25]. Potential risk assessment and biological effects of the light flickers are discussed in [26]. The IEEE 1453 standard is utilized to quantify the flicker. The IEEE 1453 standard proposes a method to quantify the light flicker, where the voltage fluctuates randomly with varying frequencies of occurrence [27]. The IEEE standard 1453 adopts the IEC 61000–4–15 Standard flicker meter. The IEC flicker meter aims to model the human visual system and quantify its response to the light flicker by applying statistical analysis to calculate the Percentile Short Term flicker severity index (P_ST) and the Percentile Long Term flicker severity index (P_LT). P_ST is computed using several supporting values over 10-min interval as in Equation (1) [28].

$${\mathrm{P}}_{\mathrm{ST}}=\sqrt{\left(0.0314\times {\mathrm{P}}_{99.9}\right)+\left(0.0525\times {\mathrm{P}}_{99}\right)+\left(0.0657\times {\mathrm{P}}_{97}\right)+\left(0.28\times {\mathrm{P}}_{90}\right)+\left(0.08\times {\mathrm{P}}_{50}\right)}$$

(1)

where P_99.9, P₉₉, P₉₇, P₉₀, and P₅₀ symbolize to the flicker levels not exceeded by 99.9%, 99%, 97%, 90%, and 50%, respectively, in the observation period and can be calculated based on the smoothed assessment as follows:

$${\mathrm{P}}_{99}=\frac{\left({\mathrm{P}}_{99.3}+{\mathrm{P}}_{99}+{\mathrm{P}}_{98.5}\right)}{3}$$

(2)

$${\mathrm{P}}_{97}=\frac{\left({\mathrm{P}}_{97.8}+{\mathrm{P}}_{97}+{\mathrm{P}}_{96}\right)}{3}$$

(3)

$${\mathrm{P}}_{90}=\frac{\left({\mathrm{P}}_{94}+{\mathrm{P}}_{92}+{\mathrm{P}}_{90}+{\mathrm{P}}_{87}+{\mathrm{P}}_{83}\right)}{3}$$

(4)

$${\mathrm{P}}_{50}=\frac{\left({\mathrm{P}}_{70}+{\mathrm{P}}_{50}+{\mathrm{P}}_{20}\right)}{3}$$

(5)

The P_ST is adequate to assess the voltage fluctuation produced by an individual source characterized by short duty-cycle. For evaluating the disturbances caused by loads with a long duty-cycle or by combined sources randomly operating, the P_LT is adopted in the standard and calculated from 12 consecutive values of P_ST (over two-hours), as in Equation (6).

$${\mathrm{P}}_{\mathrm{LT}}=\sqrt[3]{\frac{1}{12}\left({\displaystyle \sum }_{\mathrm{a}=1}^{12}{\mathrm{P}}_{\mathrm{ST}}{\left(\mathrm{a}\right)}^3\right)}$$

(6)

The compatibility level for low voltage (LV) is defined in [28] as “the specified disturbance level used as a reference level in a specified environment for coordination in the setting of emission and immunity limits. This is normally taken as the level of PST or PLT above which LV customers are likely to perceive flicker”. The compatibility levels for PST and PLT are 1.0 and 0.8 respectively [28].

3. Power Quality Mitigation

3.1. Comparison of Voltage Fluctuation Technologies

This section attempts to quantify and compare the costs of the various mitigation devices such as [29,30,31,32]: Thyristor Switched Capacitors (TSC), Fixed Capacitors/Thyristor Controlled Reactors (FC/TCR), Distribution Static Compensator (DSTATCOM), Dynamic Voltage Restorer (DVR), Unified Power Quality Conditioner (UPQC), and Fixed Series Capacitor (FSC). For these technologies, there will be two costs involved. The first is the initial purchase price of the equipment, while the second is the maintenance costs associated with the selected equipment. The cost of power quality mitigation devices is determined based on their power rating, such as USD/kVar [33]. This cost represents a rough estimate of the equipment; however, the total system cost may contain additional elements [33]. The total annual equivalent cost of installing a voltage flicker mitigation device can be found as:

$${\mathsf{\Lambda }}^{\mathrm{y}}={ℂ}^{\mathrm{y}}+{\mathrm{ℳ}}^{\mathrm{y}}$$

(7)

where ${\mathsf{\Lambda }}^{\mathrm{y}}$ is the total annual equivalent cost, USD/year, ${ℂ}^{\mathrm{y}}$ is the annual equivalent cost of capital invested, USD/year, and ${\mathrm{ℳ}}^{\mathrm{y}}$ is the annual equivalent cost of maintenance, USD/year. The annual equivalent capital cost is called capital recovery cost, ${ℂ}^{\mathrm{y}}$.

$${ℂ}^{\mathrm{y}}=\mathsf{\zeta }·{\mathsf{\mu }}^{\prime }-𝒮·{\ell }^{\prime }$$

(8)

$${\mathsf{\mu }}^{\prime }=\left(\frac{\mathsf{\lambda }·{\left(\mathsf{\lambda }+1\right)}^{\mathsf{\eta }}}{{\left(\mathsf{\lambda }+1\right)}^{\mathsf{\eta }}-1}\right)$$

(9)

$${\ell }^{\prime }=\left(\frac{\mathsf{\lambda }}{{\left(\mathsf{\lambda }+1\right)}^{\mathsf{\eta }}-1}\right)$$

(10)

$$\mathsf{\zeta }=\mathsf{\Gamma }·\mathsf{\phi }$$

(11)

$$𝒮=\mathsf{\Omega }·\mathsf{\phi }$$

(12)

where $\mathsf{\zeta }$ is the first cost of installed flicker mitigation device (USD), $𝒮$ is the estimated salvage value at the end of the device useful life (USD), ${\mathsf{\mu }}^{\prime }$ is the capital recovery factor, ${\ell }^{\prime }$ is the single-payment discount factor, $\mathsf{\lambda }$ is the fixed charge rate (%), $\mathsf{\eta }$ is the useful life in years (flicker mitigation device lifetime) (years), $\mathsf{\Gamma }$ is the cost per unit of installed flicker mitigation device (USD/kVAr), $\mathsf{\Omega }$ is the salvage value per kVAr at the end of η (USD/kVAr), and $\mathsf{\phi }$ is the operating range of the flicker mitigation device (MVAr). The cost of installation ($\mathsf{\Gamma }$) of different flicker mitigation equipment is given as follows [34,35,36,37,38].

