After deriving the close form expression of qj∗ in any power distribution network G and compromised customer set D as in (5.24), we can traverse q∗j, ∀j ∈ M on all the power lines lj and search all vulnerabilities in G.
To compute q∗j, we have to calculate σkj which has a time complexity of luM , then
inverse Z-transform which has a time complexity of lHlog(lH). luis the number of nontrivial
terms of load properties uki in (5.4) and lH is the number of nontrivial terms of hj(t).
Therefore, the computation of one q∗j has a time complexity of max{luM, lHlog(lH)}. A
naive traverse of qj∗, ∀j ∈ M has a time complexity of max{luM2, lHlog(lH)M }.
In this section, we present a DFS algorithm to traverse all the power lines for q∗j, ∀j ∈ M efficiently. Due to the space constraint, we only present the key component of this DFS algorithm, the update of σjk, in Algorithm 2. The complexity of updating σjk for all the Algorithm 2 Depth First Search of σkj
1: procedure Update σjk
2: σkj ← 0
3: for All customer i directly connected to j do
4: if i 6∈ D then
5: σkj ← σk
j + uki
6: for All power lines j0 connected to j do
7: Update σkj0
8: σk
j ← σjk+ σjk0 return σkj
power lines is reduced to luM . The resulting time complexity of the vulnerability search is
max{luM, lHlog(lH)M }. Such improvement may be unnoticeable when lHlog(lH)M is the
significant term, but it can have a big influence when the power distribution network G is large. Other values including Dj, Dj and etc can be efficiently calculated using the same
idea though they are not bottlenecking the vulnerability search time complexity.
5.5
Summary
In this work, we built a theoretical framework to evaluate the potential risks of ma- licious DSM cyber attacks with certain capabilities. A close form expression of maximum
power line load is derived when the DSM is under attack. An efficient depth first search al- gorithm is developed to search for all power grid vulnerabilities. A case study was provided to demonstrate the protocol and its effectiveness.
To continue our research, we plan to utilize our proposed vulnerability detection method to assist the design of DSM communication network planning and high value attack target protection. One naive approach is to test the vulnerabilities of different communi- cation network plans or protection plans and choose the one with minimum vulnerabilities. However, this approach is neither performance effective nor time efficient. Our objective is to develop an efficient communication network design tool to minimize the potential targets which requires a deep understanding of the vulnerability detection and a carefully designed optimization.
6.
Conclusion and Future Works
6.1
Privacy Protection in DSM
We studied the privacy protection in demand response using an in-home energy storage system. A pair of close bounds to characterize the optimal tradeoff between privacy protec- tion and cost savings were given. Although the policy that solves the optimal tradeoff be- tween privacy and cost savings remains an open problem, we believe that our bounds using the revealing state approach are quite close. Operating costs are an important consideration for the mechanism proposed in this research. While the key mathematical contributions in this work do not consider operating costs, the framework does not preclude such costs per se. For instance, a marginal amount can be added to the purchase price when charging the battery, and a marginal cost incurred every time the battery is discharged. The policy simulated with these inclusions would provide a tradeoff that is closer to practice.
Another approach of privacy protection in DSM is to tackle this issue from the metering mechanism design. When the smart metering network is under attack, the fine electricity profile transmitted upon it becomes an even greater privacy concern. The major objective of smart meter is to enable variable electricity pricing. Though reporting the electric usage in every short period of time can help the reliable and effective operation of power grid, it is not the only way. Instead of transmitting how much electricity a consumer uses every certain time period, the meter can calculate the bills of the users locally and only transmit how much money a consumer used for electricity once a week or even once a month. The variable pricing can be achieved by having the pricing plan broadcast to every smart meter and then billing on consumer’s end. Such broadcast is necessary in classical smart metering method anyway.
Though this metering scheme has some disadvantage than transmitting electricity us- age every 15 mins, it can be used as a backup plan when the communication link is exposed to cyber attacks for two benefits:
1. Longer transmission interval gives more time to eliminate the threats.
2. The aggregated electric bills are much less sensitive. The amount of money a consumer use on electricity in one week or one month reveals much less information than a detailed electricity profile.