Intrusion Detection System for Multilayer-Controlled Power Electronics-Dominated Grid

This article presents an intrusion detection system (IDS) for a multi-layer-controlled power electronics-dominated grid (PEDG). This IDS improves the situational awareness of PEDG against malicious set-points from a compromised upper control layer. Firstly, a mathematical theory is developed for deriving a safe operation region. This mathematical theory extends the stability margins inferred from $P-V$ curves to the abstract concept of morphisms. Particularly, there are two morphisms for each point of common coupling (PCC) bus when operating in the safe operation region: (Morphism 1) PCC bus voltage mapped to network set-points, and (Morphism 2) network set-points mapped to PCC bus voltage. Morphism 1 is used for anomaly detection. Explicitly, observation of a non-zero imaginary-part in the PCC voltage $L_{2}$ norm is evidence of an anomaly. Morphism 2 is utilized for independent decision making at the primary layer of the dispersed energy generator (DEG) during intrusion scenarios. Morphism 2 is an alternative for the secondary layer when the dispatched set-points are not trusted. The theoretical analysis is verified by several case studies to substantiate the situational awareness against malicious set-points and consequently enhancing the cybersecurity aspects of the PEDG.

INDEX TERMS Power electronics-dominated grid, safe operation region, intrusion detection system, situational awareness. 16 t

LIST OF SYMBOL
Time. τ Dummy intermediate variable for integrals. C DC i DC-link capacitor of the i th grid-feeding inverter.

L i
Filter inductor of the i th grid-feeding inverter.

R i
Filter inductor resistance of the i th gridfeeding inverter. ω Nominal angular frequency of the network. P i Active power of the i th grid-feeding inverter.

P Li
Active power of the i th grid-feeding inverter load. P PCCi Active power of the i th local PCC bus.

Q i
Reactive power of the i th grid-feeding inverter. 17 The associate editor coordinating the review of this manuscript and approving it for publication was Peter Palensky .

Q Li
Reactive power of the i th grid-feeding inverter load. Q PCCi Reactive power of the i th local PCC bus. S Rated Rated appeared power of the i th grid-feeding inverter. f SW Switching frequency of the i th grid-feeding inverter.

P Refi
Active power reference of the i th grid-feeding inverter.

Q Refi
Reactive power reference of the i th gridfeeding inverter. Z ij Line impedance between PCC bus i and j.

R ij
Line resistance between PCC bus i and j.

L ij
Line inductance between PCC bus i and j.  Error on active power of the i th grid-feeding inverter. e Qi Error on reactive power of the i th gridfeeding inverter. v Pi Active power control output of the i th gridfeeding inverter. v Qi Reactive power control output of the i th gridfeeding inverter.

K Ppi
Active power control proportional gain of the i th grid-feeding inverter.

K Qpi
Reactive power control proportional gain of the i th grid-feeding inverter.

K Pii
Active power control integral gain of the i th grid-feeding inverter.

K Qii
Reactive power control integral gain of the i th grid-feeding inverter. v Thi Thevenin voltage phasor seen at the i th local PCC bus. δ Thi Thevenin voltage angle seen at the i th local PCC bus. δ PCCi i th local PCC bus voltage phasor angle. V g Grid voltage peak.

A i
Real part of the i th local PCC bus phasor voltage. 19 B i Imaginary part of the i th local PCC bus phasor voltage.

R Thi
Thevenin resistance seen at the i th local PCC bus.

L Thi
Thevenin inductance seen at the i th local PCC bus. f Developed Morphism 1: Generalization of the inverse of the P-V curve. g Developed Morphism 2: Generalization of the P-V curve. h Ohm's law across linear resistor (R) as a morphism mapping current (i R ) into voltage (v R ). w Ohm's law across linear resistor (R) as a morphism mapping voltage (v R ) into current (i R ).

