Nicolas Manduley

Stephan Pack

Alain Xemard

Selle Toure

Bertrand Raison

Serge Poullain

Alain Xémard

Sellé Touré

Techniques for the improvement of the lightning back-flashover performance of double circuit HVDC lines

Keywords: HVDC, lightning, back-flashover, double circuit, surge arresters, unbalanced insulation

Introduction

This document addresses different aspects regarding the lightning performance of HVDC lines, and in particular of double circuit configurations. In such configurations, two poles may have the same rated voltage and thus present similar back-flashover risks in case of lightning strikes, potentially leading to double flashovers and causing a temporary loss of the transmitted power. Hence, special attention should be paid to the issue of double flashovers to avoid the interruption of the current on several DC poles after a lightning strike and the potential consequences to the system.

To do so, EMT simulations have been performed and thoroughly analysed considering factors such as the footing resistance of the tower, the geometric configuration of the DC poles, the coupling of the conductors, the polarity of the lightning strike and the voltage drops across the tower. Two solutions aiming to improve the lightning performance are investigated and explained in terms of the fundamental mechanisms that are directly affected by them.

The paper is structured as follows. Section 2 discusses the overall problem regarding lightning performance in HVDC systems, and techniques for its improvement. Section 3 presents the general methodology to conduct the studies presented in this paper.

Section 4 addresses all the modelling aspects related to these different study cases.

Section 5 is dedicated to the effect of the configuration of the poles on the lightning performance of the system, while section 6 studies and compares the two solutions considered in this work for the improvement of the lightning performance. The overall conclusions are listed in section 7.

HVDC Overhead Line Faults

As in HVDC systems the voltages are constant, the back-flashover risk of each DC pole is the same at any given instant, as opposed to HVAC systems, where phase angles influences the risk for each phase conductor within the tower. This section addresses the main aspects regarding the lightning performance specifically for HVDC overhead lines which were considered in this research.

Consequences of faults on a DC system

Whenever a flashover due to lightning occurs, a temporary pole-to-ground fault appears. Depending on the protection strategy of the system, an AC breaker opening may be required to interrupt the fault current [START_REF] Touré | VSC Transmission[END_REF] which can result in a significant temporary loss of transmitted power. This risk may be especially strong in multi-circuit DC transmission towers, since several DC poles can be lost at the same time due to the same lightning strike, potentially resulting in an even higher loss of transmitted power.

Lightning fault mechanism

When lightning strikes a tower, electromagnetic waves propagate through all the parts of the configuration. As the voltage across the tower structure rises, so does the voltage between the terminals of the insulator strings. In a simplified way, if this voltage reaches a critical level, a back-flashover arises [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF]. Whenever a first back-flashover occurs, a fraction of the lightning current is injected to the faulted pole, and less current contributes to the voltage rise of the tower.

Therefore, the voltage across the tower drops and more current will be required to increase the voltage of the tower sufficiently to produce a second back-flashover.

In addition, if two poles on the same cross arm are at the same instantaneous voltage at strike inception, it is likely that both insulators will flashover at the same time, thus losing both poles simultaneously. Consequently, if the circuits of a doublecircuit HVDC line have the same rated voltage, the risk of double flashovers to occur increases compared to a situation with different rated voltages.

Influence of the position of the DC poles

Another factor (among others also addressed in this work) that influences the flashover probability is the coupling between the conductors, particularly the coupling between the poles and the shield wires. Therefore, the relative position of the DC poles shall be a major determinant of the lightning performance of an HVDC line.

In [START_REF] Lu | Lightning Backflash Performance for±500kV Double Circuit Transmission Lines[END_REF], an assessment of the effect of the configuration of the DC poles on the backflashover rate has been performed quantitatively for a specific 500 kV configuration.

In the present work, different pole configurations are investigated, analysed and compared in terms of their respective performance, but also in terms of the fundamental factors that differentiate them. This study has been conducted for two different voltage levels (320 kV and 500 kV).

Improvement of the lightning performance

One of the most evident and well-known techniques to improve the lightning performance of an overhead line concerns the improvement of the grounding of the tower. This can be done by directly modifying the shape, depth or materials of the grounding grid or electrodes [START_REF] Zhenghua | Research on reducing grounding resistance of transmission line tower grounding grid[END_REF], depending on the specific case. Other solutions involve the use of counterpoise wires [START_REF] Visacro | Lightning performance of transmission lines: requirements of tower-footing electrodes consisting of long counterpoise wires[END_REF] and the installation of underbuilt wires [START_REF] Visacro | The use of underbuilt wires to improve the lightning performance of transmission lines[END_REF], which physically connect several towers in series so that the equivalent grounding resistance in case of a stroke is reduced. These solutions are well known and in many cases they can effectively help improve the back-flashover performance for areas with high soil resistivity. However, this is not always an easy task and these solutions have often a limited effect, especially for regions with poor soil resistivity.

In this work, two alternative solutions are examined. The first one involves the installation of line surge arresters, and considers different numbers and possible locations of the arresters within the considered tower. The second solution addresses the use of an unbalanced insulation design of both circuits.

Unbalanced insulation solutions have already been proposed for HVAC schemes, though their applicability seems to be complex and limited [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF][START_REF] Kawai | Design and performance of unbalanced insulation in doublecircuit transmission lines[END_REF] and more effective for configurations with several circuits in one tower [START_REF] Li | A design of unbalanced insulation to improve the lightning performance of multi-circuit transmission lines[END_REF].

An unbalanced insulation solution for HVDC systems is presented in [START_REF] Lundquist | Novel design for parallel VSC HVDC links on common overhead line towers[END_REF] for the design of the SouthWest Link with a horizontal (no cross arms) disposition of all of the DC poles within the tower. In [START_REF] Manduley | Use of Unbalanced Insulation for the Limitation of Double-Pole Lightning Flashovers in Double Circuit HVDC Overhead Lines[END_REF], a solution is investigated for a specific double circuit configuration with two cross arms for different values of the relative unbalance between both circuits. Regarding this solution, this paper aims to complement the studies started in [START_REF] Manduley | Use of Unbalanced Insulation for the Limitation of Double-Pole Lightning Flashovers in Double Circuit HVDC Overhead Lines[END_REF], and provide more evidence towards its applicability in HVDC systems in general.

Methodology for the Back-Flashover Rate Calculation

The evaluation of the back-flashover performance is based on the estimation of the critical flashover current If, which is the minimum lightning current intensity required to produce a flashover in case of direct strike on the tower or shield wires. The calculation procedure is inspired in the method presented in [START_REF]CIGRE TB 63[END_REF] but applied to DC and based on simulations to obtain the value of If. The results are then compared in terms of their corresponding back-flashover rates (BFOR) for different tower footing resistances.

Estimation of the critical flashover current If

The study cases are modelled in an EMT-like program [START_REF]EMTP (Electromagnetic Transient Program[END_REF]. Lightning strikes are applied at the top of the tower and at one third of the span length (sky wire) to determine the lowest current producing a single and a double flashover (i.e. If), namely the critical current. It is assumed that lightning strokes with a higher current will also produce a flashover.

The value of the critical current If is determined by dichotomy, and the other lightning parameters (i.e. maximum steepness and front time) are calculated as the median values of the corresponding current intensity as indicated in [START_REF]CIGRE TB 63[END_REF]. Even though these parameters are based on measurements performed for negative lightning, positive lightning has also been represented using the same distribution, under the hypothesis that it is an approximation which does not have a major influence on the results. However, it should be taken into account that the share of BFOR due to positive strikes is generally higher than the actual distribution of positive strikes. This is because positive strikes tend to be more energetic, mostly due to the more frequent presence of continuing currents and/or M-components in positive strikes [START_REF]CIGRE TB 549[END_REF], which have not been considered in this research. This is addressed further in section 4.1.

The results of the simulations are analysed to determine whether there has been at least one flashover (or two, in the double flashover case) or not.

