Propagation of Voltage Fluctuations and Assessment of LED Lamps Light Flicker in Low Voltage Networks

This paper offers an assessment of the risk and severity of light flicker, evaluated considering LED lamps as the only customer lighting technology as well as different household devices as source of voltage fluctuations. The study is based on the configuration of a real low voltage network. The results are calculated for a single-phase system without consider the impedance of the household devices themselves. The short-circuit impedances values needed for reaching the global emission limit of light flicker and the irritability threshold are at least over the $84^{th}$ percentile of a sample of short-circuit impedances from Swedish distribution networks, and in most of the cases over the $95^{th}$ percentile of the networks in Europe. The voltage fluctuations reduce in magnitude when propagating to adjacent phases, being this reduction different for each adjacent phase as has been observed from measurements in a controlled network. It has also been noted that the duration of the voltage fluctuations does not change when propagating between different points of the controlled network nor between phases. The severity of the light flicker values calculated in this study point to a ratio to estimate the severity of light flicker of a generalized LED lamp using the IEC flickermeter.


I. INTRODUCTION
This paper offers an assessment of the risk and severity of light flicker, evaluated considering LED lamps as the customer lighting technology as well as different household devices as source of voltage fluctuations.The study is based on the configuration of a real low voltage (LV) network.The light flicker severity is studied here using the P LM st index from IEC TR 61547-1 [1] to deal with the actual lighting scenario, where the penetration rate of the LED lamps in the market is expected to grow up to 75.8 % in 2025 [2].The risk and severity of light flicker are calculated based on the methodology in [3], which proposes a stochastic methodology to evaluate the light flicker from a generalized LED lamp.The limits of the global and individual emission defined in IEC TR 61000-3-14 [4], as well as the irritability The associate editor coordinating the review of this manuscript and approving it for publication was Vigna K. Ramachandaramurthy .threshold P LM st = 1) [1] are considered to evaluate the LV network according to the severity of light flicker.The global emission of the LV network and the light flicker experienced by a customer considering the contribution of neighboring customers and the customer itself are studied.
The propagation of voltage fluctuations and the severity of light flicker has previously been studied with the objective to settle the emission limits between voltage levels calculating the transfer coefficient as in [5] for Dutch networks.The severity of flicker has been studied in relation to the distance of the customer's installation from the transformer in [6], where it is pointed out that the effect of the network impedance plays an important role in the flicker level in the network.The studies in the literature consider the IEC 61000-4-15 standard [7], which defines two indexes, P st and P lt to measure the flicker severity based on the light response of a 60 W incandescent lamp to voltage fluctuations.
The objective in this paper is to study the impedance values needed to reach the flicker emission limits.It would allow to use the impedance values as references for network design purposes or to modify the currently established limits.
Several methods can be used to study the propagation of voltage fluctuations [8] depending on the configuration of the network, radial or meshed, as explained in [9] for high voltage (HV) networks.This study is based on the transfer impedance matrix calculation realized in [10] for a real LV network.
The propagation of the voltage fluctuations has been measured in a controlled network, the experiment and the conclusions are stated in Section II.Section III, IV and V state different aspects of the methodology applied.An extended explanation of the results is provided in Section VI.Section VII offers a discussion that intents to extend the understanding of the results showed.Finally, Section VIII is devoted to the conclusions.

II. PROPAGATION OF VOLTAGE FLUCTUATIONS IN A CONTROLLED LV NETWORK
The voltage fluctuations are characterized by their magnitude and rate of change [11], [12].The propagation of these two characteristics is analysed by measuring the voltage fluctuations produced by the operation of a microwave oven and a kettle.The specific household devices are chosen as the microwave oven produces three different types of voltage fluctuations and the kettle produces voltage fluctuations of significant magnitude.The measurements are done in a real but controlled LV network without any significant voltage background distortion [12].The LV network in question has three customers indicated in Fig. 1 as p1, p2 and p3 and the electrical distance between them can be varied.A Dewesoft SIRIUS ® XHS meter is connected to each customer to obtain continuous measurements of the voltage and current waveforms and the data are processed with the DewesoftX software to obtain the rms voltage and current.The cable indicated in Fig. 1 by a dashed line is extended to obtain four different network impedances up to approximately 1.46 [13].The microwave oven and the kettle were measured individually with no other connected devices in two customers, p1 and p2, indicated in Fig. 1.The three phases of the three-phase system have been measured with respect to neutral, each household device has been connected only in one of the phases.From the results of the measurements, which are not shown, it is observed that: -A device connected close to the transformer produces voltage fluctuations of lower magnitude than when it is located farther downstream.-There is a more significant reduction in the magnitude of the voltage fluctuation that is propagated from p2 to p1 than there is to p3. -The duration of the voltage fluctuations does not change so the rate of change varies with the propagation due to the voltage magnitude.
-The propagation of the magnitude between phases results in low magnitudes of the voltage fluctuation, impacting differently in each adjacent phase.