$${\mathsf{\Gamma }}_{\mathrm{UPQC}}=0.0003·{\mathsf{\phi }}_{\mathrm{UPQC}}^2-0.2691·{\mathsf{\phi }}_{\mathrm{UPQC}}+188.2$$

(13)

$${\mathsf{\Gamma }}_{\mathrm{DSTATCOM}}=0.0002478·{\mathsf{\phi }}_{\mathrm{DSTATCOM}}^2-0.2261·{\mathsf{\phi }}_{\mathrm{DSTATCOM}}+60$$

(14)

$${\mathsf{\Gamma }}_{\mathrm{TSC}}=0.0003·{\mathsf{\phi }}_{\mathrm{TSC}}^2-0.305·{\mathsf{\phi }}_{\mathrm{TSC}}+127.4$$

(15)

$${\mathsf{\Gamma }}_{\mathrm{FC}-\mathrm{TCR}}=0.0003·{\mathsf{\phi }}_{\mathrm{TSC}}^2-0.305·{\mathsf{\phi }}_{\mathrm{TSC}}+127.4$$

(16)

$${\mathsf{\Gamma }}_{\mathrm{DVR}}=0.0015·{\mathsf{\phi }}_{\mathrm{DVR}}^2-0.713·{\mathsf{\phi }}_{\mathrm{DVR}}+153.8$$

(17)

$${\mathsf{\Gamma }}_{\mathrm{FSC}}=0.000541·{\mathsf{\phi }}_{\mathrm{FSC}}^2-0.3902·{\mathsf{\phi }}_{\mathrm{FSC}}+90.8$$

(18)

where,

$${\mathsf{\Gamma }}_{\mathrm{UPQC}}:$$	the per unit cost of the Unified Power Quality Conditioner, (USD/kVAr)
$${\mathsf{\Gamma }}_{\mathrm{DSTATCOM}}:$$	the per unit cost of the Distribution Static Compensator, (USD/kVAr)
$${\mathsf{\Gamma }}_{\mathrm{TSC}}:$$	the per unit cost of the Thyristor Switched Capacitor, (USD/kVAr)
$${\mathsf{\Gamma }}_{\mathrm{FC}-\mathrm{TCR}}:$$	the per unit cost of the Fixed Capacitors/Thyristor Controlled Reactors, (USD/kVAr)
$${\mathsf{\Gamma }}_{\mathrm{DVR}}:$$	the per unit cost of the Dynamic Voltage Restorer, (USD/kVAr)
$${\mathsf{\Gamma }}_{\mathrm{FCS}}:$$	the per unit cost of the Fixed Series Capacitor, (USD/kVAr)
$${\mathsf{\phi }}_{\mathrm{UPQC}}:$$	the operating range of the Unified Power Quality Conditioner, MVAr
$${\mathsf{\phi }}_{\mathrm{DSTATCOM}}:$$	the operating range of the Distribution Static Compensator, MVAr
$${\mathsf{\phi }}_{\mathrm{TSC}}:$$	the operating range of the Thyristor Switched Capacitor, MVAr
$${\mathsf{\phi }}_{\mathrm{FCTCR}}:$$	the operating range of the Fixed Capacitors/Thyristor Controlled Reactors, MVAr
$${\mathsf{\phi }}_{\mathrm{DVR}}:$$	the operating range of the Dynamic Voltage Restorer, MVAr
$${\mathsf{\phi }}_{\mathrm{FSC}}:$$	the operating range of the Fixed Series Capacitor, MVAr

The annual equivalent cost to maintain the flicker mitigation device (${\mathrm{ℳ}}^{\mathrm{y}}$) is calculated per kVAr per year, as in Equation (19):

$${\mathrm{ℳ}}^{\mathrm{y}}=\mathsf{\gamma }·\mathsf{\Gamma }·\mathsf{\phi }·{\mathsf{\mu }}^{\prime }$$

(19)

where, $\mathsf{\gamma }$ is the maintenance cost in percent of the first cost, (%). $\mathsf{\lambda }$ is the fixed interest rate, at 6%, and $\mathsf{\eta }$ is the lifetime of the project, 10 years. If the salvage value is assumed to be negligible, the different mitigation methods are calculated, as in

Table 1. Maintenance cost for flicker mitigation devices.

Mitigation Device	% of the First Cost	The Source
${\mathrm{ℳ}}_{\mathrm{UPQC}}^{\mathrm{y}}$	10	[39]
${\mathrm{ℳ}}_{\mathrm{DSTATCOM}}^{\mathrm{y}}$	5	[40]
${\mathrm{ℳ}}_{\mathrm{TSC}}^{\mathrm{y}}$	10	[41]
${\mathrm{ℳ}}_{\mathrm{FC}-\mathrm{TCR}}^{\mathrm{y}}$	10	[41]
${\mathrm{ℳ}}_{\mathrm{DVR}}^{\mathrm{y}}$	5	[42]
${\mathrm{ℳ}}_{\mathrm{FSC}}^{\mathrm{y}}$	1	[43]

.

3.2. Comparison of Costs of Flicker Mitigation Technologies

As per the general utility practice, the annual fixed charge rate is estimated based on the summation of the following costs: costs of capital, depreciation, taxes, insurance, and operation and maintenance expenses. However, only the capital and maintenance costs are considered in calculating the ${\mathsf{\Lambda }}^y$ in Table 1. Moreover, the salvage value is assumed to be zero at the end of the project lifetime.

Table 2. Cost of voltage fluctuation mitigating devices.