Back-flashover rate (BFOR) calculation

Once the critical flashover current is determined, the back-flashover rates (BFOR) can be calculated as indicated in CIGRE TB 63 [START_REF]CIGRE TB 63[END_REF] and shown in equation (1) below:

𝐵𝐹𝑂𝑅 = 𝑁 𝐿 𝑃(𝐼 ≥ 𝐼 𝑓 ) (1)
where P(I≥If) is the probability for a lightning with an equal or higher current intensity (with respect to If) to occur, and NL represents the geometry of the line and the keraunic level of the region. These factors are calculated through equations ( 2) and

(3) below, as also indicated in [START_REF]CIGRE TB 63[END_REF]:

𝑃(𝐼 ≥ 𝐼 𝑓 ) = 1 1 + ( 𝐼 𝑓 31 ) 2.6 (2)
𝑁 𝐿 = 𝑁 𝑔 ( 28 𝐻 𝑇 0.6 + 𝑏 10 )

where HT and b are the height of the tower and the width of the line, respectively, and Ng represents the ground flash density of the region. The value of Ng was set to 1 (flashes/km²/year) so that the back-flashover rates can be easily adjusted to any particular case by just multiplying them by the corresponding ground flash density.

Separate values are calculated for positive and negative strikes and an overall value is estimated considering that approximately 90% of the strikes are negative and 10% are positive. The distribution between the strikes along the span and directly on the tower is considered by applying a factor of 0.6 to the calculated BFOR [START_REF]CIGRE TB 63[END_REF].

Modelling Aspects and Configuration Details

This section addresses the modelling aspects of the different components considered in the study. All the models are in agreement with the recommendations of IEC 60071-4 [START_REF]Insulation Coordination Part 4: Computational guide to insulation coordination and modelling of electrical network[END_REF].

Lightning strike

The lightning strike is modelled using the CIGRE concave shape. The parameters are calculated for each current intensity If by using the median values of the time to front tf and maximum steepness Sm, as indicated in [START_REF]CIGRE TB 63[END_REF]. In absence of detailed data for positive strikes, the same model has been used for both lightning polarities by just reversing the sense of the lightning current.

Different studies and measurements have determined that the resistance of the channel can be considered constant with values ranging from several hundred Ω to a few kΩ. In this work, a value of 1 kΩ has been used to represent the resistance of the channel in parallel with the ideal current source, as it is a common agreed value in the literature [START_REF]CIGRE TB 549[END_REF].

All strikes are considered to be perfectly vertical. The coupling between the channel and the overhead line or the tower has not been considered.

Transmission towers and overhead lines

The dimensions of the towers for the 320 kV and 500 kV cases are shown in Fig. 1.

For the model implementation, the tower body, including the vertical section between the upper and lower cross arms, is modelled through a lossless propagation line model to take into account the wave propagation times. The cross arms and the shield wire supports are represented by a single inductance with a value of 1 µH/m.

Insulators

Insulator strings are represented through their arcing horns using the leader model proposed by Shindo and Suzuki [START_REF] Shindo | A new calculation method of breakdown voltage-time characteristics of long air gaps[END_REF], which is recommended for long gaps and considers the streamer and leader formation phases of a flashover, as well as the polarity of the impulse. In this work, the base insulator arcing horn distances are 2.74 m and 4.16 m for the 320 kV and 500 kV systems, respectively. The model has been adjusted in order to present an accurate behaviour of the flashover voltage and current under transient conditions for this particular range of values (i.e. 2.74 m -4.16 m) by tuning the pre-discharge current levels of the flashover model. This was done by setting the capacitance between the leader and the ground of the model to

Tower grounding

In this work, a circuit approach is considered [START_REF] Grcev | Modeling of grounding electrodes under lightning currents[END_REF], consisting of a single resistance without including the ionization of the soil nor the frequency dependence of the soil parameters. In both cases the effect on the lightning performance is likely to be favourable since it tends to reduce the equivalent footing resistance of the tower [START_REF] Grcev | Modeling of grounding electrodes under lightning currents[END_REF][START_REF] Grcev | On high-frequency circuit equivalents of a vertical ground rod[END_REF]. However, the specific conditions under which the effect would not be favourable for the lightning performance have not been addressed in this work. It is thus assumed for the effects of this research that disregarding both effects yields results that are more conservative and allows studying the impact of the tower grounding on the lightning performance.

Furthermore, studies indicate that for the purpose of evaluating the lightning performance of an overhead line, a single resistance can accurately represent the effect of including the frequency dependence of the soil parameters in the analysis [START_REF] Visacro | Lightning performance of transmission lines: requirements of tower-footing electrodes consisting of long counterpoise wires[END_REF][START_REF] Visacro | The use of the Impulse Impedance as a concise representation of grounding electrodes in lightning protection applications[END_REF]. Therefore, conducting a parametric study using different values for a single resistance is considered to yield results that are valid over a wide range of conditions regarding the grounding, thus providing further justification to the hypothesis.

Surge arresters

At high frequencies, the inductive properties of surge arresters become more significant by producing a delay between the instants where the current and voltage peaks are produced. The Pinceti model is a modified version of the IEEE model in which the parameters only depend on electrical magnitudes, and thus it is easy to implement while keeping a similar accuracy to that of the IEEE model [START_REF] Pinceti | A simplified model for zinc oxide surge arresters[END_REF]. For these reasons, this model has been used in the cases involving surge arresters.

Simulation Setup

A section of eleven towers has been modelled to take into consideration the effect of successive reflections on neighbouring towers. Lightning strikes are applied at the middle of the considered line section (i.e. tower 6). For each case, a constant footing resistance has been used for every tower, ranging from 10 Ω to 100 Ω. Lightning currents up to 350 kA were considered. If no flashovers were produced at 350 kA, the corresponding value of back-flashover rate (BFOR) is considered to be zero. A long line section is placed at both ends to avoid reflections with the stations.

Effect of Pole Configuration on Back-Flashover Rate

Regarding the geometry of the towers considered in this work (see Fig. 1), there are four possible configurations for the DC poles. These configurations are illustrated in In this section, the effect of the pole configuration on the overall and double backflashover lightning performance is investigated for two voltage levels (320 kV and 500 kV) and different values of the tower resistance ranging from 10 to 100 Ω. It is worth mentioning that the overall BFOR includes all kinds of lightning flashovers.

Thus, when speaking about double back-flashover rates, it refers to the portion of the overall BFOR which is constituted by two or more flashovers.

Results: effect of the configuration of the poles

The overall and double back-flashover rates (BFOR) for the 320 kV and 500 kV systems are shown in Fig. 2 and Fig. 3, respectively, for all pole configurations. As shown in Fig. 2a and Fig. 3a, the Top and Bot configurations present the lowest overall back-flashover rates. However, these flashover rates are almost entirely constituted by double flashovers (Fig. 2b and Fig. 3b). This means that in those two configurations, the critical current If required to produce a first flashover will most likely produce a double flashover in the system.

In the case of the Side and Xed configurations, the overall BFOR tends to be slightly higher than in the above-mentioned configurations, but the proportion of double flashovers is greatly reduced.

In all cases, the results are greatly influenced by the footing resistance of the towers.

Factors influencing the results

The results illustrated in Fig. 2 and Fig. 3 can be explained by considering four main factors: the symmetry of the model, the conductor coupling, the polarity of the impulse and the voltage drops along the tower.

The model used in this work is perfectly symmetrical (i.e. the left side of the tower is mathematically identical to the right side). In real applications, small asymmetries inherent to the construction of the line and/or the dielectric properties of individual insulators may make the obtained results to differ to a certain extent from what is observed in practice. Further studies are required to determine the impact of this aspect on the validity of the results.

