工程科学与技术   2020, Vol. 52 Issue (4): 25-32

Spatial–Temporal Multi-granular Attribute Analysis and Knowledge Discovery Method for Voltage Sag
XIAO Xianyong, HU Wenxi, WANG Yang, WANG Ying, ZHANG Wenhai
College of Electrical Eng., Sichuan Univ., Chengdu 610065, China
Abstract: In order to mitigate voltage sag related problems based on power quality monitoring data, it is meaningful to improve the efficiency of power quality data analysis. Due to depending on accurate models of voltage sag, the traditional methods are inadequate for complex problems with multiple uncertainty factors. Therefore, the spatial–temporal multi-granular attribute analysis of voltage sag data and a related knowledge discovery method were proposed in this paper. Inspired by the cognitive hierarchy of complex problems, a framework consisted of “data—characteristic—index—information—knowledge” was proposed as a general technical route for voltage sag related problems. Based on the framework, to solve the problem of information loss caused by single granular, sag information in different granular was extended by voltage sag spatial–temporal multi-granular analysis. The relationship between power system structure attribute and voltage sag was discovered by granular reduction. Then, knowledge about voltage sag severity and propagation was derived. The synthetic and measured data were used to validate the effectiveness of the proposed method. Results showed that the proposed method can describe and resolve complex problems with many uncertainty factors.
Key words: power disturbance    voltage sag    spatial–temporal multi-granularity    knowledge discovery    propagation law

1 电压暂降数据分析框架 1.1 双向驱动的DCIIK架构

 图1 递进认知的DCIIK架构 Fig. 1 Progressive cognitive DCIIK framework

1.2 基于目标驱动的问题空间粒化

 $IND(B) = \{ (x,y) \in U \times U|\forall a \in B,a(x) = a(y)\}$ (1)

1.3 基于数据驱动的粒子组织

 $V = \sqrt {\frac{1}{N}\sum\limits_{i = 1 + k - N}^k {v_i^2} }$ (2)
 $T{\rm{ = }}{T_{{\rm{end}}}} - {T_{{\rm{start}}}}$ (3)

2 电压暂降时空多粒度属性分析 2.1 电压暂降时间多粒度属性

 ${E_{{\rm{se}}}}{\rm{ = }}\bigg(1 - \bigg(\frac{{{V_{\min }}}}{{{V_{{\rm{nom}}}}}}\bigg)\bigg) \cdot T$ (4)
 ${E_{{\rm{ss}}}}{\rm{ = }}\frac{{1 - {V_{\min }}}}{{1 - {V_{{\rm{curve}}}}(T)}}$ (5)

 $S\!I = \frac{1}{n}\sum\limits_{x = 1}^n {{s_i}}$ (6)

 $s = {E_{\rm{v}}} \cdot {w_1} + {E_{{\rm{sf}}}} \cdot {w_2} + {E_{{\rm{se}}}} \cdot {w_3} + {E_{{\rm{ss}}}} \cdot {w_4}$ (7)

 ${\delta _\gamma } = \left\{ {\left( {{t_1},S\!{I_1}} \right),\left( {{t_2},S\!{I_2}} \right), \cdots ,\left( {{t_i},S\!{I_i}} \right), \cdots } \right\}$ (8)

2.2 电压暂降空间多粒度属性

 $T{C_i} = \frac{{{H_i}}}{{{K_i}({K_i} - 1)}}$ (9)

 $T\!{E_i} = \frac{1}{{n - 1}}\sum\limits_{j = 1,j \ne i}^n {\frac{1}{{{l_{ij}}}}}$ (10)

 $T\!{S\!_i} = \min ({l_{ij}}),j \in \alpha$ (11)

 ${R^j} = \frac{1}{m}\sum\limits_{x = 1}^m {{r^j}(x)}$ (12)

 $\varphi _\gamma ^j = \left\{ {\left( {{{\textit{z}}_1},R_1^j} \right),\left( {{{\textit{z}}_2},R_2^j} \right), \cdots ,\left( {{{\textit{z}}_i},R_i^j} \right), \cdots } \right\}$ (13)