A CL i
Closed loop control of the i th grid-feeding inverter state matrix.
Closed loop control of the i th grid-feeding inverter states vector. P CL i Closed loop control of the i th grid-feeding inverter linear quadratic Lyapunov stability theorem P matrix.

Q CL i
Closed loop control of the i th grid-feeding inverter linear quadratic Lyapunov stability theorem Q matrix.
Lyapunov function of the i th grid-feeding inverter closed loop control. 21 The futuristic energy paradigm implicates high penetration of 22 nonsynchronous generation at the grid edge through embrac-23 ing dispersed energy generators (DEGs) [1], [2]. At the grid 24 edge, grid-feeding inverters are projected to be the prevailing 25 type of DEGs. In this mode of operation, the DEGs are 26 following the inertial response of the network and their capa- 27 bilities are confined in injecting/absorbing current into/from 28 their local point of common coupling (PCC) without con-29 sidering upstream network constrains and requirements [3]. 30 Accordingly, these DEGs are typically unobservable to the 31 upstream network and vice versa. Henceforth, real-time 32 system level coordination and management is crucial to 33 ensure the optimal utilization of unobservable DEGs that are 34 installed behind the meters and offer an additive situational 35 awareness to the system [4], [5].

36
The multi-layer-controlled power electronics-dominated 37 grid (PEDG) is demonstrating to be an effective exam-38 ple that is enabling DEGs to achieve the U.S. Depart-39 ment of Energy's 100% nonsynchronous generation based 40 U.S. power grid [6]. The  Energy is anticipated to be vulnerable to malicious cyber-53 attacks. This is because of the more dispersed generation that 54 will operate outside the realm of old-fashioned power-plant 55 administrative domain through employing more DEGs at the 56 grid edge [10], [11], [12], [13], [14]. The attack might be 57 introduced into the PEDG infrastructure through the com-58 munication medium that enables its harmonious operation.

59
Security breach in the cyber-layer of a PEDG has a direct 60 influence on its physical layer, which disrupts its nominal 61 operation. A severe stealthy cyber-attack typically spreads 62 throughout the grid steadily compromising the cyber layer.

63
This makes the detection of such a stealthy attack extremely 64 challenging at early stages using conventional protection and 65 intrusion detection schemes [15], [14], [16].  In fact, according [17], situational awareness feature offers 74 a direct improvement of the system cyber-security aspects.

75
As situational awareness does not only provide accurate 76 observation, but also ensures availability of necessary func-77 tions that support predicting operation projections and iden-78 tifying potential risks [18] In the literature, the capability of synchronous generator is 104 estimated through the concept of capability chart. This chart 105 provides the range of dispatchable PQ set-points without 106 jeopardizing the stability of the synchronous generator [19]. 107 The notion of capability chart was first time utilized for 108 multi-layer-controlled renewable based grid in [20]. This 109 capability chart was used as conventional generators capa-110 bility charts that are employed in scheduling and dispatch-111 ing optimization. In other words, set-points that belong to 112 the capability chart are guaranteed to be executable when 113 requested by the upstream network. Though, the capability 114 charts for renewable based grids are more complex compared 115 to conventional generators. This is because renewable based 116 grid capability charts are representing aggregation of vari-117 ous DEGs. An example of such capability charts is used to 118 estimate the reactive power injection capability at different 119 active power levels in [21]. Another work is suggesting a 120 methodology for approximating capability chart numerically 121 using repeated time domain simulations in [22]. In general, 122 the capability chart is obtained by repeated load flow solu-123 tions for various scenarios that often are selected randomly. 124 After that, the realistic load flow solutions consequence to 125 points that are constructing the capability chart. Another 126 approaches that are reported in the literature for approximat-127 ing the capability charts are employing geometrical hypothe-128 sis such as polyhedron, ellipse, and so on [23]. Furthermore, 129 capability charts estimation with incorporation of random-130 ness is reported in [24]. Yet, these methods extensively rely 131 on repetitive load flow solutions that needs to be executed 132 in secondary or tertiary layers, which even turns out to be 133 challenging to utilize fast load flow algorithms due to the 134 dominate resistive nature for the distribution network [25]. 135 Furthermore, the considered potential attack model, in which 136 the intruder is compromising the secondary layer controller 137 and existing load flow algorithms, mandates another sanity 138 checkpoint at the primary layer for realizing an effective 139 intrusion detection. Hence, to our knowledge, utilizing the 140 existing capability charts for intrusion detection against oper-141 ational PQ set-points manipulation is not viable from the 142 perspective of the primary layer. The contributions of this 143 paper are summarized in the following bullet points:

144
• A mathematical theory extends the stability margins 145 inferred from P − V curves to the abstract concept of 146 morphism. This morphism simplifies understanding the 147 operation limits of the unobservable DEGs without rely-148 ing on repeated load flow solution at secondary/tertiary 149 control layers, thus creating an independent framework 150 for decisions making at the primary layer.

151
• Intrusion detection by utilizing the SOR as a sanity 152 checkpoint for PQ set-points assignments by potentially 153 compromised secondary layer; thus, detecting and pre-154 venting a cyber intruder that is requesting malicious 155 set-points from the DEGs.   Consider the exemplification in Fig. 4 of the multi-layer con-200 trolled PEDG understudy shown in Fig. 1, if a stealthy cyber 201 intruder took control over the cyber layer and he is targeting 202 the i th local PCC bus in Fig. 4 by manipulating the operation 203 PQ set-points that are passing from the secondary layer to the 204 primary layer of the DEG. From the stealthy intruder perspec-205 tive, he is altering the operation set-points and observing the 206 local measurement to understand the impact of his set-points 207 manipulation. The intruder could initiate catastrophic effect 208 by pushing the targeted PCC bus to operate outside its stable 209 FIGURE 3. Grid-feeding primary control layer considered for DEGs in the PEDG: controller structure with measurements, nonlinear coordinate the transformation illustration, and the intrusion detection system. set-points domain by slowly and randomly changing the PQ 210 set-points [14]. Therefore, the hypothesis in this article is 211 that the primary layer will be equipped with the SOR, as a The structure preservation is not sustained when Morphism 234 1 is producing a non-zero imaginary valued L 2 norm. Then, 235 the decision that this anomaly is due to an intrusion or not is 236 based on authenticating the set-point passing for upper layer 237 into Morphism 2 (i.e., the generalized PV curve expressed in 238 (3)). is given by, where R Thi is the Thevenin resistance seen by the i th grid- Similarly, the Thevenin voltage is given by, To relate the local PCC voltage ( v PCCi ) to the dispatched PQ 287 set-points of the i th targeted grid-feeding inverter; the local 288 PCC current ( i PCCi ) can be written as (7). ence i th targeted grid-feeding inverter, P Li is the active power 295 load at the i th targeted local PCC bus, Q Li is the reactive power 296 load at the i th targeted local PCC bus, P PCCi is the net injected 297 active power at the i th targeted local PCC bus, and Q PCCi is 298 the net injected reactive power at the i th targeted local PCC. 299 Combining (7) and (4) results in (8).
The key point from reaching to (9) is that the left-hand side 306 (LHS) is all real valued terms. In other words, the imaginary 307 part is zero. This is an obvious resultant form multiplication 308 of the local PCC phasor voltage by its complex conjugate. 309 Thereby, (9) can be rewritten as (10).
Then, by equating the real parts of the LHS and right-hand 315 side (RHS) of (10); (11) is deduced.
Similarly, by equating the imaginary parts of the LHS and 319 RHS of (10); (12) is obtained.
For finding a solution for A i ; from combining (13) and (11) 330 this parametric quadratic equation expressed in (14) can be 331 solved.
98334 VOLUME 10, 2022 where 339 a = 1, Theoretically, equation (14) has two bifurcation solutions.  any operation set-points that satisfies v PCCi 2 / ∈ R is in 364 the UOR (see the proof in appendix D). Yet, these operation 365 regions cannot be utilized. As finding the Thevenin voltage of 366 the rest of the network requires repeated load flow solutions. 367 To extend this analysis to closed-form, the inclusion of 368 nearby PCC buses PQ set-points on the i th targeted PCC 369 bus is deliberated by finding the expression of the Thevenin 370 voltage in (6) as a function of all the other grid-feeding 371 inverters PQ set-points except the targeted i th grid-feeding 372 inverter. In fact, with such consideration the targeted PCC 373 voltage is expressed with a multi-dimensional manifold. 374 This process is repeated for every local PCC bus in the 375 network and then the intersection of all PCC buses SOR 376 is considered as the whole PEDG SOR (i.e., Morphism 377 2 expressed in (3)) Note that, Morphism 2 closed-form is 378 developed mathematically in the next subsection. Whereas, 379 Morphism 1 that is expressed in (2)) cannot be derived in 380 closed-form its R → R 2N mapping structure preservation is 381 measured through observing the imaginary-part of the PCC 382 voltage L 2 norm. The inclusion of nearby grid-feeding inverters (i.e., DEGs) 385 influence is determined by finding the closed form solution 386 of the Thevenin voltage depicted (4)- (16). To understand this, 387 an example is taken here of the PEDG network shown in 388 Fig. 5. This example can be extended to any network with 389 an arbitrary number of grid-feeding inverters. In this case, the 390 Thevenin voltage of the grid-feeding inverter at local PCC bus 391 2 is as (17), shown at the bottom of the next page. Then, this 392 Thevenin voltage is combined with (15) and (16)   Also, the voltage at main PEDG bus is a function of all PQ 399 set-points in the network and described by (19).
In this example, each PCC bus is five dimensional man-

