Patricia M Olmos

Gutiérrez Silvia

Granados

Fethi Bedioui

Sophie Griveau
email: sophie.griveau@chimieparistech.psl.eu

PEDOT/Superoxide dismutase electrode surface modification for superoxide bioelectrochemical sensing

Keywords: Superoxide sensing, Platinum, PEDOT, SOD, amperometry

An amperometric biosensor of high enzymatic response to the sensitive and selective detection of superoxide (𝑂 2 .-) was designed utilizing a drop-coating approach for immobilizing the enzyme superoxide dismutase on Pt electrode modified with a thin layer of poly (3,4-ethylenedioxythiophene) (PEDOT). The PEDOT electrodeposited layer on Pt was characterized by cyclic voltammetry and atomic force microscopy (AFM). Then, drop-coating procedure was chosen for the immobilization of superoxide dismutase, which is incorporated at the electrode surface using a solution containing SOD, glutaraldehyde and bovine serum albumin (optimization composition : SOD 0.1% -ASB 2% -GA 2.5%.) This simple procedure allows forming a reproducible enzymatic biocomposite layer that allows optimal sensitivity and limit of detection for 𝑂 2 .

-. The synergistic effect integrates an effective conductivity and permoselectivity attributed to the PEDOT, as well as the specificity and selectivity of SOD for the detection of superoxide. A high sensitivity (0.82 ± 0.01 μA / μM) and a low detection limit of 11 nM for 𝑂 2

.

-were obtained, as well as good selectivity against main interfering biological compounds such as uric acid and ascorbic acid. Our results suggest that the biosensor could be used for the detection and quantification of 𝑂 2

.

-in vitro and in vivo.

Introduction

Among the reactive oxygen species (ROS) at the biological level, the radical superoxide anion (𝑂 2

.-), is generated as a reduced intermediate of dioxygen (O2) [1], [2] . The main source of superoxide in cells comes from the electron transport chain in the mitochondria and in the endoplasmic reticulum [3] . Under normal metabolic conditions, ROS are produced at a rate which does not exceed the capacity of the cell to dismute these species [4], [5] . However, when the production of 𝑂 2

.

-exceeds the natural capacity of the organism for its dismutation, this oxidant triggers cytotoxicity processes, giving rise to several diseases, including cancer and chronic degenerative diseases [6] . Under normal physiological conditions, the basal concentration of 𝑂 2

.

-lies between 10 and 100 nmol/L [7], [8] . This low level of concentration is attributed to the great capacity of superoxide dismutase (SOD) for dismutation and also to its high reactivity with other small molecules [9] . Various technologies have been conceived to indirectly determine the level of 𝑂 2

.

-, including spin-electron resonance (ESR) [10] , [11] and semiquantitative colorimetric tests [12] , [13] . However, these technologies can not be applied for the direct detection of 𝑂 2

.

-in vitro and in vivo. Electrochemical techniques, and more specifically amperometric biosensors, have been used to detect and quantify, directly and in real time 𝑂 2

.

- [14] . First [15] , second [16] and third generation [17] , [18] biosensors have been developed using different types of transducer materials, such as Pt, Au, and carbon fiber, whose surfaces are modified incorporating different types of nanomaterials and / or certain specific biomolecules. Third generation biosensors based on SOD have high sensitivity and excellent selectivity thanks to the activity of the enzyme to convert 𝑂 2

.

-to O2 and H2O2 via a cyclic oxide-reduction mechanism [19] , [20] .

The adequate interfacial communication between the enzyme and the electrode is a key parameter to facilitate the charge transfer. Due to their large surface area, good biocompatibility and excellent stability, conducting polymers are thus used for the immobilization of redox enzymes. The combination of conductive polymer and enzyme can provide a hybrid composition that simultaneously allows a specific recognition of 𝑂 2

.

-by SOD, as well as a high electron transfer promoted by the polymer [21] , [22] . These synergistic effects favor an efficient analytical behavior. Among the main conducting polymers, poly (3, 4-ethylenedioxythiophene) (PEDOT) was already used as an electroconductive platform in the design of biosensors [23] , [24] . The main advantages of the PEDOT are its easy electropolymerisatin in aqueous medium and its stability in a wide range of pH [25] , [26] . The most common methods applied for the immobilization of enzymes, make use of membrane entrapment, cross-linking, covalent binding and physical adsorption [21] , [27] , [28] . The immobilization of SOD [29] , [19,24] , [17] on the surface, catalyzes the dismutation reaction of 𝑂 2

.

-as shown in the following equation:

2𝐻 + + 2𝑂 2 .-𝑆𝑂𝐷 → 𝐻 2 𝑂 2 + 𝑂 2 (1)
The generated H2O2 from the enzymatic reaction is reduced at the electrode interface, producing the electrochemical signal associated with the following reaction:

𝐻 2 𝑂 2 + 2𝐻 + + 2𝑒 -→ 2𝐻 2 𝑂 (2)
In this work, we report on a simple, but effective procedure for the manufacture and characterization of a specific amperometric biosensor using platinum electrode modified by PEDOT and SOD for the detection and quantification of 𝑂 2 .

-. Brett et al [20] have proposed a modification of glassy carbon electrode using multi-walled carbon nanotubes/chitosan, PEDOT and SOD for the detection of superoxide giving interesting performances. In this work, we built on this procedure and adapted it for the modification of platinum electrodes, using PEDOT and SOD, for further transposition in the long run to microelectrodes for measurements of 𝑂 2

.

-in vitro and in real time [30] , [31] . Also, the electrode surface modifications were deeply characterized by AFM and cyclic voltammetry. The analytical performances of the modified electrode towards superoxide in terms of sensitivity, selectivity and stability were assessed by chronoamperometry.

Experimental

Chemicals

Superoxide dismutase enzyme Cu-Zn (SOD) from bovine erythrocytes, potassium superoxide (KO2), 3,4ethylenedioxythiophene (EDOT), glutaraldehyde (GA), bovine serum albumin (BSA), PBS tablets, uric acid, ascorbic acid, xanthine, H2O2, sodium XTT, sodium styrene sulfonate (NaSS) and Potassium hexacyanoferrate II (K4[Fe(CN)6]), were purchased from Sigma-Aldrich and were used as received. ITO substrates were purchased from Delta Technologies and have the following characteristics: 4-10 Ω and dimensions of 150x150x1.1 mm. The solutions were prepared using ultrapure water (18.2 MΩ.cm resistivity, LabFlex system, Veolia, France). The electrochemical experiments were carried out in 0.01 mol/L phosphate buffer (pH 7.4). For the polymerization of EDOT, 0.1 mol/L NaSS containing 10 mmol/L EDOT was used. A 0.1% CuZnSOD solution was prepared at the same time, the 2% BSA protein was integrated (solution A). The 2.5% glutaraldehyde solution was prepared (solution B). At the end both solutions A and B were mixed, 1 μL of this mixture was taken which was placed as drop on the electrode PEDOT / Pt.

