Power distribution system resilience to extreme dust storms: probabilistic impact assessment and hardening planning

ABSTRACT

Extreme dust storms (EDSs) are high-impact low-probability natural disasters, and their occurrence in humid climates can damage the power distribution systems (PDSs) as a critical infrastructure. In this paper, proposed a bi-level stochastic framework for simultaneously hardening substations and distribution lines. In the first level, total capital cost is addressed for PDS hardening under the financial constraints, while in the second level, the expected operating costs are minimized in the case of an EDS under the operating constraints. In the proposed model, the location of remote-controled switches (RCSs) is determined based on the PDS hardening planning results, and the decisions at each level depend on the planning results of the other level. The simulation results at different budget levels show that simultaneous hardening planning of distribution lines and substations considering network reconfiguration can not only reduce expected operating costs, but also can reducing total capital cost to PDS resilience enhancement.

KEYWORDS:

• Resilient distribution networks
• dust storms
• gas insulated substation
• silicone rubber insulator
• network reconfiguration

Nomenclature

Sets and Indices:	=
ΩS	=	Set of scenarios indices s.
ΩT	=	Set of emergency operation durations indices t.
ΩN	=	Set of buses indices i.
ΩB	=	Set of lines indices (i,j).
ΩL	=	Set of load buses (ΩL$\subset$ ΩN).
ΩPCC	=	Set of substation buses (ΩPCC$\subset$ ΩN).
ΩSW1	=	Set of selected lines for installing RCS (ΩSW1$\subset$ ΩSW).
ΩSW2	=	Set of selected tie lines for installing RCS (ΩSW2$\subset$ ΩSW).
ΩSW	=	Set of lines with RCS (ΩSW$\subset$ ΩB).
Variables:	=
${\mathrm{C}}_{\mathit{sub}}^{\mathit{inv}}\left(x^{\mathit{sub}}\right)$	=	Total annual investment cost of substations hardening ($).
${\mathrm{C}}_{\mathit{net}}^{\mathit{inv}}\left(x^{\mathit{ins}}\right)$	=	Total annual investment cost of lines hardening ($).
${\mathrm{C}}_{\mathit{RCS}}^{\mathit{inv}}\left(x^{\mathit{sw}1}\right)$	=	Total annual investment cost of installing RCSs ($).
$C^{\mathit{op}}\left(\mathit{s}\right)$	=	Total operating cost in scenario s ($).
$C_i^{\mathit{Lsh},\mathit{s}}$	=	Total load shedding cost of bus i in scenario s ($).
$C_i^{{\mathit{r}}_{\mathit{sub}},\mathit{s}}$	=	Total restoration cost of damaged substation i in scenario s ($).
$C_{\mathit{ij}}^{{\mathit{r}}_{\mathit{net}},\mathit{s}}$	=	Total restoration cost of damaged line ij in scenario s ($).
$C_{\mathit{ij}}^{{\mathit{d}}_{\mathit{sw}},\mathit{s}}$	=	Total depreciation cost of RCS installed in line ij in scenario s ($).
${\gamma }_{\mathit{i},\mathit{t}}^{\mathit{L},\mathit{s}}$	=	Load shedding percentage of bus i at time t in scenario s.
${\zeta }_{\mathit{ij}}^{\mathit{ins}}$	=	Replacement cost of a damaged isolator in line ij ($).
$v_{\mathit{i},\mathit{t}}^s$	=	Voltage magnitude of bus i at time t in scenario s.
$P_{\mathit{ij},\mathit{t}}^s/Q_{\mathit{ij},\mathit{t}}^s$	=	Active/Reactive power flow of line ij at time t in scenario s (pu).
$P_{\mathit{i},\mathit{t}}^{\mathit{sub},\mathit{s}}/Q_{\mathit{i},\mathit{t}}^{\mathit{sub},\mathit{s}}$	=	Active/Reactive power output (pu) of substation i at time t in scenario s.
Binary Variables:	=
$x_i^{\mathit{sub}}$	=	1 if substation i is selected for hardening; 0 otherwise.
$x_{\mathit{ij}}^{\mathit{ins}}$	=	1 if line ij is selected for hardening; 0 otherwise.
$x_{\mathit{ij}}^{\mathit{sw}1}$	=	1 if line ij is selected for installing new RCS; 0 otherwise.
$x_{\mathit{ij}}^{\mathit{sw}}$	=	1 if line ij has a RCS; 0 otherwise.