III. LV NETWORKS IMPEDANCES
IEC TR 60725 [14] (published in 2012) shows the results of an international survey conducted in 1980 about the impedances of the residential customers in several countries with 50-Hz network (mostly European countries).The reference impedance for equipment with current ratings equal or below 16 A is based on the 90 th percentile values obtained in 1980.After a strengthening of the networks produced after the publication of the survey in 1980, these values are more relevant to the 95 th percentile [14].The established reference impedance is 0.4 + j0.25 , corresponding to an absolute value of 0.472 .Considering the text in [14], the reference impedance can be associated to the 95 th percentile of the impedances from residential customers in Europe.
The cumulative distribution function of short-circuit impedances of 38888 customers with a fuse size of 16 A in Swedish distribution networks is shown in Fig. 2. The reference impedance according to this distribution function is close to the 95 th percentile as shown in Fig. 2.

IV. METHODOLOGY BASED ON A PUBLIC LV NETWORK A. REAL LV NETWORK
The LV network used as reference for the study is a Swedish rural network of six customers described in [10] and [15].
129196 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
It has 230 V rms of nominal voltage at 50 Hz that is supplied by a 100 kVA transformer (10/0.4kV).The network is simplified in Fig. 3 indicating only the points of common coupling (PCC) (nodes 2-4 in Fig. 3), the point of connection (PoC) (nodes 5-10 in Fig. 3) of the customers and the transformer connection (node 1 in Fig. 3).The buses and transformer impedances are indicated in Fig. 3 considering the phase and neutral cables.

B. FLICKER EMISSION LIMITS
The emission limits for individual customers are derived from the planning levels, for this reason the same indexes are applied to evaluate the measurements against emission limits and planning levels [4].The point of evaluation (PoE) of the emission level is established at node 2 in Fig. 3, which is the PCC of all the customers in the LV network.

1) GLOBAL EMISSION LIMIT (G PstLV )
The maximum acceptable global emission to be shared between all customers in the LV network (G PstLV ) is 0.65.This limit considers the impact of the propagation of voltage fluctuations from MV.It is calculated following (1) [4] considering the following values for the parameters in the equation: -L PstLV represents the flicker planning level for LV.
The value of the flicker compatibility level in IEC 61000-2-2 standard [16] (L PstLV = 1) is used for the calculation of G PstLV .-L PstMV represents the flicker planning level for MV.
The value stated in the IEC TR 61000-3-7 [17] (L PstMV = 0.9) is used for the calculation of G PstLV .-T PstML represents the transfer coefficient from MV to LV.It is considered as equal to the unity for the calculation of G PstLV .-The summation law exponent (α) of value 3 is used as recommended in IEC TR 61000-3-7 [17] and IEC TR 61000-3-14 [4].
2) INDIVIDUAL EMISSION LIMIT (E Psti ) The individual emission limit (E Psti ) of each customer is calculated from G PstLV following (2) [4].For the calculation of E Psti , a fuse of 16 A and therefore, an agreed apparent power (S i ) of 3680 VA (S = 230 V * 16 A) are considered for each customer.The supply capacity (S t ) of the LV network studied is 100 kVA.The resulting E Psti calculated using (2) is 0.22.
The minimum E Psti stated in the IEC TR 61000-3-14 [4] is 0.3, so it is considered the individual emission limit for all the customers in the LV network.

C. ADJUSTMENTS TO THE REAL LV NETWORK
The adjustments attempt to study the conditions under which the flicker emission limits and the flicker irritability threshold are reached.