As for AC systems [START_REF] Sargent | Lightning performance of double-circuit transmission lines[END_REF][START_REF] Kawai | Design and performance of unbalanced insulation in doublecircuit transmission lines[END_REF], the coupling of the conductors causes an additional voltage to arise in the DC pole due to the induced voltage from the current flowing through the shield wires. Since this voltage rise goes in the same direction as that of the tower (see example in Fig. 4), the induced voltage provides some protection to the pole by reducing the total voltage across the insulators. As it will be shown later, the coupling between the conductors has a major influence in the differences in lightning performance of the double-circuit DC configurations analysed in this work.

Additionally, because the pole voltages are constant and the dielectric strength of an air gap is different for positive and negative impulses [START_REF]CIGRE Technical Brochure 072: Guidelines for the Evaluation of the Dielectric Strength of External Insulation[END_REF][START_REF] Cortina | Study of the Dielectric Strength of External Insulation of HVDC Systems and Application to Design and Testing[END_REF], the polarity of the lightning strike also determines which insulator strings are more susceptible to flashovers. For instance, in case of a negative lightning strike (which represents about 90% of the lightning strikes [START_REF]CIGRE TB 63[END_REF][START_REF]CIGRE TB 549[END_REF]), the positive poles are more likely to flashover first. Finally, the voltage drop across the different sections of the tower may also play a role in the performance. Since the voltage drop across the upper section concerns only the poles in the upper cross arm, the upper cross arm sees a slightly higher voltage drop of the tower than the lower cross arm. This is illustrated in Fig. 4 (red and green curves). Although less common (~10%), a positive polarity strike has been represented in the figure for the sake of clarity. As it can be noticed, the voltage drop between the cross arms counters the protective effect of the line coupling (blue and pink curves). However, this effect tends to be significantly smaller than the coupling effect for most cases. Very low values of footing resistance (under 4 Ω in the tests performed in this work) and unusually high current intensities (above 250-300 kA) are required for this effect to become more significant than the coupling effect. Therefore, this effect may be often disregarded, but could still explain the behaviour of the system under very specific conditions.

Discussion on the results

Considering all of the above, it is possible to explain the differences between the four pole configurations studied.

For instance, the fact that both the Top and Bot configurations (see Table 1) are almost entirely constituted by double flashovers is explained through the intrinsic symmetry of the model used and the coupling of the conductors. Both poles on any given cross arm will see the same voltage rise of the tower and, regardless of the polarity of the lightning strike, the protective effect of the coupling will be almost identical on both sides (because the currents flowing on both shield wires are roughly the same).

However, to explain why the Top configuration presents a better overall performance than the Bot configuration, it is required to consider the fact that most lightning strikes are negative, and that whenever a second flashover follows, it is more likely to appear in the other pole of same polarity as the conductor where the first flashover occurred. In case of direct negative strikes, the positive poles are more likely to flashover, and in the Top configuration both positive poles are located closer to the shield wires, and thus are better protected by the coupling effect than in the Bot configuration. For this same reason, the Bot configuration presents a slightly better performance than the Top configuration under positive strikes, but since this only represents about 10% of the cases, the overall performance of the Top configuration remains superior.

Similarly, the fact that both the Side and Xed configurations present the same overall BFOR, but different distributions of double flashovers, is also explained through the coupling effect. Both configurations have a positive and a negative pole in the lower cross arm. Hence, regardless of the polarity of the lightning strike, one of the lower poles will flashover first (as the upper poles are better protected by coupling effect). These effects are almost identical for both configurations during the first flashover.

However, as the first insulator flashes, a significant current is injected into the DC pole. This has two main consequences: first, the current flowing through the tower to the ground will decrease, and thus, the voltage of the tower structure will also drop, making it more difficult for a second flashover to occur. Secondly, the variation of the current being injected to the DC pole will also induce a voltage on neighbouring lines with the same polarity as the one originated by the shield wires, hence also contributing to the protection of the other insulators.

In the Side configuration, the second insulator that could flashover is right above the faulted pole, and thus closer than in the Xed configuration and better protected by the induction from the faulted DC pole. Consequently, for a second flashover to occur, a higher critical current If is required in the Side configuration than in the Xed configuration, thus producing the difference on double BFOR observed in Fig. 2 and Fig. 3.

Nevertheless, a configuration like this may present a series of practical drawbacks. In particular, the unbalanced distribution of the electric field which could result in a wider corridor [START_REF] Liu | Analysis of electric field, ion flow density, and corona loss of same-tower double-circuit HVDC lines using improved FEM[END_REF][START_REF] Yang | A calculation method for the electric field under doublecircuit HVDC transmission lines[END_REF], and the maintenance of a single circuit may be complicated because both poles would necessarily be on opposite sides of the tower. These potential drawbacks are naturally avoided with the Xed configuration.

Conclusions and final considerations

The Top configuration presents the best overall back-flashover performance mainly due to the coupling effect. However, when the critical current If is reached, it is most likely that both poles will flashover at the same time. This constitutes a major drawback since in case of flashover, 100% of the transmitted power is lost.

The Side and Xed configurations present a slightly higher BFOR than the Top and Bot configurations, but a significantly lower incidence of double flashovers. All the differences in performance between the different configurations can be analysed in terms of coupling effect, distribution of the polarity of lightning strikes and voltage drops across the tower. Nevertheless, in all cases, the dominant factor regarding lightning performance is the footing resistance of the towers.

Improvement of the Lightning Performance

In this section, two solutions are investigated for the improvement of the lightning performance: one involving the installation of line surge arresters (LSA) on specific towers along the line, and another concerning the use of an unbalanced insulation of the DC circuits. Since the overall results and behaviours were found to be identical for both system voltage levels (see previous section), both solutions were studied considering only a 500 kV system.

The base configurations to study each solution have been chosen considering the advantages and drawbacks of each configuration discussed in the previous section.

In this regard, the Xed configuration constitutes a case study where the main interest is to reduce the overall BFOR, as the incidence of double flashovers is naturally lower (as for the Side configuration but without its practical drawbacks, as discussed in section 5.3). For this reason, this configuration has been used to study the line surge arresters solution. Conversely, the Top and Bot configurations provide a good environment to study the unbalanced insulation solution. Since the Top configuration presents a naturally lower overall BFOR (due to the higher occurrence of negative strikes), this configuration has been used to study the unbalanced insulation solution.

Line surge arresters (LSA) solution

The installation of LSA aims to improve the overall lightning performance, and it is well documented in the literature [START_REF]Surge arresters -Part 9: Metal-oxide surge arresters without gaps for HVDC converter stations[END_REF][START_REF] Gu | Comparison and Analysis on Key Performance of EHV/UHV DC Transmission Line Surge Arresters[END_REF][START_REF] Visacro | Concerns on surge-arrester application for improving the backflashover rate of transmission lines[END_REF][START_REF]IEEE Std. 1243, Guide for improving the lightning performance of transmission lines[END_REF][START_REF]CIGRE TB 440[END_REF]. Even though it is a very effective solution to improve the lightning performance, it is often considered not economically viable to install LSA all along a transmission line. Therefore, this solution is implemented on specific critical points where the lightning performance is abnormally low (due to high altitude zones, mountainous regions, high soil resistivity areas, high lightning activity, etc.).

In this section, different configurations of LSA are investigated for the improvement of the lightning performance of a double-circuit HVDC line. The simulation setup is the same as in the previous section, but installing the different combinations of LSA (see Fig. 5) in the tower which is stroke by lightning (tower 6, at the middle of the eleven towers considered; see section 4.6).

Single arrester in the lower positive (LP) pole

Because 90% of the strikes are negative, back-flashovers are more likely to be produced in the positive poles. Because the upper positive pole is closer to the shield wires (and thus better protected by induction), the lower positive pole is the most likely to flashover. As it can be observed in Fig. 6, by directly protecting only the lower positive pole (LP configuration, see Fig. 5), a great improvement of both the overall and double back-flashover rates can be achieved (BFOR). Though double flashovers are still possible under positive strikes (because both negative poles remain unprotected) and very intense negative strikes (enough to make the lower negative pole flashover after the upper positive pole), the sum of the double BFOR due to these two scenarios is still significantly lower than in the base case (red bars in Fig. 6b).

