1. Introduction
Currently, the increasing penetration of small-scale renewable distributed generators (DGs), e.g., micro wind turbines, photovoltaic panels, has reshaped the medium/low voltage (MV/LV) electric distribution network from a passive system to an active network which allows coexistence of bidirectional power flows. These renewable sources exhibit intermittent and stochastic characteristics, and hence the massive DG integration across a large geographical span can bring direct operation and control challenges, e.g., voltage raise effect, increased fault level, protection degradation, and altered transient stability in [
1]. In addition, many distribution network operators (DNOs) are currently being faced with the limitation of dealing with enormous amount of operational data and control functionalities in centralized control systems. In [
2], such complexity can degrade the timely network management under anomalous or emergent conditions as approximately 75–90% faults in distribution system are temporary events. To this end, efficient supply restoration solution upon faults in guaranteeing network self-healing capability is demanded for active network management (ANM).
The power supply restoration aims to restore as much supply to demand (critical loads with higher priority) as possible and as fast as possible upon the power supply interruptions in [
3]. In Ref. [
4,
5,
6], the majority of research effort focused on addressing the power supply restoration upon faults in passive power distribution networks without DG availability. In recent years, DG plays a growing role in the issue of continuity of electricity supply in [
7,
8]. Meanwhile, a set of studies for power restoration considering the presence of DGs was exploited. In [
9], the power supply restoration using a multi-agent was studied based on optimal network topology reconfiguration considering the DGs as back-up power supplies. However, the operation of DGs simply depends on capability of backup feeders to supply de-energized loads. The study in [
10] reveals that the capability of DGs for supply restoration service was investigated and an adapted branch-and-bound algorithm was proposed to maximize the restored loads based on DGs availability. However, service areas of DGs are also decided before the restoration model according to DGs capacity, which may not be the optimal restoration scheme. A multi-agent system approach for decentralized power supply restoration was presented where the loads are resupplied by uninterruptable DGs independently in [
11]. In [
12], a novel load restoration optimization model is proposed to coordinate topology reconfiguration and microgrid formation while satisfying a variety of operational constraints. The aforementioned restoration solutions considering DG availability has not made full use of DGs in restoration process and explicit address the challenge of DG uncertainties on restoration performance.
The power restoration methods based on topology reconfiguration were extensively investigated in [
13,
14,
15]. In [
13], a comprehensive mathematical model to address the restoration problem in balanced radial distribution systems was presented, which formulated various optimization objectives into one objective function, including minimization of switcher operations, maximization of demand satisfaction, and prioritization in critical loads and automatic switcher operations. In [
14], a graph-theoretic power restoration solution that maximizes the restored load and minimizes the switching operations was presented. However, these solutions are designed and validated for single fault scenarios, and the parallel restoration mechanism to restore power loads upon multiple faults has not been studied. In literature [
15], an informed A* search-based algorithm was proposed through topology reconfiguration of radial distribution networks upon faults in partial network, including both single and multiple fault cases. The power restoration solutions based on topology reconfiguration were also studied in the context of microgrids (e.g., in [
16,
17]). The solution presented addressed the power restoration in microgrids with renewable DGs following to an unscheduled disconnection from the main grid in [
16]. It aims to determine the maximum of the expected restorative loads by choosing the best arrangement of the power network configurations immediately from the beginning of the breakdown all the way to the end of the island mode. In [
17], the solution proposed addressed the black-start restoration process in microgrids after a blackout. However, it should be noted that frequent topology reconfiguration can lead to frequent changes in power flow, which may degrade the system stability. Furthermore, malfunction in switcher operations increase the risk of cascading failure during topology reconfiguration.
In addition, most of the existing power supply restoration solutions were designed to maximize the load restoration as well as minimize the switcher operations subject to a set of operational constraints, e.g., voltage limit, line current limit and maintenance of radial topology. In [
18], a modified Viterbi algorithm was presented to identify the optimal restoration solution while minimizing the number of switching operations. In [
19], the multi-agent-based solution was implemented at two levels: zone and feeder, considering the priority of critical loads and minimization of switching operations and power loss. In [
20], a non-dominated sorting genetic algorithm-II (NSGA-II)-based power supply solution was presented considering the priority of number of manually controlled and remotely controlled switcher operations, and power loss minimization. In [
21], a service restoration model of power distribution systems incorporating load curtailment of in-service customers via direct load control considering maximization of load restoration and minimization of the number of switcher operations and total load curtailment. In fact, the existing solutions have not explicitly considered the minimization of adverse impact imposed by the power restoration actions carried out in the failed section on the failure-free sections in the distribution network, e.g., unexpected power flow changes. Our previous work (Ref. [
22]) has considered the impacts on power flow changes during the power restoration process and presented a solution combining DG-based and topology reconfiguration-based restoration with preliminarily results.
