Abstract
The increasing integration of different forms of distributed generations (DGs) into current medium- and low-voltage power distribution networks can result in increased system instability and protection performance degradation. Efficient power supply restoration upon a power outage is demanded to ensure resilient operation of power distribution networks consisting of DGs with stochastic generation and diverse characteristics. This work proposes an algorithmic solution of power supply restoration under the condition of a large-scale power blackout . The solution consists of DGs starting path searching and collective load restoration combining DG-based and topology reconfiguration strategies to improve network resilience under failures. In the DG starting path searching algorism, non-black-start DGs (NBDGs) can be started by black-start DGs (BDGs) nearby through the shortest path as much as possible. This solution enables simultaneous power restoration in the presence of multiple faults with maximized restored loads and minimized power loss and power flow changes. The developed solution of power supply restoration is evaluated on the basis of a 53-bus test distribution feeder penetrated with wind turbines (WTs) for a set of fault scenarios through simulations. The stochastic generation of WTs is fully considered using the heuristic moment matching (HMM) method. The proposed solution is assessed through mathematical simulations, and the results confirm that this solution can provide efficient supply restoration under a large-scale power blackout .
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Abbreviations
- F :
-
Utility function of the power restoration model
- \( f_{k,n} \) :
-
\( k{\text{th}} \) sub-function of function F; during the \( n{\text{th}} \) optimization, \( k \in [1,3] \), \( n \in [1,N_{change\_swi} ] \)
- \( N_{{{\text{change}}\_{\text{swi}}}} \) :
-
Number of switchers to be closed in the restoration process
- \( r_{k} \) :
-
The base value of the \( k{\text{th}} \) sub-function of function F, \( k \in [1,3] \)
- \( {\mathbf{X}}_{n} \) :
-
Switcher operation types at the \( n{\text{th}} \) iteration of optimization, \( {\mathbf{X}}_{n} = \left\{ {x_{1,n} ,x_{2,n} , \ldots ,x_{{N_{can\_swi} ,n}} } \right\} \)
- \( x_{i,n} \) :
-
Type of operation in terms of a specific optimization iteration; when \( x_{i,n} = 1 \), the candidate switcher i will be turned off; otherwise, it remains open
- \( N_{{{\text{can}}\_{\text{swi,}}i}} \) :
-
The candidate switcher number for an iteration
- \( \alpha_{m} \) :
-
The time cost for switcher m
- m :
-
Switcher operation types, \( m \in \left\{ {1,2,3} \right\} \); type 1 is bus switcher operation, type 2 is inter-switcher operation within the substation, and type 3 is across multiple substations
- \( N_{{{\text{off}}\_{\text{node}}}} \) :
-
Number of off-line buses after faults
- \( \rho_{j} \) :
-
Off-line load priority of j
- \( L_{j} \) :
-
Off-line load of j
- \( dis_{ij} \) :
-
Restoration of the \( j{\text{th}} \) off-line load when set the \( i{\text{th}} \) candidate switcher
- \( N_{{{\text{on}}\_{\text{swi}}}} \) :
-
The quantity of online buses after faults
- \( X_{i,p,n} \) :
-
Boolean value denoting if the power flow of the \( p{\text{th}} \) restored branch is affected by the \( i{\text{th}} \) off-line switcher operation at the \( n{\text{th}} \) iteration of optimization. If yes, then \( X_{i,p,n} = 1 \); else, \( X_{i,p,n} = 0 \)
- \( Y_{i,q,n} \) :
-
Whether the bus voltage of the \( q{\text{th}} \) restored bus is affected due to the \( i{\text{th}} \) off-line switcher operation at the \( n{\text{th}} \) iteration of optimization. If yes, then \( X_{i,p,n} = 1 \); else, \( X_{i,p,n} = 0 \)
- \( I_{p,n} \) :
-
Current of the \( p{\text{th}} \) restored branch at the \( n{\text{th}} \) iteration of optimization
- \( I_{{{\text{limit}},p}} \) :
-
Current limit of the \( p{\text{th}} \) branch
- \( U_{q,n} \) :
-
Voltage of the \( q{\text{th}} \) restored bus at the \( n{\text{th}} \) iteration of optimization
- \( U_{{l{\text{owerlimit}}}} \) :
-
Bus voltage lower limit
- \( U_{upperlimit} \) :
-
Bus voltage upper limit
- \( N_{\text{bus}} \) :
-
The quantity of network buses
- \( N_{\text{sub}} \) :
-
The quantity of power substations
- \( path(i,j) \) :
-
The quantity of paths between buses i and j
- \( \gamma_{{{\text{bran}}\_vw,n}} \) :
-
If buses v and w connect with each other, \( \gamma_{{{\text{bran}}\_vw,n}} = 1 \); otherwise, \( \gamma_{{{\text{bran}}\_vw,n}} = 0 \)
- \( G_{vw} \) :
-
Branch admittance from bus v to bus w
- \( \delta_{vw.n} \) :
-
Phase angle difference between branches of buses v and w at the \( n{\text{th}} \) iteration of optimization
- \( P_{v}^{L} \) :
-
Loads at bus v
- \( P_{v}^{D} \) :
-
Installed DG capacity at bus v
- \( I_{{{\text{capacity}},vw}} \) :
-
Branch capacity of bus v and bus w
- \( V_{i}^{BR} \) :
-
\( i{\text{th}} \) bus voltage in the failure-free section before the restoration process
- \( V_{i}^{AR} \) :
-
\( i{\text{th}} \) bus voltage in the failure-free section after the restoration process
- \( I_{i}^{BR} \) :
-
Current of the \( i{\text{th}} \) bus in the failure-free section before the restoration process
- \( I_{i}^{AR} \) :
-
Current of the \( i{\text{th}} \) bus in the failure-free section after the restoration process
- \( N_{\text{normal}} \) :
-
Number of buses in the failure-free section
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Xia, C., Yang, Q., Jiang, L., Ge, L., Li, W., Zomaya, A.Y. (2020). Power Restoration Approach for Resilient Active Distribution Networks in the Presence of a Large-Scale Power Blackout. In: Zobaa, A., Cao, J. (eds) Energy Internet. Springer, Cham. https://doi.org/10.1007/978-3-030-45453-1_14
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