Coordinating Self-Healing Control of Bulk Power Transmission System Based on a Hierarchical Top-Down Strategy

Xi Cao1, Hongtao Wang1*, Yutian Liu1, Rasoul Azizipanah-Abarghooee2, Vladimir Terzija2

1 Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education, Shandong University, Jinan, China

2 School of Electrical and Electronic Engineering, University of Manchester, Manchester, U.K.* E-mail address: whtwhm@sdu.edu.cn

Abstract: Top-down power system restoration following a widespread blackout begins with energization of the backbone transmission network. All interconnected regions will be restored as a whole, which needs collaboration of multiple operators. The parallel control and integrated restoration planning issues have to be addressed. In order to conduct an efficient top-down restoration process and guarantee the operational security, a hierarchical coordination mechanism and an online decision support system-based self-healing approach are proposed. Considering the multiple decision-making problems involved, an associated bi-level optimization model is built, which integrates the planning problems of backbone reconfiguration, sub-transmission system restoration, and non-black-start units start-up. Then, a solution methodology is developed to provide online decisions based on the model. Simulation results of Shandong Power System in China show that the restoration performance is significantly improved using the proposed control approach. Additionally, the decision method is proved to be efficient enough for online applications.

Keywords: Bi-level optimization, decision support system, coordination mechanism, power system restoration.

Nomenclature

nL Number of LFPs.

nC,i Number of EHV transmission lines that are energized prior to the restoration

of LFP i.

nLC,ij Number of transmission lines within the local restoration path of plant j.

nP,i Number of NBS plants in the local system where LFP i is located.

nG,ij Number of NBS units in plant j.

nGstable Total number of NBS units that reach the minimum stable output.nGtotal Total number of NBS units in the system.nB Number of nodes that needs to be restored within the local cranking paths.

Abbreviations: TSR, transmission system restoration; NBS, non-black-start; BSRs, blackstart resources; EHV, extra high voltage; LFP, local feeding point; DSS, decision support system; DTS, dispatcher training system.Funding: This work was supported by the National Key Research and Development Program of China (2016YFB0900105).

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nES Number of substations along the EHV transmission corridor.

Ptotal,i Total MW consumption in the local system where LFP i is located.

Vi,max, Vi,min Upper and lower limits of the EHV bus steady state voltage of LFP i.

Vi EHV bus voltage of LFP i.

TE, j Switching operation time for energizing line j.

TC, j Switching operation time of compensation equipment before energizing line j.

t0 Beginning time of restoration.

T Ending time of a defined restoration period.

Pk(t) Generation output function of NBS unit k.

PGstart,i Start-up power requirement of plant i.PS Current allocable MW resource of the system.PSinitial Initial MW resource of the system.PGmax,j Capacity of unit j.PGmin,j Minimum stable output of unit j.ki Indication whether unit i has got the power quota at previous stages (1 for true, 0 for false).ΩLFP Set of target LFPs.

tstart Unit start-up time.

Tstart Duration of the unit start-up process

r Ramping rate of unit.

Ts,h, Ts,cHot-start and cold-start time of unit.

TCH, TCC Maximum hot-start and minimum cold-start critical time of unit.

1. Introduction

Although modern power systems are highly reliable, catastrophic widespread blackouts still

can’t be avoided [1], [2]. When a blackout occurs, the utilities have a responsibility to restore

the power system as expeditiously as possible. During a typical restoration procedure,

transmission system restoration (TSR) is a critical stage prior to large-scale load pick-up [3],

[4]. In a TSR process, long-distance transmission lines will be energized to rebuild the bulk

power network and deliver cranking power from blackstart resources (BSRs) to major non-

black-start (NBS) plants out of service. The major concerns of a TSR problem are voltage

security and system stability, the reconfiguration strategy of transmission network, and the

start-up sequence of NBS units.

Generally, two types of restoration strategies can be deployed in the TSR procedure, i) the

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bottom-up strategy and ii) the top-down strategy [3], [5]. When internal BSRs are sufficient,

bottom-up restoration would be more efficient. By dividing the blackout area into several

subsystems, multiple independent restoration procedures can take place

simultaneously. Therefore, the total restoration process is speeded up. The technical

problems along a bottom-up restoration process are discussed in [6]. Different sectionalizing

methods are proposed in [7]-[10]. The advantage of bottom-up restoration is to decompose a

complex problem into several simpler ones [8]. The modeling and solving process are easier.

The TSR procedure will be executed in a decentralized way. So frequent interactions between

operators can be avoided.

However, when internal BSRs are insufficient, the advantage of bottom-up restoration

would not be reflected. In such circumstances, top-down restoration will be a better option,

especially when the external power support is available and a strong backbone system exists.

Some utilities also choose the top-down approach as the primary strategy as they have some

internal BSRs directly interconnected to the extra high voltage (EHV) network [11]. The

advantage of top-down restoration is the rapid deployment of MW resources by initially

energizing the EHV circuits. With considerable EHV transmission corridors, it is relatively

easy to restore the local sub-transmission systems and provide the auxiliary power to the NBS

plants that distributed in the wide area [5].

Unlike the bottom-up strategy, top-down restoration is more complex. All the operations

distributed in different regions and executed by different operators are handled as a whole.