${\pi }_{\mathit{ij},\mathit{t}}^{\mathit{c},\mathit{s}}$	=	1 if the RCS status in line ij at time t under scenario s has changed; 0 otherwise.
${\pi }_{\mathit{ij},\mathit{t}}^{\mathit{sw},\mathit{s}}$	=	1 if the RCS in line ij at time t under scenario s is close; 0 otherwise.
${\lambda }_{\mathit{ij}}^{\mathit{net},\mathit{s}}/{\lambda }_i^{\mathit{sub},\mathit{s}}$	=	1 if line ij/substation i status at time t in scenario s is damaged; 0 otherwise.
${\rho }_{\mathit{mn},\mathit{t}}^s/{\rho }_{\mathit{nm},\mathit{t}}^s$	=	1 if bus m/n at time t in scenario s is the parent bus of n/m; 0 otherwise.
Parameters:	=
${\mathrm{c}}_i^{\mathit{sub}}$	=	Annual capital cost of a GIS-substation ($).
${\mathrm{c}}_i^{\mathit{ins}}$	=	Annual capital cost of a silicone-rubber insulator for substations ($).
${\mathrm{c}}_{\mathit{ij}}^{\mathit{ins}}$	=	Annual capital cost of a silicone-rubber insulator for lines ($)
${\mathrm{c}}_{\mathit{ij}}^{\mathit{sw}}$	=	Annual capital cost of a RCS ($).
$x_{\mathit{ij}}^{\mathit{sw}0}$	=	Binary parameters indicates whether the line ij has exist switch (1) or not (0).
${\beta }_i^{\mathit{sub}}$	=	Cost recovery factor for replacing a GIS at bus i.
${\beta }_{\mathit{ij}}^{\mathit{ins}}$	=	Cost recovery factor for replacing a SRI at line ij.
${\alpha }_i^{\mathit{sub}}$	=	Cost sharing factor for GIS at bus i.
${\alpha }_{\mathit{ij}}^{\mathit{sw}}$	=	Cost sharing factor for RCS at line ij.
$N_d$	=	Average occurrences of EDS in a year.
$n_{\mathit{ij}}^{\mathit{ins}}$	=	Number of insulators at line ij.
$c_0^{\mathit{Lsh}}$	=	Base load shedding cost ($/KWh).
$c_0^w$	=	Base repair and washing cost ($).
$c_0^d$	=	Base depreciation cost of RCS for each switching action ($).
${\phi }_i^L$	=	Load importance coefficient at bus i.
Δt	=	Time period (h).
$P_{\mathit{i},\mathit{t}}^{\mathit{L},\mathit{s}}/Q_{\mathit{i},\mathit{t}}^{\mathit{L},\mathit{s}}$	=	Active/Reactive load of bus i at time t in scenario s (pu).
$V_0$	=	Reference voltage magnitude.
$m_i^{\mathit{sub},\mathit{s}}/m_{\mathit{ij}}^{\mathit{net},\mathit{s}}$	=	Number of damaged insulators at substation i/line ij in scenario s.
$\overline{{\mathit{P}}_{\mathit{ij}}}/\overline{{\mathit{Q}}_{\mathit{ij}}}$	=	Max active/reactive power limit of line ij.
$\overline{P_i}/\overline{Q_i}$	=	Max active/reactive power limit of substation i.
$\underset{\_}{V_i}/\overline{V_i}$	=	Min/Max voltage magnitude at bus i (pu).
${\lambda }_{\mathit{ij}}^{\mathit{PI},\mathit{s}}/{\lambda }_{\mathit{ij}}^{\mathit{SRI},\mathit{s}}$	=	1 if line ij with PI/SRI at time t in scenario s is damaged; 0 otherwise.
${\lambda }_i^{\mathit{AIS},\mathit{s}}/{\lambda }_i^{\mathit{GIS},\mathit{s}}$	=	1 if the AIS/GIS i at time t in scenario s is damaged; 0 otherwise.
$x_{\mathit{ij}}^{\mathit{sw}0}$	=	1 if line ij has exist switch; 0 otherwise.
$B_H^{\mathit{inv}}$	=	Resilience investment budget ($).
$R_{\mathit{ij}}/X_{\mathit{ij}}$	=	Resistance/Reactance of line ij (pu).
$\mathit{M}$	=	The positive big number.
$T_i^{{\mathit{r}}_{\mathit{sub}},\mathit{s}}/T_{\mathit{ij}}^{{\mathit{r}}_{\mathit{net}},\mathit{s}}$	=	The times riquered for whshing and repair of substation i/line ij in scenario s (h).
$t_{\mathit{ij}}^{{\mathit{d}}_{\mathit{PI}},\mathit{s}}/t_{\mathit{ij}}^{{\mathit{d}}_{\mathit{SRI}},\mathit{s}}$	=	The time that flashover is reported at line ij before/after hardening in scenario s.
$t_i^{{\mathit{d}}_{\mathit{AIS}},\mathit{s}}/t_i^{{\mathit{d}}_{\mathit{GIS}},\mathit{s}}$	=	The time that flashover is reported at AIS/GIS substation i in scenario s.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are available on request from the corresponding author.