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Modern power system reliability assessment with cyber‐intrusion on heat pump systems

In smart power systems, information and communication technologies are being broadly installed and two-way communications are being established more effectively and efficiently. However, they are vulnerable to cyber-physical interactive threats and their impact depends on the system infrastructure, degree of interaction, degree of vulnerability, and the intensity and the frequency of the attack. The study addresses this problem and proposes: (i) an innovative Markov-chain based framework of the cyber-intrusion process to implement operating conditions in a smart power system; (ii) an advanced algorithm for power system reliability assessment, incorporating cyber-intrusion process and a detailed model of a heat pump system; and (iii) a new impact assessment framework for different cyber-intrusion detection-time distributions driven by Monte Carlo simulation. The cyber-detection and system recovery process with the presence of cyber-physical interactive operation models suggest that a significant level of impacts could be generated by the interactive operation of the smart power system and a quantitative assessment is needed in order to assess true impacts.


Introduction
Over the past decade, there has been a dramatic increase in implementation of renewable energy resources such as solar photovoltaics (PV), wind power generation, coupled with a growing focus on strategic decarbonisation elements in the service sector, for instance, electric vehicles and heat pumps (HPs), have provoked a complexity in structure, and resulted in new challenges in power system operations [1]. Penetrating these cutting-edge technologies into the power grids shifts its topological configuration from being centralised with dispatchable conventional generation to being distributed with non-dispatchable intermittent generation [2]. To maintain reliable operations of the decentralised power systems, high-level monitoring and supervision practices are desired [3]. These desirable necessities are fulfilled by installing an advanced metering infrastructure (AMI) and additional components of Information and Communication Technologies (ICTs). ICT is a critical infrastructure in modern power systems. AMI is a key element in the critical infrastructure and it had been deployed almost 87 million sites in the USA by 2018, representing 50% of all USA electricity customers [4]. Increasing installations of cyberphysical-based systems such as AMI, not only bring wide-ranging benefits, but also open doors for cyber-attack agents to access critical information, force the system into abnormal conditions and even leading to power outages. On account of their harmful and unexpected nature, preventing cyber-attacks have recognised as a critical issue in power systems sector.
At the end of 2015, Ukraine's power distribution system was exposed to a sophisticated cyber-attack. The pre-attack period was started several months before the attack-day and, attackers observed and determined cyber-attack pathways in the power grid. As a result, data of key assets was manipulated and almost 225,000 customers experienced a black-out for several hours [5]. In 2017, energy companies were indirectly affected by fast-spreading encrypting malware, called 'NotPetya' [6,7]. Although there were no direct effects on operations of energy companies, this ransomware caused collateral damage that was a huge financial loss, and it was linked with the previous cyber-attack on Ukrainian power grid according to [8]. Afterwards, during the year of 2019, there were a higher number of cyber incidents on critical infrastructure that was a rising concern for power sector [7]. American power companies and Russian power plants were hacked by cyber-intruders in March and June 2019, respectively [9]. Especially, parts of power networks in three states of the USA were influenced by cyber-intruders on Supervisory Control and Data Acquisition (SCADA) systems while power utilities stayed in the control of power grid operators [7,9]. Together, these real cases show reliable operation of most of the power grids are under attack, grid resiliency is fragile, its vulnerability is rising, and preventive actions for power grids are needed for operational continuity and avoid cascading failures.
There are limited incidents that have been recorded as cyberintrusions on distributed energy resources (DER). An important example is that an electric car was hacked through a mobile application of cyber-vulnerability [10]. Hackers gained the control of the vehicle's air-conditioner in ∼10 s and drained its battery during the cyber-incident [10]. Another notable real-life example is happened through smart meters in Puerto Rico [11]. Due to infiltrating the AMI with external connection by infrared light, massive cyber-intrusion on smart meters resulted in an extremely high level of electricity theft and a large number of scam bills [11]. Puerto Rican electric utility incurred a loss of millions of dollars by the cyber-incident [12].
More recent attention has focused on the scenario-based case studies that assess the impacts of cyber-intrusion on the power grid and its response with resiliency level. To determine the effects of cyber-incident on power networks, home appliances are considered in [13]. Appliances such as air conditioners and space heaters can be dramatically affected by cyber-attacks due to manipulative action on their power demands [13]. It is shown in [14] how manipulating consumer load profiles and falsification of congestion mitigation during demand-side management (DSM) process would lead to overloading as well as power system operational issues. With these vulnerable congestion control techniques indicate how can severely affect DSM process techs affect, such as HPs. Regarding HPs, there are limited cyber-attack study cases in the literature. Only Yang and Wang [15] demonstrate how type of cyber-attacks and integrity level on HPs controller can influence electricity consumptions. High level of cyber-integrity could vary system temperature and increase the power consumption of HPs [15].
As can be noticed from these cyber incidents [5][6][7][8][9][10][11], cyber threats have different time scales, unpredictable behaviours, different reconnaissance and waiting (sojourn) times for different technologies and platforms. Unfortunately, there is limited information on the reconnaissance and sojourn time duration of cyber-attacks in the literature. These complex features increase difficulty on cyber-attack intrusion modelling for power systems significantly.
In addition, cyber-intrusion process modelling has received considerable attention. In [16], a study was conducted to quantify security failures due to cyber vulnerabilities considering conventional computer system layers. It was found that although the security failure quantification in that study was done well, the time scale identification of cyber layer's detection-attack agents was limited [16]. A recent study by Xiang et al. [17] utilised semi-Markov process in a similar way as in [16] to investigate the probability of a successful cyber-attack. The difference between cyber-intrusion methodology applied in [16,17] is that different reconnaissance and waiting time scale ranges were implemented in the former. When the detection-agent time interval was modified with different limits, the cyber-attack waiting time (sojourn) in each layer and pre-attack (reconnaissance) time were changed significantly. Thus, the changes in calculation of cyber-attack waiting and pre-attack times have an effect on cyber-attack impact analysis. In addition to [16,17], the same methodology of the cyber-intrusion process was applied in [18]. Zhang et al. [18] differ from Xiang et al. [17] only in the cyber-attack types and pathways. These previous studies [17,18] did not take into account the futuristic characteristic of system smart components, the smart capability of layers in the procedure and sophisticated attacks. This paper makes several contributions as follows: • An innovative mathematical model for HP system configuration is proposed in order to reduce assessment process complexity of cyber-physical systems. • A new algorithm is proposed for the reliability assessment of HP systems with cyber-physical interactive operations. • An enhanced cyber-intrusion process model is presented for cyber-physical system reliability analysis. This model also considers stochastic attack-detection time in the cyber-intrusion process. • Sensitivity analysis framework of attack-detection times in cyber-intrusion process for HP systems is presented.
The paper is outlined in the following structure. Section 2 delineates mathematical model of the research problem and cyberphysical interactive power system reliability framework for the heating system; Section 3 presents the case studies and analysis, and finally, Section 4 concludes the findings of the investigations.