1) SINGLE-PHASE
A single-phase network is considered for the study.This consideration avoids the uncertainty of the distribution of the household devices between phases in a three-phase system and assumes the worst possible case.

2) NUMBER OF CUSTOMERS
The maximum number of possible customers (N max ) in the LV network is determined in (3) by the supply capacity of the transformer (S t = 100 kVA) and the agreed apparent power per customer (S i = 3680 VA is assumed) rounding to the nearest integer.In this paper, the LV network studied can host 27 customers as maximum.
The LV network has been adjusted to have 27 and 13 customers, as well as the original 6 customers.The 'extra' customers are added to node 2 in Fig. 3 (PCC of all customers).

3) RESISTANCE OF THE BUSES
The resistance of the bus from node 1 to 2 (Z 1,2 ) impacts the short-circuit impedance of all customers, since node 2 is the PCC of all the customers.For this reason, node 2 is chosen as PoE of the global emission of light flicker.The short-circuit impedance of customer C3 in Fig. 3 is the addition of the impedance of the transformer (Z 0 ), Z 1,2 upstream node 2 (PCC of all customers) and Z 2,7 downstream this node.Customer C3 has been chosen for the study of the light flicker experienced by a customer since this situation simplifies the study, facilitating the understanding of the results of the study.

D. SOURCE OF VOLTAGE FLUCTUATIONS
The source of voltage fluctuations considered for the study are household devices connected to each customer.The same stochastic model for the use of the household devices in [3] is used for every customer in the LV network, as well as the same type and number of devices per customer.The stochastic models of the voltage fluctuations produced by each household device in [3] are also considered for this study.
The network impedance at a customer connection will vary depending on size of the network, i.e., length of cables and transformer size, but also on the devices connected at the customers.Fig. 4 shows the variation of the network impedance with the power consumption of a customer starting from different values of the network impedances without devices connected (P = 0 W).The presence of household devices in the network reduces the total network impedance.Connected devices cause a greater reduction in overall impedance on higher impedance networks (as percent of the original value), as shown in Fig. 4. The impedance of the household devices has been neglected in this study implying the consideration of the highest impedance for the configuration of the LV network, i.e., the worst case for propagation of the voltage fluctuations (highest impedance).The maximum variation of the network impedances due to shunt inductances and capacitances at 50 Hz calculated from the model [10] is on the fourth decimal, so they are neglected.

E. TRANSFER IMPEDANCE MATRIX
The transfer impedance matrix of the 6 customers in the LV network is calculated using the principle of superposition as explained in [10].The transfer impedance matrix is calculated every time that the impedance of the buses is modified.For the real impedance of the buses (shown in Fig. 3), the resulting transfer impedance matrix is represented in Table 1.
The transfer impedances between the customers that have the same value are shown in Table 1 with the same color.They correspond to customers connected in the same PCC.Therefore, the PCC has special relevance in the propagation of voltage fluctuations.As stated in [15], the voltage fluctuation magnitude propagated to every customer in the LV network can be obtained as the transfer impedance (Z tr ) relates the voltage fluctuation at a given location (V r ) in the network to the current injected at another location (I s ) according to (4).
The source current (I s ) here is the current fluctuation magnitude obtained based on the measurement of household devices described in [12].
Customer C3 has the same transfer impedance with all the neighboring customers as observed in Table 1, i.e., the impedances involved in the propagation of the voltage fluctuations are the impedances from the PCC at node 2 to upstream (Z 0 and Z 1,2 ).The transfer impedance for customer C3 calculates the voltage fluctuation magnitude at node 2.

