Advanced modeling and mapping of severe pollution stress required for outdoor insulation coordination

Abstract

Severe pollution environment over the Israel Electric (IECo) Power Grid is created by synergy between Saharan dust and sea-salt aerosols (SSA) originated from the Mediterranean Sea. In the presence of high air humidity, the resultant pollution stress remains one of the major factors affecting operational reliability of ceramic insulators in the IECo Network. In respect with the severe polluted conditions, the outdoor insulation coordination requires detailed statistical studies and refined geographic mapping of the natural pollution deposit. This paper presents numeric maps of Sea-Salt Sedimentation Rate (SSSR) that was developed for the Eastern Mediterranean region including Israel. The paper demonstrates an adopted meteorological model, calculating algorithm and spatial–temporal characteristics of sea-salt aerosols within the considered domain. The acquired SSSR-Maps have been verified against the Equivalent Salt Deposit Density (ESDD) field-data and available ground-level measurements of SSA-concentrations. Good agreement was obtained between SSA model predictions and ground-based measurements on a daily and monthly basis. A case-study of a joint analysis of desertdust and sea-salt deposition along the selected overhead line was presented. The effect of the sea-salt deposit on the pollution flashover risk of ceramic insulators has been demonstrated. It is showed that the predicted ESDD-values might quite commensurate those ESDD-portions absorbed by desert dust. Hence, the contribution of sea-salt deposit cannot be neglected when evaluating pollution flashover risk for local outdoor insulators, especially in coastal areas. The study outcomes have demonstrated that the proposed SSA-modeling approach has sufficient meaningfulness to be implemented in practical tasks of outdoor insulation coordination and insulators dimensioning.

Appendices

Appendix A

1.1 Chemical structure of the local SSA and sea-water

The chemical structure of sea-salt particles is similar to that of sea-water. According to Nessim et al. [23], the following six major ions: Na + , Cl-, SO4-2, Mg + 2, Ca + 2 and K + , make up > 99% of the total dissolved salts in the Eastern Mediterranean Sea-water. Based on our long-term measurements, Table 2 presents typical chemical components of the coastal sea-water.

Table 2 Major chemical components of the coastal sea-water

The representative mass-relations, as per Table 2 can be characterized as very stable, which have fairly low monthly and directional variations along the local 230-km-shoreline. The data from Table 2 enable direct evaluation of the key-index γ that represents specific weight of NaCl in the total mass of sea-salts (see Eq. (4)). As per our estimates, the γ-index can be reliably assigned to be 0.85 for local conditions. The latter ratio causes a respective very high salinity (~ 40-g/kg) of the Eastern Mediterranean Sea-water which is one of the most saline sea areas in the world [24].

Appendix B

2.1 The ‘Dream-Salt’ model

Below we will briefly explain a principal Flowchart, as per Fig. 13, which depicts the involved modules, data-exchange and calculating algorithm.

Fig. 13

Data-processing flowchart of the TAU/DREAM SSA-deposit calculation module

At the 1-st step, the NCEP/Eta meteorological model is initialized with the NCEP analysis [20, 25]. Boundary conditions are updated every 6 h by the NCEP Global Forecast System [25] meteorological model (Fig. 13, PREPROCESSING).

At the 2-nd step, the Eta (η) meteorological model [20, 21] solves the system of hydrodynamic equations as per (B1)–(B9), which describe basic meteorological parameters, such as winds, temperature, pressure, etc. (Fig. 13, ATMOSPHERIC MODELING).

$$ \frac{{{\text{d}}v}}{{{\text{d}}t}} + f \cdot \user2{k} \times \user2{v} + ~\nabla {{\Phi ~}} + ~\frac{{R \cdot T}}{p} \cdot \nabla p = 0~ $$

(B1)

$$ \frac{{{\text{d}}T}}{{{\text{d}}t}} - \frac{{k \cdot T \cdot \omega }}{p} = 0~ $$

(B2)

$$ \frac{\partial }{{\partial \eta }}\left( {\frac{{\partial p}}{{\partial t}}} \right) + ~\nabla \cdot \left( {\user2{v} \cdot \frac{{\partial p}}{{\partial \eta }}} \right) + ~\frac{\partial }{{\partial \eta }}\left( {\eta \cdot \frac{{\partial p}}{{\partial \eta }}} \right) = 0 $$

(B3)

$$ \frac{{\partial {{\Phi }}}}{{\partial \eta }}~ = - \frac{{R \cdot T}}{p} \cdot \frac{{\partial p}}{{\partial \eta }} $$