Mathematical model
The aim of this section is to present cyber-intrusion process models combined with HP reliability assessment framework applied to a smart power grid. In order to design the framework, at first, an intrusion path model is demonstrated. Then, a new cyber-intrusion process is introduced showing calculation steps of attack-detection times that are essential parts for the calculation of cyber-physical system failures. Next, a generic component-based reliability model of an HP system is presented for cyber-physical system availability analysis of HP, incorporating Monte Carlo simulation for composite reliability assessment.

State transition model for smart grid
As reported by the National Electric Sector Cybersecurity Organization Resource (NESCOR) in [19], power systems need a different manner to preserve critical infrastructures for present and future developments. Hence, power system studies also require distinctive approaches in order to assess the futuristic features of smart grid elements. As stated in Fig. 1, the study considers three different typical process ways to reach successful cyber intrusion for the smart grid. All three-intrusion pathways have equal probabilities to compromise a cyber-attack. This paper selected only intrusion path 1 (Fig. 1) through the DER SCADA (supervisory control and data acquisition of distributed energy resources) to show the cyber-attack process in a power grid. Path 1 is chosen due to SCADA systems is one of the most vulnerable ICT components in the energy sector. Additionally, there has been a considerable amount of real cyber-incidents are happening through SCADA systems [20,21]. There are six distinctive phases that P 1 -P 6 are defined as secure and failed system states, respectively. In this cyber-intrusion process, a cyber-attack tries to get an advantageous status to pass to the next phase. Thus, P 1 , P 2 , P 3 , P 4 , and P 5 demonstrate the probability of each phase for cyberintrusion to pass to the next state (Fig. 2). The cyber-intrusion process is successful only if the attack reaches the absorption state P 6 of the system