V. RISK AND SEVERITY OF LIGHT FLICKER
For the assessment of the severity of light flicker, the P LM st from the light flickermeter [1] is used.The methodology of the stochastic assessment of risk of light flicker developed in [3] is used to assess the risk of light flicker produced by devices in a household, considering the contribution of voltage fluctuations originated by other household devices from neighboring customers in the LV network.
Following the methodology in [3], the severity of the voltage fluctuations is measured by the severity factor (SF).The severity factor of a voltage fluctuation can be equal to 1, 2 or 3 (from lowest to highest severity), each value has an associated probability (P SF1 , P SF2 , P SF3 ) of producing light flicker equal to or over the perception threshold (P LM inst = 1) in a generalized LED lamp of 5 %, 25 % and 50 % respectively.The severity factor of a voltage fluctuation depends on the P LM inst,max values that a set of LED lamps, sensitive to voltage fluctuations and representative of the market, have with respect to the perception threshold.The P LM inst,max values associated to the magnitude of a voltage fluctuation calculated with the transfer impedance matrix are obtained from the voltage fluctuation of the synthetic voltage profile of steps in [12] with the closest magnitude in a range of ± 0.25 V.The steps of the synthetic voltage profile are considered to have the most severe rate of change [18].
The risk of light flicker index [3] expresses the probabilistic number of voltage fluctuations in a 10-minute interval producing light flicker equal to or over the perception threshold (P LM inst = 1) in a generalized LED lamp, i.e., this index 129198 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
represents the light flicker response of a generalized LED lamp to voltage fluctuations.As explained in [3], the risk of light flicker index (risk f ) is calculated following (5), which is applied within a 10-minute interval.N SF1 , N SF2 and N SF3 represent the number of voltage fluctuations with SF=1, SF=2 and SF=3 respectively during the 10-minute interval.These quantities are multiplied by the probabilities per unit of producing light flicker equal to or over the perception threshold (P LM inst = 1) in a generalized LED lamp, that corresponds to P SF1 = 0.05, P SF2 = 0.25 and P SF3 = 0.5 in (5) for the respective values of severity factor.risk f = N SF1 P SF1 + N SF2 P SF2 + N SF3 P SF3 (5) The stochastic assessment explained in [3] is then applied.Fig. 5 provides a simplified explanation of the necessary calculations.The maximum total risk is used for the analysis of the results as done in [3].An average P LM st (P LM st ) value with the standard deviation (std) are calculated for the probabilistic number of voltage fluctuations in a 10-minute interval given by the maximum total risk obtained.The P LM inst,max values assigned to the probabilistic number of voltage fluctuations are stochastically calculated from the distribution of P LM inst,max values that are equal to or over the perception threshold obtained, for every LED lamp from the set used, due to the voltage fluctuations as in [3].It is considered that there is no overlap of the P LM inst response produced by the voltage fluctuations during the 10-minute interval for which the P LM st is calculated.Due to the response time of the P LM inst to each voltage fluctuation, the P LM st can be calculated up to a value of the maximum total risk equal to 294 following the methodology in [3].

A. LIGHT FLICKER ACCURACY
The P LM inst,max is obtained from the synthetic profile of voltage steps in [12], while the methodology in [3] is mainly based on measurements of household devices.The accuracy of the approach with a synthetic profile is tested calculating the difference between the P LM st values obtained from all the possible values of risk f for a single customer in a network with a resistance of 1.46 , and the P LM st values obtained with the approach in [3].The difference between the P LM st values for each risk f value is represented in Fig. 6, where it is observed that the maximum difference between the P LM st values for the same value of risk f is 0.0908.Positive values indicate that the P LM st values obtained based on the synthetic profile are higher than the obtained in [3].This is expected since the voltage steps of the synthetic profile always represent the most severe rate of change [18].The uncertainty of the use of the household devices by each customer in the LV network, the use of simplified voltage fluctuation patterns and household devices considered are present in the methodology of [3] as well as in this study.The calculation of the P LM st associated with the maximum total risk values obtained implies an uncertainty that can be quantified by the standard deviation shown in the results.This calculation does not consider the overlap of the light flicker response due to different voltage fluctuations.The set of LED lamps selected for the study influences the results, though it is considered as representative of the actual market.

VI. RESULTS
The results obtained are based on customer C3 due to the characteristics of the connection of this customer to the network described in Section IV.
The individual emission limit (E Psti = 0.3) is reached at customer C3 adjusting Z 1,2 to 0.4405 as shown in Table 2.This impedance is close to the reference impedance (0.472 ) stated in Section III, but higher than the real Z 1,2 = 0.1578 .The reference impedance is associated to a 95 th percentile of the short-circuit impedances of residential customers in Europe.

