Cyber defense analysis of smart grid including renewable energy resources based on coalitional game theory

2.1 Wind turbine model

Wind power depends on several factors like speed of wind, wind direction and location, but the main factor is wind speed. Wind speed for any wind farm is time varying. There are several methods for modelling of wind speed [19].

Wind power simulation, v _t is derived as Equation (1) [20]: v t = μ t + σ t × y t(1)

The μ _t is the mean value of recorded wind speed in hour t and σ _t represents standard deviation. The output power of a wind turbine generator P _W (v _t ) could be formulated as a nonlinear function of wind speed. P W ( v t ) = { arraycolsep = 3 pt 0 v t < v ci av t 3 + bv t 2 + cv t + d v ci ≤ v t < v r P r v r ≤ v t < v ∞ 0 v t > v co(2)

In Equation (2) v _c i, v _r and v _c o indicate of cut in wind speed, nominal wind speed and cut out wind speed respectively. P _r is nominal power, (a, b, c and d) are the parameters which should be defined by the factory [21, 22].

Power from photovoltaic mostly depends on sunlight and temperature. The temperature impact in solar power generation is normally modeled as a nonlinear relation. Solar radiation data is used to determine the probability distribution of the photovoltaic characteristics. Photovoltaic output power is related to location of PV arrays [23]. Photovoltaic cell produce current I as Equation (3). I = I PV - I 0 [ exp ( V + R S I ) / - ( ( kT / - q ) a ) - 1 ] - ( V + R S I ) / - R P(3)

Where V and I are terminal voltage and current of the solar cell. I _P V is produced current by sunlight, I₀ stands for leakage current in diodes, R _S and R _P series and parallel resistances of the equivalent circuit, q denotes electric charge (1.60217646 * 10–19C), k is Boltzmann constant (1.3806503 * 10–23), T shows p-n junction temperature and a is an ideality factor of the diode. The output power of solar cell will be calculated by Equation (4) [24]. P solar cell = V [ I PV - I 0 [ exp ( V + R S I ) / - ( ( kT / - q ) a ) - 1 ] - ( V + R S I ) / - R P ](4)

CHP as a clean and effective approach for heat and electricity production has benefits such as increasing efficiency, reduction of air pollution, reliability improvement. Natural gas, biomass and biogas as a clean energy resources can be used in CHP. Total efficiency of CHP is calculated by Equation (5) [25]. η CHP = 3.6 E Gen + T Gen l fuel × LHV fuel(5) where:

E _Gen : the total yearly electricity generation (kWh/yr)

T _Gen : the total yearly thermal generation of generator (kWh/yr)

l _fuel : the total yearly fuel consumption level of CHP generator (kg/yr)

LHV _fuel : the lower heating value of fuel

Attackers may provide more computational resources and advanced attack tools by allocating sufficient money. The probability of a successful attack on a system depends on the cyber defense equipment. A probability function shows the relationship between attacker and defender [26, 27]. It is assumed that there is N target (MG _i microgrid). The attacker has a total budget for attack (BA) and the defender has a total budget for defending (BD) to protect the system under attacks. The probability of a successful attack is calculated with the assumption of allocating BA and BD to N target. P i ( A i ) = 1 - e - λ i A i 0 < P i ( A i ) ≤ 1(6) where A _i is the attack resource dedicated to target i by the attackers (i.e. the budget or the amount of investment for attack) which shows the level of attacker’s capabilities. λ _i is the vulnerability factor that shows the level of difficulty of the attack and will be designated by the defense and countermeasures relating to each stage of the attack. The probability of a successful attack depends on the defender vulnerability. Such vulnerability is decreased by the defender investment (i.e. increase of D _i ) and is modeled by the below equation: P i ( D i ) = e - α i D i 0 < P i ( D i ) ≤ 1(7) where D _i is the least defense resources allocated to target i and α _i is the vulnerability factor. The joint probability of successful attack for any target is a product of Equations (6 and 7). P i ( A i , D i ) = ( 1 - e - λ i A i ) ( e - α i D i )(8)