The restoration can be vulnerable to uncertainties and delays. Decentralized control is not

suitable anymore since all the involved regions are directly interconnected. A hierarchical

organizational structure is essential. Normally, a central coordinator, e.g. Reliability

Coordinator in North America or higher-level Dispatch Center in China, is designated to lead

the whole restoration procedure. The key challenges of conducting a top-down TSR include:

i) centralized restoration planning from a global perspective, and ii) efficient coordination

control among multiple parallel restoration processes.

Multiple decision-making problems will be involved in the planning process. First, the

restoration paths and the NBS units start-up sequence should be carefully determined. These

two problems have been widely discussed in previous studies. In [12]-[14], the concepts of

power transfer distribution factor and electrical betweenness are used respectively to

determine the restoration path. The node importance assessment-based network

reconfiguration strategies are proposed in [15] and [16]. In [17] and [18], different models are

presented to solve the start-up sequence problem of NBS units. However, since the top-down

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TSR is organized in a hierarchical manner, these methods cannot be directly utilized.

Generally, a coarse-grained optimization is required at the central level to determine an

energization direction. Then, the restoration paths and sequence will be arranged based on

this guideline. Another critical concern during this process is reactive power balance and

overvoltage control. Specific compensation and voltage regulation measures should be

determined before energizing the EHV transmission circuits. These issues have been

discussed in [19] and [20]. Since voltage control is essential and time consuming in top-down

TSR, it should be integrated into the determination of restoration paths.

A top-down TSR may cover several independent control areas and require collaboration of

multiple utilities. The coordination issues should be carefully considered. As the initial

supply of cranking power is limited and all will be allocated through the EHV network, it is

important to properly organize the restoration actions that distributed in different regions. In

[21], a tie line-based collaboration strategy is presented to share BSRs among neighboring

systems. Such collaboration is still based on a bottom-up strategy. Considering the tight

coupling of operations in a top-down TSR, specific mechanism for coordination control should be developed. On the other hand, as the spatial

and temporal span of top-down TSR is large, reasonable and timely response to various

contingencies is also essential. Traditional ‘manual’ restoration based on offline decision

tools cannot manage the uncertainties well. Development of online decision support system

(DSS) provides a solution for this problem [22], [23]. In order to achieve a robust control

process, a specific response mechanism for triggering such a DSS is required. It is also

important to guarantee the flexibility and efficiency of such DSS.

Taking into account the above concerns, a coordinating self-healing control method of top-

down TSR is proposed in this paper. First, the general implementation strategy and the

involved multiple restoration tasks are analyzed. Then, a novel hierarchical coordination

mechanism among the operators is established. By introducing a local feeding point (LFP)

concept and setting up associated indexes, specific strategies of cranking power allocation,

overvoltage prevention, information sharing and contingency handling are provided. Under

this mechanism, a DSS-based self-healing approach is proposed to facilitate the decision-

making and execution of top-down TSR. In order to provide comprehensive and optimal

decisions from the whole system perspective, restoration planning of top-down TSR is

modelled as a bi-level optimization problem and an efficient solution methodology is

proposed. A case study of Shandong Power System in China is presented to verify the

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efficacy of the method.

The paper is organized as follows. Section 2 introduces the control framework of top-down

TSR. Section 3 describes the bi-level optimization model. In Section 4, the associated

algorithms are introduced. The case study results are presented and discussed in Section 5,

followed by conclusions.

2. Control Framework of Top-Down TSR

In this section, a general implementation strategy of top-down TSR is described and a

corresponding hierarchical coordination mechanism is proposed. The associated decision-

making problems are analysed. Moreover, an online DSS-based restoration planning and self-

healing control framework is presented.

2.1.General Implementation Strategy

The goal of top-down TSR is to reconfigure the EHV backbone and restore the major

generation facilities distributed in different regions. As the spatial span is large, multiple local

operators together with the central coordinator will participate in this process. Hierarchical

and distributed operations with close coordination are required. A general implementation

strategy is described as follows.

The upper-layer operator, e.g. a central dispatcher or a coordinator of interconnection, acts

as a leader of the overall restoration actions, is responsible for rebuilding the EHV backbone

and monitoring the restoration progress of other operators. The lower-layer operator, e.g. a

regional dispatcher or transmission owner, is responsible for establishing a local transmission

corridor to the NBS plants located in its service area after i) the associated EHV substations

have been restored, ii) the operator has got permission from the upper-layer. The plant

operator is responsible for restarting the NBS units after getting the cranking power. After a

unit is synchronized, the load pick-up procedure will be activated. Then, load restoration

control will be implemented in parallel with the TSR process.

2.2.Hierarchical Coordination Mechanism

In order to achieve smooth collaboration and guarantee the operational security, the mutual coupling relationship between multiple restoration tasks, both in the decision-making and execution process, should be properly addressed. In other word, the objectives and constraints of each operator as well as

the specific interaction and communication strategies should be clarified. For this purpose, a

hierarchical coordination mechanism is proposed.

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1) Power Quota Allocation

In top-down TSR, the EHV substations act as the interfaces for power exchange. In the

initial stage of restoration, the external power support or internal generation capacity is very

limited. The upper-layer operator has to decide which regions have the priority to get the

cranking power. A LFP is defined as an EHV substation selected by the lower-layer operator

as the local power source. Power allocation with fixed value among the LFPs is a

straightforward approach for the coordination of MW resources use. Meanwhile, power

exchange through other EHV substations is not allowed.