Definitions and assumptions for intrusion process:
The mission of an attack-agent is to gain a privilege status in a particular period against the detection agent. A smart-attack agent needs to help to the attack agent for simplifying cyber-intrusion preparations in a certain amount of time. In addition, the detection agent must spend some time to detect the cyber-intrusion to isolate the attack and limit to successful-attack intrusion in each cyberlayer. By means of playing this cyber game in between agents, MTTC Cyber (mean time to compromise for cyber-attack) can be computed. It is defined as a statistical time-variant that is to obtain the required mean time value to go from the normal status to the abnormal status of the system. Moreover, MTTD Cyber (mean time to detection for cyber-attack) refers to another statistical time value that is cyber-forensic with physical restoration time and this is necessary for the statistical probability evaluation of a successful cyber-attack intrusion (P Cyber-attack ). These two statistical values of threats can vary with attack type, frequency, strength and severity of layers etc. Their statistical relation is presented as follows: Statistical calculation of P Cyber-attack in (2) can be utilised in power system reliability and resiliency. The investigation aim is to present the smart attack agent role in the process of intrusion and to assess the impact on the statistical value of MTTC Cyber . Additionally, the study has some assumptions related to the cyber-intrusion process. They are as follows: • The investigation considered the mission of a cyber-attack is to force the system to the abnormal states. The system has a detection agent in each cyber layer that adversely affects the detection of threats and preserves the system at normal conditions. • Available detection systems in the cyber-security sector have been designed with available cyber-attack data, which are assumed as normal attacks, in a data set [22]. Intelligent attacks or smart-attacks are accepted as unknown and unseen attacks. • The investigation assumed component characteristics of a power system would change with smart features that would include subordinate smart firewalls and smart detection assets. As a result, the investigation includes the detection agents for cyberattack detection. Each cyber layer has a smart detection system and different ability against threats in order to minimise their impacts on the system. Thus, the detection time is considered in a random manner. • The attacker agent needs to spend some time to gain the trust of the cyber layer in order to get an authorisation for passing to the next stage of the smart grid. Additionally, it is assumed that the target of the attacker is to cause harm to a smart meter or control panel of HP for energy theft from end-users. • The intruder is presumed to inject bad data into the system for the manipulation of energy reading measurements and the detector is supposed to have a capability of anomaly behaviour detection because of generic MTTD Cyber estimation for this study.