	Mitigation Techniques
Parameters	UPQC	DSTATCOM	TSC	FC-TCR	DVR	FSC
$\mathrm{Lifetime}\mathsf{\eta }$, (years)	20	20	20	20	20	20
$\mathrm{Charge}\mathrm{rate}\mathsf{\lambda }$, (%)	6	6	6	6	6	6
$\mathrm{Maintenance}\cos \mathrm{t}\mathrm{in}\%\mathrm{of}\mathrm{first}\mathrm{cost}\mathsf{\gamma }$, (%)	10	5	10	10	5	1
$\mathrm{Reactive}\mathrm{power}\mathrm{range}\mathsf{\phi }$, (MVAr)	2	2	2	2	2	2
$\mathrm{The}\mathrm{per}\mathrm{kVAr}\mathrm{cost}\mathsf{\Gamma }$, (USD/kVAr)	187.66	79.55	126.8	126.8	153.3	89.97
$\mathrm{Cost}\mathrm{of}\mathrm{installation},\mathsf{\zeta },\left(\mathrm{USD}\right)$	375,320	159,100	253,600	253,600	306,600	179,940
$\mathrm{capital}\mathrm{recovery}\mathrm{factor},{\mathsf{\mu }}^{\prime }$	0.0872	0.0872	0.0872	0.0872	0.0872	0.0872
$\mathrm{Sin}\mathrm{gle}-\mathrm{payment}\mathrm{discount}\mathrm{factor},{\ell }^{\prime }$	0.0272	0.0272	0.0272	0.0272	0.0272	0.0272
$\mathrm{Capital}\mathrm{recovery}\mathrm{cost},{ℂ}^{\mathrm{y}}$$,\left(\mathrm{USD}/\mathrm{year}\right)$	32,728	13,874	22,114	22,114	26,735	15,691
$\mathrm{Annual}\mathrm{maintenance}\mathrm{cost},{\mathrm{ℳ}}^{\mathrm{y}}$$,(\mathrm{USD}/\mathrm{year})$	3,272	694	2,211	2,211	1,337	157
$\mathrm{Total}\mathrm{annual}\mathrm{equivalent}\mathrm{cost},{\mathsf{\Lambda }}^{\mathrm{y}}\left(\mathrm{USD}/\mathrm{year}\right)$	36,000	14,568	24,325	24,325	28,072	15,848

shows a range of costs for a number of the mitigation technologies discussed above. According to the comparison, DSTATCOM is the cheapest mitigation technology on a cost per kVAr basis and is based on the total annual equivalent cost (14,568 USD/year). In contrast, the UPQC has the highest annual cost and per kVAr cost.

3.3. Comparison of Advantages and Disadvantages of Mitigation Technologies

A comparative summary of different types of compensation technologies is given in

Table 3. Comparison of different voltage fluctuation mitigation devices [34,44,45,46,47].

	I	II	III	IV	V	VI
	FSC	FC/TCR	TSC	DSTACOM	DVR	UPQC
Steady state Characteristic	Self-regulation	Controller easily adjustable	Controller easily adjustable	Controller easily adjustable	Controller easily adjustable	Controller easily adjustable
Control range	Capacitive	generation and absorption	Capacitive	Both generation and absorption	Both generation and absorption	Both generation and absorption.
Harmonic content	Negligible	Requires filters	Negligible	Small low order. Large: high order	Small; depends on the hardware	Small low order; eliminated by a shunt filter
Losses	Negligible	Low at full generation. High at full absorption	High at full output. Low at zero var output	High at full output. Low at zero var output	Low	Low
Overload capability	Limited to capacitor rating	Limited to capacitor rating	Limited to capacitor rating	Limited to rating of shunt compensator	Up to 150% for 30 s	Up to 150%
Response time in the system	0–0.05 s	0.02–0.06 s	0.02–0.06 s	0.01–0.02 s	0.01–0.02 s	0.01–0.02 s
Maintenance requirements	Moderate	Moderate as for electronic indoor equipment	Moderate	Moderate	Moderate	Moderate
Response to rapidly fluctuating load	Inherently fast	Less rapid than I	Slower than II	Faster than III	Faster than III	Faster than III
Voltage control under line outage	Requires metal varistor for protection	Require switched capacitors to support voltage	Require switched capacitors to support voltage	Require switched capacitors to support voltage	Require energy storage to provide power	Require a DC capacitor to support voltage
Behavior following system fault	Cannot tolerate fault current; automatic switch required	Auxiliary controls used to damp load swings	Auxiliary controls used to damp load swings	Auxiliary controls used to damp load swings	Auxiliary controls used against overcurrent	Series converter utilized to improve system stability

. Besides,

Table 4. Advantages and disadvantages of different types of compensating devices.

Mitigation Techniques	Advantages	Disadvantages
TSC	▪ Fast response time, less than 20 ms. ▪ Effective in reducing the impacts of fast load fluctuations and flicker. ▪ Free harmonic generation. ▪ No switching transients. ▪ Effective control to prevent overcurrents and overvoltages.	▪ Susceptible to series resonance, appropriate connection is required to prevent it. ▪ A delay in the response time may occur due to complicated control system. ▪ Higher losses than that in pure capacitor losses.
FC/TCR	▪ Operate in inductive and capacitive modes. ▪ Flexible control during light and heavy loading periods.	▪ High steady-state losses ▪ Limitation in the injections or the absorption of reactive power. ▪ Cannot disconnect the capacitor in exigencies.
Dynamic Voltage Restorer	▪ Fast dynamic response to the disturbance. ▪ Different modes of operations. ▪ Compensate for the inductive drop in the line. ▪ Limiting fault current by providing a leading voltage.	▪ Requires active power during the compensation. ▪ Causes phase jump at load voltage. ▪ Partially provides power to the load during extreme variations.
DSTATCOMs	▪ Ability to perform different functions at the same time. ▪ Ability to follow rapid load variations. ▪ Smaller than that of corresponding SVC systems.	▪ Compensates only for reactive power at the fundamental frequency. ▪ Limited overload capability.
Series capacitors	▪ Minimizing light flicker on redial feeders. ▪ Improving voltage regulation on radial feeders. ▪ Increasing power transfer ability. ▪ Controlling load sharing between parallel feeders.	▪ Compensation available only downstream the capacitor. ▪ May cause resonance phenomena. ▪ Affecting distance estimation for distance relay. ▪ Self-excitation of synchronous machines.
UPQC	▪ Perform shunt and series compensation. ▪ Flexible overall control. ▪ Efficient runs near nominal operating point. ▪ Small physical size and light weight.	▪ Low efficiency when load power is low. ▪ Limited lifetime of the electrolyte capacitor.

illustrates the advantages and the disadvantages of each flicker mitigation technique explained in this chapter.