422
Without loss of generality, let us consider Q PCC2 and 423 Q PCC3 are zero. Then, the realization of the different opera-424 tion regions for each local PCC bus in Fig. 5 is reduced from 425 a five-dimensional manifold to a three-dimensional surface 426 depicted in Fig. 8(a), (b) and (c) for each PCC bus. Let SOR 1 427 be the projection of the surface v PCC 1 on the P PCC2 and P PCC3 428 plane. Then, SOR for PCC 1 bus described by (20).

452
The network SOR ( SOR ) is depicted in Fig. 8  → R mapping; the set-points passing 480 from the secondary layer are disregarded and the grid-feeding 481 inverters are changing the set-points and monitor if the local 482 PCC voltage of the bus is regaining safe operation (i.e., 483 move the network to SOR).

484
The steps to generate the analytic expression of each PCC 485 bus in the single-phase PEDG as a function of all the network 486 DEGs' PQ operation set-points are as follows:   (15) and (16).    The challenge that might arise is what if finding the 513 Thevenin impedance or reduction of the impedance network 514 during each stage of superposition is non-solvable due to 515 network connection complexity. This can be elucidated with 516 using the general two point impedance theory introduced in 517 [26], [27] by using the network Laplacian matrix.

519
The theoretical analyses established are validated by simu-520 lation of two scenarios. In these two scenarios, the DEGs in 521 the multi-layer controlled PEDG network are rated according 522 to Table 1. Particularly, the inverters representing DEGs in 523 the PEDG are rated to 10 kVA, 60 Hz nominal frequency 524 operation, 10 kHz switching frequency, 420 V nominal DC 525 link voltage, and 0.5 mH filter inductor. These DEGs are 526 controlled in grid-feeding mode of operation through the 527 primary current control scheme illustrated above in Fig. 3. Now, for the scenario of the PEDG with seven buses that 560 is shown in Fig. 10, each local PCC bus is described with 561 eleven dimensional manifolds. Furthermore, in this scenario 562 initially the PEDG is operating in the SNOR of the network 563 (see Fig. 11 before time instant 0.3 s). All consumers DEGs 564 are meeting their local loads and not injecting any power into 565 their local PCC terminals. After that, power reversal occurs 566 at PCC2 and PCC3 after time instant 0.3 s in Fig. 11 due to 567 a manipulation by a cyber intruder at the secondary layer. 568 At this duration, the set-points 2 kW for PCC2 4 kW for 569 PCC3 belong to the SOR and the intruder fails to jeopardize 570 the network operation. Then, after 0.4 s in Fig. 11, PCC2 571 and PCC3 are pushed to unstable operation by the intruder. 572 This new operation set-point −5 kW for PCC2 and PCC3 573 are in the UOR and the intruder is successful to induce 574 an unstable operation. The IDS will alert the DEG that an 575 anomalous voltage is detected, then the DEGs are moved to 576 local primary control mode based on PCC voltage condition 577 to push the PEDG to the SNOR (see Fig. 11 after time instant 578 0.5 s). For this example, the local PCC buses and the main 579 PEDG bus eleven dimensional manifolds are described by 580 (28)-(33), as shown at the bottom of the page.

