Estimates of Atmospheric Aerosols Adhered to the High Voltage Electric Wire in the Yangtze River Delta Region of China

Atmospheric aerosol particles can collect on and adhere to high voltage electrical wires, causing power loss as well as other detrimental effects on electrical insulation. The mass of fine particles (PM2.5) adhering to wires has been estimated using a modified size-resolved particle dry deposition model and a range of annual average PM2.5 concentrations found in literature for the Yangtze River Delta region of China. Annual mass collected by the surface of a unit length (1 m) of wire with a radius of 0.5 cm is estimated to be in the range 1.56 × 10–1.46 × 10 μg. The actual mass adhering to the wire may be reduced by 85% of these estimated values considering the washing-off effects of rain. For a wire of 1.0 cm in radius, the annual mass on the wire is estimated to be in the range of 4.68 × 10–4.35 × 10 μg after considering the effects of rain. This study provides a first estimation of particle mass collected by electrical wires, although with large uncertainties, which can be used for subsequent impact studies of aerosol pollution on electricity transfer.


INTRODUCTION
Mass concentrations in air of atmospheric aerosol particles have been at high levels across China (Tao et al., 2017) in the most recent decades due to increasing energy consumption (Wang et al., 2016;Ma et al., 2017) and rapid economic growth (Liu et al., 2016;He et al., 2017;Sun et al., 2017).Increased aerosol air concentrations can enhanced particle deposition amounts to any surfaces including high voltage electric wires with the power loss.In particular, particle deposition on insulator can decrease flashover voltage and increase leakage current, posing a threat to electric power supply safety (Wu et al., 2004;Zhao et al., 2007;Li et al., 2014;Hu et al., 2015).Particle deposition (marine salt, industrial and agricultural pollutants), in the presence of elevated humidity levels, greatly increase the surface conductivity of lines and substations insulators and can lead to surface discharges and electrical short-circuits.The persistence of these conditions poses a threat to the continuity of service of the electrical grid and may produce extended blackouts in large areas of the network such as the blackout phenomena due to pollution on the whole island of Sardinia, Italy (Troccoli et al., 2014).
Some efforts have been made to simulate the impact of particle pollution on flashover incidents (Gençoğlu et al., 2008;Jiang et al., 2010), but little has been done to estimate the amount of particle mass deposition on electric wires.The purpose of the present study aims to provide a rough estimation of particle mass adhered to high-voltage electric wires in the Yangtze River Delta region of China.To do this, the size-resolved particle dry deposition model of Zhang et al. (2001) is first modified to include the effect of electric charge since this mechanism might be important in the collection of fine particles by electric wires.Modeled dry deposition velocities under typical turbulent conditions are then combined with a range of annual average PM 2.5 concentrations found in this region, as documented in Tao et al. (2017).Coarse particles are not considered here since they may not be adhered to the wire permanently due to blowing off effects by strong winds and washing off effects by rain.Uncertainty analyses have also been conducted to provide a range of possible values for the estimated annual particle mass adhered to different sizes of wires.

METHODOLOGY
Dry deposition flux to various land surfaces is commonly based on unit land surface area.Electric wire is in cylinder shape so the particle mass adhered to electric wire is calculated based on a unit length in this study with surface area as a function of wire diameter.The size-resolved particle dry deposition model of Zhang et al. (2001) is modified to estimate the rate of particles adhered to surface of electric wire.The collection efficiencies of particles by electric wire surface are certainly different from those by land surfaces so modifications are made as detailed below.
According to Zhang et al. (2001), particle dry deposition velocity (V d ) is calculated as: where R a and R s are aerodynamic and surface resistance, respectively.Because wire is installed at high levels in the sky where winds are generally strong, R a should be negligible in most cases.A value of 10 s -1 m is used throughout the study.Note that the gravitational setting velocity in the original formula was excluded here considering the cylinder shaper of the wire surface may not collect all the particles through this mechanism.Besides, gravitational setting is a minor contributor to the deposition of fine particles (Zhang and He, 2014), which is the focus of the present study as further explained below.The surface resistance is parameterized as a function of various collection mechanisms: where ε 0 is an empirical constant (0.3), u * is friction velocity, E B , E IM , E IN and E E are collection efficiencies by Brownian diffusion, impaction, interception, and electric charge, respectively.R 1 is the factor considering particle rebound (the fraction of particles collide with the surface and not bounced back).E B and E IM by electric wire surface are considered to be smaller than any land surface described in Zhang et al. (2001) so the minimum values (such as over bares soil) are used here for these two terms.E IN is calculated as a function of particle diameter and wire radius.A value of 0.5 cm is used for wire radius as the base case in the present study based on a survey in the studied region.E E is a new term added in this study, representing the collection efficiency by electric force generated by wire on particles.According to Wang et al. (2010), E E is parameterized as: where K = 9 × 10 9 (N m 2 C -2 ), C C is Cunningham correction factor as a function of particle diameter and the mean free path of air molecules, Q and q are the surface charge of high voltage wire and particle, respectively, µ a is air viscosity, V is gravitational setting velocity of particles, and D and d p are the diameters of wire and particle, respectively.Q was expressed as: where σ is surface charge density of high voltage wire and the value was taken from Jiang et al. (2015) as 12 × 10 -6 (C m -2 ).S can be calculated as a product of section girth and length of wire.Here, the length of wire was chosen as 100 times of particle size in order to generate effective electric force between wire and any size particles.q can be calculated according to Wang et al. (2010): where a = 0.83 × 10 -6 and ∂ (C m -2 ) is an empirical parameter that can vary between 0 and 7.Here ∂ is taken as 7 because the electric field around high voltage wire is very strong.
Particle mass deposit and adhere to a wire (M) can then be estimated as: where C is the mass concentration of particles in air, r is the wire radius, L is wire length, t is the time period.
Considering that large particles collide with wire may not easily adhere to the wire since they can easily be blown away by strong winds or washed off by rain, only fine particles (PM 2.5 ) are considered in Eq. ( 6).Since particle size distribution is needed for calculating size-resolved V d , a log-normal size distribution is assumed following Zhang and He (2014) with geometric mass median diameter and geometric standard deviation chosen as 0.4 µm and 2.2, respectively.