3.4. Technology Selection

In this comparison, several parameters are utilized to select the best flicker mitigation device. These parameters are as follows:

• Overload capability;
• Losses;
• Response time;
• Reactive power range;
• Investment costs;
• Control interaction;
• Special requirements (i.e., protection devices; special connection; customization);
• Efficiency during low/high loading;
• Single-phase control;
• Energization.

In choosing the best option for reducing voltage flicker caused by the FCS, it is important to consider the cost and benefit of each method that is available. In this study, two stages are utilized to select the best flicker mitigation technique. In the first stage, a linguistic comparative is utilized to compare between each mitigation method, as shown in

Table 5. Comparison of different voltage mitigating devices.

	Mitigating Techniques
	FSC	FC/TCR	TSC	DSTATCOMs	DVR	UPQC
Overload capability	Limited	Limited	Limited	Limited	Good	Good
Losses	small	Moderate	Small	Small	Small	Small
Response Time	Very fast	fast	fast	fast	Very fast	Very fast
Reactive power range	Capacitive	Capacitive inductive	Capacitive	Capacitive inductive	Capacitive inductive	Capacitive inductive
Capital costs	Good	High	High	Good	Very high	Very high
Maintenance costs	Very good	Good	Good	Good	Very high	Very high
Control interaction	Limited	Good	Good	Good	Good	Good
Special requirements	Overvoltage resonance	Harmonic	Resonance	Short-circuit	Short-circuit	Short-circuit
Efficiency during low/high loading	Good	Good	Good	Good	Good	Limited
Single-Phase control	Yes	Yes	Yes	Yes	Yes	Yes
Energization	Fast and direct	Fast w/control	Fast w/control	Fast w/control	Fast w/control	Fast w/control

. The first column in Table 5 represents parameters utilized to differentiate between each mitigation technique listed in the first row. Then, each linguistic comparator, utilized in Table 5, is given a score based on a user-defined criterion. Four types of scores are utilized to distinguish between each mitigation method, which are: −, − −, +, and + +. This method of comparison has been utilized in the literature, as per [48]. The value (score) of each group of linguistic comparators is shown in

Table 6. Weighting of the comparators in Table 5.

Given Weight
+	−	+ +	− −
Cheap	High	Very fast	Very high
Fast	Slow	Fast and direct	Very slow
Fast w/control	Short-circuit	Very good	$\mathrm{Cost}\mathrm{USD}/\mathrm{kVA}>150$
Capacitive	Moderate	$\mathrm{Cost}\mathrm{USD}/\mathrm{kVA}\le 50$	$7.5<\mathsf{\gamma }\le 10\%$
Yes	Limited	$\mathsf{\gamma }\le 2.5\%$
Good	Resonance
Small	Harmonic
Inductive	$100<\mathrm{Cost}\mathrm{USD}/\mathrm{kVA}\le 150$
$50<\mathrm{Cost}\mathrm{USD}/\mathrm{kVA}\le 100$	Overvoltage
$2.5\%<\mathsf{\gamma }\le 5\%$	No
	$5\%<\mathsf{\gamma }\le 7.5\%$

. In the second stages, the linguistic comparators are mapped based on their given score, as shown in

Table 7. Grading of the selected mitigation devices.

	Mitigation Techniques
	FSC	FC/TCR	TSC	DSTATCOMs	DVR	UPQC
Overload capability	−	−	−	−	+	+
Losses	+	−	+	+	+	+
Response Time	+ +	+	+	+	+ +	+ +
Reactive power range	+	+ +	+	+ +	+ +	+ +
Cost per kVAr	+	−	−	+	− −	− −
Maintenance Cost	+ +	− −	− −	+	+	− −
Control interaction	−	+	+	+	+	+
Single-Phase control	+	+	+	+	+	+
Special requirements	− −	−	−	−	−	−
low/high loading Eff.	+	+	+	+	+	−
Energization	+ +	+	+	+	+	+
Sum (-)	−4	−6	−5	−2	−3	−6
Sum (+)	11	7	7	10	11	9
Sum (total)	7	1	2	8	8	3

. Each mitigation technique is given a weight based on the difference of its total positive scores and its total negative scores. The mitigation technique that possesses the maximum positive weight is considered the best flicker mitigation option, as per the parameters defined in this study.

In Table 7, the results show that DSTATCOM and DVR have equivalent positive weights. This means that both represent the best mitigation solutions based on the defined criteria. However, their capital costs are distinctly varied. If the highest priority is to minimize cost, DSTATCOM has lower cost per kVAr than DVR, and, thus, it represents the preferred solution. In contrast, if the priority is efficiency and fast action, DVR represents the best solution. Therefore, DSTATCOM is utilized in this work to mitigate the adverse impact of FCS on voltage quality.

4. Probabilistic Load Charging Modelling

4.1. Commercial Load Profiles

Based on the geographic coordinates, cities can be classified into different climate zones. The cities can be projected into 16 different climate zones [49]. If the climate is mixed-marine, it is classified as 4C. The electrical loads and their peaks are impacted by the weather (climate). Reference [49] reported annual profiles for different loads in different climate zones. The idea of indicating that the residential and commercial loads profiles utilized in the test-bed of the study is to make it easier for researchers who want to duplicate the results of the paper. Annual load profiles for two commercial facilities, a medium office and a quick service restaurant, which are characterized based on their geographic coordinates as mixed-marine (climate zone 4C), are utilized to represent the three-phase base load in the distribution system proposed in study. The commercial load profiles are probabilistically extracted as illustrated in detail in [50]. The weekly, daily, and hourly peak loads for these commercial profiles are shown in [49].