Preparation of superoxide biosensor

PEDOT was electrodeposited on Pt (d = 1mm) electrode by sweeping the potential from -0.6 to 1.2 V vs. SCE at 50 mV s -1 in a 10 mmol/L EDOT + 0.1 mol/L NaSS aqueous solution for 10 cycles. These modified electrode is named as PEDOT/Pt. Then, the SOD solution was prepared in a bovine albumin serum medium (0.1% SOD + 2% BSA). It was mixed with a 2.5% GA solution in a 2:1 (v / v) enzyme: GA ratio, and a 5 μL drop was placed on the surface of the PEDOT/Pt electrodes; it was let on to dry for 4 h at room temperature. Before use, the obtained biosensor was kept immerged in a 0.01 mol/L PBS solution, pH 7.4 at 4 ° C.

Instrumentation

The electrochemical experiments were carried out with a potentiostat-galvanostat Uniscan instruments (Ametek, France). A three-electrode conventional cell was used as electrochemical system, using disc-shaped Pt as working electrode (1 mm diameter), platinum wire as counter electrode, and a Saturated Calomel Electrode (SCE) as the reference electrode (Hach Lange, France). The pH measurements were carried out with Radiometer analytical (France) pH meter. An Electronic Scanning Microscope (SEM) model SIGMA-HDVP Field Emission of the brand Carl Zeiss was used to characterize the electropolymerized PEDOT film on ITO substrates. The Atomic Force Microscopy (AFM) experiments were carried out with an AFM Nanosurf easyscan 2 with a contact tip. The processing of the AFM images was done with the Gwyddion software.

Spectrophotometric determination of superoxide

A stock solution of KO2 was prepared in NaOH medium, pH 12.3. Its concentration was determined from the absorbance value at λ = 245 nm using an extinction coefficient of ε = 2350 M -1 cm -1 [32] . The spectra were recorded using a UV-visible spectrophotometer (UVIKON XL, BIO-TEK, France)

Results and discussion

Electropolymerization of EDOT on platinum electrodes.

Figure1 shows typical successive cyclic voltammograms obtained during the electropolymerization of the PEDOT on Pt electrode. The anodic oxidation of EDOT monomer is observed above +0.9 V vs SCE on the first cycle. Then, the characteristic increase of the anodic and cathodic current on each cycle can be observed around 0 V and -0.3 V respectively, indicating the formation of the PEDOT polymer at the electrode surface [33] .

Characterization of the PEDOT / Pt modified electrodes

After electropolymerization, the electrode was characterized by SEM, AFM and cyclic voltammetry. Figure 2-a shows a picture of ITO electrodes modified with PEDOT electrodeposited layer, showing a stable brownish deposit on the electrode surface. Figure 2-b shows the SEM images of the ITO modified electrode.

The electrodeposited polymer exhibits a homogeneous coverage on the ITO substrate.

Electrochemical detection of Superoxide

Enzymatic activity of SOD immobilized in the SOD/PEDOT/Pt biosensor

In solution, SOD efficiently dismutates 𝑂 2 .

-to O2 and H2O2 via a redox cycle attributed to the Cu I/ II metal center couple, which acts as a redox mediator in the Cu-Zn SOD enzyme complex, as follows [29] :

𝑆𝑂𝐷(𝐶𝑢 𝐼 ) + 𝑂 2 .-+ 2𝐻 + → 𝑆𝑂𝐷(𝐶𝑢 𝐼𝐼 ) + 𝐻 2 𝑂 2 (3) 𝑆𝑂𝐷(𝐶𝑢 𝐼𝐼 ) + 𝑂 2 .-→ 𝑆𝑂𝐷(𝐶𝑢 𝐼 ) + 𝑂 2 (4)
The working principle of the biosensor developed here is based on the amperometic signal linked to the electrochemical reduction of H2O2 generated by the enzymatic reaction (3) [34] . The SOD enzyme was immobilized on the biocompatible coating of PEDOT / Pt, using the drop-coating method, to ensure a good accessibility of the superoxide anion to the immobilized SOD enzyme. The enzyme solution was prepared by adding BSA, which helps in maintaining the enzymatic activity of SOD. Subsequently, glutaraldehyde (GA) was integrated as a cross-linking promoting agent to provide stability to the enzyme. Glutaraldehyde carries out the cross-linking with the lysine residues present in the BAS, generally located on its surface. These interactions prevent the direct linkage of GA with the lysine residues contained in the SOD thus preserving the activity and configuration of the SOD enzyme [35] . KO2 solution in NaOH was dissolved in PBS as the superoxide source. The amperometric response of the developed biosensor was recorded in PBS at -0.30V vs. SCE following consecutive additions of aliquots of KO2 (0.09 μmol/L each). As illustrated on Figure 4-a, after each addition of KO2, a simultaneous increase of the cathodic current is observed. The biosensor, therefore, efficiently carries out the dismutation of 𝑂 2 .

-and the continuous detection of H2O2 as an analytical signal. By introducing catalase in the electrochemical cell allows to ensure that the detected analyte is H2O2. Indeed, the main action of catalase is the capture of H2O2 present in the electrochemical cell, converting it into water and oxygen. As observed on Figure 4-a, the addition of catalase induces a large decrease of the analytical signal practically coming back to the baseline. A control experiment was also conducted using a modified electrode in absence of the SOD enzyme (GA 2.5% _BSA 2%) / PEDOT / Pt electrode) by performing an amperometric analysis upon successive addition of KO2. The typical amperometric response following additions of KO2 aliquots is reported on Figure 4-b. No faradaic signal could be observed that reflects any electrochemical reaction. This result is important since it rules out the intervention of H2O2 produced by the spontaneous decomposition of 𝑂 2

.

-in the electrolyte. Indeed, H2O2 produced in the bulk solution by dismutation of 𝑂 2

.

-is diluted is the solution explaining that it is not detected. H2O2, generated from the enzymatic reaction in the vicinity of the membrane, leads to large local concentrations of H2O2 and is thus detected. -concentration levels in the extracellular environment lie between 10 to 100 nmol/L [7] . Consideration of these values is critical, when designing biosensors for superoxide detection in vitro and in vivo. In this work, the optimization of a proposed amperometric biosensor, designed based on (SOD 0.1% _BAS 2% _GA 2.5%) / PEDOT/Pt, has been made. Calibration of the biosensor was thus performed by addition of KO2 which produced 𝑂 2

.

