Load Shed Recovery With Transmission Switching and Intentional Islanding Methods After (N-2) Line Contingencies

Changing power system configuration may result in load shed recovery (LSR) because topology change can provide power flow control in meshed network. Some topologies may favor generation redispatch as compared to others and can eliminate line congestion which leads to LSR. One of the known methods for topology change is called transmission switching (TS) and research conducted in the past showed that TS is an effective means of mitigating load shedding. However, another method of topology control also exits and it is referred as intentional islanding (IIS). In this manuscript, we explore IIS as a potential solution for LSR. IIS based on generator coherency has been presented in literature for mitigating cascading failures. However, IIS has not been explored solely as a LSR mechanism. In this paper, we compare the LSR based on IIS with well known LSR algorithm based on TS. The comparison is performed for IEEE 39-bus system and IEEE 118-bus system. The results show that IIS has a potential to perform better than TS in terms of computational efficiency and LSR.

being used by industries on limited occasions [9], [26]. One 91 of the main reasons for its limited use is the complex or 92 computationally expensive algorithms proposed in literature 93 to find the best TS candidate for larger systems [26]. 94 Complete enumeration (CE), [9], or exhaustive search 95 method (ESM) [10] is one of the well known methods to 96 find the best TS candidate. This method involves switching 97 lines, one by one, one at a time to find the best TS candidate. 98 Fig. 1 shows a flowchart for CE/ESM. For understanding, 99 consider CE/ESM as a two step process, where the first level 100 (shaded green color) determines the list of unfaulted branches 101 that needs to be checked. The blocks shown in shaded color 102 (orange) represent the choice of either the ACOPF or DCOPF 103 formulation. Note that the CE/ESM algorithm is agnostic to 104 the choice of formulation. In the second step, the branches 105 from the list will be tested to find the best TS candidate with 106 minimum load shedding. Assuming that electrical power sys-107 tem is N-1 compliant, we consider non-trivial N-2 contingen-108 cies. Non-trivial contingencies are a subset of contingencies 109 that require load shedding even after generation redispatch. 110 Note that the proposed algorithm is valid for any N-k line 111 contingencies, where k = 1,2,3,..n. After detecting a non-112 trivial contingency, the algorithm removes/switches a line to 113 check whether load shedding is improved or not. This process 114 is repeated for all healthy lines in the system. Switching a 115 line that results in minimum amount of load shed is the best 116 TS candidate. An advantage of CE/ESM is the guarantee of 117 finding a TS candidate for LSR, thus making it the standard 118 base case for comparing newer algorithms [9], [10]. CE/ESM 119 performs well for small systems but for larger systems, with 120 a multitude of lines, the process of switching each line and 121 running DC optimal power flow (DCOPF) to find the best 122 TS candidate is computationally expensive and potentially 123 intractable in time. 124 In [11], a computationally less expensive mixed integer 125 program heuristic algorithm (MIP-H) is presented. But, large-126 scale test of MIP-H algorithm showed that it is not scalable. 127 Researchers in [10] presented a mixed-integer programming 128 model for AC power flows (MIPAC). MIPAC is a modifica-129 tion of an existing mixed-integer linear optimization model 130 called linear-programming approximation of AC power flows 131 (LPAC) model [27]. LPAC is computationally slower than 132 CE/ESM. When seeking the best single switching action for 133 IEEE 118-bus system, replacing CE/ESM by MIPAC resulted 134 in an average speedup of approximately 2.3 times. 135 In [13], researchers presented the limit branches TS 136 (LBTS) algorithm, based on line flow thresholds, which per-137 forms approximately 108 times faster than the CE/ESM for 138 the IEEE 118-bus system. Although LBTS is computationally 139 fast, results showed that it is capable of recovering only 5.2% 140 of load shed compared to CE/ESM after (N-2) line contingen-141 cies for the IEEE 118-bus system. In [12], authors proposed 142 the LSB max algorithm based on selecting the candidate for 143 TS using proximity to the load shedding bus where the most 144 load is expected to be shed after a contingency. The LSB max 145 algorithm performs approximately 22 times faster than the 146  In order to avoid cascading failures, IIS is utilized to stabilize 155 the system [7], [8], [28], [29]. IIS divides the power system 156 into smaller independent subsystems, which are disconnected  The IIS algorithms proposed in [28] and [29] to mitigate 163 cascading failures, focus on power system stability and are 164 based on generator coherency. We propose to divide the 165 power system into a pre-deterministic islands such that gen-166 eration is greater than demand, i.e., i∈N G P G i > j∈N D P D j 167 in each island, as explained in Section IV-C. Moreover, in this 168 work we develop four cases of creating islands to show that 169 specific topologies may result in different amount of LSR. 170 We leave the optimal method of creating islands for future predetermined islands as explained later in subsection IV-C. 174 We then find the total load shedding by summing the load 175 shedding in each island. The aim is to compare this total 176 load shedding in IIS case with the load shedding achieved 177 in TS case.