Due to the great advantages of protecting the lower positive pole, all configurations with two surge arresters considered in this section are obtained by placing an additional arrester to the LP configuration on each of the other three poles of the tower (see Fig. 5).

LPLN configuration

The poles in the lower cross arm are the ones with the highest probability to flashover because the protective coupling effect from the shield wires is weaker than for the poles in the upper arm. If both positive and negative lower poles are protected, as it can be observed in Fig. 6a, there is a significant improvement of the overall performance (especially at higher values of the footing resistance).

Even more interesting is the fact that, with this configuration, the probability of double flashovers is almost zero for the studied system and the footing resistances considered (see Fig. 6b). Since the surge arresters, regardless of the polarity of the strike, directly protect the lower positive and negative poles it is in the upper pole where the first flashover must be produced. Therefore, for a double flashover to occur, the current crest value must be sufficiently high to produce the second flashover in the pole with the opposite polarity, while also countering the coupling effect from the shield wires.

LPUP configuration

If the second arrester is placed on the upper positive pole, the tower is almost perfectly protected against any negative strike (except for strikes sufficiently intense to produce a back-flashover in the negative poles). The overall back-flashover rate (BFOR) is significantly lower than in the LP configuration (>50% lower) and it is the lowest among all the studied configurations (Fig. 6a). The portion of the overall BFOR constituted by double flashovers is also among the lowest obtained, right after the LPLN configuration (Fig. 6b).

LPUN configuration

Generally, the upper negative pole is not very likely to flashover except in the case of very intense positive strikes producing double flashovers (since under normal conditions, the lower pole will flashover first). Therefore, as it is shown in Fig. 6, the LPUN configuration does limit the occurrence of double flashovers, but the overall improvement compared to the LP configuration is not very significant.

Final considerations and partial conclusions

In most cases, a single arrester in the pole with the highest probability of flashover may be enough to significantly improve the lightning performance of a given tower.

In case a single arrester is not enough to reach the desired lightning performance (e.g. because of very high soil resistivity), the LPLN configuration seems to be the best option as it significantly reduces the BFOR, and the probability of having double flashovers drops to practically zero. However, if double flashovers are not a great issue, the LPUP configuration provides the maximum reduction of the overall BFOR, since it protects the configuration completely against any flashover originated by negative strikes.

Unbalanced insulation

The unbalanced insulation solution consists in using different insulator arcing horn distances for each circuit in the tower. This way, it is possible to determine in advance which circuit will flashover first in case of lightning strike, and thus prevent the incidence of flashovers on the other circuit. The base arcing horn distance is 4.16 m, and the unbalance has been introduced by reducing the distance on one of the sides by 10, 30 and 50 cm. The study case considered is illustrated in Fig. 7. It is observed in Fig. 8a that reducing the arcing horn distance on one side increases, as expected, the overall back-flashover rate. The increase is significant for a difference of 50 cm, small for 30 cm and not very significant for 10 cm. However, for all cases, a significant reduction of the occurrence of double flashovers is obtained, which is the main focus of this solution.

It is also noticed that when increasing the difference from 30 to 50 cm, the increase in the overall back-flashover rate (BFOR) begins to be more significant than the reduction of the double BFOR. From 10 to 30 cm, both the increase of the overall BFOR and the reduction of the double BFOR are smaller, but significant.

Based on these results and considerations, it is concluded that an optimal value may range between 30 and 50 cm.

In [START_REF] Manduley | Use of Unbalanced Insulation for the Limitation of Double-Pole Lightning Flashovers in Double Circuit HVDC Overhead Lines[END_REF], it was concluded that huge differences between the lengths of both circuits (above 80 cm) may not necessarily contribute significantly to the improvement of the lightning performance, and that an optimal value may be close to 40 cm. In [START_REF] Lundquist | Novel design for parallel VSC HVDC links on common overhead line towers[END_REF], a difference of 50 cm was found to be optimal for the design used in SouthWest Link.

Therefore, it can be concluded that the results obtained in this work are in agreement with the existing studies available in the literature, and provides further evidence supporting that the optimal value for an unbalanced insulation solution should range between 30 cm and 50 cm.

Overall comparison

Taking into account the results and conclusions from this section, a general comparison between both solutions and their respective base cases is shown in Fig. 9. It features the solutions considered as the best alternatives for each case: the LP and LPLN configurations for the surge arrester solution, and differences of 30-50 cm in the arcing horn distance for the unbalanced insulation solution. As expected, the surge arrester solution is much more effective in improving the lightning performance. However, this solution is only economically viable to improve the performance of some critical towers along the line. The unbalanced solution, on the other hand, can be implemented and studied along the whole line from the initial design.

From the results presented in Fig. 9, it is noticed that a pole configuration with both positives on the upper arm (Top), combined with the unbalanced insulation solution, can present a slightly better overall lightning performance for unbalances between 30 and 50 cm. The resulting incidence of double flashovers reaches similar values as in the crossed (Xed) configuration, where the unbalance is naturally introduced by placing both poles of the same polarity at different heights.

It should be also noted that the increase in the BFOR observed in the unbalanced insulation solution is due to the fact that the arcing horn distance is reduced (with respect to the base value) on one side. If the solution is considered from the conception of the line (as it is intended to be), the alternative of increasing the arcing horn distance on one side should be prioritized whenever possible. In that case, the overall BFOR would remain exactly the same as in the base case, as also seen in [START_REF] Manduley | Use of Unbalanced Insulation for the Limitation of Double-Pole Lightning Flashovers in Double Circuit HVDC Overhead Lines[END_REF], and even better performances can be achieved. In the worst case scenario, only slight modifications to the design of the tower shall be made to guarantee that all the minimum clearances are respected.

With a proper design of the insulation, the Top configuration may present better lightning performances than the most typically used crossed (Xed) configuration, as found for example in [START_REF] Dong | Protection of±500 kV HVDC Double-circuit Converter Station from Lightning Induced Overvoltage[END_REF][START_REF] Hu | Reliability Evaluation and Weak Component Identification of±500kV HVDC Transmission Systems with Double-Circuit Lines on the Same Tower[END_REF][START_REF] Ma | Fault Analysis and Traveling-Wave-Based Protection Scheme for Double-Circuit LCC-HVDC Transmission Lines With Shared Towers[END_REF][START_REF] Li | Research on Lightning Performance of Back-flashover of UHV Direct Current Double-circuit Mixed-voltage Transmission Lines on the Same Tower[END_REF]. A technical and economic study shall determine which solution best improves or satisfies the lightning performance requirements for a specific project.

Conclusions

In this paper, several aspects regarding the back-flashover performance of double circuit HVDC lines have been investigated. In particular, the effect of the geometrical configuration of the DC poles within a tower has been analysed thoroughly, as well as two different solutions to improve the lightning performance under different scenarios regarding grounding conditions, lightning polarities and location of the impact.

The main issues addressed during this work are the coupling between the conductors, the effect of the polarity of the lightning impulse, the voltage drop across the tower sections, the overall dynamics during a lightning strike within a given overhead line section to explain the BFOR results and two solutions for the improvement of the lightning performance.

The position of the DC poles in a double-circuit configuration plays a major role in the overall and double back-flashover rates, mainly because of the effect of the conductor coupling and the polarity of the lightning strike. All four possible DC pole configurations for a double circuit scheme with two cross arms have been studied in detail in order to identify the mechanisms leading to their differences in lightning performance.

A proper implementation of an unbalanced insulation solution can effectively improve the double back-flashover performance of a system in which both poles of the same polarity are placed at the same height. An unbalance of about 30 to 50 cm seems to be optimal. A significant improvement can also be achieved by installing only one surge arrester on the most vulnerable pole of the configuration, based on the conclusions of the analysis of the DC pole configurations.

With a proper design, a configuration with both positives on the upper cross arm (Top configuration), combined with an unbalanced insulation solution, can achieve similar or better lightning performances than the typical configuration with the polarities crossed (Xed configuration).