A. GLOBAL EMISSION OF LIGHT FLICKER
The global emission of light flicker is considered at node 2 (PCC for all the customers).The voltage fluctuations magnitude at node 2 is given by the transfer impedance calculated for customer C3 (which is the same for all customers) as explained in Section IV.The results in Table 3 and Fig. 7 are obtained for values of Z 1,2 that result in an individual emission of customer C3 equal to or less than the limit (0.3 calculated in Sub-section VI-B2).The results in Table 3 shows that the maximum total risk with 13 customers is double the value obtained with 6 customers, while the ratio between the P LM st values is 1.17.The global emission of light flicker is below the limit in both cases.
The results of the global emission calculated for 27 customers in the network are shown in Fig. 7.The original impedance of Z 1,2 in the LV network is 0.1578 (see Fig. 3).With this impedance, there is a risk of light flicker although there is no P LM st value equal to or over the perception threshold found with the set of LED lamps tested.The calculation of the P LM st is limited to a value of the maximum total risk below 294 as explained in Section V.The highest value of Z 1,2 for which the P LM st can be calculated is 0.3187 , obtaining a P LM st value of 0.4792 as shown in Fig. 7, not reaching the global emission limit.This impedance is at the 84 th percentile of the Swedish distribution networks as indicated in Fig. 2. When the individual emission of customer C3 is at the limit (Z 1,2 modified to 0.4405 ), the maximum total risk obtained is of almost a probabilistic number of 500 voltage fluctuations producing perceptible flicker for an average observer in 50 % of the cases in a 10-minute interval.
Fig. 7 shows that with 27 customers, the maximum total risk increases 4.8 times for a small difference (0.002 ) of Z 1,2 .This abrupt change in the maximum total risk is due to the fact that the most frequent voltage fluctuation in the washing machine, which is the most influential household device in terms of risk of light flicker, is at the limit to be considered a severity factor 1 or 2.
The global emission reaches the irritability threshold (P LM st = 1) only if customer C3 exceeds the individual emission limit.It happens if Z 1,2 is 1.4201 with 6 customers in the LV network or Z 1,2 is 1.0802 with 13 customers (without considering the light flicker propagated from MV) as shown in Table 4.These values are over the 99.8 th percentile of the short-circuit impedances from Swedish distribution networks shown in Fig. 2.

B. LIGHT FLICKER EXPERIENCED BY A CUSTOMER
The contribution to the severity of light flicker of the customer itself (P LM st customer itself ) and the contribution of neighboring customers (P LM st neighboring customers ) are studied for customer C3 for the reasons stated in Section IV.The total severity of light flicker (P LM st total ) experienced by customer C3 is calculated applying the cubic summation law recommended in the IEC TR 61000-3-7 [17] as expressed in (5).
The short-circuit impedance of customer C3 is the addition of Z 0 , Z 1,2 and Z 2,7 (see Fig. 3).The impedance Z 1,2 is modified to 0.4405 and kept constant maintaining the individual emission of customer C3 close to the limit.This value is close to the reference impedance (0.472 ), which is associated to 129200 VOLUME 11, 2023 Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
a 95 th percentile of the short-circuit impedances of residential customers in Europe.

1) CONTRIBUTION OF THE CUSTOMER ITSELF
Different short-circuit impedances are obtained varying the value of Z 2,7 to study the contribution of the customer itself (at node 7) on the severity of light flicker experienced.The results are shown in Fig. 8.It is observed that a customer itself does not produce light flicker over the irritability threshold (P LM st = 1) for short-circuit impedances up to 1.6944 , with includes almost all the short-circuit impedances of Swedish networks in Fig. 2.

2) CONTRIBUTION OF THE NEIGHBORING CUSTOMERS
The magnitude of the voltage fluctuations at customer C3 produced by neighboring customers depends on Z 0 and Z 1,2 as seen in Table 1.Z 1,2 is modified to 0.4405 and kept constant, maintaining the individual emission of customer C3 close to the limit.The number of neighboring customers is varied to study their contribution to the severity of light flicker at customer C3.The results are shown in Fig. 9.The contribution of 5 and 12 neighboring customers is below the irritability threshold (P LM st = 1).It is shown that 26 customers contribute to the risk of light flicker with a probabilistic number of 480.35 voltage fluctuations perceived by an average observer in 50 % of the cases in a 10-minute interval.The calculation of the P LM st is limited to a value of the maximum total risk below 294 as explained in Section V.For this reason, the contribution to the severity of light flicker (P LM st ) of 26 neighboring customers does not appear in Fig. 9.

