圖1 配電網(wǎng)地震災(zāi)害下韌性評(píng)估流程圖Fig.1 Flow chart of resilience assessment of distribution network

圖2 配電網(wǎng)與交通網(wǎng)損壞概率與震中距關(guān)系Fig.2 Probability of road damage degree depending on earthquake grade and epicenter distance

表1 地震災(zāi)害下道路破壞程度Tab.1 Road damage degrees due to earthquake disasters

表2 交通-配電網(wǎng)空間耦合情況Tab.2 Spatial coupling of transportation-distribution networks

表3 故障線路與道路的受損情況Tab.3 Situation of faulty lines and damage roads

表4 不同策略下故障搶修順序及應(yīng)急電源車調(diào)度方案Tab.4 Sequence of fault repair and dispatching scheme of emergency power vehicle of different strategies

為了便于計(jì)算及交通-配電網(wǎng)耦合圖像辨識(shí),將該算例的地震能量在該區(qū)域的傳播范圍以塊狀形式劃分.

圖4 交通-配電網(wǎng)故障場(chǎng)景Fig.4 Transportation-distribution network fault scenario

附錄A

下層省間問題的拉格朗日函數(shù)為

(A1)

(1) 拉格朗日平穩(wěn)性約束:

?j∈J, ?s∈S, ?n∈Ns,

?t∈T

(A2)

(2) 拉格朗日系數(shù)約束:

(A3)

(3) 互補(bǔ)松弛條件:

(A4)

(4) 原問題等式約束條件

?j∈J, ?t∈T

(A5)

利用KKT條件將雙層模型轉(zhuǎn)換為單層模型式(1),約束條件包括:上層問題約束條件式(2)～(6),下層問題約束條件式(A2)～(A5).此時(shí)模型為非線性優(yōu)化問題,進(jìn)一步采用大M法對(duì)KKT條件中的互補(bǔ)松弛等式約束(A4)進(jìn)行線性化處理:

(A6)

(A7)

根據(jù)強(qiáng)對(duì)偶理論,原問題和對(duì)偶問題的目標(biāo)函數(shù)在取到最優(yōu)值時(shí),最優(yōu)值大小相等,即

(A8)

(A9)

(A10)

經(jīng)由上述步驟,雙層模型可轉(zhuǎn)換為單層線性模型,目標(biāo)函數(shù)為式(A10),約束條件包括式(2)～(6),式(A2)～(A3),式(A5)～(A6).

附錄 B

圖B1 A省和B省的負(fù)荷、新能源和凈負(fù)荷Fig.B1 Load, renewable energy and net load of province A and province B

表B1 送端省份發(fā)電機(jī)組參與省間市場(chǎng)的容量Tab.B1 Capacity of sending provincial generators in the inter-provincial market MW