4.2. Residential Load Profiles

Three types of residential load profiles corresponding to three different load models are in [51]. The residential load models include: the high load model, the low load model, and the base load model. The base load model in 4C climate zone is proposed in this study and is probabilistically generated, as demonstrated in [50], to represent the single-phase base load in the distribution system under study. The weekly, daily, and hourly peak loads for these residential profiles are presented in [49].

4.3. Type Selction of Electric Vehicles

Probabilistic charging profile is proposed in this study to represent the FCSs energy requirements when they are utilized by one type of Plug-in Battery Electric Vehicles (PBEVs), a Chevrolet Bolt. The battery capacity of this PBEV is 66.6 kWh, selected because of its high market share in the Canadian market, which almost amounts to 26% [52]. Three different parameters are considered: the battery state-of-charge, the daily distance traveled, and the arrival time at the FCSs. The minimum and maximum battery SOC are assumed to be 5% and 80%, respectively, as in [53].

4.4. Type Selction of Electric Vehicles

Typical data, for a period of three years, from seven FCSs, are individually extracted and analyzed for distribution fittings. These FCSs are located in different locations such as workplaces, retail locations, and malls; however, all of them are in Vancouver, British Colombia, where its climate zone is characterized as 4C, mixed and marine [54]. These data are utilized to obtain arrival time distributions, which, in turn, are utilized to select the best standard distribution function that fits them. The typical datasets are extracted for the years of 2015, 2016, 2017, and 2018 [55]. The dataset for each year includes the number of charging times in each hour (24 hours) of each day (365 days). Each yearly dataset (365 days) is divided into 12 months, and, then, all the datasets are grouped based on their monthly basis. Therefore, each hour is represented by the accumulated number of charging times from the same hour from different months (12 months) from different years (3 years). Figure 2 shows the number of charging times (left y-axis) and the percentage of charge times (right y-axis) versus the time of day. As a result, Figure 2 can be used to represent the arrival time probability distribution at the FSC. In total, 14 arrival time probability distributions corresponding to seven different FCSs are generated using the same approach. Half of these represent the weekday distributions, whereas the other half represent the weekend distributions. The utilized FCSs have the same number of ports (one port) and the same maximum power (50 kW), so, thus, their charging events are not affected by these factors.

For each distribution of the 14 arrival time distributions, the empirical CDF will be calculated and, then, compared to theoretical CDFs calculated from seven standard distribution functions, whereas their dissimilarity is evaluated using the calculating of the Sum of Squares Error (SSE), as illustrated in [56]. For each arrival time distribution, seven SSE values will be obtained of the comparison, whereas one of the theoretical CDFs will be selected to represent that arrival time distribution based on its minimum SSE value. The 14 selected theoretical CDFs are utilized to represent the 14-typical arrival time distribution functions, and their frequency of occurrences are tabulated. In all comparative cases, the Birnbaum–Saunders distribution function is the winning distribution and is, therefore, utilized in this work to represent the arrival time distribution at the FCS.

4.5. Markov Chain Monte Carlo Approach

The Markov Chain Monte Carlo (MCMC) in this study is used to generate a sample (random variable) representing the daily distance traveled, derived from a given standard distribution function, as illustrated in [56]. A Monte Carlo is a general term used to generate outcomes from random sampling. A sequence of random samples is called a Markov chain. A Markov chain is a stochastic process, in which the state of the current sequence is influenced only by the latest state. The MCMC, relying on a Metropolis–Hastings sampler, is applied to estimate the daily mileage traveled and the arrival time distribution based on their distributions (e.g., exponential, Birnbaum–Saunders). The convergence of the algorithm is assessed based on the Gelman and Rubin approach [57].

4.6. Rated Power of FCSs

The arrival time at the FCS shapes the start point of the charging event, contrary to the rated power of the FCS, which is an essential factor contributing to shape the end point of the charging event (departure time). If, for example, a PBEV charges from an FCS with a rated power of 50 kW starting from a specific time, it means that the power consumed from the electric grid at that instant will jump by an amount equal to or less than the rated power of the FCS. The PBEV will be charged until it reaches its maximum amount of SOC. When the rated power of the FCS is high, the period of charge will be less, especially in the case of low battery capacity or high SOC level. Two different scenarios related to the rated power of the FCS are considered in this study; these are the estimated charging rates and the actual charging rates of the FCS, as explained below.

Estimated Charging Rate of FCSs: In this case, the FCS with 50 kW rated power is utilized to charge one type of PBEV, the Chevy Bolt. The output power of the FCS is assumed to be constant and will not be changed over time as the Chevy Bolt battery SOC changes. It is assumed that the battery of the Chevy Bolt is charged linearly until it reaches to its maximum amount of SOC. For instance, the day is represented by 2880 samples (1 sample/30 s). If a Chevy Bolt arrives at FCS at 14:50 p.m. with 10% SOC (6.66 kW), then it requires 51.8 kWh to reach 80% of its capacity. The required charging time is equal to $\frac{51.8 \mathrm{kWh}}{{\mathsf{\eta }}_{\mathrm{FCS}}}\times 50 \mathrm{kW}\cong 1.15 \mathrm{h}$, which means 138 samples, based on our resolution. The end time of charging is at 16:05 p.m., which corresponds to the sample number 1918 in our daily profile. It means that the FCS will draw a constant power from the electric grid equals to 50 kW from 14:50 p.m. to 16:05 p.m. The FCS efficiency ${\mathsf{\eta }}_{\mathrm{FCS}}$ is specified to be 90% of its rated power as in [58].

