黄光球 谢蓉

摘 要：为提高突发事件级联失效对现实碳排放关联系统破坏程度的评估可信性，在传统复杂网络的“负载容量”级联失效模型基础上，考虑个体成员对负载的冗余能力，提出一种过载失效概率，构建了考虑节点过载状态的级联失效模型，并基于节点特性提出了6种过载节点负载分配策略。仿真结果表明：在过载节点负载分配策略中，综合分配策略整体上较优，能够有效控制级联失效的规模，增加网络鲁棒性;在一定范围内提升过载参数有助于降低级联失效的影响，但提升到一定程度时改善效果不明显;在不同负载分配策略下，剩余系数存在一个最优值，容量可调参数存在最优区间，可以使碳排放关联网络保持较好鲁棒性的同时，花费较小的构建成本，其中紧密度分配策略对应的网络构建成本较高。

关键词：碳排放关联网络;级联失效模型;过载节点;负载分配;魯棒性

中图分类号： TP393

文献标志码：A

Abstract： In order to increase the creability of the damage degree evaluation of cascading failure caused by emergency to carbon emission correlation system， considering the redundancy ability of individual members to load， an overload failure probability was proposed based on “load-capacity” cascade failure model of traditional complex network， and a cascading failure model was constructed considering load overload. Then， based on the characteristics of nodes， six load allocation strategies for overloaded nodes were raised. The simulation results show that， in the load allocation strategies of the overloaded nodes， the integrated allocation strategy is superior in general， which can effectively control the scale of cascading failure and increase the robustness of network; increasing the overloaded parameters in a certain range can help to reduce the impact of cascading failure， while the improvement effect is not significant when the parameters are too large; under different load allocation strategies， the residual coefficient has an optimal value and capacity adjustable parameters have optimal ranges which can keep the carbon emission correlation network in good robustness with low construction cost while the tight allocation strategy means high costruction cost.

Key words： carbon emission correlation network; cascading failure model; overloaded node; load distribution; robustness

0 引言

现实社会中，产生碳排放的主体彼此相互依赖，它们通过资金、技术等经济往来联系在一起，逐渐形成一个复杂化、规模化的碳排放关联系统，但系统本身常表现出不稳定的情况，如能源短缺、经济危机等;同时当主体的碳排放水平过高时，政府或企业便会响应节能减排号召采取一定措施，如搬迁出高耗能企业、改革产业结构等，以降低碳排放，此时主体成员“故障失效”，继而影响到与其他主体成员间的经济往来，特别是当系统内重要的参与主体或主要的环节“失效”时，关键链路消失，级联失效传播，严重时可导致整个网络的瘫痪，如图1所示。……