3 电压暂降传播规律多粒度知识发现 3.1 多粒度信息系统

 $S = \langle U,A\rangle = \langle U,\{ a_j^k|k = 1,2, \cdots ,m\} \rangle$ (14)

 $a_j^{k + 1}(x) = g_j^{k,k + 1}(a_j^k(x)),x \in U$ (15)

 $P(x) = \sum\limits_{i = 1}^T {{w_i}P(x|{\mu _i},{\sigma _i})}$ (16)

 $P(x){\rm{ = }}\frac{1}{{\sqrt {2{\text{π}}} \sigma }}\exp \bigg[ - \frac{{{{(x - \mu )}^2}}}{{2{\sigma ^2}}}\bigg]$ (17)

3.2 基于粗糙集的粒度约简方法

 $IND(P) = IND(P - \{ a\} )$ (18)

 ${\underline {\sum\limits_{i = 1}^m {{A_i}^{}(X)} }} = \left\{ {x \in U{\rm{|}}{{\left[ x \right]}_{{A_1}}} \subseteq X \wedge \cdots \wedge {{\left[ x \right]}_{{A_m}}} \subseteq X} \right\}$ (19)
 ${\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\overline {\sum\limits_{i = 1}^m {{A_i}^{}} (X)}} = \sim \underline {\sum\limits_{i = 1}^m {{A_i}^{}} ( \sim X)}$ (20)

 ${\mu _{A'}}(U,D) = \left\{ {\underline {\sum\limits_{i = 1}^m {{A_i}({Y_1})} } ,\underline {\sum\limits_{i = 1}^m {{A_i}({Y_2})} } , \cdots ,\underline {\sum\limits_{i = 1}^m {{A_i}({Y_r})} } } \right\}$ (21)

${\;\mu _{A'}}(U,D) = {\mu _A}(U,D)$ ，则称 $A'$ $A$ 粒度下的近似分布一致集；若对 $\; \forall A' \subset A$ ，都有 ${\;\mu _{A'}}(U,D) \ne {\mu _A}(U,D)$ ，则 $A'$ $A$ 粒度下的近似分布约简。可以证明，粒度下近似分布一致集保证了每个目标决策的下近似保持不变，即可保持分类不改变[21]。因此，以此为判据，可使得约简后的多粒度空间具有和原始粒度空间相同的目标决策能力。

 $\underline {\sum\limits_{i = 1}^m {A_i^P(X)} } \subset \underline {\sum\limits_{i = 1,{A_i} \in A'}^m {A_i^P(X)} }$ (22)

 $\underline {\sum\limits_{i = 1}^m {A_i^P(X)} } {\rm{ = }}\underline {\sum\limits_{i = 1,{A_i} \in A'}^m {A_i^P(X)} }$ (23)

 图2 暂降传播规律知识发现流程图 Fig. 2 Flowchart of knowledge discovery for voltage sag propagation

4 算例分析 4.1 电压暂降影响程度多粒度评估

 图3 IEEE 30节点测试系统 Fig. 3 IEEE 30-bus test system

 图4 不同加权方法下的电压暂降综合评估排序结果 Fig. 4 Evaluation results for voltage sags based on different weighting methods

 图5 供电园区电网简化示意图 Fig. 5 Simplified diagram of a power grid

 图6 时间多粒度评估结果 Fig. 6 Multi-temporal granular evaluation results

4.2 电压暂降传播规律挖掘

 $\beta({X_i} \to {Y_j}) = \frac{{{N_{({C_i} \cap {D_j})}}}}{{{N_{{D_j}}}}}$ (24)

5 结　论

1）将数据、特征、指标和信息看作知识的不同粒度表现形式，从复杂问题认知层次出发，提出双向驱动的DCIIK架构，作为知识发现的一般思路流程。

2）对电压暂降幅值、频次、能量和严重程度等属性进行时间多粒度拓展。既能捕获短时间内暂降水平升高的准确时间，又有助于分析暂降水平长期变化规律。

3）对节点规模、聚集程度、传播效率和支撑能力等电网结构属性进行空间多粒度拓展，有助于从节点、区域等不同层面分析电压暂降传播规律。

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