Actual Charging Rates of FCSs: A typical FCS profile is used in this case. The profile is generated when a depleted battery of a Chevy Bolt was charged from an FCS with a rated power of 50 kW. The FCS was connected to the secondary of a distribution pad-mounted transformer, characterized as (4.16Y/0.6Y KV) with 50 kVA. The output power of the FCS will not be constant over time as the Chevy Bolt battery SOC increases, according to the typical profile depicted in Figure 3, which shows the active power per phase and its corresponding power factor. It clearly shows the variation of the output power over time. This work presumes that the Chevy Bolt will be charged based on a linear rate. For example, the FCS takes 119 min or 238 samples, as the profile indicates, to charge 80% of the battery capacity. Then, the battery SOC will increase based on constant rate equal to $\frac{{\mathsf{\gamma }}_{PBEV}}{238}$, where in this case the maximum battery SOC ${\mathsf{\gamma }}_{PBEV}=53.25$, and the charging rate is equal to 0.223. This means that, based on the charging rate, the depleted Chevy Bolt requires 119 min or 238 charging samples to reach 80% of its battery capacity. In the first minute of the charge time, the FCS draws a minimum power of 12.48 kW/phase, whereas in the last minute of charge time it draws a maximum power of less than 2 kW/phase, as shown in Figure 3. If the same Chevy Bolt used in the previous section arrived at this FCS with 10% SOC (6.66 kW), then it needs 208 charging samples to reach 80% of its capacity. The output of the FCS for each phase will be identical to the profile, as demonstrated in Figure 3, but it starts after the first 15 min, since the Chevy Bolt arrived with 10% SOC. This means that the FCS will draw variable power from the electric grid starting from 14:50 p.m. and ending at 16:34 p.m. In this case, the end time of charging is 16:34 p.m., while it was 16:04 p.m. in the previous case. This is because the battery requires more time with 208 charging samples to reach the same level of its SOC, compared to 138 charging samples in the case of charging with a constant charging rate.

5. Results and Discussion

5.1. Test System Description and Modification

The IEEE 123-Node standard distribution test feeder, published in [59], is utilized in this research to conduct the study. The proposed system shown in Figure 4 includes three-phase and single-phase spot loads. The three-phase loads are replaced with multiple three-phase distribution transformers utilized to supply the FCSs and commercial facilities. The rated power of these three-phase distribution transformers are 50 kVA, 30 kVA, and 15 kVA. The test system has six loads of this types, three of which are unbalanced spot loads. Moreover, the system contains 31 and 47 single-phase spot loads, rated 22.36 kVA and 44.72 kVA. These spot loads are replaced with 31 center-tapped distribution transformers, rated 25 kVA and 47 rated 50 kVA. These 78 center-tapped distribution transformers are utilized to feed the secondary distribution circuits, which are used to flow electrical power to residential homes.

Residential Homes: Each center-tapped distribution transformer, rated 50 kVA and 25 kVA, is utilized to feed a group of 12 residential homes and a group of 6 residential houses, as shown in Figure 5. The number of homes served by each distribution transformer is equivalent to the corresponding single-phase spot load in the primary system. Therefore, a total of 750 residential homes are connected to 78 distribution transformers via service drops with random lengths between 80 to 100 feet; this = emanates from a routing single-phase triplex 120/240 V secondary main, with a length of 125 feet. This study presumes that all residential houses are in the same climate zone, namely a 4C, and, thus, their daily load profile are specified accordingly. According to the residential yearly load profiles in [51], all dwellings located in climate zone 4C are equipped with gas heaters, but without electric water heaters. In [60], findings show that the median of the annual peak demand for similar dwellings is 4.93 kVA. Thus, 4.93 kVA, at 0.9 lagging power factor, is assigned to represent the required peak load of each residential house in this study.

Commercial Facilities: Four commercial facilities are utilized in this work; three of these are quick service restaurants connected to the test system at nodes 47, 49, and 65, and one is a medium office connected at node 48. These commercial loads are connected to the primary distribution system using three-phase two-winding distribution transformers, of which three are rated 30 kVA and one is rated 15 kVA, as depicted in Figure 6. The peak load of each type of commercial building is assigned by analyzing the annual load profile as in [50], relying on the median of the maximum demand values. The peak load for a quick service restaurant is 28.56 kVA, while it is 13.33 kVA for a medium office, which is at 0.9 lagging power factor for both.

Fast-Charging Stations’ Inclusion: There are two approaches to represent the output power of FCSs: charging with a real profile and charging with an estimated profile. Each FCS is connected to the primary main feeder using a three-phase distribution transformer rated 50 kVA. The number of FCSs utilized in this work and their locations are illustrated in

Table 8. Location and numbers of FCSs.

Location	Number of FCSs	Number of Ports
Node 47	2	2
Node 48	5	5
Node 49	2	2
Node 65	2	2
Node 76	5	5
Node 610	3	3

. This study assumes that only 15% of the total number of residential homes have EVs and recharge them at the FCSs. The 15% represents the electric portion of new passenger car sales in British Columbia in 2018, as in [61].

Distribution-Static Compensators’ Placement: Distribution Static Compensator (D-STATCOM) is a shunt device utilized to regulate the bus voltage to which the device is connected. The aim of using D-STATCOMs in this study is to maintain the bus voltages to which D-STATCOMs are placed; this is either by producing or absorbing reactive power to alleviate the effect of FCSs on the primary and secondary distribution systems. Multiple three-phase D-STATCOMs are connected to the primary side and the secondary side of the three-phase distribution transformers. It is assumed that the reactive power of each D-STATCOM that can be absorbed or injected into the system varies from −50 kVAr to 2000 kVAr.

5.2. Voltage Quality Assessment Results and Discussion

The impact of FCSs on the modified system is analyzed and quantified using three different assessment methods: the voltage range, the voltage unbalance, and the voltage fluctuation. In the case of voltage range, the undervoltage and the overvoltage limits are utilized and compared, respectively, with the minimum voltage and the maximum voltage experienced by each node in the primary distribution system. In the case of voltage unbalance, the unbalance limit is compared with the maximum deviation from the average of each three-phase primary voltage divided by the average of the corresponding three-phase primary voltage. In the case of voltage fluctuation, the percentile of short- and long-term flicker severity indices are calculated and compared with the compatibility levels, as was explained in Section 2.3. The node 48 is utilized to compare between the two methods of charging and to compare between the effectiveness of the considered scenarios on the system. Node 48 is used to apply the comparisons because it is a primary node, where the voltage is 4.16 kV and represents a point of common coupling, to which six different three-phase distribution transformers are connected to supply five FCSs operating at 600 V and one medium office operating at 208 V.