III. OPF FORMULATION FOR TS AND IIS
The electricity network is a set of N buses (or nodes) con-181 nected by a set of L transmission lines (or edges or branches), 182 with controllable generators G and dispatchable demand D 183 located at a subset N G ⊆ N and N D ⊆ N of the buses, 184 respectively. The operating cost of a generator is a function of 185 its active output power c i P G i where i ∈ N G [30]. The cost of 186 load shedding is given by c j P D j where j ∈ N D . The objective 187 is to minimize the cost of generation and load shedding. 188 DCOPF based formulation is given below: All variables are either presented as matrices or vectors. P G i is 197 the output of each generator and P D j is the power delivered at 198 each load. P D j is dispatchable load and is modeled as ''nega-199 tive generation'' with negative cost in the objective function. and constraints (4)-(7) remains unchanged. Additional con-216 straints are given below:   [11], our emergency 246 ratings are set to 125% of normal ratings. Table 1 shows the 247 details of the test systems used.

248
Authors in [38] removed the elements of the radial trans-249 mission system while using the IEEE 118-bus system in CL. 250 This was done as the system would not be considered as 251 N-1 compliant without the removal of the radial transmission 252 elements in the N-1 CL and these elements are not subject 253 to any standards of reliability as standardized by Federal 254 Energy Regulatory Commission (FERC). Hence, we consid-255 ered N-2 non-trivial line contingencies (L1 & L2) without 256 including the radial transmission lines for the same reason 257 mentioned in [38]. We developed a contingency list (CL) 258 based on DCOPF and ACOPF formulation. CL is a list of 259 contingencies that will overload the remaining components 260 of power system. Non-trivial contingencies is a subset of 261 CL that will result in nonzero load shed after a generation 262 redispatch [11].

263
Note that we only considered N-2 non-trivial line contin-264 gencies (L1 & L2). N-2 contingencies that involve generator, 265 i.e., G1 & L1 and G1 & G2, are beyond the scope of this 266 work. The reason of not including generator contingencies in 267 present work is that islands considered in this work are prede-268 termined and a generator contingency might impact the rule 269 on which islands are formed, i.e., i∈N G P G i > j∈N D P D j in 270 each island. Hence, forming optimal islands for contingencies 271 involving generators is left for future work. Table 2 shows the 272 non-trivial CL for the two test systems.

274
We divided IEEE 39-bus system and IEEE 118-bus system 275 into three pre-determined areas as shown in Figs. 7 and 4. 276 Note that division of these areas are not optimal but based on a 277 rule mentioned in section II-B, i.e., i∈N G P G i > j∈N D P D j 278 in each area. For IEEE 39-bus system, we modified the areas 279  Table 3. Similarly, the cut set used for IEEE 118-  Table 4.  islands where each island is equal to an area. Note that all 292 three areas have i∈N G P G i > j∈N D P D j . ''Islanding 1'' is 293 created by dividing the system in two islands, i.e., combining 294 area 1 and area 2 as one island while area 3 is considered a 295 separate island. Similarly, ''islanding 2'' and ''islanding 3'' 296 have two islands in each case as shown in Table 3. Transmis-297 sion line cut set in Table 3 shows which transmission lines 298 are required to cut to obtain the four cases of islanding. The 299 idea here is to show that different way of islanding a power    in Table 4. Transmission line cut set in Table 4 shows which 314 transmission lines are required to cut to obtain the four cases 315 of islanding.