Calculation of MTTC Cyber :
This sub-section aims to introduce statistical calculation of cyber-attack waiting (sojourn) times in each cyber layer and the total intrusion process time. A fundamental instrument is to develop cyber intrusion occurrence and its waiting time in each cyber-physical layer. Hence, it is vital to point out the calculation of required time for each attack phase as well as full attack process. In order to quantify security levels of cyber-physical components on the smart grid, the MTTC Cyber , refers to requisite time to go from secure to failure status of the system that is implemented for power system reliability evaluations. As previously mentioned, normal attack f (X i n ), smartattack f (X i s ), and detection agents f Y i are introduced. Almasizadeh and Azgomi [16] quantify security failures with conventional computer layers, and detection time of cyberintrusion has a restriction in the time scaling identification of detection process. Similarly, Xiang et al. [17] utilise semi-Markov chain for cyber-attack process, except adding a clear identification on lower boundary limit of cyber-intrusion process time, though utilising a constant value for detection time in [16,17], which is a unreal approach that it should be assigned as a variable value in each intrusion attempt. The differences between our approach and previous studies in [16,17] on MTTC Cyber calculation are: (i) considered the implementation of a smart-attack agent in each layer that has different boundary limits for detection time (as noted in Fig. 3); (ii) new lower-upper boundary limits have been implemented for cyber-attack process (as in Fig. 3); and (iii) added variable detection time of cyber-intrusion established that brings novelty to the cyber-threat modelling framework. Fig. 3 shows the difference between the previous studies' approaches on calculation of MTTA (mean time to attack) [16,17] and the proposed approach on MTTC Cyber . This study models attack and defense times incorporating with uniform distributions. To begin the calculation process, let X i n and X i s denote normal attack and smart-attack time needed during ith phase of cyber intrusion for attack and smartattack agent, respectively. Therefore, the total attack time equals to the normal attack time plus smart-attack time of each phase. In this study, corresponding attack intervals are selected from uniformly distributed random numbers. Time range and density functions can be expressed by (3)- (5): As described in (4) and (5), τ a, i , τ a, i max and τ s, i min , τ s, i max are utilised for lower-upper boundary limits of X i n and X i s in each phase, respectively. Whereas X i n and X i s refer to the total operation of attack times of normal operation and smart operation, respectively, Y i refers to the detection time of the cyber intrusion during the ith phase for detection agent. To select appropriate time intervals for Y i , the uniform distribution function is applied in this study. The Y i detection time interval is chosen as τ s, i min , τ a, i max for each cyber layer. In each phase of the system, relation on determination of successful attack intrusion and detection probability is presented in (6): As stated in (7), the probability of successful detection, where P Y i < X i n + X i s , is computed by using conditional probability theorem. While the probability of successful detection at each phase of the system is as in (8), waiting (sojourn) time W i at each phase of the system is referred to (7)) The procedure of MTTC Cyber depends on the study of queening theory, that is, predicting waiting time and queue lengths [23]. Thus, the semi-Markov model ( Fig. 2) (1) is constructed with intrusion path calculation procedure steps of the MTTC Cyber . In addition, after identification of time boundaries of each cyber layer, waiting time (W i ) (8) at each phase is calculated for the transient state by the help of calculation steps of [16]. Due to different boundary limits in our approach, the final formula of waiting time (W i ) (8) differs than [16]. First, the final canonical form of transition matrix of K is presented as similar as in [16,24]. It (K) is written as: where T represents state transition probabilities that [23] demonstrates state transitions of the presented model for smart grid, and sub-matrix C refers to transition probabilities between the cyber-layers. Secondly, combining (1)- (8) and (9), MTTC Cyber is finally calculated as in (10): where N i is expected statistical number of times in i transient state phase that the system reaches failure state finally. It is written as in (11): (11) where q i denotes the probability of the process starts from state i. It is assumed that the initial status is the secure state. As explained previously, the calculation process of MTTC Cyber needs to be carefully examined due to disparities (time intervals, severity of layers etc.) between each cyber/system layer characteristics. Taking into consideration of these disparities, security of each cyber layer could be quantified more accurately with this process. We assumed that each layer behaves differently against cyber intrusion during the process due to future characteristics of smart grids. Each layer could have a different impact on the statistical calculation of MTTC Cyber . For this reason, the calculation process of cyber intrusion probability (P Cyber-attack ) is carefully examined with the effect of MTTD Cyber .
As far as MTTC Cyber is concerned, MTTD Cyber plays an essential role when evaluating P Cyber-attack as well as cyberphysical system reliability. It is important to highlight that the system will remain in the failure status in a certain amount of time until the detection agent catches the attacker. In this study, detection time denotes detection time plus recovery time of the system. Therefore, it is necessary that detection time (MTTD Cyber ) identification for P Cyber-attack calculations is essential. This unique value could change according to attack type, frequency, strength and severity of layers etc. As previous studies stated in [17,18], there is no available real data for detection time. These studies [17,18] utilise a constant number for MTTD Cyber , which should be a different statistical value in each system. For this reason, the mean detection time needs to be determined according to a statistical analysis of the detection agent's capabilities. Within this target, our study investigates the fundamental behaviour of the detection process and the underlying distribution of detection time. There is a large volume of published studies describing the role of intrusion detection in the context of computer science. Intrusion detection studies are mainly classified into two types: misuse and anomaly detection [25,26]. As the aim of the attacker could be the energy theft from consumers with false data injection, the study considers it as an anomaly detection of the detection time. In the anomalybased detection mechanism, the intruder can only be detected if it acts in a different way compared to legitimate behaviour of the system. Thus far, several studies have indicated that the intrusion detection process could obey heavy-tail distribution characteristics [27][28][29]. Heavy-tail distributions are probability density functions and their tails are not limited by an exponential distribution. The results in [28] show that detection time follows the heavy-tail distribution. Sampling path of a heavy-tailed featuring system reduces slowly, and its efficacy falls over time. Therefore, heavy tail distributions have been utilised for sampling of many extreme events such as floods, tsunamis etc. Since cyber-attacks are considered as rare and extreme events and they are less extreme over time due to not being anymore as unseen threats [27,29], the marginal distribution of intrusion detection times may follow a heavy tail pattern. On the other hand, some previous studies confirmed the effectiveness of Gaussian distribution on the intrusion detection process [30,31]. As in [32], a system error is assumed to follow a normal distribution. Yu et al. [32] confirmed that manipulated data may pursue Gaussian distribution if the adversary has information on the detection technique. As a result of many variables and uncertainties in the relation of adversary and detection, the statistical value of MTTD Cyber is considered as a random number. By using MATLAB, these random numbers are determined from a pool that has a specific range and distribution technique. MTTD Cyber is carefully chosen from the following pool with pre-defined distribution: rand p randn gprnd stblrnd (12) For this study, heavy tail (General Pareto, Stable [33], Pareto distributions) and Gaussian distributions are utilised for the selection of MTTD Cyber in each case. Having discussed how to calculate MTTC Cyber and MTTD Cyber , the following section of this paper addresses the component-based reliability model for the heating system.