Overall relation of risk for any target is calculated based on Equation (9). R ( A i , D i ) = ∑ i = 1 N P i ( A i , D i ) . d i = ∑ i = 1 N ( 1 - e - λ i A i ) ( e - α i D i ) . d i(9) where d _i is consequence or the impact on the target i while an attack is done successfully. N is the number of targets covered by attackers. Risk R (A _i , D _i ) may change by the amount of attack resource A _i or defense resource D _i . The optimum allocation of resources of attackers and defenders is derived by Equations (10–12). D i min [ A i M a x R ( A i , D i ) ] = D i min [ A i M a x { ∑ i = 1 N ( 1 − e − λ i A i ) ( e − α i D i ) } . d i ](10) ∑ i = 1 N A i = BA , A i ≥ 0(11) ∑ i = 1 N D i = BD , D i ≥ 0(12)

Threats belong to cyber-attacks have been increased due to more communication and telecommunication. Microgrids have potential for cyber-attacks based on their type and location. There are some methods for improving the security level of microgrids.

Control Panel of each generator in microgrid includes a monitoring and control unit with display screen and operation keys. The configuration operation of each generator can be done through a control panel, as well as access to the instantaneous operation and measuring values. It is assumed that the attacker will be able to reach directly to the control panel by bypassing the cyber defense like firewalls.

3.2 Attack on local control LAN of a microgrid

The attacker tries to intrude to the microgrid workstation in the control room. When the attacker successfully penetrates to the control room with the bypassing of default cyber defense program, the application and communication server could be cracked. Then the attacker sends fake trip commands to generators of microgrids.

3.3 Attack on the communication link of microgrids

The communication link between the LAN of control center and LAN of local control of microgrids as well as the links between generators are good opportunities for attackers. The attacker may inject false command to the communication link. Traffic patterns are detected by traffic monitoring and communication link analysis.

3.4 Attack on the control center LAN of microgrids

The attacker may penetrate to the user interface with the highest access and would be able to use the console to discover the network data. Similar to other scenarios, the attacker will be able to send commands to open the breakers [31].

3.5 Access to Intelligent Electronic Device (IED) of each microgrid

A successful crack of password and access to IEDs in any microgrid enables the attacker to have access to the microgrid configuration, such as single line diagrams, communication network and IED schemes.

4.1 Non-cooperative model

A weighted directed graph, G (N _M , ɛ _M ) is considered where N _M is the nodes quantity and ɛ _M is the edge of the graph. Each node shows a microgrid and any connection between microgrids represents a type of dependency. Impact of i node on j node is given with e _ij . For each edge, there is a weight y _ij ∈ R which shows the link strength between the mentioned nodes. These weights are defined by the matrix W ^M ∈ R^N×N in Equation (15). W ij M : = { 1 if i = j , y ij if e ij ∈ ɛ M i , j = 1 , … , N 0 Elseways ,(15)

Which 0 < y _ij < 1 is the impact degree of microgrid i on microgrid j and the e _ij is the edge between microgrids. Therefore, the investigated distribution network is connected to the main grid via a substation and also is connected to a grid of N renewable microgrids [32]. Figure 2 shows the method that the cyber intruders use to attack lead to blackout a part of a microgrid. OPEN IN VIEWER

The important points for microgrid security are:

The placement of each microgrid in geostrategic areas such as borders, islands, regions far from urban centers and areas with critical loads make them prone to cyber-attacks.

The security resource vector of all the microgrids is D : = [BD₁, BD₂, …, BD _N ] which could be used for defense against security threats and A : = [BA₁, BA₂, …, BA _N ] is the threat vector of microgrids. Therefore, effective security resources of each microgrid i ∈ N are ((W ^M ) ^T . D)) _i . For any microgrid i ∈ N with its own threat and effective security, utility of that microgrid could be expressed by Equation (16). v ( { i } ) = p ( ( W M T . D ) i ) - c ( A i )(16)

The functions p (.) and c (.) are profit of resources and threat cost in each microgrid i respectively.