581
The SOR and SNOR of each PCC bus is described in (34) 582 and (35), as shown at the bottom of the page, respectively.
By differentiating equations (A.1) and (A.2), the state-space 644 model that includes active and reactive power as state vari-645 ables can be determined, loop of common coupling depicted in Fig. 1. Hence, the PCC 654 currents derivatives are as (A.5) and (A.6).
If the parameters K Ppi , K Pii , K Qpi and K Qii are designed 733 respecting the conditions shown in (A.26),

742
The Lyapunov candidate energy function is mathematically To retrieve the original system inputs which are the inverter The controller structure is illustrated in Fig. 3.
L 2 norm ∈ C ∈ C means singularity, which results in 775 non-existing stationary reference modulation indices (i.e., 776 no solution for (A.26)). Also, with no PCC voltage, measur-777 ing the active and reactive power by (A.1) and (A.2) for the 778 primary controller feedback will not be possible. Hence, these 779 unstable conditions will cause PEDG DEGs operation failure. 780 Hence, this proves that any instability witnessed in this PEDG 781 is originated from unstable network conditions and not from 782 the primary control layer.

786
A morphism is a structure-preserving map from one mathe-787 matical structure to another mathematical structure. In con-788 temporary mathematics, the terminology morphism is an 789 abstraction for any sort of mapping concept. For example, 790 in linear algebra, the linear transformation is a special type 791 In other words, morphism is a generalization of all map- holds. The theoretical proof behind having a none-zero imaginary 849 part in the L 2 norm of the local PCC voltage results in 850 concluding that the set-points belong to unstable operation 851 region (UOR) can be understood from the following exam-852 ple of Fig. 5    is no way to express the derivative of the i th PCC bus volt-880 age with respect to the j th PCC bus active power set-point.

881
Nevertheless, for a given network that is shown in Fig. 5 Fig. 5. Furthermore, this Morphism 2 is plotted in Fig. 13. 896 Specifically, the Morphism 2 structure preservation is not 897 sustained as seen in Fig. 13 after passing the set-point that 898 belongs to the UOR. Moreover, the stability margin can be 899 found in closed-form as in (A.43) for bus 3 with respect to 900 bus 2 of Fig. 5 network. now, P PCC2 value that makes ∂P PCC2 /∂ v PCC3 2 equal to 917 zero in (A.44) is the stability margin for bus 3 with respect to 918 active power change at bus 2 of Fig. 5 network. Unfortunately, 919 this involves polynomial with an order higher than 5, finding 920 the deterministic roots of this polynomial is not feasible. 921 This is proved by the fundamental theorem of Galois [28]. 922 Galois theory provides a connection between field theory 923 and group theory. This connection allows reducing certain 924 problems (i.e., polynomial roots finding for our case) in field 925 theory to group theory such as permutation group of their 926 roots. By Galois theory, it was proven that for a polynomial 927 roots' to be solvable by radicals and the main operations