Component-based reliability modelling for heating system
The study utilises a common implementation model of a heating system in a power grid to compute composite system availability with piecewise element consideration [34]. By doing so, the heating system model is divided into three sub-sections as in Fig. 4. It consists of a control panel ( λ C , μ C ), HP and auxiliary heater with switch ( λ H , μ H ), and storage ( λ Str , μ Str ) as a series system, respectively. This system is modelled with the eight-state Markov transition matrix (14) if there is a successful cyber-intrusion. Whether there is a cyber-intrusion, availability calculation takes consideration of four-state Markov model (13) that involves subsections 2 and 3. The sub-section 1 of the heating system is considered as a control panel that has a capability of two-way communication and stores consumer reading data. Its statistical value of failure-recovery against cyber-intrusion plays a key role for availability analysis of all systems. For this purpose, we introduce P Cyber-attack calculation in previous parts. By means of P Cyber-attack , the study estimates λ C , μ C composite availability analysis of the cyber-physical system. Following that, the sub- section 2 is composed of HP (λ HP , μ HP ), switch ( λ Switch , μ Switch ) and auxiliary heater (λ AH , μ AH ). In addition, estimated availability of HP is determined with its internal elements that includes an evaporator λ Eva , μ Eva , compressor λ Comp , μ Comp , condenser λ Cond , μ Cond , and expansion valve ( λ Evalve , μ Evalve ) as a series internal system. One of the generic HP models [34] is demonstrated in Fig. 5.
Once the reliability of internal components of HP is computed, a series arranged auxiliary heater with switch must be involved in reliability calculations by (19)- (21): After completion of reliability calculation of series arranged components (λ HP , μ HP − λ AH Total , μ AH Total ), the parallel arrangement of estimated failure-repair rates is used to reach the final calculation of (λ H , μ H ) via (22)- (24): The final sub-section is assumed as heat storage of which the failure and repair rates are denoted by λ Str , μ Str , respectively. Taken together all, piecewise reliability calculation will incorporate the Markov model of heating system to compute the system availability at a top down level.