Dry Deposition Velocity
Fig. 1 shows a comparison of size-resolved V d calculated using the modified and the original models with a u * value of 0.5 m s -1 .It is seen that adding electric charge only affect V d of particles in the size range of 0.2-6 µm, for which V d can be increased by up to two times.However, V d for this size range of particles are at the minimum values so the overall effect on the bulk V d of all particles should be very small.To verify this, bulk V d of PM 2.5 is obtained by integrating the size-resolved V d using the sizedistribution assumed above.The differences in the bulk V d between the modified (0.062 cm s -1 ) and original model (0.06 cm s -1 ) was only 3.3%.
The size-resolved V d from the modified model under different u * conditions are shown in Fig. 2. V d increases with increasing u * for all particle sizes.When u * increased from 0.2 to 1.0 m s -1 (or five times), V d also increased by up to five times for most particle sizes.The bulk V d for PM 2.5 shows an almost perfect linear relationship between  V d and u * (Table 1), e.g., V d (cm s -1 ) = 0.1226 u * , similar to what was found in an earlier study (Zhang and He, 2014).

Aerosol Mass Adhered to Electric Wire
Eq. ( 6) is used to estimate particle mass adhered to a wire accumulated during one year period (t = 1 year).A unit length of wire (L = 1 m) with a radius of 0.5 cm is chosen as the base case.A range of V d values (0.025-0.122 cm s -1 ) is applied to two different PM 2.5 concentration scenarios (63-121 µg m -3 ), which represent lower-and upper-end annual average concentrations found in the Yangtze River Delta region of China (Tao et al., 2017).Annual mass of PM 2.5 collected by the unit-length wire is estimated to be in the range of 1.56 × 10 4 -1.46 × 10 5 µg.This large range is due the large range of the estimated V d as well as the variations in PM 2.5 mass concentration.

Uncertainty Analysis
There are many uncertainties in the above estimated aerosol mass adhered to the wire.To explore how sensitive the estimated mass to various assumed variables, sensitivity tests are conducted below on model parameters as well as environmental factors, such as considering washing off effects by rain, using higher collection efficiencies (E B and E IM ), and estimating for a different size of wire.Potter et al. (1991) estimated that 85% particle mass deposited to forest leaves can be washed off by rain.The percentage can be even higher for the case of wire-adsorbed particles.Using the same percentage number, the mass of PM 2.5 adhered to an unit-length wire with a radius of 0.5 cm should then be revised to 2.34 × 10 3 -2.19× 10 4 µg (Case 1 in Table 1).In Eq. ( 2), the lowest E B and E IM values over land surface (except water) were chosen for the case of wire surface assuming wire collects particles slower than any land surface by these two mechanisms.If these two values were adjusted to medium values shown in Zhang et al. (2001), the revised estimation would be in the range of 9.30 × 10 3 -8.89× 10 4 µg, (Case 2 in Table 1), which are about three times higher of the original estimation (Case 1 in Table 1).
If considering a thicker wire such as using a wire radius of 1 cm, the annual mass adhered to the wire is estimated to be in the range of 4.68 × 10 3 -4.35× 10 4 µg (Case 3 in Table 1), basically double of those from Case 1, as is supported by from Eq. ( 6).

CONCLUSIONS
Under typical aerosol pollution conditions in the Yangtze River Delta region of China, particle mass collecting on and adhering to high-voltage electrical wires is estimated to be on the order 10 3 -10 4 µg per unit length (1 m) wire during a one year period.These numbers can be used as a first estimation for studying the impact of aerosol deposition on issues related to electrical wiring, keeping in mind that such an estimation does not include contributions from fog, humidity, or icy conditions when aerosol deposition might be substantially enhanced.Future studies may focus on chemically resolved particle mass deposited on wires, as charged ions potentially have the strongest negative impact on insulators, as well as introduce the deposition scheme into a 3-D air quality model.
This study provides a first estimation of particle mass collected on electrical wires, although with large uncertainties in the physical and chemical physical interaction between the aerosols and the wire surface, which can be used for subsequent impact studies of aerosol pollution on electricity transfer.Flashovers caused by long-term dust contamination mainly take place on dirty insulators rather than on power lines, which have a simpler shape than those of insulators.

Fig. 1 .
Fig. 1.Size-resolved V d from the modified and the original models.

Table 1 .
The modeled bulk V d of PM 2.5 under five different u * conditions and estimated PM 2.5 mass adhered to unit-length wire (1 m) during one year period under five different u * and two different PM 2.5 concentration scenarios.