A power quota index, IL, is defined as the MW resource allocated to the LFP. When a LFP

gets the power quota from the upper layer, the associated lower-layer operator gets

permission to activate the local restoration process after the LFP is restored. However, the

active power absorbed by this LFP is not allowed to exceed the index limit,

(1)

Once the LFPs and associated power quotas are determined, the restoration targets of the

upper-layer operator will be clarified. The future MW consumption in each region will also

be constrained. If violation is detected by the upper-layer operator, the associated local

restoration actions will be ordered to stop.

2) Overvoltage Prevention

Restoration of long-distance no-loaded EHV transmission lines may result in serious over-

voltages. In order to guarantee the operational security respected at both layers, the bus

voltage of each EHV substation should be controlled properly by the upper-layer operator.

Particularly, if the bus voltage of a LFP is too high, the associated lower-layer restoration

procedure cannot be implemented. In order to prevent the occurrence of such circumstance, a

bus voltage index, VL, is defined as a given EHV bus voltage upper limit of each LFP,

(2)

Vi,max and Vi,min are normally determined by the utilities. They represent an acceptable

voltage profile of the EHV bus voltage during restoration (generally 90% to 110% of

nominal).

Specific voltage control measures, e.g. connecting shunt reactors and regulating terminal

voltage of generators, should be taken before energizing an EHV line. The closer VL,i is to

Vi,max, the less burden of such voltage control operations, meanwhile, the less security margin

for local restoration actions. For each LFP, this voltage limit will be maintained until a local

NBS unit is synchronized to the system.

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3) Information Sharing

In top-down TSR, the operators at different layers should be informed of the restoration

performance of others so that they can estimate the progress of related restoration processes

and organize the field crews in advance. In order to reduce the communications among the

operators, three kinds of indexes for evaluating the performance of different tasks are defined

and an information sharing strategy is carried out.

A recharge time index, TL, is defined as the expected time cost for recharging the EHV bus

of a LFP,

(3)

A waiting time index, TP, is defined as the expected waiting time of a NBS plant before

activating the unit start-up procedure,

(4)

A generation capability index, EP, is defined as the expected total MWh output provided by

a NBS plant during a specified period,

(5)

These three indexes represent the restoration performance of upper-layer operator, lower-

layer operator and plant operator, respectively. By estimating and sharing these indexes, a

commitment to undertake specified restoration actions is made by the operators. Restoration

progresses can be predicted by each other and thus frequent communications during the TSR

process can be avoided. With index TL and TP, the activation time of each local restoration

procedure is clear. In particular, as the NBS units have different physical start-up

characteristics, the plant operator is able to arrange the start-up sequence more reasonably.

With index EP, the benefit of restoring this plant can be assessed. Moreover, the associated

load pick-up procedures can be prepared in advance by the lower-layer operators.

4) Contingency Handling

Under a realistic scenario, the restoration actions may face various uncertainties. When an

unplanned incident happens, the restoration plan may need to be changed. However, frequent

restoration interruption and plan alteration will increase the communication and time cost,

which should be avoided in a top-down TSR. Hence, the contingencies with different

categories should be managed differently. Once a contingency happens at the backbone layer,

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e.g. an EHV cranking path is failed to be restored, all restoration processes will be ordered to

pause. A decision-making process will be triggered to update the five indexes defined above.

Once a contingency happens during a local restoration process, e.g. an operation failure in a

local substation or a power plant, only the associated local restoration plans as well as the

index TP and EP will be updated. Other restoration processes will not be affected.

2.3.DSS-Based Self-Healing Control

Under the proposed coordination mechanism, specific decision-making problems will be

involved. In particular, the value of the power quota index and bus voltage index of each LFP

should be carefully determined. In order to make comprehensive decisions from a global

perspective, centralized restoration planning is recommended in a top-down TSR. In addition,

as the system state changes dynamically, the plan may need to be adjusted and updated along

the restoration progress. The timeliness and flexibility of such centralized decision-making

are of critical importance. An online DSS equipped with situational awareness and efficient

decision-making functions can be a solution to this problem. Together with auto-generation

of operation order and remotely controlled automatic switches, the DSS is able to provide a

self-healing control service of a bulk power transmission system. An online DSS-based self-

healing control process can be summarized as shown in Fig. 1.

Fig. 1. Control framework of top-down TSR

The DSS should be efficient and smart enough to provide rapid and optimal decisions.

Specific optimization model and algorithms are required. Generally, the optimization

problem of a top-down TSR can be described as,

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The overall objective is defined as maximize generation capability E, which represents the

total MWh output provided by the system during a specified restoration period. The allocable

MW capacity represents the total cranking power source that the system or neighbouring

system can provide currently.

3. Bi-Level Optimization Model

The decision-making process of top-down TSR can be considered as determination of the

index matrix. As a result, the restoration-planning problem can be decoupled into multiple

sub-problems with different concerns. The optimization of backbone reconfiguration, local

network restoration and NBS units start-up can be modelled separately. In order to provide

global optimal decisions, a bi-level optimization model is built as follows.