To the author’s best knowledge, the existing power supply restoration solutions have not been able to fully exploit the potential benefit of DGs in supporting restoration process under DG generation uncertainties and carry out fault restoration in parallel in multiple fault scenarios. To this end, this work presents a parallel joint power supply restoration through combining the DG local restoration and switcher operation-based restoration to enhance the self-healing capability in active distribution networks considering stochastic distributed generation. The key technical contributions made in this paper can be summarized as follows: (1) the restoration algorithmic solution carry out power restoration jointly based on DG local restoration and switcher operation-based restoration (topology reconfiguration) which is able to restore power supply in parallel upon multiple simultaneous faults; and (2) The minimization of adverse impact of power restoration on failure-free section of distribution network is explicitly included in the optimization utility function in power restoration process; Finally, the robustness of the proposed solution is validated through extensive simulation experiments for a range of fault scenarios and DG scenarios. The DG scenarios are generated based on HMM method to fully consider the randomness of the DG uncertainties.
The reminder of the paper is organized as follows.
Section 2 formulates the power supply restoration problem and presents the proposed algorithmic solution;
Section 3 discusses the heuristic moment matching-based scenario generation technique; the performance is assessed through simulations for a range of fault scenarios in
Section 4; finally, the conclusive remarks are given in
Section 5.
3. DG Uncertainty Characterization Based on HMM Method
The distribution network with penetration of wind turbines (WTs) was considered in this paper. The stochastic power generation of WTs needs to be fully considered in the validation of the proposed parallel supply restoration approach. The HMM method is adopted in [
24,
25] to generate sufficient number of scenarios to capture such uncertainties, which consists of two transformation processes: matrix transformation and cubic transformation, discussed as follows.
1. Matrix transformation: it aims to obtain an n-dimensional matrix
with a given correlation matrix
R = LLT, where
is a lower-triangle matrix. An
n-dimensional random matrix
subjected to normal distribution was generated first, which includes independent column vector
. Then
can be calculated as (15)
2. Cubic transformation: a univariate normal random column vector
with given four moments can be transformed from a column vector
subjected to normal distribution through cubic transformation. Four moments (expectation, standard deviation, skewness and kurtosis) are considered and the transformation can be formulated as (16)
where,
,
,
and
are the coefficients of transformation, which can be obtained by solving a set of nonlinear equations given in (17)
where
is the given
kth moment of
ith column vector, known as target moment.
is
kth moment of column vector
.
Step 1.
Initialization: calculate the moments and correlation matrix
R of historical wind power generation statistics as target moments and target correlation matrix, and normalize the target moments based on (18)
where,
and
are the
kth normalized moment and target moments of
ith column vector, respectively.
Step 2. Randomly generate scenarios: given the number of wind turbine and the expected number of scenarios Nh, randomly generate matrix , subjected to .
Step 3. Matrix transformation: matrix is transformed into to satisfy the correlation of historical statistics through the matrix transformation based on (1).
Step 4. Cubic transformation: calculate the coefficients , , and in (16) by solving (17), and then matrix is transformed into to satisfy the moments of historical statistics through the cubic transformation based on (2).
Step 5.
Justification: calculate the moment error (
) and correlation error (
) based on (19) and (20), respectively. The calculated errors are used to justify the eligibility of generated scenarios through comparison with the predefined thresholds (
,
).
where,
is
kth moment of
ith column vector generated by HMM method.
is the correlation matrix of matrix generated by HMM method.
is the target correlation matrix.
Step 6.
Inversion: invert the normalized scenarios
to satisfy the target moments
using (21).
5. Conclusions and Future Work
This paper presents an algorithmic solution for power supply restoration for active distribution networks through combining the DG local restoration and topology reconfiguration-based restoration with full consideration of availability and stochastic characteristics of distributed generation. The proposed solution carries out power restoration in parallel upon multiple simultaneous faults to maximize the load restoration as well as while minimizing power loss, topology variation and power flow changes. The performance of the proposed solution is assessed based on a 53-bus distribution network with WTs through extensive simulation experiments for a range of fault and DG scenarios and the result confirms the effectiveness of the proposed solution.
Based on the insights obtained from this work, two research directions are considered to be worth further exploitation. The proposed parallel fault restoration of distribution networks need to be further studied and validated considering the availability of mixture of different renewable DGs (e.g., solar PVs, WTs) as well as onsite diesel generators; also, one of the insights of this study is that the DG installation with appropriate capacity and loacation can further improve the performance of the proposed restoration solution. Thus, the optimal planning of distribution networks or network expansion, e.g., placement and capacity of DGs as well as feeder line reinforcement, considering the network self-healing capability needs to be investigated.