Fig. 1 .

 1 Fig. 1. Tower geometry and dimensions considered for the study cases Overhead lines are represented using a frequency-dependent (FD) model to account

  a) Overall and b) double back-flashover rates for all configurations in the 320 kV system a) b) Fig. 3. a) Overall and b) double back-flashover rates for all configurations in the 500 kV system

  . 4. a) Upper section: CIGRE concave shape model for a lightning strike of +120 kA. Lower section: potential rise of the tower at the upper and lower cross arms (red and green curves) and effect of the inductive coupling between the lines (blue and pink curves); b) Voltage measurements in the crossed (Xed) configuration used for this example. For this particular example, I = +120 kA and Rgnd = 40 Ω.

Fig. 5 .

 5 Fig. 5. The different surge arrester configurations considered. Each configuration is named based on its respective cross arm (upper or lower) and the polarity of the pole (positive or negative).The results and comparisons of the obtained overall and double back-flashover rates

Fig. 7 .

 7 Fig. 7. Study case for the unbalanced insulation solution including a reduced arcing horn distance on a complete circuit. All cases are performed on a configuration with both positives in the upper cross arm. The obtained results are shown in Fig. 8.

9 .

 9 Comparison of the overall (left) and double (right) back-flashover rates of the surge arrester and unbalanced insulation solutions.

Table 1 ,

 1 and are labelled with respect to the position of the positive poles in the

	Top	Bot		Side	Xed
	+	+	-	-	+	-	+	-
	-	-	+	+	+	-	-	+

arrangement: Top (both positives on top), Bot (both positives on bottom), Side (both positives on one side of the tower) and Xed (both positives crossed).

Table 1 .

 1 Different pole configurations considered


F Charru
email: francois.charru@imft.fr

Sand transport over a barchan dune

The present work investigates an important and yet unsolved issue: the relationship between the sand flux and the fluid shear stress over a spatially varying bed of particles. It is now recognized that over such a bed, the particle flux is not in equilibrium with the shear stress: there is some lag related to the particle inertia or particle settling. A confident modelling of this relaxation phenomena and the corresponding length scales, is still lacking (Charru, Andreotti and Claudin 2013). This question is investigated here from experiments on barchan dunes in a closed-conduit water flow. From visualizations with a high-speed camera and a tracking algorithm, the particle motion over the whole dune surface is determined: particle trajectories, local velocity and surface density of the moving particles, and local particle flux. The relationship between the local particle flux and local shear stress (estimated from previous analyses) is investigated. Surprisingly, the particle flux appears to be out-ofequilibrium over the whole dune surface, with saturation length much larger than expected.

INTRODUCTION

When a fluid flows over an erodible bed (e. g. in a channel, river, or marine current), particles forming the bed are eroded and transported downstream. As a consequence, an intially flat bed generally does not remain flat: bedforms such as ripples and dunes are observed to grow and propagate.

Although these phenomena are known for a long time, and have been widely studied both in the natural environment and laboratory flumes, their understanding is far from complete. From the experimental point of view, wavelength measurements exhibit large scatter, over one order of magnitude [START_REF] Yalin | On the determination of ripple geometry[END_REF]. From the theoretical point of view, the modelling of the bed shear stress τ b exerted by the fluid flow on the bed is dependent on uncertain knowledge about the turbulence over an undulated wall [START_REF] Abrams | Relaxation effects observed for turbulent flow over a wavy surface[END_REF]. Moreover, the sediment transport over a variable bed is not well-known, and the use of the classical laws q sat (τ b ) for the particle flux, which assume q sat to be in equilibrium with τ b , is now recognized to lead to wrong predictions, i.e. ripple lengths much to small [START_REF] Charru | Sand ripples and dunes[END_REF].

Crucial improvements for the sand transport law have been proposed during the last decade, based on the idea that as the shear stress varies, the particle flux does not adapt immediately, but after a certain relaxation time of length. The simplest transport law accounting for this relaxation is the first-order equation [START_REF] Sauermann | Continuum saltation model for sand dunes[END_REF][START_REF] Andreotti | Selection of dune shapes and velocities. Part 2: A two-dimensional modelling[END_REF]:

L sat ∂ x q = q sat (τ b ) -q.
(1)

This law states that when the actual flux q differs from the saturated --or equilibrium --flux q sat (τ b ), it relaxes exponentially towards q sat (τ b ) over the relaxation length L sat (figure 1). This equation holds for quasistatic situations where time variations of the bed are slow, i.e. when the bedform velocity is much smaller that the particle velocity, which is generally the case. For situations where such a condition would not be met, the term T sat ∂ t q should be added to the l.h.s. of Eq. ( 1), where T sat is a relaxation time.

Eq. ( 1) has been first introduced from phenomenological considerations. A different introduction of this equation was proposed by [START_REF] Charru | Ripple formation on a particle bed sheared by a viscous liquid. Part 1. Steady flow[END_REF] and [START_REF] Charru | Selection of the ripple length on a granular bed sheared by a liquid flow[END_REF], based on the modelling of the erosion and deposition rates (Figure 2). The expression of the saturation length is discussed below.

Figure 1. Fluid flow coming over an erodible bed (for x > 0) and corresponding particle flux increasing from zero to q sat over the length L sat .. When Eq. ( 1) is used in bed stability calculations (instead of the usual equilibrium law q = q sat (τ b ) which corresponds to L sat = 0), ripple length predictions are much improved [START_REF] Charru | Selection of the ripple length on a granular bed sheared by a liquid flow[END_REF]). Indeed, bed instability is rooted in the fact that the phase of the bed shear stress leads that of the bed deformation, due to fluid inertia. Within the equilbrium assumption, the phase of the particle flux is the same as that of the bed shear stress, so that particles are dragged from troughs to crests (figure 3a). Accounting from the stabilizing (diffusive) effect of gravity on inclined slopes, a cut-off wavenumber arises, which defines the most amplified wavelength which can be compared to ripple length measurements. Within the new nonequilibrium model (figure 3b), the particle flux lags, which corresponds to a stabilizing effect : a relaxation length L sat larger than the fluid inertia length L τ carries the maximum particle flux downstream of the crest of the disturbance, so that the bed deformation vanishes and the flat bed is stable. Predictions of the most amplified wavelength imply that some expression is given for L sat . Two heuristic models have been proposed. When particle inertia dominates, L sat scales with the acceleration length (ρ p /ρ) d, where ρ p and ρ are the particle and fluid density and d is the particle diameter [START_REF] Andreotti | Measurements of the aeolian sand transport saturation length[END_REF]. When settling effects dominate, L sat scales with the deposition length (u * /V fall ) d, where u * is the friction velocity (which is a scale for the particle velocity) and V fall is the settling velocity of the particles [START_REF] Charru | Selection of the ripple length on a granular bed sheared by a liquid flow[END_REF]. The first situation is more likely relevant for aeolian transport (where the ratio ρ p /ρ is large), whereas the second is expected to hold for aqueous transport where ρ p /ρ is about two. Thorough measurements in water and oil, of the erosion and deposition processes at the particle scale, have allowed some determination of L sat , for both laminar flow (Charru, Mouilleron and Eiff 2004) and turbulent flow (Lajeunesse, Malverti and Charru 2010).

However, direct measurements of L sat in non equilibrium conditions have never been performed. The aim of this paper is to present such measurements.