-and measuring the changes in the anodic current as a consequence of the electroquemical reduction of the H2O2. The amperometric response of the developed biosensor was recorded in PBS at -0.30 V vs SCE. The current versus the response time of the electrode for successive additions of 𝑂 2

.

-is shown in Figure 5a.

The calibration curve deduced from amperometric analysis is reported on Figure 5-b, showing that the biosensor display a linear response between 0.175 and 2.8 μmol/L. The experimental conditions were optimized such that, the analytical parameters of the biosensor show high sensitivity for 𝑂 2 .-(0.82 μA/ μM), and a low detection limit of ca. 11 nmol/L (using S/N= 3). These results suggest the biosensors potential use for monitoring 𝑂 2

.

-in vitro and in vivo. Repeatability was verified constructing three new electrodes and testing them in the same conditions. The points are obtained from the mean of the values for the three electrodes and the error bars represent the standard deviations for each point. The RSD was 0.03%.

Selectivity and Stability study

When designing amperometric biosensors, one of the challenges consists in minimizing and preferably avoiding the effect of electroactive species that may be present, in addition to the target analyte, in the biological fluids. The compounds that can interfere in the amperometric determination of 𝑂 2

.

-include uric acid (UA), xanthine (XA) and ascorbic acid (AA). To confirm the selectivity of the biosensor to superoxide, we used cyclic voltammetry to evaluate the electrochemical behavior in the presence of specific interferents. The electrochemical data were obtained for each compound at a concentration of 1mM (Figure 6). In the sensing media did not cause a significant signal for UA and XA since the registered Ipc = 0 for these interfering species. However, for AA, a signal of Ipc = 8.4 μA was recorded at Ecat = 0.01 V. In spite of this, the biosensor remains selective for 𝑂 2

.

-. This is due first, to the high current intensity signal registered, Ipc = 175 μ at Ecat = -0.30 V; and second, because the amperometric measurements are done at a fixed potential Ecat = -0.30, limiting the possibility that notwanted electrochemical reactions occur. The amperometric measurements at a fixed potential of -0.30 V are presented in Figure 7. The 𝑂 2 .

-was added twice for a final concentration of 25 μmol/L in the cell before the interfering components (UA, AA, XA) were added. These were then added sequentially. This procedure was done to corroborate the amperometric signal for the detection of 𝑂 2

.

-in a concentration ratio (1:4), 𝑂 2

.-: interferents (100 μmol/L). It should be noticed that none of these compounds was oxidized or reduced at E= -0.30 V (data not shown). Aliquots of 𝑂 2

.

-are subsequently injected again, resulting in the recorded signals corresponding to the analyte. This confirms that UA, AA, XA compounds will not be interferents for the final detection of 𝑂 2

.-using the biosensor. For the stability study we recorded, during a period of 28 days, the amperometric signals obtained for the detection and quantification of 𝑂 2 .-, by means of calibration curves. Was evaluated recording a 10-point calibration plot in the concentration range 0.175 to 1.575 μM for 𝑂 2

.

-three times a week. Figure 8 presents the calibration curves corresponding to the results obtained for current at 8, 12 and 28 days after the first use of the biosensor for the analysis. It is observed that the measured current decreases up to 27% as time progresses. This is reflected in the slight decrease in the sensors sensitivity (0.597 μA / μmol/L), while keeping a good detection limit (15 nmol/L).

Modified Electrode Ework (V) Sensitivity LoD (nM) Reference

Cyt c functionalized nanopipette -1 to 1 V vs. Ag --------147 [22] (SOD 0.1%_BAS 2%_GA 2.5%)/PEDOT/Pt -0.30 vs. SCE 104.2 µA cm -2 µM -1 11 This work

For sake of comparison, a few analytical parameters of superoxide biosensors based on SOD are summarized in Table 2. Our results are comparable to the ones reported in the recent literature. We must consider, however, the nanostructured materials used for the construction of both biosensors, which require the use of nanoparticles of Fe3O4 and Au respectively. Our proposed design and construction of superoxide biosensor has a simpler configuration, exhibits good analytical results for the detection and quantification of 𝑂 2 .

-in terms of limit of detection, which is the third best LOD reported in the literature.

Conclusions

A selective and sensitive biosensor for 𝑂 2

.

-, based on superoxide dismutase, is presented. The sensor was developed by immobilizing the SOD enzyme using the drop coating method on Pt modified with a thin layer of PEDOT. The incorporation of glutaraldehyde and bovine serum albumin provided and preserved the integrity, activity and stability of the enzyme, which contributed to the sensors good sensitivity and analytical parameters. PEDOT electropolymerization on the platinum surface shows an efficient surface coating method that contributes to the synergistic increase in interfacial charge transfer. This in turn, produces a significant increase in analytical signals. In addition, the PEDOT coating acts simultaneously, as a permoselective layer to the passage of H2O2, and as a barrier to avoid the passage of interfering species such as UA, AA, XA, KO2. This procedure dispenses with the use of sophisticated nanomaterials useful in the manufacture of similar sensing devices. Finally our analytical results indicate that the designed biosensor can be used in the future to monitor 𝑂 2

.

-for biological models in vitro and in vivo.

Figure 1 .

 1 Figure 1. Successive cyclic voltammograms on Pt electrode in aqueous solution containing 10 mmol/L EDOT and 0.1 M NaSS. Scan rate 50 mVs -1 , 10 cycles.

Figure 2 -

 2 c shows the 3D topographic profile of the PEDOT over ITO coating obtained by AFM measurements. A quadratic mean roughness value of 35 nm and an average thickness of 280 nm were obtained for the PEDOT film over ITO surface (calculated from triplicate measurements at several points in the PEDOT film). The observed roughness is characteristic of the electrodeposited layer of PEDOT since the roughness of the bare ITO surface is 2 nm only.

Figure 2 .

