Over the past number of decades, the electric grid has been modernized, becoming more decarbonized, distributed and digitalized. Consequently, modern day electric grid systems have evolved to become smart grids allowing: two-way flow of electricity and data enabling applications such as smart metering. While smart meters provide benefits to consumers through better tracking and use of energy, more accurate billing and increased tariff options, they have also brought concerns related to privacy and data integrity over the use of personal data collected. Over the past number of years various privacy preserving techniques have been proposed to address this concern to prevent the invasion of privacy by smart meters, which include cryptography and data perturbation methods^1,2.

To date much of the literature has focused on analysing the benefits of increased complexity and computation introduced through cryptography-based encryption methods versus the trade-off between privacy and utility introduced by data perturbation techniques such as Differential Privacy (DP). In addition, several works have assessed the robustness of these techniques against privacy attacks such as data reconstruction, linking, inference, differencing and correlation attacks³. While all these attacks differ, the goal of the adversary is to gain knowledge that was not intended to be shared. Such knowledge can be related to the data usage allowing an adversary to identify patterns and behaviours and to infer sensitive information form it.

Chamikara et al.⁴ outlined how data perturbation techniques are vulnerable to specific data reconstruction attacks such as naïve estimation, independent component analysis (ICA) and Input/Output (I/O) attacks such as eigen analysis, distribution analysis attacks and spectral filtering. The goal of all these attacks is that the adversary attempts to reconstruct the original data from perturbed data. Setting a strong perturbation has been proven to be effective against these types of attacks in advance adversarial environments. Other data perturbation attacks have focused on removing the level of noise on masked data such as Filtering Attack⁵ and Negative Noise Reduction⁶ attacks, which used in combination with other attacks could increase their efficacy.

Purpose

To date there has been no evaluation on how the privacy models that uses pure perturbation techniques such as Differential Privacy (DP) are resistant to collusion attacks. In this specific type of attack, a group of smart meters and/or (third party) aggregators collectively work together to leak sensitive information with the aim of reconstructing private data or injecting false packets with the aim of modifying the integrity of the data sent to the utility provider. The use of trusted third party aggregators in smart grid systems make it particularly vulnerable to these types of data reconstruction/privacy and integrity attacks. The existing privacy solutions for smart grids that are collusion resistant either uses hybrid (DP with encryption) or pure encryption based solutions^{3,7,8,9,10,11}, which have high computation and communication cost.

Given the above context, in this paper we present a collusion resistant Enhanced Differential Privacy with Noise Cancellation Technique (E-DPNCT) scheme, that not only preserves the privacy of smart meter, but also protects the data from being reconstructed by colluding entities such as smart meters and trusted third party aggregators. E-DPNCT extends previous work, DPNCT¹² ( A preliminary version has been published by IEEE International Conference on Communications (ICC) - Workshop on Communication, Computing, and Networking in Cyber-Physical Systems (IEEE CCN-CPS ), Montreal, Canada, June 2021, entitled “DPNCT: A Differential Private Noise Cancellation Model for Load Monitoring and Billing for Smart Meters”), whose core contribution removed the use of a trusted third party aggregator in DP scheme and enabling the calculation of highly accurate billing using a periodic noise cancellation technique at a low computational cost. In this extended work, we have modified DPNCT with split noise distribution over multiple smart meters, increasing the approach resilience against collusion attacks. We assess E-DPNCT performance, by comparing it against a lightweight encryption based collusion resistant privacy solution, EPIC⁹. We chose EPIC as a comparison due to the lack of alternative DP collusion resistant approaches. We demonstrate through our analysis that E-DPNCT is collusion attack resistant, yields highly accurate results in billing and load monitoring with low computational cost.

Contributions

Our contributions are highlighted as follows:

• We present E-DPNCT that is collusion attack resistant by splitting the noise over multiple master smart meters (MSMs). This, to the best of the authors knowledge, is the first data perturbation DP scheme for smart grids that does not make an assumption of trusted entities and that is resilient against collusion attacks.

• We assess the performance of our E-DPNCT against the state of the art encryption collusion resistant approach EPIC⁹.