Assessment and Discussion of Undervoltage and Overvoltage: Figure 7, Figure 8, Figure 9, Figure 10 and Figure 11 depict the assessment in this subsection. Figure 7 represents the evaluation when only FCSs are connected to the modified system, showing the minimum and maximum line-to-neutral voltages experienced during the day by each node in the primary of the system under study. Moreover, the minimum and maximum limits are illustrated in Figure 7. Exceeding the minimum limit means that there is undervoltage, while exceeding the maximum limit indicates an overvoltage. Figure 7 clarifies that none of the primary nodes violate the limits of undervoltage or overvoltage. Regarding the output power of the FCSs, Figure 8 compares between two methods of charging: a charging with constant rate and a charging with variant rate, representing the estimated and the actual charging profiles, respectively. Figure 8 consists of three graphs: the first graph represents the voltage measured at the primary side of the distribution transformers, the second graph explains the voltage profile measured at the secondary side of one of the five distribution transformers connected to the FCSs, and the third graph shows the voltage profile measured at the secondary side of the distribution transformer used to supply the medium office. The nominal voltage of each graph is shown in the y-axis, whereas the x-axis represents the time of day. Although both charging methods operate within the service voltage limits, charging with constant rates has more effect, as can be seen in Figure 8. When referring to the voltage waveform for a 600-voltage base in Figure 7, the FCS is represented in the modified system as a constant real and reactive power load, and its voltage is required at each time. When the output power of the FCS is increased, the voltage at the FCS bus is decreased, and vice versa. In the case of estimated charging rates, the output power always equals the rated power of the FCS, which is 50 kW. Therefore, the voltage in this case is mainly affected by the rated power of the FCS and not by the SOC of the PBEV. In case of variant charging rates, the output power of the FCS is a function of the battery SOC. When the battery SOC is increased, the required power from the FCS is reduced, as shown by the typical profile in Figure 3. Accordingly, there is an obvious distinction in the voltage profiles corresponding to the two methods of charging. The primary voltage profiles in Figure 7 are influenced by the demand on their corresponding FCSs. There are some variations in the pattern between the primary voltage profiles and their corresponding secondary profiles. The variations in the pattern of the primary and secondary voltages in Figure 8 are produced due to the demand on their corresponding FCSs supplied from the same primary node.

Figure 9 illustrates the effect when D-STATCOMs are connected to the secondary side of the distribution transformers from which the FCSs are supplied. Instead of using BESUs to produce active power, D-STATCOMs are utilized to inject a reactive power to mitigate the impact of the FCSs. Figure 9 clearly shows that D-STATCOMs are able to maintain the voltage at the point of common coupling and, hence, mitigate the impact of FCSs. Although both methods of charging in Figure 9 depict a similar voltage profile, the voltages at the primary side of distribution transformers are not maintained at their nominal values. Figure 10 depicts the outcome when different D-STATCOMs are connected to the primary and the secondary sides of the distribution transformers connected to the FCSs. In this case, the Figure 10 clearly indicates that D-STATCOMs are effective in improving the voltage magnitudes and maintaining them at their nominal values. The minimum and the maximum line-to-neutral voltages encountered during the day, corresponding to this case, are shown in Figure 11.

Every group of points in Figure 11 that is lined vertically represents the minimum or maximum voltage values experienced corresponding to a specific node (phases). It is deduced from Figure 11 that the difference in the voltage magnitudes, corresponding to a three- or two-phase node, is reduced on the test system under study. Not only is the impact of the FCSs mitigated, but also the voltage of the nodes is enhanced.

Assessment and Discussion of Voltage Unbalance: 

Table 9. The maximum voltage unbalance encountered for each scenario.

Scenarios	Charging Methods	Maximum VU (%)	Time (hh:mm:ss)
First	Estimated charging rates	2.079	19:03
	Actual charging rates	1.965	19:01
Second	Estimated charging rates	1.609	19:02:30
	Actual charging rates	1.558	19:01
Third	Estimated charging rates	0.948	19:01
	Actual charging rates	0.930	19:01

shows the maximum voltage unbalance that occurred in each scenario and its corresponding time of the day. The voltage unbalance is calculated for each node, and, then, the maximum value of each scenario is recorded in Table 9.

Inspecting the values of maximum voltage unbalance demonstrates that none of the conducted scenarios violate the limit of voltage unbalance. This is due to the connection of FCSs as balanced three-phase components, and, thus, they impact the unbalanced phases of the system under study by the same degree. Moreover, the outcome of the table implies that in the case of estimated charging rates, the effects on the voltage unbalance is more than the effects in the case of variants’ charging rates. Moreover, D-STATCOMs are connected as balanced three-phase components. When D-STATCOMs are utilized, the system’s voltage is improved, and the deviation between its phases is reduced. Accordingly, this may lead to a decrease in the system’s power losses.

Assessment and Discussion of Voltage Fluctuation and Light Flicker: The results of voltage fluctuations and light flickers are summarized in

Table 10. Statistics for voltage fluctuation and light flicker indices.