 2 Figure 2. (a) Picture of the ITO substrate modified with PEDOT (left) and ITO without surface modification (right). (b) SEM images of the PEDOT coating on ITO, a "close up" on the polymer from 2 μm to 200 nm is shown. (c) 3D AFM image of 50 μm x 50 μm.Cyclic voltammogram was also recorded at the PEDOT/Pt modified electrode in 5 mM K4[Fe(CN)6] aqueous solution, and compared to the one obtained at bare Pt electrode, as illustrated on Figure3-a. This shows the large increase in the intensity of anodic and cathodic peak currents for PEDOT/Pt electrode in comparison to those obtained at bare Pt. This difference can be attributed to the large increase in the electroactive area promoted by the PEDOT film on the Pt substrate, in accordance with the roughness of the PEDOT film deduced from AFM measurements. The slope of 0.5 obtained from the representation log Ip vs. log ν at increasing scanning rate (figure3-b) indicates that the behavior of the soluble redox system is governed by the diffusion at the electrical interface. Figure 3-c shows the evolution of the anodic peak current as a function of the square root of the scan rate (20 to 200 mV s -1 ) for ferrocyanide oxidation on PEDOT / Pt electrode. Using the Randles-Sevcik equation, the values of the electrochemical active surface area of the PEDOT/Pt and Pt bare were estimated as 0.034 cm 2 and 0.006 cm 2 , respectively showing an increase of the surface of 5.6 times between bare and modified electrode. The stability of the PEDOT / Pt electrodes as a function of time was also investigated. During a period of one month, the peak current intensity signals of ferri/ferrocyanide redox couple did not change. The described results show that the PEDOT / Pt modified

Figure 3 -Figure 3 .

 33 Figure 3. (a) Cyclic voltammograms for bare Pt and PEDOT / Pt electrodes in the presence of K4[Fe(CN)6] 5 mmol/L in PBS pH 7.4; scan rate 50 mV / s. (b) Graph of log Ip vs log v for electrodes modified PEDOT / Pt in the presence of 5 mM K4[Fe(CN)6] in PBS pH 7.4 at increasing scanning rate. (c) Graph of Ip vs v 1/2 for PEDOT / Pt electrodes in the presence of 5 mM K4[Fe(CN)6] in PBS pH 7.4, at different scan rates of 20 to 200 mVs -1 .

Figure 4 .

 4 Figure 4. (a) Typical amperometric response for the reaction H2O2 + Catalase at -0.30 V vs SCE in buffer PBS 0.01 mol/L, pH 7.4. The orange arrows represent the sequential addition of 0.1, 0.18, 0.26, 0.35, 0.44 μmol/L of 𝑂 2 .-The source of superoxide production was KO2 in NaOH, pH 12.3. The blue arrow indicates the injection of 200 μL of 0.1% catalase. (b) Amperometric response of the modified electrode (GA 2.5% _BSA 2%) / PEDOT / Pt (red line) in PBS 0.01 mol/L, pH 7.4 and KO2 (black line) to 0.175, 0.35, 0.7, 0.875 μmol/L at -0.30 V vs SCE in PBS 0.01 M, pH 7.4.

Figure 5 .

 5 Figure 5. (a) Amperometric response of the biosensor for the successive addition of 𝑂 2 .-from an mother solution of KO2 for concentration ranging from to 2.8 μmol/L. Applied potential -0.30 V vs SCE in PBS 0.01 mol/L, pH 7.4. (b) Corresponding calibration curve (cathodic current in absolute value).

Figure 6 .

 6 Figure 6. Electrochemical study of possible interferent compounds such as uric acid (UA) and ascorbic acid (AA), xanthine (XA) in the final determination of the anion-radical superoxide.

2 Figure 7 .

 27 Figure 7. Amperometric response of the interferents (UA, AA, XA) using the modified electrode PEDOT / Pt at -0.30 V vs SCE in PBS 0.01 mol/L. pH 7.4, molar ratio H2O2 : interfering (1: 4). This information was used to evaluate the electroactive influence of the interferents in the detection of H2O2.

Table 2 .

 2 Comparison of results recently reported for biosensors based on the use of SOD enzyme on nanostructured materials (from 2010 to date).

	start measure
	after 8 days
	after 12 days
	after 28 days


Book Review

Paolo Bory, 2020, The Internet Myth: From the Internet Imaginary to Network Ideologies, London: University of Westminster Press. DOI: https://doi.org/10.16997/book48. Open Access with license CC-BY-NC-ND 4.0. 169 p.

By Francesca Musiani

Centre for Internet and Society, CNRS francesca.musiani@cnrs.fr Notions such as imaginary, myth, ideology, utopia… have been mobilized with notable success in the social sciences throughout the past years and decades, as they are useful to incorporate in an anthropological perspective the forms of doing-together and beingtogether, the discourses and the objects of contemporary societies. These notionsoftentimes interchangeably, and oftentimes wrongly so -have been frequently used, in particular, in the studies of relations between technology and society. As Françoise Massit-Folléa pointed out in 2008 (critically assessing a body of work on Internet imaginaries which originated in France with Patrice Flichy's 2001 seminal volume), such words allow for "a kind of 're-enchantment' of a world which is uncertain, complex and sometimes anxiety-filled, that of technology," and even more so when it comes to the Internet and other information and communication technologies (ICTs) -an ensemble of artifacts that have long been supposed to provide a limitless horizon of progress for human societies.

Yet, these concepts have also been questioned at their core and in their relation to the Internet as a research subject, with critics pondering whether using such terms as "imaginary" or "myth" as an analytical framework is not, most often, an a priori assumption about ongoing fieldwork dynamics rather than a problematization tool. In this regard, Laurence [START_REF] Monnoyer-Smith | Postface. La notion d'imaginaire : mauvaise réponse à une bonne question ?[END_REF] points out that these notions could be a "bad response to a good question," as they appear insufficient to capture the ways in which social constructs are configured by a variety of mediations and intermediations, or to understand how actors actually appropriate technologies to foster their arguments and values, and what is revealed by the forms of communication established between them.

While Paolo Bory's volume re-mobilizes the terms of both myth and imaginary in its title and subtitle, his enterprise is actually mostly one of 'de-mythization' and 'de-imaginarization', with an interdisciplinary approach, spearheaded by media history, in its toolbox. What the author is most interested in in this volume is to examine in a very concrete way how networks were imagined, designed and promoted in specific socio-cultural contexts, so as to unveil the foundations of what he calls "network ideologies," i.e. "the idea that networks, by themselves, are the main agents of social, economic, political and cultural change" (p. 1). In Paolo Bory's work -informed in particular by Cornelius Castoriadis' and Paul Ricoeur's dialogue (2016) on imaginaries as ways to define and institutionalize the integration of the experiences of the past and the vision of the future -imaginations, imaginaries and mythologies are re-configured and understood as key elements in the social construction of reality, and in particular, in the very practical, and infrastructure-embedded, struggles for control that permeated the Internet since its very early days.

The Internet Myth is one of the most recent and notable additions to a field of study, that of Internet history, that -as préfacier Gabriele Balbi, former supervisor of the PhD dissertation the book is based on, points out -is acquiring increased importance and nuance around the work of a growing community of researchers, exemplified by the recent creation of the journal that publishes this book review. However, there are important touches of interdisciplinarity in the book, including elements of sociology, science and technology studies, political economy and media archaeology, and this interdisciplinary glance is applied to a variety of sources including the more classical semi-structured interviews and archival documents, but also more "discipline-specific" materials belonging to digital-born heritage.