Composite system availability analysis for heating system with cyber-physical component
In this study, a framework is presented to calculate overall system availability, and it is an indicator of system reliability. Four-state (M 4 ) and eight-state (M 8 ) stochastic transition matrices represent system state probabilities. To determine and simplify these system state probability vectors [36] and Markov transition matrices are modelled in (25): where v represents the eigenvalues of the transpose matrix of M, vī s the eigenvectors of the transpose matrix M and S denotes a constant that is calculated according to the initial system state.
In general, the system availability is evaluated as one of the factors for reliability determinant. It can be defined with all the probability states. Availability and unavailability of the system can be represented by operational and non-operational system states of probabilities, respectively. They are written as in (26): To calculate S 1 , …, S n constant values for availability calculation, considering the system at t = 0 is in the fully-operational state P 1 t = 0 = 1; P 2 t = 0 = 0; ⋯; P n t = 0 = 0, is expressed as in (27):

Fig. 5 Generic HP's components
The solution for any n-state Markov chain is given as in (28): P 1 (t) = S 1 n 11 e n 1 t + S 2 n 12 e n 2 t + ⋯ + S n n 1n e n n t P 2 (t) = S 1 n 21 e n 1 t + S 1 n 22 e n 2 t + ⋯ + S n n 2n e n n t ⋮ ⋮ ⋮ ⋱ ⋮ P n (t) = S 1 n n1 e n 1 τ + S 1 n n2 e n 2 t + ⋯ + S n n nn e n n t . (28)

Power system reliability assessment in a smart grid environment
This study has considered composite-system availability as a factor of power system reliability analysis with cyber-intrusion effects. If there are external effects on a power system from the latest system drivers which could be a control panel of heating system, then traditional power system reliability analysis should evolve to assess the impact of these cyber-physical components of the control panel.
It is considered that the control panel of the heating system is linked to smart meters. System designers and decision-makers of power grids generally examine the operational reliability even if there is not a cyber-intrusion through a heating system. On the other hand, regular assessment can help to avoid system losses and large system disturbances. Composite system availability analysis and its reliability calculation procedure are described in Fig. 6 and its steps are given as follows: i. Select the relevant reliability data for each component of the heating system, generators, transformers, lines and power system components and then determine the HP pool profile and time intervals for each cyber-layer transitions. ii. Randomly select a day and an HP user for initiating an HP load profile. iii. Extract HP load for time t from the selected profile and initialise the number of intrusion attempts. iv. Model MTTC Cyber and MTTD Cyber with given time intervals for each cyber-layer transitions. v. Check the number of successful cyber-intrusions within 100 attempts (assumed number) in time t. This process is described as in (29): where F Cyber denotes number of successful cyber-intrusion attempts within 100 attempts and r is a random number. F Cyber is a function that helps to estimate failures of the cyberphysical system. Initial condition of successful cyber-intrusion attempt A succesful is set to zero. If a success of an attempt is larger than r, A succesful is increased. Failure rate of the control panel is expressed as λ C = 1/ A succesful for time t. vi. By constraining as r < P Cyber − attack , the relevant stochastic transition matrix is determined. vii .
According to the identified transition matrix, calculate updated failure-repair rates of heating sub-systems as described in Section 2.3. vii i.
Then, compute the eigenvectors and the eigenvalues of the system as in Section 2.4. ix. Build relevant composite system availability function at time t.
x. Quantify availability function according to the system state. xi. The study assumes that a target of the attacker is to manipulate data on the control panel readings. If the attacker has successfully intruded into the control panel, the attacker transforms the original load data of HP and increases meter reading into the unavailability level (%) of the system at time t. xii .
Re-generate HP load value and re-produce it for time t. Next, extract re-generated HP load profiles. xii i. Select the physical system state randomly.
xi v. Perform power flow considering power balance with voltage limits as a constraint. xv. If the solution is not converged, go to the step xi. xv i.
Compute load curtailment of the whole system. xv ii. Estimate the expected energy not supplied (EENS).

Case studies and analysis
The aim of the case studies is to investigate how cyber-intrusion on HP systems affect power system reliability considering different attack-detection time distributions. To investigate its effects on power system reliability, two 'what if' scenarios are implemented. Scenario 1 reflects how cyber manipulation on the electricity usage of each HP user can affect system reliability with different detection time distributions. Scenario 2 reflects continues-time range effect of cyber-intrusions on HP systems which is different from scenario 1 where discrete-time range effect of cyberintrusions on peak times are considered. In this section, the case studies are performed with Roy Bilinton Test System (RBTS) [37]. The RBTS consist of 6 buses that include 11 generators and 9 power transmission lines. The voltage at the power distribution system was 11 kV and HP sites operate at 400 V. The total installed generation capacity and peak load are 240 and 185 MW, respectively. The RBTS topology is extended with 100 HP users (Fig. 7). They are integrated on Buses 2 and 3. Although there are different HP capacity sizes, we assumed the nominal rated capacity of a utilised HPs is 5 kW considering the weather conditions in London, (UK).