3.1.The Upper-Level Problem: Allocation of Cranking Power

For the upper-layer operator, the primary challenge is how to allocate cranking power

among the LFPs. Hence, optimization of power quota index vector IL is formulated as the

upper-level problem.

1) Objective: As discussed in subsection 2.3, the objective of the upper-level problem is to

maximize the total generation capability E, which is the sum of EP of all NBS plants,

(6)

During the TSR process, power quota is consumed mainly by the NBS plants. Since the

system scale is large, in order to reduce the search space, binary decision variables wL are

introduced in this problem,

(7)

wL,i=1 means LFP i gets the power quota and the associated lower-layer operator will get

permission to restore all the NBS plants in this region. Generally, only one NBS unit of each

power plant will be selected as the target. Other NBS units will be restarted after the target

unit is synchronized and be able to provide the cranking power.

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2) Allocable MW capacity constraint: The decision variables wL should satisfy the

following constraint,

(8)

PS represents the current allocable MW resource of the system. The value of PS changes

dynamically along the restoration progress. In this paper, we assume the allocable MW

resource will be supplemented when a NBS unit is synchronized and has ramped to the

minimum stable output. So the value of PS can be calculated by,

(9)

3.2.The Lower-Level Problem 1: Local Network Restoration

For the LFPs that get the power quota, the associated lower-layer operator’s mission is to

send cranking power from the LFP to each NBS plant as soon as possible. Since the number

of NBS plants in each local system is very limited, a “parallel” restoration strategy is

adopted, which means the corridors to all NBS plants are energized in parallel. The key

challenge is how to determine this radial cranking path within each local system and

guarantee operational security. The problem is described as follows.

1) Objective: Within each local system, the primary measure for overvoltage regulation is

motor load pick-up. However, in order to ensure all NBS plants to be restored, additional

power quota consumption should be avoided during the network restoration process. As a

result, the value of VL becomes crucial for guaranteeing the voltage security. The objective of

local network restoration is to obtain an acceptable maximum value of VL within the range

defined in (2),

(10)

2) Connectivity constraint: Interconnections between LFP and each NBS plant should be

guaranteed. The power network can be abstracted as an undirected connected graph. Hence,

this constraint can be checked based on the graph theory [9].

3) Steady state voltage constraint: The steady state voltage security during the energization

process should be guaranteed. This constraint can be checked by calculating the power flow,

(11)

At the lower-layer, LFP can be viewed as a constant voltage source. As a result, the LFP

EHV bus is set as the swing bus and the bus voltage magnitude is set as VL.

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3.3.The Lower-Level Problem 2: Backbone Reconfiguration

With a specific allocation plan of power quota, the upper-layer operator’s mission is to

reconfigure the backbone by restoring the target LFPs (LFPs that get the power quota).

Normally, a “serial” restoration strategy is adopted, which means the EHV transmission lines

will be energized one by one to reduce the security risk. The key challenge is how to establish

this EHV transmission corridor and determine the restoration sequence of the target LFPs.

The problem is described as follows.

1) Objective: The objective of backbone reconfiguration is to minimize the total restoration

time,

(12)

2) Connectivity constraint: Interconnections between power sources and target LFPs

should be guaranteed.

3) Power flow constraint: In each line-charging process, power flow should be calculated

and the steady state voltage of every node should be checked,

(13)

The branch power capacity constraint is neglected in this problem because the transmission

power is normally very limited during the TSR process.

4) Switching overvoltage constraint: Transient voltage security should be guaranteed. At

the EHV level, switching operations of long-distance transmission lines may lead to

extensive transient overvoltage. A quick check of switching overvoltage can be implemented

based on the formula presented in [19].

3.4.The Lower-Level Problem 3: NBS Units Start-Up

In each power plant, the NBS units start-up procedure will begin after the start-up/standby

transformer gets charged. Normally, the number of field crews in a power plant is limited.

The NBS units are assumed to be restarted one by one. The start-up sequence and the specific

auxiliary loads restoration procedure should be arranged properly. The problem is described

as follows.

1) Objective: The objective of NBS units start-up in each power plant is to obtain the

maximum value of generation capability index EP,

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(14)

The value of EP is related to the waiting time index of this plant and the start-up

characteristic of each unit. In order to estimate the value of EP, the simplified generation

output function of NBS unit is utilized in this problem, which is depicted in Fig. 2.

Fig. 2. Simplified generation capability curve

2) Critical time constraint of unit: Thermal units have maximum and minimum critical

time limits during start-up process. This constraint can be reflected in the calculation of EP.

The duration of the unit start-up process, Tstart, varies as,

(15)

3) Operational security constraint: Motor start-up may lead to transient voltage and

frequency drop. It can be mitigated by arranging the unit auxiliary start-up sequence properly.

As a result, this constraint is neglected in this problem.

4. Solution Techniques

In order to generate a feasible and optimal restoration plan based on the bi-level

optimization model, the problems of combinatorial optimization, graph search, security check

and voltage regulation should be carefully addressed. Specific solution techniques are

proposed as follows.