BARCHAN DUNES

A nice situation of non-equilibrium particle flux is provided by barchan dunes. Such dunes form when sand is transported by a fluid flow (gas or liquid) over a non-erodible bed. These dunes exhibit a remarkable crescentic shape with horns pointing downstream (figure 4). They are commonly observed in deserts, with height of a few meters and velocity of a few tens of meters per year. In his famous book, [START_REF] Bagnold | The physics of blown sand and desert dunes[END_REF] first pointed out their significance for understanding the physics of blown sand. Their outstanding shape and stability properties have triggered a number of studies, aiming at understanding the conditions for their formation, their migration velocity and time evolution, and also the striking existence of a minimum length, of about ten meters in air, below which no dune is observed. A model accounting for their main properties was derived by Kroy, Sauermann and Hermann (2002) and [START_REF] Andreotti | Selection of dune shapes and velocities. Part 2: A two-dimensional modelling[END_REF], from calculations of the shear stress at the dune surface by [START_REF] Hunt | Turbulent shear flows over low hills[END_REF] and Eq. (1) for the sand flux accounting for the retarding effect of grain inertia (Sauermann, Kroy and Hermann 2001). Similar barchan dunes have also been observed under water flows when, again, the sediment supply is limited. The size of these aquaeous dunes is however much shorter than in air, of a few centimeters, say. Such dunes formed in an open channel flow are reported by [START_REF] Mantz | Bedforms produced by fine, cohesionless, granular and flakey sediments under subcritical water flows[END_REF], with typical width of about three centimeters; in this paper the resemblance with the aeolian dunes observed by Bagnold was noted. This resemblance was investigated further by [START_REF] Hersen | Flow effects on the morphology and dynamics of aeolian and subaqueous barchan dunes[END_REF] from experiments in which the dunes were formed on a tray oscillating asymmetrically in a water tank. Barchan dunes also form in circular pipes where they may cause damages to industrial installations [START_REF] Al-Lababidi | Sand transport characteristics in water and two-phase air/water flows in pipelines[END_REF]). An extensive study of barchan dunes in water has been performed by [START_REF] Franklin | Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion[END_REF], discussing their geometry, velocity, and long time evolution. The existence of a smallest dune size of about one centimeter was evidenced, supporting the idea that the relaxation length scsale on the deposition length (u * /V fall )d rather than the acceleration length (ρ p /ρ)d. Again, no direct measurement of L sat was provided.

EXPERIMENTAL RESULTS

1.1.

Experimental arrangement The experimental arrangement mainly consists of a horizontal plexiglass channel, six meters long, with rectangular cross-section of height 2δ = 60 mm and width b = 120. Water flows from a head-tank with free surface 2.5 meters above the channel, and enters the channel through a divergent-convergent device with a honeycomb section in order to suppress large eddies and homogeneize the smallscale turbulence. At the open end of the channel, particles are separated by sedimentation in a large tank, and a pump drives the water up to the headtank. The volumetric flow rate is measured with an electromagnetic flow-meter. For more details see [START_REF] Franklin | Subaqueous barchan dunes in turbulent shear flow. Part 1. Dune motion[END_REF].

The particles (glass beads, with diameter d = 1.1, 0.2 or 0.5 mm) were deposited in the channel, previously filled with water, with the help of a syringe through a small hole in the upper wall located at 4.15 m form the entrance. The sand settles in the water at rest and forms a conical heap. Then the flow is started up, and the heap deforms. A slip face develops on the lee-side where particles avalanche, and horns grow on both sides. The equilibrium shape of the dune is quickly reached, as it has travelled over a distance of the order of its own size. Varying the shape of the initial heap does not change the final dune shape. When the heap is large, it may split and form several interacting barchan dunes, as shown in Figure 4.

The evolution of the shape of the dune was recorded with a video camera placed above the channel and mounted on a travelling system. The resolution of the camera was 2048x2048 pixels, with field of view at the bottom wall of about 140x140 mm 2 . The side view of the dune was recorded on the same images thanks to a mirror inclined at 45°.

Particle motion

Figure 5. A barchan dune seen from above, and the particle velocity field averaged over a rectangular mesh (green arrows).

The motion of a few dyed particles (5%) was recorded, allowing the determination of the surface density of the moving particles (number of moving particles per unit horizontal area) and their velocity. Figure 5 displays a typical particle velocity field over a moving barchan dune, where the measured velocity of individual particles has been averaged over a rectangular area with size of 1/10 and 1/6 of the length and width of the dune, respectively. The velocity increases from the upstream foot of the dune towards the crest, and is larger in the central part of the dune than at the horns, as expected.

From the velocity u(x, y) and moving particle density n(x, y), the field of the particle flux, q(x, y) = n(x, y) u(x, y), can be obtained. An example of the resulting profiles is shown in figure 6, along three slices : (i) the central part of the dune, (ii) the side parts, and (iii) the horns. It can be seen that, firstly, the flux increases from the dune foot towards the crest (located at x = 40 mm), as expected. Secondly, the flux is the largest in the central part, and minimum over the horns. Thirdly, the flux increases everywhere, with no indication of saturation in the vicinity of the crest.

RELAXATION LENGTH

The above measurements may be put together by (i) shifting the x-origin of each slice, initially at x d (y), up to the foot of the slice, and (ii) normalizing the flux in each slice by a saturated flux q sat (y) obtained by fitting the data points with Eq. ( 1). The result is shown in figure 7. It can be seen that the data points nicely fall close to the exponential relaxation curve corresponding to Eq. (1) (except very near the foot), with

L sat = 300 (u * /V fall ) d
where u * is the friction velocity on the bottom wall of the channel. This length appears to be one of magnitude larger than those obtained from measurements of the equilibrium erosion and deposition rates. Further investigation is needed here to clarify this point.

CONCLUSIONS

Understanding relaxation effects of the particle flux over a variable erodible bottom is a key point for confident prediction of the sediment transport over a variable bottom. In particular, such an understanding is necessary for predictions of the ripple length under water. We have shown here that field measurements of the particle flux q(x, y) over barchan dunes allows the determination of the relaxation length. Our results show that the particle flux increases from the dune foot up to the crest, where it is not yet saturated. Fitting these measurements with the non-equilibrium model corresponding to Eq. ( 1) provides a relaxation length much larger than expected from previous analyses. Further analyses are in progress, which include the variations of the shear stress over the dune.

Figure 2 .

 2 Figure 2. Sketch of the mass conservation balance between the flux divergence ∂ x q, and the erosion and deposition rates n e and n d , from which Eq. (1) may be derived.

Figure 3 .

 3 Figure 3. (a) Within the equilibrium assumption q = q sat (τ b ), the shear stress and particle flux disturbances are in phase and the flat bed is unstable. (b) Accounting for relaxation effects stabilizes the bed (apart from gravity effects).

Figure 4 .

 4 Figure 4. Three barchan dunes under a water flow, seen from above. Top of the photo: side view from an inclined mirror. The width of the largest dune is 4 cm (photograph from V. Laval, IMFT).

Figure 6 .

 6 Figure 6. Sand flux along the dune (cm -1 ), with x=0 at the dune foot. Red: central part ; blue : side part ; green: horns.

Figure 7 .

 7 Figure 7. Normalized sand flux along the dune (see text for the normalizations). Red: central part ; blue : side part ; green: horns. Solid line: Eq. (1) with L d = 300 (u * /V fall ) d.


Salman Muhammad
email: muhammad-salman.shahid@g2elab.grenoble-inp.fr

Shahid

Benoît Delinchant

Frédéric Wurtz

Daniel Llerena

Béatrice Roussillon

Designing and Experimenting Nudge Signals to Act on the Energy Signature of Households and Optimizing Building Network Interaction

Keywords: d'Energie Renouvelables, Flexibilité Indirecte, « Nudge », Secteur Résidentiel Renewable Energy Sources, Indirect Flexibility, Nudge, Residential Sector 1

RESUME. La transition énergétique en Europe conduit à la production décentralisée par des sources renouvelables intermittentes. Lorsque ce paysage énergétique changeant exerce certaines contraintes sur le réseau énergétique, il exige intensément une flexibilité dans la consommation d'énergie. La flexibilité directe (généralement sous forme de demande réponse) est déjà en place, tandis que l'impact de la flexibilité indirecte n'est pas très clair. Selon RTE, le secteur résidentiel est le plus gros consommateur d'énergie en France, il est donc important pour l'application de la flexibilité indirecte. Dans ce travail de recherche, nous avons testé notre hypothèse de flexibilité indirecte par des signaux « Nudge » pour un groupe de ménages. L'impact des signaux est mesuré en comparant le groupe traité avec le groupe contrôle et en comparant la courbe de charge de consommation avec une courbe de charge de référence pour chaque ménage de groupe traité. Dans une perspective future, cette étude aidera les gestionnaires de réseau à minimiser la congestion grâce à flexibilité indirecte pour le secteur résidentiel.

