在真實網路中，一個節點或連結的損壞可能會造成網路大規模崩解，這現象亦出現在過去許多電力系統的大停電事件中。因此由網路的觀點對電力系統是否安全和穩定之研究一直是備受探討。在本論文中使用複雜網路方法對台灣電力網路進行脆弱性分析，並由攻擊者的角度使用多重攻擊策略探討網路脆弱性。 本論文中使用了拓樸性效率脆弱性(efficiency vulnerability)和四種連鎖性失效模型針對台灣電力網路進行分析，其中包含三種靜態負載的連鎖性失效模型(static load cascading failure model)和一種動態負載的連鎖性失效模型(dynamic load cascading failure model)，藉由這些不同觀點檢視台灣電力網路的脆弱性。 以上模擬皆為攻擊單一連結，但若以攻擊者的觀點，其可以同時對多個連結進行破壞，因此最後部分為如何有效對網路造成傷害的多重攻擊策略，我們應用此攻擊策略於隨機網路(random network)以及無尺度網路(scale-free network)測試其有效性，最後將此攻擊策略應用於台灣電力網路，並從結果中透露出台灣電力網路相當脆弱。

於歷史事件中我們知道電力網路中些許的傷害會導致大停電事件的發生，而電力網路的安全是學者們一直以來關心的議題，複雜網路發展至今，已有不少研究人員利用複雜網路的方法來分析電力網路，本論文即利用複雜網路的分析方法，分析台灣電力網路脆弱性，並提出一新穎的保護策略。 文章中引用三種分析方法分析台灣電力網路的脆弱性，第一為根據網路效率(efficiency of complex network)，第二為根據靜態負載的連鎖性失效(static load cascading failure)，第三為根據動態負載的連鎖性失效(dynamic load cascading failure)，三種脆弱性分析的方法得到結果的交集處，在文中被認為是電力網路中最具風險的變電站。根據靜態負載的連鎖性失效的結果，我們在不改變網路結構和整體網路的負載量之下，提出一新穎的安全策略，試圖降低靜態負載時連鎖性失效帶來的傷害，並分析此安全策應用至ER隨機網路(ER random network)、BA無尺度網路(BA scale-free network)和台灣電力網路，且量化其結果。 三種脆弱分析的結果皆有共通的部份，表示台灣電力網路在拓樸分析下並不堅固，其結果顯示此安全策略是有效的。本篇論文分析的網路均是無權重也無方向性的網路，如此，未來在網路脆弱性與安全策略的研究還有進一步的研究空間。 / From blackout events in history, we know the damage of a few substations or transmission lines can lead to a big blackout, and the robustness of power grids are always a great concern. Recently the topological analyses of power grid network have developed rapidly and its achievements have become a center of attention. This thesis aims to investigate the vulnerability of Taiwan’s power grid through topological analyses and propose a novel protection strategy. This thesis introduces three methods to investigate the vulnerability of Taiwan’s power grid. The first method is based on efficiency of complex network. The second method is based on static load cascading failure. The third method is based on dynamic load cascading failure. The common results of the three results are considered the high risks in Taiwan’s power grid. According to the static load cascading failure, we propose a protection strategy against cascading failure without changing the structure of network and the whole load of the network, and then demonstrate the effectiveness of this strategy on an ER random network, a BA scale-free network and Taiwan’s power grid numerically. The three methods having the common results, one may say Taiwan’s power grid isn’t robust under the topological analyses, and our protection strategy may be useful for decreasing the damage after cascading failure.

現實社會中，有時會發生大規模的停電事件，一經調查後才瞭解，只是因為一根電纜線、一根高壓電塔或是一個變電站故障導致，令人好奇電力系統的運作模式。因此藉由拓蹼網路的特性去研究電力系統的安全性及穩定性，一直受到人們的關注和討論。本篇論文利用動態負載去模擬現實中的電流，並藉由連鎖性失效的攻擊策略對於網路效率的影響，去判斷其網路的脆弱性分析。 本論文利用網路效率的(efficiency)影響來作為網路脆弱性(vulnerability)的分析，藉由在靜態負載中連鎖性失效的模型(static load cascading failure model)和動態負載中連鎖性失效的模型(dynamic load cascading failure model)來判斷及討論，其中動態負載為不同發電量及消耗量的狀況，藉此觀察台灣的電力網路系統在狀況下的結果。 此外以攻擊方來思考，單一攻擊、多重攻擊和策略性的多重攻擊的狀況底下，網路效率的變化，並將此運用在台灣電力網路系統上，發現台灣電力網路相當脆弱。 / In the real world, sometimes there will be black out (power shortage) happening in large scale areas. After investigating, we found out that it was cause by either a broken transmission line, a high-voltage tower or a substation. We are very interesting to know how the operation scheme of power system works. Therefore, we study the safety and the stability in power system by the characteristics of topology network. This subject is always concerned and discussed by the society. The thesis use dynamic load to simulate current in real world. We foc us effect on network efficiency by the strategy of cascading failure, analyze the vulnerability of network. The thesis use the variation of network efficiency as index to analyze network. According to determining and discussing by static load cascading failure model and dynamic load cascading failure model, dynamic load is the situation in different amount of generating and consumption of electrical energy. We used the data to observe the result of Taiwan power system under the situation. In addition to, changing of internet efficiency by single attack, multi-attack and strategic multi-attack in attacker method of thinking. We found that Taiwan power system is weak after we used the statistics on it.