Usually, coalitional game theory is utilized to investigate microgrid cooperative behaviors [33]. A coalitional game is defined as (N, v) in which N is the set of players and v : 2 ^N → R is a function for any coalition S ⊆ N. v represents the total benefit which is obtained by any coalition. In order to construct a coalitional game between MGs for any coalition S ⊆ N, it should be defined the value function v (S). A simple scenario for attack on the microgrids when coalition of microgrids is surveyed can be considered. This approach is applied to achieve appropriate utility and optimized defense budget [33]. Microgrids can be make cooperative groups (i.e. coalition) to improve the security resources (i.e. optimal defense budget) and to reduce effective threats. The matrix W ^M is defined in Equation (17) for a coalition S ⊆ N and two section i, j ∈ N. W ¯ ij M : = { arraycolsep = 3 pt 1 if i = j , W ij M if i ∉ S or j ∉ S , i , j = 1 , … , N f ( W ij M ) if i , j ∈ S ,(17) where f ( W ij M ) ≥ W ij M is the cooperation improvement in positive effect when i and j be in the same coalition. Equation (17) shows that two members of the same coalition can improve their cooperation based on f. In ideal condition, any coalition of microgrids may maximize the positive effects of cooperation, therefore f ( W ij M ) = 1 ∀ i , j ∈ S . When coalition is formed, in spite of the whole benefits, the cost will be imposed due to particular cultural, social and economic reasons. Thus, it is obvious that there are many friction between several microgrids with several aspects. In order to model the friction between microgrids, a friction graph, F (N, ɛ _F ) is introduced which N is set of microgrids. The effects of friction graph have been formulated in a friction matrix F which F is an N-by-N matrix. Every element of such matrix has a real value r _ij > 0 which defines the degree of friction between sections i and j as Equation (18) [34]. F ij = { arraycolsep = 3 pt r ij if e ij ∈ ɛ F and i ≠ j 0 Otherwise(18)

A cost function e (F, S) is defined based on friction matrix F and the degree of coalition S. By implementation this concept in the prospective of microgrids, there are microgrids with a suitable organization in comparison with the microgrids that do not have such an infrastructure thus strong microgrid should consider more cost for the coalition. While the organization is grown up, friction is normally increased. Therefore due to variety of idea, possibility of members’ cooperation will be reduced. It causes a coalition formed with few members. In most of real situations, the cost function of coalition S could be specified as a linear function of total friction and size of the coalition which is expressed in Equation (19) [35]. e ( F , S ) = { arraycolsep = 3 pt μ 1 ∑ i ∈ S ∑ j ∈ S F ij + μ 2 | S | , if | S | > 1 0 Otherwise(19) where F _i j is a component of friction matrix F extracted from friction graph F. The parameter μ₁ ≥ 0 is per unit cost of formation of a coalition with |S|>1 and parameter μ₂ is per unit cost of coalition size. Friction between two microgrids can be defined as the percentage of the total lost load due to coalition effective connection. Thus definition will be modeled by load shedding procedure that amount of forced load shedding is taken to account as main criteria. There are two essential factors for identification of load shedding value, firstly load types, secondly the vulnerability rate of cooperative microgrids from cyber-attack. Some loads are deenergized (i.e. load shedding should be applied) while the microgrid frequency drops to a value under acceptable limits [36]. A forecast of overload per unit L for load shedding modeling can be given as Equation (20): L = Total Load Demand - Total Power Supplied Total Power Supplied(20)

The total amount of demand which should be removed can be represented by LD index (in per unit) in Equation (21). For maximum value of L, LD keeps the frequency in an acceptable limit [37]. LD = L L + 1 - d ( 1 - f f n ) 1 - d ( 1 - f f n )(21)

Parameter d is a load reduction factor, f is the minimum allowable frequency and f _n is the rated system frequency. A new algorithm for elements identification of matrix F is presented in Fig. 3. According to this algorithm, it is assumed that in an attack scenario to a microgrid, the largest generation unit loses the supply in the worst case. OPEN IN VIEWER

In this condition, if microgrid i try to compensate part of lost load of microgrid j, the total amount of load shedding will be defined according to Equations 20 and 21. The values of F _ij are calculated based on the load ratio of each microgrid and load reduction factor. The cost is an incremental function of the total friction of graph F (N, ɛ _F ) and the size of the coalition |S|. Therefore, for any coalition S ⊆ N the value of characteristic function in coalitional game theory is stated byEquation (22): v ( S ) = p ( ( W ¯ M T . D ) S ) - c ( A S ) - e ( F , S )(22) where F is the friction graph.