Input data for cyber-intrusion process in smart grid
This part describes the data utilised for reliability assessment. The reliability assessment framework of a heating system in Section 2 incorporated the data are given in Table 1 and the data is sourced from [38]. Time intervals for calculating MTTC Cyber are randomly selected from Table 2 for each phase. The study assumed that each cyber layer has its own time characteristic and the capability of an attacker will have a different approach on waiting (sojourn) time. HP load profile data is sourced from the open-source in [39]. This data consists of HP load profiles of 19 customers over a month during the heating season in 2014. The study only uses HP load data of ten customers for re-generating HP load profile. Utilised HP data has been randomly selected from 350 HP load profile samples of the data pool.

Scenario: 1 cyber-attack on HP during the peak times
The aim of an attacker is to malfunction an HP user site and manipulate electricity usage of each HP user. This scenario does not only help compares different detection time distributions but also demonstrates the attacker's behaviour on the manipulation of HP load and its disparity compared to the peak time of electricity consumption. It is essential that 'same original HP load profile' is necessary to be incorporated in all figures to show readers a clearer distinction in load difference in each time interval during the cyberintrusion, attack timing effects on load manipulation and calculation of EENS. Attacked HP site includes 100 users in total. Due to not being caught by the system operator, hacker affects the operation of HP during the peak times with 20-min intervals. The objective of the scenario is to investigate what happens on the system reliability if a cyber-attack can intrude a heating system in a small discrete-time range during the peak hours. According to original HP load profiles, the peak hours are divided into two parts: morning (03.00-09.00) and night-time (18.00-22.30). The detection-recovery time calculations are developed with four different distribution techniques for this study. The availability calculation of heating system relies on random number generation of detection time by means of following distributions: A-General Pareto, B-Gaussian, C-Pareto, and D-Stable. Fig. 8 shows a comparison of aggregated original HP load profile and HP load profile with cyber-intrusion in consideration of different distributions of MTTD Cyber . As can be seen from Fig. 8, the main character of the threat's impact is to increase the load demand of HP during morning and night peak times. Increment on utilised electricity in each aggregated profile follows a slight change. There is a clear and discrete increasing trend of electricity utilisation roughly 0.1-0.3 kW during peak hours. This is because of the unavailability ratio of the heating system as a result of an attack. Figs. 8a and c follow a similar pattern and the peak load demand reaches around 2.5 kW. On the other side, aggregated HP load profiles with Gaussian (Fig. 8b) and Stable (Fig. 8d) distribution random numbers have a higher peak (2.9 kW) than Pareto distributions related HP load profiles. It appears that the impact of intrusion on electricity consumption remains in a low-level of increase for all the experiments. Fig. 8 illustrates some of the main impacts of the discrete-time cyber-intrusion on power system reliability. What stands out in Table 3 the is that increment on EENS is in a slight change for all the experiments. In all cases, disparity range of EENS between affected and original HP load profiles changes between 6.459 and 35.407 MWh/year. Fig. 8 shows a comparison of aggregated original HP load profile and HP load profile with cyber-intrusion in consideration of different distributions of MTTD Cyber . As can be seen from Fig. 8, the main character of the threat's impact is to increase the load demand of HP during morning and night peak times. Increment on utilised electricity in each aggregated profile follows a slight change. There is a clear and discrete increasing trend of electricity utilisation roughly 0.1-0.3 kW during peak hours. This is because of the unavailability ratio of the heating system as a result of an attack. Figs. 8a and c follow a similar pattern and the peak load demand reaches around 2.5 kW. On another side, aggregated HP load profiles with Gaussian (Fig. 8b) and Stable (Fig. 8d) distribution random numbers have a higher peak (2.9 kW) than Pareto distributions related HP load profiles. It appears that the impact of intrusion on electricity consumption remains in a lowlevel of increase for all the experiments. Fig. 8 illustrates some of the main impacts of the discrete-time cyber-intrusion on power system reliability. What stands out in Table 3 is that increment on EENS is in a slight change for all the experiments. In all cases, disparity range of EENS between affected and original HP load   profiles changes between 6.459 and 35.407 MWh/year. Results suggest that Bus 3 is more impacted than Bus 2 in the context of reliability performance. General Pareto and Pareto distributions follow very similar patterns too. However, unavailability rate of the heating system with these distributions is higher than Stable and Gaussian methods of both buses. It is apparent from results that unavailability rate of heating system with stable distributiondetection time technique is less than other techniques for both buses. It means that the performance adaptation of stable detection time on this cyber intrusion process is slightly better than Gaussian detection-time method and others.