As the Internet is now several decades old, scholars can start interrogating its historical dimension in all its complexity -and geographical diversity, and this book provides a contribution towards this endeavor (Gabriele Balbi refers to it in his preface quite explicitly as a "de-Americanization" of the field, referring to a dominant narrative and mythological apparatus that has long been focused primarily on the United States). Paolo Bory tackles this challenge by putting together two case studies, at first glance vastly different in scope, aims and nature: one of the most successful technologies of recent history, the World Wide Web, is immediately followed by two "failed" networking projects in Italy, Socrate and Iperbole. While this pairing could bring some perplexity to several readers' minds (it did to mine initially), credit should go to the author for boldly using it to serve a demonstration of the vast differences -often embedded in national realities, infrastructures and economiessubtending networking projects, and the expectations, imaginations and design choices that made them what they are (or were). Furthermore, the two empirical chapters of the book are linked in other subtle ways, including a focus on the European dimension of Internet history and an exploration of the 1990s as a crucial period in this history, one when the Internet increasingly came to be understood as a need -as put by the author; other discussions that come to mind are those on the Internet as a (human) right [START_REF] Best | Can the internet be a human right?[END_REF] or as a global facility [START_REF] Musiani | Cyberhandshakes: How the Internet Challenges Dispute Resolution[END_REF].

The book has a simple structure that includes four chapters. The first chapter makes a casequite familiar to this journal's readers -for a theoretical perspective on Internet history able to move beyond the linear, deterministic, US-dominated perspective on the evolution of networking technologies, and for the need to highlight a series of alternative and competing histories. The different sections of this chapter examine the consequences of this pluralistic vision for the very concept of Internet imaginary -which in the author's view entails a shift towards network imaginaries -and establishes the link between network imaginaries, the political economy of media and the emergence of "network ideologies" (p. 31).

The second chapter, the first of two empirical ones, examines the narratives and the imaginary constructed around the birth of the World Wide Web. It is an examination of the ensemble of narratives constructed and disseminated to promote the Web during and after its invention. This chapter interestingly shows the extent to which the enormous success of the Web does not only, and perhaps not primarily, rely on its technical qualities, but on its framing as a "good, egalitarian and revolutionary invention" (p. 41), strongly supported by the story of its creator, Tim Berners-Lee, as a quiet and unique hero -in the long tradition of media history heroes such as Edison, Marconi and Jobs who are well accounted for by Joseph Campbell's "monomyth" [START_REF] Campbell | The Hero with a Thousand Faces[END_REF]. As the author argues, "to overcome the monolithic and linear path of the Web, and the ideological consequences of such a partial history, is essential to recognize how this story has been recounted as part of the dominant narrative of Internet history" (p. 66); a narrative that can and should be countered, or at least complemented, with "other" case studies and interpretive lenses.

The third chapter intends to show how to do just that -and to do so, picks two examples of "lost networks," the institutions-driven Socrate and the grassroots Iperbole projects in Italy: two European histories of networking linked to particular political and infrastructural visions, and aimed at demonstrating how "national and local cultures, political and economic traditions, and media landscapes impacted on the current state of digitization far beyond the Web's invention" (p. 70). Despite the previous chapter's ingenious take on Web history, this is the chapter I enjoyed the most, thoroughly original in its choice of case study in a vastly understudied country from the standpoint of technological and networking development, well-written and engaging. The author weaves together seamlessly visions, narratives and documental evidence to make a case for the power of the "hidden sides" of the history of networking.

The final Chapter 4 brings together insights from previous chapters, the case studies in particular, to refine the theoretical perspective of the book. In particular, it makes a case for exploring the limits of networks and of the imaginaries founded on networking models, as a means to "accept the constant tension between the past and the future, between the dreams of a networked society and those socio-technical, cultural, economic and political constraints that are able to regulate, shape and control networked societies" (p. 6). This book is an interesting and timely reading, of which I particularly appreciated the interdisciplinary perspective and mastery of different sources and materials. A part of me wonders whether its transition from a PhD thesis to a book should have entailed the hardest thing to do for a scholar -leaving behind part of his work to concentrate on the other. While, as previously mentioned, the author's Chapter 2 take on the Web is interesting and well-presented, I am not sure that the Italian case studies -which are indeed the "hidden treasure" of this study, covering completely new territory and unveiling private archives well-deserving to be unveiled -actually needed it as a prelude to convey the book's core message and make a case for looking beyond dominant technologies, their narratives and imaginaries. I would perhaps have been a more satisfied reader if the two central chapters had been dedicated one to Socrate, one to Iperbole (it seems to me that the author had largely the material and depth to do so), and more time and space had been dedicated to compare their "network ideologies", including their consequences for Italian Internet governance, and to the implications of this comparison for the book's underlying thesis. Perhaps, this would also have allowed for a more detailed discussion not only about the power of limits, but about the power of failures -an incredibly fascinating subtopic of media history and media archeology to which the author has contributed elsewhere [START_REF] Bory | La mancata disseminazione di Socrate. La storia dimenticata della rete a banda larga di Telecom Italia[END_REF] and, so it appears to this reviewer, is one of the most innovative recent contributions to the 'pluralistic history' this book is part of. That being said, I would like to reiterate my appreciation and admiration for this volume, and my pleasure in reading it as one of the most important recent contributions to the plural, non-deterministic, alternative Internet history this journal is also a testament to.


Trung Ferréol Binot
email: ferreol.binot@centralesupelec.fr

Dung Le

Marc Petit

Impact of environmental conditions on the voltage profile of LV networks

Keywords: Voltage profile, low voltage networks, temperature, ground resistivity, grounding resistance. I

European distribution system operators (DSOs) should meet EN 50160 standard requirements on the whole network. With the development of distributed energy resources (DER), DSOs need to have a better insight of their low voltage (LV) networks.

In this paper, we study the joint impact of external conditions (cable temperature, the ground resistivity and the ground resistances) on the voltage profile of three LV networks in four cases. The results show that some voltage problems cannot be seen by using only usual values of those external conditions. By considering the values that are closer to the real conditions, the voltage analysis will be more accurate and in some cases, additional problems can be detected. To be sure that the EN 50160 standard is met, a global study of LV networks including the external conditions should be done.