The overall cooperation effective security resources can be written as Equation (23): ( W ¯ M T . D ) S : = ∑ i ∈ S ( W ¯ M T . D ) i(23)

The overall vulnerabilities and threats for coalition S is derived from Equation (24). A S : = ∑ i ∈ S A i(24)

To simplify the analysis, it is supposed in the rest of the paper that profit function p (.) and threat cost function c (.) are linear that v ( S ) = ( W ¯ M T . D ) S - ( A S ) - e ( F , S )(25)

The value function in Equation (25) is the maximum total utilities by each coalition S ⊂ N. In coalitional game, it is essential to introduce a rule which extracts the value of Equation (25) with the vector ∅ (S). The ∅ _i (S) is the utility of player i ∈ S or the share of MG i ∈ S in the total value v (S). Since the Equation (25) shows the paid cost by a coalition, i.e., a definite amount of money, can be arbitrarily divided between members that it introduce a game with Transferable Utility (TU). There are some fairness criteria (e.g. egalitarian fair, Shapley, nucleolus, proportional fairness and etc.) for sharing the utilities. In this paper proportional fairness (PF) is used for modeling of microgrid utility from Equation (26) [38–40]. Φ i = κ i ( v ( S ) - ∑ j ∈ S v ( { j } ) + v ( { i } ) )(26) where κ i κ j = v ( { i } ) v ( { j } ) , ∑ i ∈ S κ i = 1 .

As a conclusion, a new structural method for microgrids cooperation in accordance with the coalition game during a cyber - attack is suggested as shown in Fig. 4. OPEN IN VIEWER

According to the proposed algorithm, steps to determine the optimal coalition are as follows.

Based on practical approaches of cyber defense and Equations (13 and 14), the defense budget is calculated in each micro grid. It should be noted that the defense budget can be always considered more than the attack budget. Therefore, the attack budget also is estimated.

For a coalitional game with characteristic form and TU, the summation relationship for two coalition S1 and S2 is as Equation (27) [35]. v ( S 1 ∪ S 2 ) ≥ v ( S 1 ) + v ( S 2 ) ∀ S 1 ⊂ N , S 2 ⊂ N s . t . S 1 ∩ S 2 = ∅(27)

When merging of two coalitions in a network (or its microgrids) is beneficial, the Equation (27) expresses a quantified criterion.

Besides the great benefits of renewable energy resources, there is actually uncertainty in them. According to studies, the coalition and the combination of microgrids with renewable resources have the least uncertainty. Employing more microgrids with a combination of different types can result in minimum uncertainty. Basically, in the grand type of coalition, there is no any uncertainty [41]. However, according to using microgrids with limited size in our study, the terms of uncertainty has been investigated.

For this aim, in the case of using wind turbine power, it is essential to study the uncertainty of the wind speed. According to the Equations (1 and 2), the wind turbine output power can be determined based on the percentage of its rated power. Also in case of solar PV, the radiation characteristics of the sun can be obtained from a multimode probability model, and the output of the PV modules will be calculated. The PV output power can be attained according to the relation (3) and (4) which is based on the conditions of temperature and radiation of the sun. According to past studies and scenarios about uncertainties of renewable resources, it has been estimated that the deviation of the yearly mean power output from one 20-year period to the next has a standard deviation of 10% or less. Therefore, over the lifetime of a wind turbine, the uncertainty of the wind resource is not considerable [42]. In [43] uncertainty of the wind is considered about (8–10%). Also, different amounts of uncertainty have been estimated for PV resources. For example, the considered value for uncertainty in [44] is about (5% –17%).

Accordingly, the maximum uncertainty for the wind and solar resources is considered 20 percent in this paper. The average output power is considered equal to 0.8 of rated power. Consequently, the proposed coalition game theory method is analyzed with 20 percent as a maximum of uncertainty. Despite of the fact that uncertainty will be reduced in composition of microgrids, but the same value for uncertainty is also considered in the coalitionalgorithm.

Determination of matrix F based on proposed algorithm: There are two assumptions, firstly the largest generator of each microgrids will lose the supply after a cyber-attack, and secondly there is no priority for the loads. The other microgrid which should compensate the shortage in supply of the infected microgrid has no option except load shedding for a portion of its load. According to the proposed algorithm, load reduction factor can be determined with the assumption (f _n = 50Hz, f = 48Hz, LD = 0.2).