4.1.Global Search for Optimal Index IL

It is well known that even the linear bi-level programming problem is NP-hard [24]. In

order to solve the problem with a complex structure like this and find feasible solutions

within acceptable computation scale, two search strategies for upper-level decision variables

wL are introduced: i) backtracking search, and ii) genetic algorithm (GA) based heuristic

search. When the number of LFPs is limited, the size of the search tree will be small enough

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for applying a backtracking search [25]. However, when the number of LFPs is large,

heuristic search technique can be used to avoid combinatorial explosion. GA is a commonly

used evolutionary algorithm for optimization and search problems [26]. Binary encoding is

adopted and the chromosome can be encoded as (wL,1, wL,2, …, wL,nL). The fitness function is

the upper-level objective function as shown in (6). Roulette wheel selection, multi-point

crossover, random inversion mutation and elite preserving strategy are used. For the

chromosomes that not satisfy the constraint, the fitness is set to a small value. For other

chromosomes, the three lower-level problems will be solved to calculate the fitness.

4.2.Determination of Index VL

With a specific vector wL, the index VL is determined at first. For the LFPs that don’t get

the power quota, the value of VL is directly set as Vmax. For others, the value of VL is

determined by solving the lower-level problem 1. For each local system, in order to maximize

the value of VL of associated LFP, a local cranking path with minimum charging power

should be found. The Dijkstra algorithm is used [27]. And the edge weight is set to the

charging power of a transmission line with considering compensation reactors. The paths to

all NBS plants in this region will be determined sequentially. Then, to calculate the specific

maximum value of VL, a linear search process is implemented. The value of VL is initially set

to Vmax and the power flow of the local system is calculated. If the constraint in (11) is not

satisfied, VL will be set to a smaller value and the power flow is calculated again. This

process terminates until the voltage constraint in (11) is satisfied.

4.3.Determination of Index TL

After the index VL is given, the index TL is determined by solving the lower-level problem

2. Firstly, in order to obtain a restoration corridor, a tree of the backbone network that

connecting all target LFPs and power sources should be constructed, which is a typical

Steiner tree problem [28].

A Steiner tree problem is NP-hard [28]. Hence, an approximation method is used: First,

construct the minimum spanning tree using the Prim algorithm [27]. Then, remove the edges

that don’t need to be restored by pruning operation, which guarantees all leaf nodes are the

target LFPs. At the backbone layer, voltage regulation operations will slow down the

restoration progress. In order to reduce the total restoration time, a restoration corridor with a

minimal overvoltage risk should be determined. Therefore, the edge weight is set to the

charging power of a transmission line.

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Then, a rule-based breadth-first search is implemented to determine the restoration

sequence. The tree root is a virtual power source node formed by node contraction. In each

search step, the target node is determined based on the following rules: i) giving preference to

target LFPs, ii) giving preference to the node with highest value of the defined importance

degree η,

(16)

where ω is the load importance degree of the region where the node is located, α is the

topological node degree, i.e. the number of edges that are directly connected to the node.

Each time a target node is determined, the voltage constraints should be checked. If

violations are detected, the sensitivity method in [20] is adopted to determine a regulation

plan. If the feasible regulation plan doesn’t exist, an alternative target node will be selected.

After the backbone reconfiguration plan is generated, TL of each LFP can be estimated based

on the total number of switching operations.

4.4.Determination of Index EP

After the above mentioned steps, the index TP of each target NBS plant can be obtained.

Then, the index value EP is determined by solving the lower-level problem 3. If the NBS

units number in the power plant beyond 3, a traversal search of the start-up sequence will be

implemented to obtain the maximum value of EP.

In summary, the solving process of this bi-level optimization problem is shown in Fig. 3.

In order to reduce the computation cost, some repeat computations can be avoided during this

process. Specifically, the minimum spanning tree and VL of each LFP can be predetermined

and stored before the iteration. The detailed algorithm performance will be analyzed in the

next Section.

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Fig. 3. Flow chart of the solving process Fig. 4. Shandong power system in China

5. Case Study and Discussions

5.1.Case Study of Shandong Power System in China

In order to demonstrate the efficacy of the control framework and associated decision-

making method, the Shandong Power System in China is used to carry out case studies. The

Shandong Power System is a provincial-level system with typical hierarchical network

structure and managed by vertically integrated utilities. 73 EHV transmission lines constitute

the backbone of the system and connect multiple local subtransmission systems distributed in

17 city regions. Fig. 4 shows the network topology.

A total blackout happens at t=0:00(h). The internal BSR, Taishan pumped storage station,

will then activate a blackstart procedure. A stable local system is expected to be formed at

t=2:30(h). Moreover, we assume the external power support is available immediately after

the blackout. The EHV substation Liaocheng is restored at t=0:10(h) by energizing the tie

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line. The allocable MW resource provided by external power sources is 300MW. As a result,

a top-down TSR procedure is implemented.

1) Decision-making process: By reading the system data, the blackout scenario and

network topology will be analyzed at first. Then, a centralized decision-making process based

on the bi-level optimization method will be implemented. In this case, we assume no

transmission facilities are damaged. The LFP of each region and the target NBS unit of each

power plant are selected as shown in Table I. The computation parameters are set as follows:

i) the restoration time of each branch is set as 10min, ii) the maximum voltage deviation of

500kV and 220kV buses are set as 10% and 8%, iii) the switching time of each unit of shunt

reactor is set as 5min, iv) the ending time T is set as 24:00(h). The optimal solution of LFP

Index IL is obtained as shown in Table II.