• We compared our results in accuracy with DP based model “Differentially Private Demand Side Management for Incentivized Dynamic Pricing in Smart Grid (DRDP)”¹³.

• We experimented with multiple sensitivity values and study their impact on privacy and accuracy/utility of the data.

The rest of the paper is organized as follows. The related work is discussed in “Literature review”. The threat model and Preliminary Knowledge are introduced in “Threat model and attacks” and “Preliminary knowledge” respectively. After that proposed solution is introduced in “Methods”. Finally, The paper is concluded with “Conclusion and future work” that includes summary of analysis on E-DPNCT and the future directions.

The literature review is further divided into two parts. The first part provides an overview of existing privacy models for smart grids based on (a) privacy technique i.e. DP, encryption, and hybrid; and (b) aggregator type i.e. trusted and un-trusted third party aggregator, is presented. In the second part, a discussion on the security analysis (i.e., their resistance against collusion attacks) of these privacy models is presented.

Privacy models for smart grid

Paverd et al.¹⁴ use a remote trusted entity to add Laplacian noise in smart meters data. This remote trusted entity is responsible for bi-directional communication between the power grid and the smart meter for an effective Demand Response (DR) mechanism. Dynamic billing to reward correct behaviour and enforce demand response model is proposed by the authors from^13,15. They provide DP at aggregator level where a trusted aggregator collects original data and Laplacian noise is generated and added to the original data. Dynamic bills are calculated using original data and only the customers responsible for peak load are charged with peak factor price to ensure fair billing. However, a trusted entity is required in both¹⁴ and¹⁵ models to mask the original data and follow the demand response protocol honestly. Liu et al.¹⁸ uses zero knowledge proof and a trusted authority which is responsible for registering users and public and private key management.

The solutions with non trusted third party including¹⁶ and⁶ used infinite divisibility of Laplacian distribution and point-wise sensitivity to generate and add noise at the smart meter level. The contributions in¹⁶ and⁶ were limited in that DP was discussed only within the context of aggregated data for load monitoring, and did not detail the subsequent impact of the noise and accuracy of billing to the end user, nor was a security analysis of the approach presented. The BDP model presented in⁵ also uses DP for the preservation of appliance usage privacy. BDP privacy preservation model is focused on masking appliance usage of a households by choosing sensitivity as the maximum wattage of the heaviest electrical appliance. Ren et al.¹⁹ uses a novel measurement based perturbation for accuracy in bills. However, the paper did not discuss the impact of noise addition on load monitoring in the experiments.

Similar to^6,16 and⁵, EPIC by Alsharif et al.⁹ and Wang et al.³ use a non trusted aggregator. They differ in their privacy mechanism as they only use compute intensive encryption based on a key exchange mechanism which has a greater communication and computation overhead as compared to pure DP based solutions. Similar to^6,16 and⁵, EPIC by Alsharif et al.⁹, Wu et al.²⁰, and Wang et al.³ use a non trusted aggregator. They differ in their privacy mechanism as they only use compute intensive encryption based on a key exchange mechanism which has a greater communication and computation overhead as compared to pure DP based solutions. Zhang et al.²¹ proposed service model that trains the neural network models locally, and only model parameters are shared with the central server instead of sending private energy data to the cloud server. The goal of the paper is however forecasting of energy demand and federated learning model predicts future energy demand based on multiple features including current demand, weather etc.

Acs et al.⁷ and Won et al.¹⁷ also use a non trusted aggregator in their approach. They differ though in that as they proposed a hybrid approach, using encryption in addition to differential private noise between the smart meters and aggregator, to mask the data. However, these solutions are computationally complex and consume extra bandwidth in the network to send ciphertexts information. The authors from⁸ make use of encryption and scheduling of charging batteries as a privacy mechanism without a trusted third party. This solution requires extra material cost for installing and maintaining energy storage devices such as batteries.

DPNCT¹² used DP with noise cancellation without a trusted third party for accurate and private load monitoring and billing. This model is put under the test of collusion attacks in this paper and it proves to be vulnerable to collusion attacks in case of malicious smart meters. Enhancing the attack resistance of the noise cancellation model, E-DPNCT makes use of split noise cancellation and variable privacy selection for the electricity consumers which makes it resistant to collusion attacks.