Scenario 2: cyber-attack on heat pump all day along
In this scenario, the target of the intruder is to disturb HP consumers continuously and re-shape the data by making unavailability of the HP system. The number of HP users and detection-recovery time methods are the same as in scenario 1. Fig. 9 presents an overview of the aggregated original HP load profile and HP load profile with continues effect of cyberintrusions. Compared to scenario 1, it can be clearly seen in Fig. 9 that there is some amount of electricity rise on HP load demand with each detection time method. This increase trend varies between 0.15 and 0.4 kW for each aggregated HP load profile. After the cyber-intrusion on HP user site, the peak HP load reaches almost 3 kW in all cases, except in Gaussian detection-time method. As shown in Fig. 9b, the peak load hits on 3.1 kW in the afternoon. The most striking result to emerge from both Figs. 8 and 9 is that there is another peak time for this HP site, which is at around 13.00-14.00. It is because of the size of the data pool and the increment can be decreased. Table 4 gives EENS changes in between aggregated original HP load profile and HP load profile with cyber-intrusion. Table 4 also gives different detection-time distribution effects on system reliability. EENS disparity ranges are in between 76.366 and 161.703 MWh/year. It is apparent that EENS disparity range is much higher than scenario 1 for both buses. Nevertheless, Bus 2 is more impacted than Bus 3 in the context of the impacts on reliability performance. The reaction of both general Pareto and Pareto distribution-related detection time method on EENS changes is similar as in scenario 1. However, General Pareto and Pareto distributions have a better EENS performance on detection time compared to others. These depict that unavailability of the heating system with Pareto distribution is less than other methods. The results also suggest that General Pareto detection time technique on cyber intrusion process provides better performance in calculating the reliability of the system. These results suggest several outcomes. At first, performance efficacy of detection time technique can rely on the discrete or continuous impact of cyber-intrusions due to the number of iterations of detection time in the analysis. A higher number of iterations increases the performance of Pareto distribution on reliability assessment framework and reflects less

Future works
This study is set out to investigate reliability levels of cyberphysical interactive operation of power systems with HPs. Further investigations, using a broader range of detection modelling, could shed more lights on the security of cyber-physical power systems. A greater focus on cyber-security of energy-sucking components of power systems such as temperature sensors of heating, ventilation, and air conditioning and communication sensors of vehicle-to-grid could help to understand interactions with power system operational security. Additionally, future research could also investigate closer links between vulnerability-reliability and resiliency of smart power grids with extensive cyber-attacks which cascade effects through multiple appliances connected at active customers.

Conclusion
A composite approach for cyber-physical interactive operation with HP systems is proposed with detailed features of cyber-intrusions. The studies justified the effectiveness of the approach for quantifying the cyber-intrusion impacts on power systems. Sensitivity analysis framework of cyber-intrusion detectiontime distributions on a cyber-physical interactive power system is also proposed as an extension to the approach to justify the effectiveness models to estimate mean time to detection for cyberattack (MTTD Cyber ). Heavy tail distribution applied in the detection-time calculation validated the effectiveness of the models. Investigations further suggest that cyber-intrusion effects on heating systems could bring a considerable impact on the operational reliability of a smart power system.
The proposed approach could serve modern power system engineers to plan and operate their systems considering cyberphysical interactive operating conditions and to plan remedial actions based on prevailing impacts.