		Statistics	First Scenario FCS Only			Second Scenario FCS and D-STATCOMs in Secondary Nodes			Third Scenario FCS and D-STATCOMs in Primary–Secondary Nodes
			Ph. A	Ph. B	Ph. C	Ph. A	Ph. B	Ph. C	Ph. A	Ph. B	Ph. C
Estimated Charging Rates	PLT	Minimum	0.801	0.801	0.012	0.801	0.801	0.012	0.012	0.012	0.012
		Average	1.034	1.226	0.236	0.884	0.872	0.284	0.196	0.236	0.284
		95%	1.272	1.503	0.612	0.977	0.965	0.720	0.485	0.612	0.720
		Maximum	1.383	1.637	0.648	0.977	0.977	0.737	0.610	0.648	0.737
		Location	Node 49	Node 51	Node 1	Node 28	Node 150	Node 1	Node 150	Node 1	Node 1
	PST	Minimum	1.000	1.000	0.007	0.003	0.003	0.010	0.007	0.007	0.010
		Average	1.149	1.320	0.235	0371	0.456	0.282	0.194	0.235	0.282
		95%	1.321	1.539	0.613	0.784	0.942	0.721	0.486	0.613	0.721
		Maximum	1.434	1.682	0.652	0.977	0.978	0.741	0.671	0.652	0.741
		Location	Node 48	Node 51	Node 53	Node 150	Node 150	Node 53	Node 150	Node 53	Node 53
Actual Charging Rates	PLT	Minimum	0.800	0.802	0.011	0.901	0.802	0.011	0.011	0.011	0.011
		Average	0.934	0.898	0.234	0.952	0.876	0.291	0.192	0.234	0.291
		95%	1.086	1.097	0.609	0.977	0.969	0.719	0.479	0.609	0.719
		Maximum	1.123	1.123	0.639	0.977	0.977	0.733	0.609	0.639	0.733
		Location	Node 150	Node 150	Node 1	Node 150	Node 150	Node 1	Node 150	Node 1	Node 1
	PST	Minimum	1.000	1.003	0.007	0.001	0.001	0.010	0.006	0.007	0.010
		Average	1.072	1.082	0.232	0.362	0.423	0.289	0.190	0.232	0.289
		95%	1.123	1.131	0.610	0.783	0.944	0.720	0.479	0.610	0.720
		Maximum	1.123	1.157	0.643	0.977	0.977	0.738	0.671	0.643	0.738
		Location	Node 150	Node 51	Node 54	Node 150	Node 150	Node 53	Node 150	Node 54	Node 53

. Four types of descriptive statistics are presented in each table: the minimum, the average, the 95th percentile, and the maximum values, in addition to the locations of the maximum values encountered. The results compare two methods of charging using two indices: the Percentile Long Term (P_LT) flicker severity index and the Percentile Short Term (P_ST) flicker severity index. If the presented minimum value in the tables below is less than the limit corresponding to one of these indices, then there is no light flicker, according to the indicator for that specified scenario. The results shown in Table 10 reveal that the light flicker is due to fluctuating the voltage in the first scenario, which exceed the limits of all two indices in all phases. In the case of estimated charging rates, the violations are more than those caused by variant charging rates. Likewise, the results indicate that the flicker sensation indices were exceeded mostly in phase C, as illustrated in Table 10. The results of the second scenario are demonstrated in Table 10. The voltage is improved in this scenario, as the P_ST was not violated by both methods of charging. However, the limit of P_LT was exceeded. Moreover, Table 10 shows the results when D-STATCOMs are connected to the primary and secondary systems. The statistics of Table 10 clearly indicate that no light flicker was encountered by any phase at all when monitored by nodes in the system. The overall impacts of the first scenario, when only FCSs are connected on the system under study, are summarized in Figure 12; it depicts the P_LT values for the primary and FCS nodes and the P_ST values for the FCS nodes only, for two methods of charging. A visual inspection for Figure 12 shows that the values of P_LT and P_ST exceed their corresponding limits. The P_LT and P_ST values are increased at the substation and at the point of common coupling, to which the FCSs are connected. In contrast, Figure 13 reveals an overview of the improvement caused by connecting D-STATCOMs on both the secondary and primary sides of the distribution transformers. The P_LT and P_ST values are extremely minimized at the point of common coupling, as shown in Figure 13. The P_ST represent the values only for the nodes, to which the FCSs are connected. It is worth mentioning that the maximum P_ST value in Figure 13 is less than 0.1; this does not match the value presented in Table 10, in which the maximum value was calculated for both the FCS and primary nodes that are not displayed in a graph due to the graphic complexity. Instead, the statistics in Table 10 include both the primary and FCS nodes.

6. Conclusions

The research presented in this paper is focused on the impacts of FCSs on three power quality aspects: voltage magnitude variations, voltage unbalance, and voltage fluctuation. The main objective of this work is to quantify and mitigate these impacts, whether on the point of common coupling in which FCSs are connected or on the upstream nodes supplied from the main distribution feeder. In order to quantify the impacts of FCSs, a distribution test system is utilized and modified to include three main components required in this study: commercial loads, residential loads, and FCSs. In order to alleviate the anticipated impacts resulting from connecting FCSs, mitigation devices, such as distribution static compensators, are placed independently in the primary and secondary systems, beside the three main components mentioned above. Two charging methods are implemented in this work: charging with an estimated output power and charging with an actual output power, for each FCS. The simulation results revealed that there are no impacts of FCSs on the system’s undervoltage or overvoltage. However, the minimum line-to-neutral voltages experienced when charging with an estimated output power is less than the values when charging with an actual output power. Moreover, the findings showed that the system unbalance is not affected by installing fast-charging stations, due to their connection as three-phase components. The system unbalance is improved to 0.948% and 0.930%, when D-STATCOMs are connected to the primary and secondary sides of distribution transformers, when charging with an estimated and an actual output power of the FCSs, respectively. Moreover, the outcomes demonstrated that when FSCs are connected to the system, the system’s voltage will fluctuate to a level more than the allowable limits in all phases. When D-STATCOMs are connected to the secondary side of the distribution transformers, the voltage is improved only at the point of common coupling, and, thus, the voltage fluctuation is reduced. Overall, the results confirmed that placing D-STATCOMs at both sides of the distribution transformers is an effective mitigation technique to improve voltage and minimize its fluctuation, which results in removing all light flickers previously encountered in the system. Furthermore, without including D-STATCOMs in the primary and secondary system, the maximum values of the flicker sensation index, according to the GE flicker curve, are 5.814 when charging with an estimated output power and 2.694 when charging with an actual output power. Furthermore, without including D-STATCOMs in the primary and secondary system, the maximum values of the flicker sensation index according to the P_LT are 1.637 and 1.123, and the values of P_ST are 1.682 and 1.157, for both methods of charging, respectively. In contrast, when D-STATCOMs are included in the primary and secondary side of the distribution transformers, the results according to P_LT and P_ST are minimized to 0.737 and 0.741, when charging with an estimated rate; this is similar to the values when charging with actual rates, which are 0.738 and 0.738.