INTRODUCTION

In Europe, distribution system operators (DSOs) should meet the EN 50160 standard requirements. The main ones for low voltage (LV) networks are that:  Line-to-neutral voltages must be 95% of the time within the range of ± 10% of nominal voltage  Line-to-neutral negative-sequence voltage must be 95% of the time less than 2% of the positivesequence voltage

This standard has been in use for several years. With the arrival of Smart Grids and fast development of distributed energy resources (DERs), more and more new components are connected to distribution networks. They are often single-phase components, thus potentially increase unbalance and reverse power flows. This increases the risk that DSOs no longer meet the standard [START_REF] Liu | Distribution network voltage control by active power/reactive power injection from PV inverters[END_REF]. To address future network constraints, network codes applied in Europe define the requirements enforced to significant grid users and DSOs [START_REF]Electricity network codes and guidelines[END_REF]. Furthermore, new methods for LV network planning [START_REF] Frame | The uncertainties of probabilistic LV network analysis[END_REF] and even for network real-time management [START_REF] Angioni | Real-Time Monitoring of Distribution System Based on State Estimation[END_REF] have been proposed. To be able to effectively implement these methods, DSOs should have a better knowledge of LV networks. In this paper, cable models and their impact to the voltage profile will be discussed. Obviously, the cable impedance matrix depends on environmental conditions. In LV network studies, reference values for external conditions (temperature, ground resistivity and earthing resistance) are commonly used and considered as constants [START_REF] Kersting | A three-phase unbalanced line model with grounded neutrals through a resistance[END_REF]. However, these values are not well adapted for all networks. It could result in non-negligible errors in network analysis. The importance of studying the impact of their environment on LV cable models and voltage profiles has been highlighted in [START_REF] Urquhart | Accuracy of Low Voltage Electricity Distribution Network Modelling[END_REF]- [START_REF] Olivier | Modelling of three-phase fourwire low-voltage cables taking into account the neutral connection to the earth[END_REF]. The summary of those studies are presented in Table I.

Article

External condition Affected parameter Limits of the study [START_REF] Urquhart | Accuracy of Low Voltage Electricity Distribution Network Modelling[END_REF] Cable temperature

Sequence impedance

Not on line-toneutral voltage Not with 4x4 matrix [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF] Ground resistivity Positive sequence impedance [START_REF] Olivier | Modelling of three-phase fourwire low-voltage cables taking into account the neutral connection to the earth[END_REF] Ground resistances

Line-to-neutral voltage

Only one external condition

In [START_REF] Urquhart | Accuracy of Low Voltage Electricity Distribution Network Modelling[END_REF] and [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF], the impact of external conditions is only studied on sequence impedances and not on line-to-neutral voltages. It is difficult to isolate the impact of only one external factor by using the sequence impedances [START_REF] Moreno-Díaz | Accuracy of Electrical Feeder Models for Distribution Systems Analysis[END_REF]. To highlight this impact, we propose to use the 4x4 impedance matrix. It gives a better insight of the impact of the external conditions and is able to model more accurately a LV cable. All the existing works are limited insofar as they focus on each condition separately. However, we argue that they should rather be studied jointly. To our knowledge, this work has not been done yet.

The main originality of this paper is to study the joint impact of external conditions on the line-to-neutral voltages. Moreover, our work enables DSOs to know which condition has a bigger impact on line-to-neutral voltages and to check that each network with its own particularities meets the EN 50160 standard requirements. The cable model is presented in Section II. Its dependencies to the external conditions are introduced in Section III. The test cases are described in Section IV. Results and discussions are shown in Sections V and VI.

II. CABLE MODEL

In this section, the cable model is described. The value of cable impedance is calculated for a LV cable used in many French networks.

A. Theoretical study

In France, LV electric cables are composed of 4 conductors (Phases A, B, C and the neutral N). As a current can flow through the ground (G), a fifth wire is considered for the cable model. This gives a 5x5 impedance matrix. However, the 5x5 impedance matrix is rarely used [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. Usually, as the sum of the currents flowing in five wires is supposed to be zero, the 5x5 matrix is reduced to a 4x4 matrix by removing the ground wire. (1)

Ohm's law on a section of LV cable between 𝑙 and 𝑘 gives the equation ( 1) following the configuration given in Fig. 1. 𝑅 𝑒 𝑙 and 𝑅 𝑒 𝑘 are the earthing resistances of 𝑙 and 𝑘. The ground wire impedance is included in the 4x4 matrix terms. We still define 𝐷 𝑔 (m), the ground radius and 𝑟 𝑔 the ground per unit length resistance equals to 𝑟 𝑔 = 𝜇 0 𝜔 8 (Ω/m). We also define 𝐷 𝑖𝑗 the distance between 𝑖 and 𝑗 conductors (including the ground conductor), 𝐷 𝑖 (m) the geometrical mean radius given by 𝐷 𝑖 = 𝑒 -1 4

⁄ 𝑅 𝑖 where 𝑅 𝑖 is the physical radius 𝑖 of conductor , and the per unit length resistance 𝑟 𝑖 = 𝜌 𝑖 𝜋𝑅 2 (Ω/m). The different terms of the 4x4 per-unit-length impedance matrix were calculated in [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. Their expressions are as follows (Ω/m):

𝑧 𝑖𝑖 = (𝑟 𝑖 + 𝑟 𝑔 ) + 𝑗𝜔 𝜇 0 2𝜋 * 𝑙𝑛 ( 𝐷 𝑖𝑔 𝐷 𝑔𝑖 𝐷 𝑖 𝐷 𝑔 ) (3)
𝑧 𝑖𝑗 = 𝑟 𝑔 + 𝑗𝜔 𝜇 0 2𝜋 * 𝑙𝑛 ( 𝐷 𝑖𝑔 𝐷 𝑔𝑗 𝐷 𝑖𝑗 𝐷 𝑔 ) ( 4
)
Where i, j = a, b, c, n and i ≠ j.

As explained in [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF], it is usually to consider 𝐷 𝑔 = 1 𝑚. In this case, [START_REF] Urquhart | Series impedance of distribution cables with sector-shaped conductors[END_REF] has determined [START_REF] Kersting | A three-phase unbalanced line model with grounded neutrals through a resistance[END_REF].

𝐷 𝑖𝑔 𝐷 𝑔𝑗 𝐷 𝑔 = 658,9 √𝑓 𝜌 𝑔𝑟𝑜𝑢𝑛𝑑 ⁄ (𝑚) (5)
Generally, the Kron reduction can be applied to the 4x4 matrix to remove the neutral conductor and obtain a 3x3 impedance matrix [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. In the same way, the 3x3 matrix can be transformed in a diagonal 3x3 series impedance matrix via the method of symmetrical components [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. But, neither the Kron reduction, nor the symmetrical components transform are well adapted for such networks because of highly unbalanced currents in LV networks and asymmetry in LV cables geometry [START_REF] Moreno-Díaz | Accuracy of Electrical Feeder Models for Distribution Systems Analysis[END_REF]. Moreover, we can no longer determine the neutral-toground voltage if 3x3 impedance matrices were used. We thus choose to keep the 4x4 matrix in the following sections.