317
As mentioned above, if there exists the best TS candidate, 318 the base case (i.e., CE/ESM) will find it. Hence, we assume 319 that the maximum LSR (i.e., 100%) is achieved by the base 320 case and we will compare the IIS algorithm with the base 321 case. Three solution metrics from [12], namely the percentage 322 load shed reduction (%LSR), the worst speedup (WS), and the 323 average speedup are used to compare LSR and computational 324 efficiency of the IIS algorithm with base case.

325
The idea is to see if IIS algorithm performs faster than the 326 CE/ESM, but should be capable of achieving the %LSR of 327 the CE/ESM. LSR in the CE/ESM and the IIS is given by 328 (15), where τ is ESM or IIS and (LS i ) is load shed during 329 contingency i where, i ∈ {CL}.               islanding topology is not optimal for every contingency. Simi-444 lar to finding best TS candidate, there is a need to find optimal 445 islanding for each contingency, and is left for future work.   Fig. 6 shows that, for DCOPF formulation based %LSR, 448 islanding A performed better than islandings B, C, and D. 449 Fig. 13 presents the contingency by contingency comparison 450 of islanding A with islandings B, C, and D. Out of 368 total 451 N-2 non-trivial L1 & L2 contingency cases, islanding A 452 recovered less load shedding than islanding D in 147 cases. 453 These results showed that islanding A is not the optimal 454 islanding topology for 147 cases. On the other hand, out 455 of 368 total N-2 non-trivial L1 & L2 contingency cases, 456 islanding A recovered higher load shedding than islanding D 457 in 40 cases. But, the difference in LSR between islanding A 458 vs. islanding D for these 40 cases is higher than compared 459 to 147 cases. That is the reason why the overall result for 460 islanding A is better than islanding D. Fig. 14 shows the violin 461 plot for the distribution of the difference of LSR achieved (in 462 MW) for the cases where islanding A performs better or worst 463 than islanding B, C, and D, respectively.    39-bus system is three times higher than the the DCOPF for-496 mulation based complete enumeration or exhaustive search 497 algorithm. The %LSR achieved by the DCOPF formula-498 tion based intentional islanding for IEEE 118-bus system 499 is 1.2 times higher than the the DCOPF formulation based 500 complete enumeration or exhaustive search algorithm. Simi-501 larly, the %LSR achieved by the ACOPF formulation based 502 intentional islanding for IEEE 118-bus system is two times 503 higher than the the ACOPF formulation based complete 504 enumeration or exhaustive search algorithm. These results 505 show that intentional islanding can be a potential solution 506 for load shed recovery with notable speedup. The speedup 507 of intentional islanding algorithm increases as we move from 508 smaller system to larger system which is a good indication 509 that intentional islanding based load shed recovery algorithm 510 is scalable. Comparison of the intentional islanding algo-511 rithm with existing TS algorithms showed the computational 512 superiority of the intentional islanding algorithm. In future, 513 we will use parallel programming to further increase the 514 achieved speedup.

516
The authors would like to thank Dr. Robert Fourney from 517 South Dakota State University for discussions on intentional 518 islanding during the course EE-692.   interests include different microgrid aspects, including power electronics, 750 distributed energy-storage systems, hierarchical and cooperative control, 751 energy management systems, smart metering, the Internet of Things for 752 AC/DC microgrid clusters, and islanded minigrids. Specially focused on 753 microgrid technologies applied to offshore wind, maritime microgrids for 754 electrical ships, vessels, ferries and seaports, and space microgrids applied 755 to nanosatellites and spacecrafts. He has published more than 600 journal 756 articles in the fields of microgrids and renewable energy systems, which are 757 cited more than 50,000 times.