INTRODUCTION

The decentralization of renewable energy tends the consumers to produce and consume energy locally (also known as auto-consumption). The energy surplus can either be sold to the energy grid through net metering or through P2P (peer-to-peer) transaction in real time. Energy flexibility is inevitable to maintain equilibrium in the network, as this intermittent energy poses constraints of energy scarcity or network congestion. According to the French national grid operator (RTE), the residential sector consumed 36% of the total annual energy consumption in 2019 (RTE France 2020); therefore, it is a key sector to implement energy flexibility at consumer side.

The DSO/aggregator can implement energy flexibility in two ways. Direct flexibility allows the DSO to curtail remote loads through a switch installed in the grid. It is expensive because it requires installation of protection switches at consumer end. The estimated time of execution is from 10 seconds to 30 seconds (IRENA 2018). The remote switching causes loss of comfort, therefore, it is not pleasant for residential consumers. Alternatively, the indirect flexibility prompts the occupant to manage energy consumption through behavior change. In this case, the occupant needs occasional notification from the DSO for either upward flexibility (load shifting towards the interval of auto-consumption) or downward flexibility (curtailing partial load during peak hours). The estimated time of execution of indirect flexibility is 1 hour to several days and can be used for load curtailment, load shifting and valley filling.

Certain DSOs and research centers have carried out interdisciplinary research to quantify consumer behavior towards energy consumption. Usually, a monetary gain or competition incentivizes the subjects to achieve energy flexibility. These experiments remained effective for the intended duration; however, they do not have a lasting impact. Nudge is a tool of behavioral economics, "which is an aspect of the choice architecture that alters people's behavior in a predictable way without forbidding any options or economic incentives." [START_REF] Thaler | Nudge: Improving Decisions about Health, Wealth, and Happiness. Nudge: Improving Decisions about Health, Wealth, and Happiness[END_REF]. "The choice architecture refers to the practice of influencing choice by organizing the context in which people make decisions" [START_REF] Shafir | The Behavioral Foundations of Public Policy[END_REF].

This article deals with an experiment regarding energy consumption behavior of households. The objective is to test a hypothesis that the knowledge of energy intermittency would influence energy consumption behavior of households and use of nudge would bring a positive reinforcement in the energy consumption behavior. The following section presents a literature review of earlier research experiments and the current mechanisms for energy flexibility in France. Section 3 presents the design of experiment and section 4 presents the comparison of control group and treated group. The formulation of reference load curve is significant to measure the impact of nudge signal; therefore, section 5 demonstrates different techniques considered for the formulation of reference load curve. Section 6 and section 7 presents the results and conclusion respectively.

LITERATURE REVIEW OF INDIRECT FLEXIBILITY

The energy crisis in 1970s forced North America to experiment energy flexibility. In this context, (Ehrhardt-Martinez and Donnelly 2010) classified the energy flexibility experiments into two eras namely; energy crisis era (between 1974 and 1994) and climate change era (from 1995 onwards). These experiments obliged the experimenters either to provide feedback to their subjects in real time (direct flexibility) or to send feedback after consumption (indirect flexibility). These subjects are collectively called treated group. Figure 1 classifies these early experiments according to the type of feedback.

Figure 1: Feedback delivery mechanism spectrum [START_REF] Neenan | Residential Electricity Use Feedback: A Research Synthesis and Economic Framework[END_REF] In a number of experiments, a control group is created with similar characteristics of treated group. "The control group is not subjected to any treatment and it is needed to acquire an average load curve similar to the treated group" [START_REF] Lesgards | La Gestion de La Demande Résidentielle d'électricité: Retour Sur 30 Ans d'expérimentations Mondiales[END_REF]. However, it is not realistic to make two groups with same characteristics; therefore, a reference load curve for each subject was needed. The reference load curve was compared with measured load curve in order to evaluate energy flexibility. It was either formulated on normal distribution or leptokurtic distribution [START_REF] Lesgards | La Gestion de La Demande Résidentielle d'électricité: Retour Sur 30 Ans d'expérimentations Mondiales[END_REF]. In terms of energy saving, a method called "Difference of differences" is used to measure the impact of energy flexibility. With an assumption that the consumption of both groups is identical over the same period, the differences ΔT and ΔC eliminate the temporal effects linked to the evolution of both groups while the second difference ΔT -ΔC eliminates the selection bias between the groups [START_REF] Hatton | Système électrique français : estimation de l'effacement des clients résidentiels[END_REF]. Figure 2 illustrates the difference of differences method.

2: Difference of differences method

Energy flexibility is in practice for many decades in France. TEMPO is a mechanism of critical peak pricing introduced by EDF (Electricité de France), in which the tariff for color-coded day D varies according to the color assigned on day D-1. The tariff on day D is cheaper than TOU price for blue color, slightly expensive than TOU price for white color and very expensive for red color (Albadi and El-Saadany 2007). EJP (peak day curtailment) is another instrument of critical peak pricing, in which the peak consumption day is color-coded in red and the subscribers pay a low tariff all year round, except for the 21 red days with higher tariff [START_REF] Bivas | La production d'effacement : comment offrir des économies d'électricité à des millions de foyers[END_REF]. EDF notifies subscribers on day D-1 about the color of TEMPO for day D. PP1/PP2 (peak period 1/peak period 2) are the days of high electricity consumption as determined by RTE. PP1 corresponds to extreme weather forecast (maximum 15 days/year) while PP2 corresponds to the network congestion (maximum 25 days/year).

DESIGN OF EXPERIMENT

For this experiment, GAEL lab recruited 175 households (equipped with LINKY smart meter) around a medium French city. LINKY transmits the daily measured load curve at a sampling period of 30 minutes to ENEDIS server [START_REF] Duplex | A Better Knowledge of Electricity Consumption for Residential Customers through the Linky Smart Meter[END_REF]. G2ELab fetches the daily load curve of each subject from ENEDIS server and anonymizes the data as per GDPR consent signed with each subject. The participants of treated group also signed a commitment form, stating the appliances that they will use or not use during green or orange period respectively. The commitment form consists of a list of all the appliances that consumes energy in each subject's household and the timeslots during which these appliances are used.

Two types of alerts are defined i.e. green alert (for load shifting) and orange alert (for load curtailment). The green alert is based on forecast of zero nebulosity in Grenoble and the forecasted consumption of each subject for next day. The orange alert is based on the declaration of PP1/PP2, EJP or TEMPO for next day. Subsequently, the green period refers to the duration between noon and 3:00 PM on green alert day while orange period refers to the duration between 6:00 PM and 8:00 PM on orange alert day. For the sake of comprehension, Figure 3 illustrates the timeline of orange alert. -Information related to energy production and its environmental impact i.e. elevated production of thermal power plants for orange period and maximum use of renewables for green period.

-A customized set of advice for each subject about how to optimize energy consumption with commitments. The subjects must commit themselves to the actions they think they will take during orange or green period. For this purpose, a URL is added in the message that permits the subjects to modify their default commitment by accessing their personal account.

-Regular feedback to the subjects in the form of an image of the measured and reference load curve.

COMPARISON OF CONTROL AND TREATED GROUP

Before formulating the reference load curve, it is essential to evaluate the habitual energy consumption behavior of both groups. For this purpose, an average of daily load curves of control group (comprising of 79 subjects) and treated group (comprising of 96 subjects) is taken between 1 st September 2019 and 28 th February 2020 with a sampling rate of 30 minutes. Figure 4(a) demonstrates that the average daily load curve of both groups is similar in the evening. The two box plots in figure 4(b) represents the distribution of energy consumption for both groups between 6:00 PM and 8:00 PM. The two box plots have surprisingly similar distribution and very close median values, which validates our assumption that the two groups are identical in terms of energy consumption in the evening.