(B4)

$$ \omega ~ \equiv ~\frac{{{\text{d}}p}}{{{\text{d}}t}} = ~ - \mathop \smallint \limits_{0}^{\eta } \nabla \cdot \left( {\user2{v} \cdot \frac{{\partial p}}{{\partial \eta }}} \right) \cdot {\text{d}}\eta + \user2{v} \cdot \nabla p $$

(B5)

$$ \frac{{{\text{d}}p_{S} }}{{{\text{d}}t}} = ~ - \mathop \smallint \limits_{0}^{{\eta _{S} }} \nabla \cdot \left( {\user2{v} \cdot \frac{{\partial p}}{{\partial \eta }}} \right) \cdot {\text{d}}\eta $$

(B6)

$$ \eta \cdot \frac{{{\text{d}}p}}{{{\text{d}}\eta }} = ~ - \frac{{{\text{d}}p}}{{{\text{d}}t}}~ - \mathop \smallint \limits_{0}^{\eta } \nabla \cdot \left( {\user2{v} \cdot \frac{{\partial p}}{{\partial \eta }}} \right) \cdot {\text{d}}\eta $$

(B7)

Here v is the horizontal velocity vector, f is the Coriolis parameter, k is the vertical unit vector, Φ is geopotential, R is the gas constant, and k is R/C_P, where C_P is the specific heat at constant pressure. Eta uses the η-vertical coordinate written as [20, 21]:

$$ \eta ~ = ~\frac{{p~ - ~p_{T} }}{{p_{S} ~ - ~~p_{T} }} \cdot \frac{{p_{{rf~}} \left( {Z_{S} } \right)~ - ~p_{T} }}{{p_{{rf~}} \left( 0 \right)~ - ~~p_{T} }} $$

(B8)

where p is pressure; the subscripts T and S stand for the top and the ground surface values of the model atmosphere, respectively; Z is geometric height, and p_rf (Z) is a reference pressure as a function of Z. The η-coordinate improves the calculation of horizontal derivatives near steep topographic areas.

At the 3-rd step, the DREAM Sea-salt module is initialized with 3-D sea-salt distributions obtained from previous sea-salt forecasts (i.e., previous model runs) (Fig. 13, SEA-SALT MODELING). Each run-session starts at 12:00 UTC and sea-salt predictions were performed for 6-h periods up to 72 h ahead. The sea-salt module of DREAM-Salt solves the Euler-type partial differential nonlinear equations for sea-salt mass continuity. The Eulerian concentration equation is given by the following expression:

$$ \begin{aligned} \frac{{\partial C_{k} }}{{\partial t}}~ = & - u \cdot \frac{{\partial C_{k} }}{{\partial x}} - \nu \cdot \frac{{\partial C_{k} }}{{\partial y}} - \left( {w - \nu _{{gk}} } \right) \cdot \frac{{\partial C_{k} }}{{\partial z}} \\ & \quad - ~\nabla \left( {K_{H} \cdot \nabla C_{k} } \right) - ~\frac{\partial }{{\partial z}}\left( {K_{Z} \cdot \frac{{\partial C_{k} }}{{\partial z}}} \right) + \left( {\frac{{\partial C_{k} }}{{\partial t}}} \right)_{{{\text{SOURCE}}}} - \left( {\frac{{\partial C_{k} }}{{\partial t}}} \right)_{{{\text{SINK}}}} ~ \\ \end{aligned} $$

(B9)

where k indicates the number of particle size classes; C_k is the sea-salt concentration of a k-th particle size class; u and ν are components of horizontal wind velocity; w is the vertical velocity; K_H is the lateral diffusion coefficient, K_Z is the turbulent exchange coefficient. ν_gk is the gravitational settling velocity, SINK is the sink term which includes both wet and dry deposition [26]. SOURCE is meaning sea-salt emissions. Eight size bins covering the particle effective sizes from 0.1 μm to 7 μm are used in the model.

At the 4-th step, the DREAM-Salt output files are created (Fig. 13, POSTPROCESSING). The Grid Analysis and Display System Software (GRADS) has been used for creating DREAM-Salt output files [27]. The output files contain space–time distribution of sea-salt concentration/deposition over the modeled domain for every six hours, starting from 12:00 UTC and up to 72 h ahead.

At the 5-th step, the DREAM-Salt output files that were generated in the GRADS format are now compressed and archived in the Multi-Year Archive of SSA-deposition over the modeled domain (Fig. 13, Multi-Year ARCHIVE).

The last 6-th step of the modeling procedure (Fig. 13, MAPPING) is described in Chapter 4.