The results create matrix F that stands for different level of friction between microgrids. F = [ arraycolsep = 3 pt 0 1.52 1.74 1.82 0.52 0 1.03 1.38 2.4 2.78 0 5.2 0 0 0 0 ](29)

Table 2 summarizes PF criteria results for different microgrid combinations.

This table is arranged for unit price (μ₁= 500, μ₂= 100). The best dual coalition is the coalition between MG02 and MG03 which has more utility over other arrangements. In other word, the combinations with other microgrids do not obtain more utilities. It is observed that the combination of optimum state, i.e. S = {MG02, MG03} with the other microgrids e.g. {MG02, MG03} and {MG01, MG04} do not lead to significant increase of PF criteria. Triple combination of microgrids, also, does not bring about any increase. Therefore, the best coalition of the microgrids in case of the cyber-attack, is the coalition of microgrids {MG02, MG03}. It can be concluded to achieve more utility, two microgrids MG02 and MG03 should be formed coalition and there is no need for the coalition of MG01 and MG04. In this situation, the ability of the network against cyber-attacks will be increased. As shown in Table 2, coalition {MG02, MG03} represents the highest utility.

Figure 6 illustrates the total utility of optimal coalition in comparison with grand coalition and non-coalition state in relation to friction variation. This graph implies when the friction rate (μ₁) is increased, the maximum total utility and size of coalition will be decreased. For example, for μ₁ < 631, the formed grand coalition is optimal, it maximizes the total utility for the network. It is essential to emphasise that lower value for friction is not practical value, so formation of grand coalition rarely happens. For 631 ≤ μ₁ < 2860, desired coalition is set of MG02 and MG03. It is so crucial to understand that for the grand coalition of μ₁= 1500, the utility is only 24015 $ while optimized coalition has the utility of 36685$ which has 53% improvement of utility in comparison with grand coalition. OPEN IN VIEWER

In the values of μ₁ above 2860, optimal case is the situation that all microgrids remain non-cooperative.

The results of the calculations according to the considering uncertainties will be as follows. The calculated Friction matrix (F) is resultedbelow. F = [ arraycolsep = 3 pt 0 2.66 2.39 2.77 1.77 0 1.81 2.59 3.55 3.73 0 4.45 0.49 1.04 0.55 0 ](30)

Coalition payoffs and PF criteria result with considering uncertainty are shown in Table 3. As it can be observed, despite the change in the optimal amount of the coalition utility, the optimal coalition is {MG02, MG03}.

To validate investigated results, probability of attack simulation on optimal coalition microgrids {MG02, MG03} based on Equations (6–12) is carried out. This simulation is performed via given defense budget for each microgrids, by changing of the attack resource to a maximum resource level. The results for two states of non-coalition and coalition are illustrated in Fig. 7. OPEN IN VIEWER

Figure 7(a) depicts that in non-coalitional state, the attack probability to the micro grids 2 and 3 would be 0.13 and 0.34 respectively while the maximum assigned budget by the attacker is 2000$.

According to Fig. 7(b), and considering the same situation, the attack probability would be 0.13 and 0.37 with a budget of 4000$. Figure 7(c) and (d) illustrate that the attack probability in coalitional state yields a maximum of 0.15 and 0.19 for the budget of 2000$ and 4000$ respectively. Finally, comparing the results of simulation in Fig. 7 reveals that forming the optimal coalition would affect the enemy cyber-attack probability and wouldlimit it.

One of the other approaches to validate investigated results is using the LOLP reliability index. It has been prepared the method of Monte Carlo simulation (MCS). Simulation has been implemented for the optimal coalition of MG02and MG03.

Figures 8, 9 illustrate the LOLP for MG02 and MG03 before the coalition while Fig. 10 shows the LOLP of the coalition of MG02 and MG03. Figure 10 shows a significant reduction in LOLP in the optimal coalition mode. OPEN IN VIEWER

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Fig. 9

LOLP of MG03 in Non-Coalitional mode.

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Fig. 10

LOLP of MG02 and MG03 in Coalitional mode.