B. Analytical and finite element values

In this section, we consider the following LV cable which is used in French LV networks (Fig. 2b). The phases and neutral cross-sections are typically: 95/70, 150/95 and 240/115mm². A reference case described in [START_REF] Urquhart | Series impedance of distribution cables with sector-shaped conductors[END_REF] is considered to model LV cables and to simulate LV networks. The parameters of the reference case are defined in Table II. We also use this reference case to determine the 4x4 impedance matrix with analytical and finite element (FE) methods. Using analytical equations ( 3) and (4), the 4 x 4 matrix of 150/95mm² cable is (Ω/km): For the FE method, we consider a cable length of 1000 m and an insulation resistivity of 10 16 Ω-m modeled in the FE method magnetics (FEMM) software [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. The mean error between analytical and FE methods is equal to 1.4%. As results of both models are similar, we consider that the analytical model has good accuracy and can be used to model the cable. We choose to keep using this model in the following sections.

𝑧 𝑎𝑛𝑎𝑙𝑦 = [ 0.

III. DEPENDENCIES ON ENVIRONMENTAL CONDITIONS

If the dependencies on environmental conditions are not considered in the previous section, this section analyses three types of external conditions: ground electrical resistivity, aluminum electrical resistivity and earthing resistances.

A. Dependency on ground electrical resistivity

Considering (5), the imaginary parts of ( 3) and ( 4) are function of the ground resistivity. In the literature, various approaches of ground resistivity determination are proposed: geological approach [START_REF] Samouëlian | Electrical resistivity survey in soil science: a review[END_REF], experimental measures [START_REF]Rural Electrification Administration[END_REF] and manufacturers specifications [START_REF] Fluke | Earth Grounding Resistance[END_REF]. They give different ranges of ground electrical resistivity. In [START_REF] Samouëlian | Electrical resistivity survey in soil science: a review[END_REF], the authors describe the measurement of ground resistivity as a great method to determine soil characteristics. In that way, ground resistivity is very influenced by the soil type and varies from 1 to 10 000 Ohm-m (fig. 3).

Figure 3 Typical ranges of electrical resistivity of earth materials [START_REF] Samouëlian | Electrical resistivity survey in soil science: a review[END_REF] Unfortunately, ground resistivity is also influenced by ground temperature, moisture, water conductivity and local heterogeneities (e.g. conductive pipes in the neighboring soil) [START_REF] Samouëlian | Electrical resistivity survey in soil science: a review[END_REF]. It is difficult to model all these conditions to obtain a global probability density function. Moreover, the geological composition of soil is not uniform within a country. Experimental measurements of ground resistivity have been conducted in the USA [START_REF]Rural Electrification Administration[END_REF]. These measurements enabled us to draw the probability density function of ground resistivity reproduced in fig. 4. The main value of ground resistivity is around 150 Ω/m which is higher than the reference value. Finally, a manufacturer provides in Table III the ground electrical resistivity of more familiarly named soils [START_REF] Fluke | Earth Grounding Resistance[END_REF].

B. Dependancy on earthing resistances

Earthing resistances do not have an impact on equations ( 3) and (4). However, the resistances impact the neutral-to-ground and line-to-ground voltages [START_REF] Olivier | Modelling of three-phase fourwire low-voltage cables taking into account the neutral connection to the earth[END_REF]. These resistances are function of the soil type and the earthing techniques. Common values of earthing resistance are shown in Table III.

C. Dependency on aluminum electrical resistivity

This last dependency variation is better known. In fact, the real parts of ( 3) and ( 4) are a linear function of the aluminum electrical resistivity, i.e. the main cable material. Aluminum resistivity is mainly temperature dependent:

𝜌 𝑎𝑙𝑢 (𝑇) = 𝜌 0 [1 + 𝛼 * (𝑇 -𝑇 0 )] ( 6
)
Where 𝛼 = 3,63 × 10 -3 𝐾 -1 and 𝜌 0 = 2,86 × 10 -8 Ω𝑚 at 𝑇 0 = 273 𝐾.

The cable temperature may vary between 0 and 100°C [START_REF] Angioni | Real-Time Monitoring of Distribution System Based on State Estimation[END_REF]. Intuitively, a part of this temperature variation results from Joule effect. As described in [START_REF] Li | The use of reflective and permeable pavements as a potential practice for heat island mitigation and stormwater management[END_REF], pavement also has an impact on the ground and the cable temperatures. This impact is not linear and is function of the network layout. We then present a time dependent thermal FE study in the following section.

IV. METHODOLOGY AND TEST CASES

The proportion of LV underground cables is significant in Europe. Impact of external factors described in section III cannot be directly measured. In this section, we present the method developed to analyze jointly these external effects on a 4x4 matrix and on a line-to-neutral voltage. The three external conditions discussed before are also influenced by other external factors such as soil surface color, soil type, air temperature, solar energy, soil moisture and electric losses, as shows Fig. 5. The probability density function of all these factors is difficult to determine and all these factors are interdependent. Therefore, we consider three types of network (urban, semi-rural and rural) and simulate each of them in four types of cases (reference winter, winter, reference summer and summer).

A. Global approach

B. Studied networks

Parameters of the studied networks (urban, semi-rural and rural) are presented in Table IV. These LV networks are part of the distribution dataset used in the CGMES 2.4.1 interoperability tests performed in 2016 [START_REF] Entsoe | INTEROPERABILITY TEST 'CIM FOR SYSTEM DEVELOPMENT AND OPERATIONS[END_REF]. For the ground electrical resistivity, we consider that urban, semi-rural and rural ground are respectively sandy clay soil, moist gravel and very moist soil. We also suppose that the ground electrode is 3 meters in depth and the neutral wire is not grounded at every node.

C. Studied cases

We consider four type of cases (reference winter, winter, reference summer and summer) to illustrate the impact of the external factors. Table V gives the values of external conditions used in different configurations. Consumption and production profile are specified using data from [START_REF]Results of electricity cost-benefit analysis, customer behavior trials and technology trials[END_REF] and [START_REF]Electricity smart metering customer behavior trials findings report[END_REF]: for the 2 winter cases, we consider the most critical moments of winter, i.e. the 24 highest successive consumption values in winter (winter profile), and for the 2 summer cases, we consider the most critical moments of summer, i.e. the 24 highest production values in summer (summer profile). The calculated temperature in the more realistic cases are from a COMSOL time dependent thermal model. V. RESULTS The load flow is computed by EPRI's OpenDSS [START_REF]OpenDSS[END_REF] on the three test networks presented previously. We analyze the impact of external conditions on voltage limits and voltage unbalance of the 24 summer moments and 24 winter moments.