TABLE INBS UNITS AND SELECTED LFPS OF SHANDON POWER SYSTEM

Number Target NBS unit LFP Importance

degree ωCapacity

/MWPGstart

/MWRamping Rate

/MW/minTs,h/Ts,c

/minTCH/TCC

/min1 Liaore#8 Liaocheng 1 330 20 5 90/420 300/2402 Liaocheng#1 Liaocheng 1 600 36 12 120/600 480/3003 Huangtai#7 Jinan 3 330 20 5 90/420 300/2404 Zhangqiu#3 Jinan 3 330 20 5 90/420 300/2405 Huade#1 Huade 1 330 20 5 90/420 300/2406 Yangcheng#1 Wenshang 2 150 9 1.5 60/300 180/607 Jiaxiang#2 Wenshang 2 330 20 5 90/420 300/2408 Yunhe#5 Wenshang 2 330 20 5 90/420 300/2409 Zouxian#4 Zouxian 2 335 20 5 90/420 300/240

10 Jining#1 Zouxian 2 350 21 5 90/420 300/24011 Liyan#3 Zouxian 2 145 9 1.5 60/300 180/6012 Heze#6 Yuncheng 1 330 20 5 90/420 300/24013 Runze#1 Yuncheng 1 600 36 3 120/600 480/30014 Laiwu#5 Luzhong 2 330 20 5 90/420 300/24015 Laicheng#1 Luzhong 2 300 18 4 90/420 300/24016 Tengzhou#3 Zaozhuang 1 350 21 5.5 90/420 300/24017 Shiliquan#6 Zaozhuang 1 330 20 5 90/420 300/24018 Feixian#1 Yimeng 2 600 39 9 120/600 480/30019 Linyi#3 Yimeng 2 140 8 2.5 60/300 180/6020 Rizhao#3 Rizhao 1 350 41 7 90/420 300/24021 Xindian#5 Zibo 2 300 18 4.5 90/420 300/24022 Nanding#3 Zibo 2 145 9 1.5 60/300 180/6023 Zhanhua#3 Binzhou 1 165 10 1.65 60/300 180/6024 Lubei#1 Binzhou 1 300 20 3.3 90/420 300/24025 Shengli#3 Youcheng 2 300 18 3 90/420 300/24026 Weifang#1 Weifang 2 330 20 5 90/420 300/24027 Huangdao#4 Langya 3 225 13 4.5 60/300 180/6028 Qingdao#3 Laoshan 3 300 18 3 90/420 300/24029 Penglai#1 Qixia 2 330 20 5 90/420 300/24030 Yantai#5 Qixia 2 160 10 1.6 60/300 180/6031 Longkou#3 Qixia 2 220 13 3.3 60/300 180/6032 Weihai#4 Kunyu 1 220 19 5 60/300 180/60

TABLE IITHE OPTIMAL LFP INDEX VECTOR IL

LFP Liaocheng Jinan Huade Wenshang Zouxian Yuncheng Luzhong Zaozhuang Yimeng

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IL/MW 56 40 20 49 50 0 38 0 0LFP Rizhao Zibo Binzhou Youcheng Weifang Langya Laoshan Qixia Kunyu

IL/MW 0 27 0 0 20 0 0 0 0

The corresponding bus voltage index of each LFP and the restoration plans of backbone

reconfiguration and each local system restoration are shown in Table III and Table IV. 8

LFPs will get the power quota in the first round of restoration. 16 NBS plants can be restored.

With the restoration plans, specific operation orders will be generated and then a top-down

TSR procedure is activated.

TABLE IIIRESTORATION PLAN OF BACKBONE SYSTEM

Sequence Substation VL/p.u. TL/min Shunt reactor Sequence Substation VL/p.u. TL/min Shunt reactor1 Liaocheng 1.0326 10 - 7 Zouxian 1.0308 90 3*60MVar2 Wenshao - - - 8 Wenshang 1.0476 105 -3 Jinan 1.0324 30 3*60Mvar 9 Luzhong 1.0318 125 1*60MVar4 Zibo 1.0476 40 - 10 Dezhou - - -5 Weifang 1.0476 60 - 11 Huade 1.0476 145 -6 Taishan - - -

TABLE IVRESTORATION PLAN OF EACH LOCAL SYSTEM

NBS plant LFP EP/MW*min TP/min Cranking path tstart

Liaore Liaocheng 414810 60 Liaocheng → Guangyue → Liaore 1:00Liaocheng Liaocheng 759000 30 Liaocheng → Liaocheng plant 0:30Huangtai Jinan 408210 80 Jinan → Feiying → Huangtai 1:20Zhangqiu Jinan 411510 70 Jinan → Zhangqiu 1:10Xindian Zibo 368000 90 Zibo → Jinling → Xindian 1:30Nanding Zibo 180041.7 90 Zibo → Fujia → Nanding 1:30Weifang Weifang 401610 100 Weifang → Weifang plant 1:40Zouxian Zouxian 407527.5 100 - 1:40Jining Zouxian 411250 140 Zouxian → Jiezhuang → Jining 2:20Liyan Zouxian 171341.7 150 Zouxian →Beisu → Luochang →Liyan 2:30