這篇論文主要可以分成兩個部分。第一部分，我們整理了關於複雜網路的初步研討。最重要的特性有：小世界網路、無尺度度分布。並且介紹了三種模型：BA 模型、EBA模型，以及W-S small world model。接著對於一份實際的社會網路資料—台灣業餘桌球選手對戰網路，做網路的結構分析，試驗其是否具有上述的兩種特性。透過兩種可以模擬出無尺度度分布特性的模型：BA以及EBA模型。我們藉由這兩種模型模擬的結果，以及和競賽網路的比較，試者去闡述模型與理論間為何有些相似，卻又如此不同。並討論了賽制設計對於結構的影響。 在第二部分裡，我們回顧了一些對於網路的拓樸性效率以及可靠度效率的研討，並且討論了兩種不同負載定義下的連鎖故障行為。最後我們使用其中三種方法：拓樸性效率脆弱性、參與中間度(betweenness)過載引發的連鎖性故障行為，以及電力網路的動態電流變化造成的連鎖性故障，對於一個假想的電網做傳輸線的弱點排序。其中由動態電流過載(transient dynamic overload)造成的連鎖性故障可以視為一個簡化後的電力動態網路模型，藉由這三者間排序的不同，我們可以看到複雜網路分析以及基於電力網路傳輸特性所模擬的結果差異。 / This thesis can be divided into two parts. In the first part, we review some basic properties of the complex networks. The most important features are: small world networks and scale-free degree distribution. Then, we introduce three complex models : BA model, EBA model, and W-S small world model. Next, we analyze a real data—CTTC network to test if it has the features we have mentioned above. By the EBA and BA model simulations, we try to illustrate why there are some similarities between the simulations and real data, but they are still so different in most of aspects. In the second part, we review the definitions of the topology and reliable efficiency of a network structure. Next, we discuss two cascading failure model based on different definitions of load of a transmission line in a power grid. Finally, we use three different ways: topology efficiency vulnerability, cascading failure triggered by betweenness overload, and cascading failure triggered by the transient dynamics overload to test the vulnerability of edges in an assuming power grid. The cascading failure triggered by the transient dynamic overload can be viewed as a simplified power flow model. We sort the most vulnerable edges in three different ways. By this, we can observe the difference of the vulnerability analysis based on the complex network and the characteristic of the power transmission..

擴散權重影像與神經纖維追蹤可以用來探討腦區域之間的連結性，目前透過網路分析方式已經證實腦網路是有小世界的特性，最近也有研究不同受試者或者是病人之間的網路連結量測集中程度，但是擴散權重影像所運算出來的網路參數中間要經過很多步驟，這些中間步驟可能會影響到網路參數。所以有必要對於量測網路參數的受試者間變異性和重複量測重現性進行研究。本研究的目標是利用機率式神經纖維追蹤術量測大腦網路參數的重現性，探討三個會影響計算網路參數的重現性的變因，分別是，路徑定義方式、有無損耗正規化、受試者群體的網路連結篩選機制。變異係數定義（Coefficient of Variance, CV）為標準差除以平均值，分別計算二次量測之間的變異係數（CVwithin），以及受試者之間的變異係數（CVbetween），另外也計算組內相關係數（Intraclass correlation coefficient, ICC）。 掃描30受試者（15男，15女，年齡20~26）。每人掃描二次，並利用機率式神經纖維追蹤術計算網路連結，網路節點則是使用AAL標準模板定義的節點。若使用Wij = 1 – Pij定義長度，三項網路參數（區域效率、全域效率及損耗）重現性皆可接受（CVwithin<1.08%, CVwithin ≤ 10% and ICC > 0.7）。如果使用Wij=1/Pij定義長度，其損耗的CVwithin相較於Wij = 1 – Pij的大。如果長度的全距大，區域效率會不尋常地增加。如果二次掃描分別實施連結篩選，全域效率的CVwithin會較大。 本研究探討不同的網路建構方式將會影響測試內重現度，不同的研究團隊，縱使是採用相同的受試者群體和相同的儀器，所發表出來的網路參數可能會因為纖維追蹤術造成的誤差而不一致，因此實驗必須謹慎的分析資料以及闡述結果。 / Diffusion tensor imaging (DTI) with associate tractography can be used to access the connectivity of cortical regions in brain. Network analysis applied to connectivity matrix has demonstrated that brain has small world property. Recent studies also use network analysis to study the variation of concentricity among different group of subjects and patients. However the estimation of network metrics from DTI takes sophisticated processing steps. These intermediate steps may influence the estimation of network metric. It is therefore needed to investigate the potential variation of estimated network metrics using reproducibility test. The goal is to study the reproducibility of network properties derived from diffusion connectivity matrix constructed using probabilistic tractography. The effects of three factors on the reproducibility of network metrics estimation were studied. They are definition of path lengths of network matrix, path with and without cost normalization, the application of threshold to subjects groups. Coefficient of Variation (CV) defined as standard deviation divided by mean is used to test the intra-session (CVwithin) and inter subject (CVbetween) variability. Intra-class correlation coefficient (ICC) was also calculated. Images were acquired from 30 healthy participants (15 male, 15 female, aged 20-26 years). Each subject was scanned twice, denoted as N1 and N2. Probabilistic tractography was performed to mapping of cortico-cortical anatomical connections between regions defined from an anatomical atlas. All three of the tested network metrics (local efficiency, global efficiency and cost) were identified as acceptable (CVwithin < 1.08%, CVwithin ≤ 10% and ICC > 0.7) using path length defined as Wij = 1 – Pij. When the path length is defined as Wij = 1/Pij, cost showed higher CVwithin compared to Wij = 1 – Pij. It is unusual that local efficiency increase when the range of path length of edges is large. Global efficiency showed higher CVwithin as threshold is applied to N1 and N2 separately compared to both scans together. The present study revealed that different ways to construct cortical network had an effect on intra-session reproducibility. Our study also showed that despite evaluation of identical subjects using the same MRI system, variation of network metrics may be found by different research groups due to the potential errors from tractography. Replication of the experiment need to be carefully analyzed and interpreted.