3) TOTAL SEVERITY OF LIGHT FLICKER AT CUSTOMER POINT OF CONNECTION
As shown in Fig. 10, the total severity of light flicker experienced by customer C3 reaches the irritability threshold (P LM st = 1) with a short-circuit impedance of 1.6745 with 12 neighboring customers, and of 1.6944 with 5 neighboring customers.These values of short-circuit impedances are over 99.98 th percentile of Swedish networks in Fig. 2 and are associated to less than 5 % of the networks of residential customers in Europe [14].For the reason given in Section V and as it is stated in Sub-section VI-B2, it is not possible to calculate the contribution of 26 neighboring customers, nor the total severity of light flicker at customer C3 associated with this number of customers.
The maximum difference of the severity of light flicker due to the number of neighboring customers is 0.0962 with a short-circuit impedance of 0.4715 , and it decreases to 0.0317 with a short-circuit impedance of 1.6944 .It indicates that the contribution to the severity of light flicker of the neighboring customers weights less for higher values of the short-circuit impedance than the contribution of the customer itself if the value of the transfer impedance is kept constant, as observed in Fig. 10.This holds under the assumption that the contribution of the neighboring customers and the customers itself aggregates as proposed in IEC TR 61000-3-7 [17].

C. COMPARISON BETWEEN LED LAMPS AND INCANDESCENT LAMPS 1) GLOBAL EMISSION OF LIGHT FLICKER
Fig. 11 shows the global emission of light flicker (at node 2) of an incandescent lamp and a generalized LED lamp to compare the results.The global emission for Z 1,2 modified to 0.4405 (for the reasons explained in Section VI) is 2.94 times higher for an incandescent lamp and the maximum total risk is 2.03 times higher.A similar proportion for the global emission (2.95 times higher for incandescent lamps) is obtained for Z 1,2 modified to 0.2409 , but the maximum total risk is 8.8 times higher for an incandescent lamp.The irritability threshold is reached for a Z 1,2 impedance 4.72 times lower than for a generalized LED lamp and the maximum total risk is 1.86 times higher than for a generalized LED lamp.

FIGURE Comparison of global emission between an incandescent
and a generalized LED lamp.

2) LIGHT FLICKER EXPERIENCED BY A CUSTOMER
Table shows the severity of light flicker experienced by a customer from an incandescent lamp and a generalized LED lamp.The real impedances of the LV network with 6 customers shown in Fig. 3 are used.Customer C4 is chosen for the assessment since it has the highest short-circuit impedance.
Comparing the contribution of neighboring customers, the maximum total risk of light flicker increases.There is a probabilistic number of 5 voltage fluctuations more perceived by an average observer in 50 % of the cases.
The contribution of the customer itself to the severity of light flicker is 3.18 times higher with an incandescent lamp.The total severity of light flicker experienced by customer C4 is over the irritability threshold with the real impedances indicated in Fig. 3.

VII. DISCUSSION
A. LIGHT FLICKER AT FULL SUPPLY CAPACITY Z 1,2 modified to 0.3187 is the maximum impedance for which is possible to calculate the global emission of 27 customers (full supply capacity of the transformer) and the respective contribution to light flicker of 26 customers to another customer (customer C3 selected).It is indicated in Sub-section VI-A where Fig. 7 shows the global emission obtained for this value of Z 1,2 .In Sub-section VI-B, this limitation is indicated but no results are given.Therefore, the contribution to light flicker of 26 customers to customer C3, the contribution of customer C3 itself and the total severity are calculated in Table 6 for this impedance (Z 1,2 modified to 0.3187 ).

B. SEVERITY OF LIGHT FLICKER IN A 3-PHASE NETWORK
The values of the severity of light flicker are expected to be lower than the ones obtained if the household devices are distributed between the three phases.All household devices are considered connected to the same phase in this study, giving the worst case.The propagation between phases of the voltage fluctuations reduces the magnitude of the voltage fluctuations as experienced in the measurements of the propagation of voltage fluctuations in Section II.It means that the impedances that lead to reach the limits studied may be even higher.