Yangcheng Wenshang 176250 155 Wenshang → Zhongdu → Yangcheng 2:35Jiaxiang Wenshang 393360 122 Wenshang → Jiaxiang 2:05Yunhe Wenshang 393360 122 Wenshang → Yunhe 2:05Laiwu Luzhong 376860 175 Luzhong → Qishan → Laiwu 2:55

Laicheng Luzhong 344250 165 Luzhong → Laicheng 2:45Huade Huade 383460 155 - 2:35

2) Execution process: In order to simulate an execution process of top-down TSR, a

Dispatcher Training System (DTS) for Shandong Power System restoration is used. With the

DTS, specific restoration cases can be produced, stored, and simulated based on the custom

blackout scenarios. In this case, a total blackout scenario is set and the operation orders

within each substation are produced based on the aforementioned restoration plans. The

beginning time of simulation is set as t=0:00(h). Each time a target LFP is restored, the

associated local network restoration process will be activated.

The simulation time of single switching operation is set as 5min. After every operation, a

power flow calculation of the synchronized system will be automatically implemented. The

simulation result shows no overvoltage is detected during the restoration. The operational

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security of the plan is verified.

On the simulation platform, the top-down TSR is implemented as a whole. However, under

a realistic scenario, multiple restoration tasks will be handled by different operators. The

proposed coordination mechanism ensures that the top-down TSR can be implemented in a

distributed and parallel manner. The operators are able to do their duty without frequent

interactions with others. The upper-layer operator considers the LFPs as terminals with fixed

voltage constraint. Despite the large spatial span, the workload can be substantially

decreased. The lower-layer operators consider the LFPs as constant voltage sources with

fixed capacity. The voltage regulation issues can be omitted and the total active power

consumption is restricted. With information sharing, every operator will be aware of the

restoration progresses. Disorders in the execution process can be avoided.

Fig. 5. The simulated restoration progress

3) Restoration monitoring: Considering the dynamic change of system state and multiple

uncertainties of TSR, the index value and associated restoration plans should be updated in

time. In this case, we assume the island that restored by the internal BSR will be

synchronized with the system at t=2:30(h). Meanwhile, the NBS unit Liaore#8

ramps to the minimum stable output (30% of capacity in this case) at the same time. Hence,

the restoration will pause for a new round of decision-making process. The simulated

restoration progress at t=2:30(h) is shown in Fig. 5. The labelled start-up time of each plant is

the time when the associated start-up/standby transformer gets charged. The allocable MW

resource at this time is 506MW, which is calculated using (9). By reading the current system

data and implementing a decision-making process again, the restoration plans are adjusted

and supplemented as shown in Table V-VII.

TABLE VTHE LFP INDEX VECTOR IL IN ROUND 2

LFP Liaocheng Jinan Huade Wenshang Zouxian Yuncheng Luzhong Zaozhuang Yimeng

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TABLE VIRESTORATION PLAN OF BACKBONE SYSTEM IN ROUND 2

Sequence Substation VL/p.u. TL/min Shunt reactor Sequence Substation VL/p.u. TL/min Shunt reactor1 Binzhou 1.0292 10 2*60Mvar 9 Kunyu 1.0314 125 2*60Mvar2 Youcheng 1.0316 25 - 10 Yuncheng 1.0308 145 2*60Mvar3 Laoshan 1.0476 40 1*60Mvar 11 Luzhong 1.0302 160 1*60Mvar4 Daze - - - 12 Zaozhuang 1.0318 175 -5 Jiaodong - - - 13 Yimeng 1.0301 190 1*60Mvar6 Langya 1.0476 80 1*60Mvar 14 Rizhao 1.0311 205 1*60Mvar7 Guangzhou - - 1*60Mvar 15 Dezhou - - -8 Qixia 1.0476 110 1*60Mvar 16 Huade 1.0476 225 -

TABLE VIIRESTORATION PLAN OF EACH LOCAL SYSTEM IN ROUND 2

NBS plant LFP EP/MW*min TP/min Cranking path tstart

Liyan Zouxian 169891.7 10 Luochang →Liyan 2:40Yangcheng Wenshang 124500 30 Wenshang → Zhongdu → Yangcheng 3:00

Zhanhua Binzhou 140250 60 Binzhou → Dongtang → Zhanhua 3:30Lubei Binzhou 328363.6 60 Binzhou → Dayang → Lubei 3:30

Shengli Youcheng 322500 75 Youcheng → Dongcheng → Shengli 3:45Qingdao Laoshan 318000 90 Laoshan → Lishan → Qingdao 4:00

Huangdao Langya 185625 140 Langya → Zhushan → Qianwan → Huangdao 4:50

Penglai Qixia 147510 160 Qixia → Shenyu → Penglai 5:10Yantai Qixia 124800 160 Qixia → Chongyi → Yantai 5:10

Longkou Qixia 175266.7 160 Qixia → Shenyu → Longkou 5:10Weihai Kunyu 176660 165 Kunyu → Weihai 5:15Heze Yuncheng 147510 195 Yuncheng → Shuihu → Heze 5:45

Runze Yuncheng 543000 165 Yuncheng → Runze 5:15Laiwu Luzhong 147510 210 Luzhong → Qishan → Laiwu 6:00

Laicheng Luzhong 132750 200 Luzhong → Laicheng 5:50Tengzhou Zaozhuang 156863.6 215 Zaozhuang → Tengzhou 6:05

Shiliquan Zaozhuang 147510 235 Zaozhuang → Fengze → Jianguo → Shiliquan 6:25

Feixian Yimeng 587527.8 230 Yimeng → Feixian 6:20Linyi Yimeng 99680 250 Yimeng → Linyi → Shenquan → Linyi plant 6:40

Rizhao Rizhao 159250 255 Rizhao → Houcun → Rizhao plant 6:45Huade Huade 147510 235 - 6:25

It can be seen that all the rest NBS units will be restored in the second round of restoration.