A. Voltage limits

A voltage problem occurs when a line-to-neutral voltage exceeds the range of ± 10%, Fig. 6 and7 show the ratio of voltage problem 𝜏 𝑣 defined in [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF].

𝜏 𝑣 =

𝑁 𝑝𝑏𝑟 𝑁 𝑛𝑜𝑑𝑒 * 𝑁 𝑝ℎ𝑎𝑠𝑒 * 𝑁 𝑚𝑜𝑚𝑒𝑛𝑡 [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF] Where 𝑁 𝑝𝑏𝑟 : the number of voltage problems, 𝑁 𝑛𝑜𝑑𝑒 : number of nodes, 𝑁 𝑝ℎ𝑎𝑠𝑒 : the number of phases and 𝑁 𝑚𝑜𝑚𝑒𝑛𝑡 : the number of studied moments. In Fig. 6, the upper limit of the standard is exceeded only in summer. Production units are only connected to the urban and rural networks. Hence, the presence of producers increases the risk to exceed the EN 50160 standard requirements in summer. The increase is higher in the rural than in the urban network. In Fig. 7, the lower limit is never reached in summer. In all networks, the number of cases where line-to-neutral voltages are below 0.9 pu rises from the reference winter case to the winter case. The increase is similar in the rural and in the semirural networks but higher than in the urban network.

B. Voltage unbalance

A voltage unbalance problem occurs when the negativesequence voltage is above 2% of the positive-sequence voltage. Fig. 8 shows the ratio of voltage problem 𝜏 𝑣 defined in [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF]. The impact of external conditions is visible in the urban network, where the number of critical situations rises from 1.33% to 1.84% in winter. In the other situations, the impact is negligible.

C. Results analysis

We also study the impact of temperature alone on the 4x4 impedance matrix and on the voltage profile. Only the real part of 𝒛 𝒂𝒂 is influenced by the cable temperature [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF]. Table VI shows the proportionality of these quantities in regards to the temperature in the rural network. Similar results are obtained for the two other networks. The impact of external conditions is easily observable by using the 4x4 impedance matrix [START_REF] Binot | Modélisation de l'impédance des câbles : Étude de sensibilité et impact sur le réseau BT[END_REF] instead of using the diagonal 3x3 series impedance matrix [START_REF] Urquhart | Accuracy of Low Voltage Electricity Distribution Network Modelling[END_REF], [START_REF] Keshtkar | Improving the Accuracy of Impedance Calculation for Distribution Power System[END_REF]. However, the impact of external conditions on voltage problems depends also on the network type. Rural network feeders are often longer than urban network ones and their cable cross-sections are often smaller. Hence, line-to-neutral voltages of rural networks are usually closer to the EN 50160 standard voltage limits than urban networks. Thus the impedance matrix of rural networks should be known with higher precision than that of urban networks.

VI. CONCLUSION

In this paper, the impact of three external conditions on the voltage profile of three LV networks is jointly studied. For each network, four cases are considered: winter, reference winter, summer, and reference summer. The results show that some voltage problems cannot be seen by using only usual values of those external conditions. By considering the values that are closer to the real conditions, the cable model parameters can be more accurately estimated. As a result, the voltage analysis will be more accurate and in some cases, additional problems can be detected. The authors recommend the use of 4x4 impedance matrix with an earthing resistance instead of the sequence impedances to describe more precisely LV networks. Besides, results show also that rural and some semi-rural networks are more prone to voltage problems than urban networks. To be sure that the EN50160 standard is met, a global study of LV networks including the external conditions should be done. In practice, it is difficult to determine the exact value of external conditions for each network or each cable section. Then a LV parameter estimator could be an interesting solution to deal with this problem.

  𝑎𝑏 𝑍 𝑎𝑐 𝑍 𝑎𝑛 𝑍 𝑏𝑎 𝑍 𝑏𝑏 𝑍 𝑏𝑏 𝑍 𝑏𝑛 𝑍 𝑐𝑎 𝑍 𝑐𝑏 𝑍 𝑐𝑐 𝑍 𝑐𝑛 𝑍 𝑛𝑎 𝑍 𝑛𝑏 𝑍 𝑛𝑐 𝑍 𝑛𝑛]

Figure 1 .

 1 Figure 1. LV cable model

Figure 2 .

 2 Figure 2. French 150/95mm² LV cable a: Picture of studied cable b: Finite element geometry c: Analytical geometry

Figure 4

 4 Figure 4 Probability density function of ground resistivity

Figure 5

 5 Figure 5 Factors, conditions and configurations for sensibility analysis

  𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 20°𝐶 𝜌 𝑔 = 100 Ω𝑚 winter profile 𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 20°𝐶 𝜌 𝑔 = 100 Ω𝑚 winter profile 𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 20°𝐶 𝜌 𝑔 = 100 Ω𝑚 winter profile Winter 𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 35°𝐶 𝜌 𝑔 = 150 Ω𝑚 winter profile 𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 25°𝐶 𝜌 𝑔 = 500 Ω𝑚 winter profile 𝑅 𝑒 = 1Ω 𝑇 𝑐𝑎𝑏𝑙𝑒 = 15°𝐶 𝜌 𝑔 = 30 Ω𝑚 winter profile

Figure 6

 6 Figure 6 Percentage of upper voltage problem

Figure 7

 7 Figure 7 Percentage of lower voltage problem

Figure 8

 8 Figure 8 Percentage of voltage unbalance problem

TABLE I IMPACT

 I

OF EXTERNAL CONDITIONS IN THE LITERATURE

TABLE III EARTHING

 III RESISTANCE OF DIFFERENT SOILS

	Type of soil	Soil resistivity	Earthing resistance (Ω) Ground electrode depth
		(Ω-m)	3 (m)	6 (m)	10 (m)
	Very moist soil	30	10	5	3
	Farming soil	100	33	17	10
	Sandy clay soil	150	50	25	15
	Moist gravel	500	160	80	48
	Dry gravel	1000	330	165	100
	Stoney soil	30,000	1000	500	300

TABLE IV LV

 IV NETWORKS TYPES PARAMETERS

	Networks types	Urban	Semi-rural	Rural
	Nominal power of transformer	400 kVA	250 kVA	100 kVA
	Consumers number	148	31	4
	Annual mean consumption	65.7 kW	24.3 kW	5 kW
	Producers number	9	0	1
	DER contract power	105.4 kW	0 kW	18 kW
	Network length	4.0 km	4.0 km	1.0 km

TABLE V VALUES

 V OF EXTERNAL CONDITIONS IN DIFFERENT CONFIGURATIONS