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐷𝑎𝑖𝑙𝑦 𝐿𝑜𝑎𝑑 𝐶𝑢𝑟𝑣𝑒 𝑜𝑓 𝐺𝑟𝑜𝑢𝑝|

FORMULATION OF REFERENCE LOAD CURVE

A reference load curve has an important role in this study. It helps in scientific evaluation of the efficiency of nudge signal. Besides, the reference load curve is itself a nudge. On day D+2, each subject views his/her measured load curve against reference load curve and measures the impact of his/her effort. Three techniques that are compared to formulate the reference load curve are given below.

-Using Kernel Density Estimation: For each half-hourly timestamp of (green or orange) period, the peak value of the kernel density estimation of historical data is taken as reference data point for reference load curve.

-Using newly devised BM technique: For each (green or orange) period on day D, the load curve of day D-1 for the same half-hourly timestamp is taken. In addition to that, the load curve with maximum energy consumption between days D-2 to D-5 is taken. The average of the two load curve yields the reference load curve.

-Using the maximum values occurred in last 5 days: For each half-hourly timestamp of the (green or orange) period, the maximum value of last 5 days is taken as reference data point for reference load curve.

To select one of the method as reference load curve, the performance of energy difference indicator for each method is observed. The following steps are taken to evaluate the performance of indicator for each method given above. Note that this analysis is only performed for orange period.

-The historical consumption data of treated group between 1 st September 2019 and 28 th February 2020 is taken with a sampling rate of 30 minutes. The data of weekend and school vacations is removed from the taken sample. After this step, we are left with historical data of 126 days.

-A reference load curve is generated for each method using the historical consumption data.

-By taking the difference of reference load curve and measured load curve, a difference load curve is generated. The energy difference indicator for orange period is calculated by taking the sum of difference load curve of each day between 6:00 PM and 8:00 PM.

-The energy difference is positive, if the measured energy consumption during the period is less than the reference energy consumption.

-The energy difference is negative, if the measured energy consumption during the period is greater than the reference energy consumption.

Figure 5 illustrates a distribution of energy difference indicator using each method. The boxplot for Kernel density estimation method demonstrates that energy difference for most days and the median value is negative. If we select this method, the measured load curve will be often greater than the reference load curve, and therefore the action of the treated group for each nudge signal will be underestimated. Hence, this method is not suitable for nudging the subjects as it underestimates their efforts. The boxplots for 2 nd and 3 rd method depicts that the energy difference is predominantly positive (with most of the data lying above zero and positive median value). Both methods over-estimates the action of treated group towards nudge signal and therefore suitable method should be selected.

Figure 5: The distribution of energy difference indicator for treated group w.r.t three methods

The data of 3 rd method is widely dispersed as it takes maximum values during the previous 5 days. The maximum value of energy consumption may occur at D-4 or D-5, hence this method may not take evolving energy consumption as function of temperature and time. The boxplot of 2 nd method shows that the energy difference indicator of treated group is not widely dispersed. It helps in better prediction through reference load curve since the historical data points are more closer to median value than 3 rd method. It takes into account the evolution of energy consumption with respect to time as it includes the energy consumption of day D-1. Besides, it does not nullify the effect of maximum energy consumption occurred at any day D-n (where 2≤ n ≤ 5). Therefore, 2 nd method (also named as BM technique) is selected as reference load curve for better estimation of the effort of each subject.

RESULTS AND DISCUSSION

It is necessary to evaluate the impact of nudge to validate the endogenous and exogenous of the results. The endogenous verification makes it possible to establish that a cause and effect relationship within the experiment has attracted attention of subjects. The exogenous factor verifies the extent to which the results obtained during the experiment is applicable to a bigger population than sample size. Therefore, two key performance indicators are used to evaluate the result of 6 alert days for which the nudge signals were sent. These nudge signals were sent between 1 st September 2019 and 28 th February 2020 on the days when one of the three declarations of PP1/PP2, EJP or TEMPO was TRUE.

COMPARISON BETWEEN ENERGY CONSUMPTION OF BOTH GROUPS ON ALERT DAYS

This indicator compares the energy consumption of control group and treated group during orange period against the nudge signal. This comparison is significant to extrapolate the exogenous impact of the experiment. Figure 6

COMPARISON OF ENERGY DIFFERENCE INDICATOR

The energy difference indicator is calculated for 6 alert days and 120 non-alert days by taking the difference of reference load curve and measured load curve. This endogenous indicator measures the impact of nudge signals on the subjects for decreasing their energy consumption during the orange period. Figure 7 illustrates the actions of some subjects who responded positively and those did not responded positively. Note that the box plot representing the energy consumption during alert days is lower than the box plot representing energy consumption on non-alert days for positively responded subjects. This means that the subjects who responded positively have consumed less energy than their reference energy consumption. The case is inverse for subjects who consumed more energy on alert days than on non alert days. Overall, the difference of medians between alert days and non-alert days reveals that 60% subjects (58 out of 96 subjects) responded positively to the nudge signal by decreasing their energy consumption during orange period and the rest of the subjects consumed more than the reference on alert days.

CONCLUSION

Indirect flexibility can be implemented to residential sector for upward flexibility (load shifting) or downward flexibility (load curtailment). In this experiment, we tested a hypothesis that the forecasted information of intermittent energy generation and network congestion could nudge the residential consumers to implement indirect flexibility. The performance of treated group is compared with control group to evaluate the exogenous impact of the signals. An extrapolation of result reveals that a significant amount of energy can be saved through nudge signals during the peak consumption days (i.e. the days when peak power plants are running).

An image containing a reference load curve superposed on measured load curve is presented to each subject of the treated group, so that each subject can view the impact of his/her effort against the nudge signal. This may positively reinforce him/her to act better next time. The reference load curve also helps to calculate an energy difference indicator to measure the extent of energy saving. The analysis of energy difference indicator yields that a good number of subjects responded positively by implementing downward flexibility, whereas the impact of upward flexibility is yet to be seen. In nutshell, the nudges might be impactful to implement indirect flexibility for energy equilibrium in the grid.

8.

ACKNOWLEDGEMENT:

Figure 3 :

 3 Figure 3: Timeline of orange alertThe subjects are categorized into control group and treated group. The control group represents as a reference for electrical consumption of households in treated group. It ensures that the energy consumption of treated group is only influenced by the nudge during alert day. The treated group receives a set of SMS as nudge signal for each alert day. Alerts are not triggered for weekend and school vacations. The nudge has three elements, which are given as follows.

Figure 4 :

 4 Figure 4: (a) The average daily consumption load curve of control group and treated group, (b) The distribution of energy consumption for both groups between 6:00 PM and 8:00 PM

  illustrates that energy consumption of treated group remained less than energy consumption of control group on alert days. The difference of median values of box plot yields that the treated group saved 0.62 kWh of energy per orange period. The individual effort generated different values however, extrapolating cumulative energy saving of 0.31 kWh per hour (0.62 kWh per orange period) for 29 million French households (INSEE France 2019) gives an energy saving of 8.7 GWh per hour (between 6 PM and 8 PM), which is significant in terms of indirect energy flexibility at peak hours.

Figure 6 :

 6 Figure 6: The comparison of energy consumption of control group and treated group for alert days

Figure 7 :

 7 Figure 7: The comparison of energy difference indicator between alert days and non-alert days of top five positively responded subjects, stable subjects and negatively responded subjects

This work has been supported by the Auvergne Rhône-Alpes region, "Pack Ambition Recherche 2017 -Expesigno projet" (17 01110301). This work has also been partially supported by the CDP Eco-SESA receiving fund from the French National Research Agency in the framework of the "Investissements d'avenir" program (ANR-15-IDEX-02).