Particularly, the identity of substation Liaocheng will change from a LFP to a power source.

The simulation result on the DTS is shown in Fig. 5. The TSR process is accomplished at

t=7:40(h).

By repeatedly triggering the decision-making process, various contingencies can be also

managed during the TSR process. For example, if a failure happens to cut off the backbone

restoration path, an alternative path will be generated. Accordingly, the power quota index

and bus voltage index of each LFP as well as the restoration plan of each operator will all be

updated. If a contingency happens in a local system, only the lower-level problem 1 described

in subsection 3.2 will be solved to generate an alternative plan under the constraints of IL and

VL.

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5.2.Discussions

As shown in the above case, various kinds of restoration tasks during a top-down TSR are

organized as a whole under the proposed control framework. By using the bi-level

optimization method, comprehensive decisions can be made from a global perspective. On

the other hand, unlike offline restoration planning, online decision support provides more

specific and flexible operation strategies rather than a general guideline. The applicability and

timeliness of the decisions are guaranteed, which make the restoration more efficient and

secure.

In order to achieve online decision support, the algorithm performance should be

guaranteed. Decision-making of top-down TSR is an integrated solving process of multiple

problems, as shown in Section 4. In this case, the performance of the proposed algorithms,

especially the backtracking search and GA based heuristic search, are tested on a desktop

computer with Core i5 3.2Hz processor and 4G RAM. The test result is shown in Table VIII.

TABLE VIIITEST RESULT OF THE ALGORITHM PERFORMANCE

LFP number 18 17 16 15 14Computation time of backtracking 997s 452s 214s 99s 39sAverage computation time of GA 117s 105s 91s 62s 52s

Average generations of GA 17 16 14 10 9

By removing the LFP one by one from the bottom of Table I, different problem scales can

be simulated. The result shows that the computation time of backtracking search decreases

exponentially as the LFP number reduces. Apparently, it would be feasible for online

application if the blackout range is small. On the other hand, the computation time of GA has

smaller sensitivity to the problem scale. The convergence performance of GA is proved

efficient when the population size is set to 500. 50 times of calculation are implemented for

each problem scale. The result shows the computation speed is acceptable. Moreover, the

performance of GA fairly depends on the CPU resources. Particularly, in a multi-CPU

environment, e.g. a computer cluster, a linear speedup can be achieved using parallel

computing techniques.

In practical application, the backtracking search and GA based heuristic search can be

selected based on the specific blackout range and LFP numbers. Moreover, a maximum

iteration number of GA should be given with the consideration of the heuristic search

uncertainty.

As shown in the case study, the most important characteristic of top-down restoration is

the rapid deployment of MW resources by making full use of the backbone network. To

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achieve that, the restoration actions handled by different operators and distributed in different

regions should be implemented in parallel. However, during the TSR stage, the decision

makers in the dispatch centers are normally risk-averse. Without efficient collaboration

strategy, the top-down restoration cannot be implemented smoothly. The significance of the

proposed coordination mechanism is highlighted.

In order to further demonstrate the advantage of a coordinated top-down TSR, a

conventional bottom-up restoration is also simulated in this case. The performance of these

two restoration strategies are compared as shown in Fig. 6. In a bottom-up TSR process,

energization of EHV network is not a high-priority option. The restoration will start from an

internal blackstart procedure. External power support is not considered. Considering the large

spatial span, the duration of such restoration procedure is too long. Since the system has only

one internal BSR, the advantages of bottom-up restoration cannot be reflected. Therefore, the

top-down restoration strategy should be the first choice in such circumstances.

Fig. 6. Statistics of restored units and system capacity

6. Conclusion

This paper proposes a coordination control framework and an associated dynamic

decision-making approach for large-scale top-down TSR. By introducing the LFP concept

and establishing the coordination mechanism, each operator’s responsibility during the TSR

process is identified. The specific interactive manner is defined and the various contingencies

can be properly handled. The DSS-based restoration control is an automated iteration process

of decision-making, execution and monitoring, which provides a solution to achieve self-

healing of bulk power transmission system. The bi-level optimization model and associated

algorithms is used to make integrated online decisions from a global perspective and help

operators generate the restoration plans. With the coordination approach, smooth

collaboration among the operators can be realized and the top-down TSR can be implemented

in parallel, which significantly improves the restoration efficiency. With the decision-making

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approach, the restoration planning problem can be rapidly solved and the restoration plan can

be flexibly adjusted in a dynamic environment, which guarantees the decision-making

efficiency and the robustness of the control process.

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