C. IEC FLICKERMETER AND LIGHT FLICKERMETER RELATIONSHIP
The P LM st from a generalized LED lamp showed to be around 3 times lower than that from an incandescent lamp.A conclusion of this result is that the severity of flicker (P st ) measured by the IEC flickermeter [7] divided by 3 would be the severity of light flicker experienced from a generalized LED lamp.It could be used as an approach to know the severity of light flicker experienced by the customers using the IEC flickermeter [7].This proportion may be a result of or influenced by the methodology used in the study, the set of LED lamps used, the assumption that the same household devices are considered for each customer, or the types of household devices considered as the source of voltage fluctuations.The severity of light flicker is not studied for changes in these parameters in this study.

VIII. CONCLUSION
An assessment of the risk and severity of light flicker considering LED lamps as the customer lighting technology and household devices as source of voltage fluctuations is developed based on the configuration of a real LV network.The global emission of light flicker and the light flicker experienced by a customer are studied for values close to the global emission limit, individual emission limit and the irritability threshold (P LM st = 1).The assessment shows that to reach the global emission limit (G PstLV = 0.65), with 27 customers (full capacity of the LV grid studied) the impedance needed from the transformer to the PoE considered is at least over the 84 th percentile of a sample of 38888 short-circuit impedances from a Swedish grid, and with up to 13 customers an impedance higher than the one associated to the 95 th percentile of the grids in Europe is needed.The same holds for the transfer impedances and short-circuit impedances values that are found to reach the severity threshold (P LM st = 1) at customer PoC considering the contribution from neighboring customers and the customer itself.The results are calculated for a single-phase system without considering the impedance of the operating household devices.The consideration of the household devices impedance would decrease the transfer and short-circuit impedances, what may result in the need of even higher impedances of the LV network than the shown in this study for reaching the global and individual emission limits, as well as the irritability threshold.The distribution of the household devices in a 3-phase system may also lead to the need of higher impedance of the cables in the LV network to reach the aforementioned limits, since the voltage fluctuations are expected to reduce in magnitude when they propagate between adjacent phases as observed in the measurements explained in Section II although this reduction being different for each adjacent phase.The duration of the voltage fluctuations does not change neither propagating between different points of the network nor between phases according to the measurements in Section II.
The contribution to the severity of light flicker of a customer itself weights more for higher values the short-circuit impedance than the contribution of neighboring customers when the transfer impedance is kept constant.This conclusion holds under the assumption that the contribution of the neighboring customers and the customers itself aggregates as proposed in IEC TR 61000-3-7 [17].
The severity of light flicker obtained with a generalized LED lamp and an incandescent lamp have been compared.The relationship between P LM st values obtained applying the methodology described and based on [3] is that the severity of light flicker is approximately three times higher with an incandescent lamp.It points that may be possible to obtain a ratio to estimate the severity of light flicker experienced from a generalized LED lamp [3] using the IEC flickermeter [7].

FIGURE 2 .
FIGURE 2. Cumulative distribution function of short-circuit impedances of 38888 real residential customers in Sweden.

FIGURE 4 .
FIGURE 4. Maximum network impedance against power consumption.

FIGURE 5 .
FIGURE 5. Simplified explanation of the stochastic assessment of the risk of light flicker.

FIGURE 6 .
FIGURE 6. P LMst difference between the values obtained in this study and the values obtained in[3] for each possible value of the risk of light flicker index.

FIGURE 7 .
FIGURE 7. Global emission of light flicker assessed using the risk light flicker index.

FIGURE 8 .
FIGURE 8. Contribution of customer C3 itself for different short-circuit impedances.

FIGURE 10 .
FIGURE 10.Severity of light flicker in customer C3.

TABLE 1 .
Transfer impedance matrix in ohms of the real LV network.

TABLE 2 .
Individual emission from a customer at node 2.

TABLE 3 .
Global emission of light flicker.

TABLE 4 .
Global emission of light flicker exceeding the individual emission limit.

TABLE 5 .
Severity of light flicker emitted by a generalized led lamp and an incandescent lamp at customer C4.

TABLE 6 .
Light flicker at customer C3 with 26 neighboring customers.