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MATEC Web of Conferences 336, 05020 (2021) https://doi.org/10.1051/matecconf/202133605020 CSCNS2020

The interconnection exchange and complex systems properties in power grid network

Piotr Hadaj*, Marek Nowak1, and Dominik Strzałka1 1Faculty of Electrical and Computer Engineering, Rzeszów University of Technology, Al. Powstańców Warszawy 12, 35-959 Rzeszów, Poland

Abstract. A case study based on the real data obtained from the Polish PSE System Operator of the highest voltages electrical energy network is shown. The data about the interconnection exchange and some complex networks (graphs) parameters were examined, after the removal of selected nodes. This allowed to test selected network parameters and to show that the breakdown of only three nodes in this network can cause significant drop of its average efficiency.

1 Introduction The concept of complex systems and related theory give many interesting applications in modelling different real systems [1]. One of examples are power systems which can be exposed on different threats even leading to the risk of potential blackouts [2]. In this short paper, the real electrical network as a graph of nodes and edges is shown. Some of this network topological parameters are given and the interconnection exchange as an example of the power system security is shown. Selected parameters of complex networks are calculated and the removal of some network nodes caused by failure was done. This leads to the changes in the whole network topology shown in tables. The most important is the drop of network efficiency and in turn, the increase of transmission costs. The paper is organized as follows: after the short Introduction in Section 2 we show the complex systems and networks theory. Section 3 gives the shape of the EU-PL electricity exchange system. The analysis of real source data based on Network Workbench and Gephi software packages is given in Section 4. Section 5 shows the paper summary.

2 Complex systems and networks The idea of complex systems refers to the concept of systems S understood as beings B, which consist of n elements E = {e1, e2, …, en}, that pose m attributes A = {a1, a2, …, am} with k possible long- or short-range relations R = {r1, r2, …, rk}, finally giving S = B(E, A, R) [3,4]. Usually, the definition of complex systems is referred to the Aristotle’s rule: the whole is more than the sum of its parts [5].

* Corresponding author: [email protected]

© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). MATEC Web of Conferences 336, 05020 (2021) https://doi.org/10.1051/matecconf/202133605020 CSCNS2020

3 The interconnection exchange between systems The interconnection exchange is an inseparable element of the power system operation. From the system point of view, it allows, during the high demand, to import energy from another county in order to provide electricity supply to consumers, and to transfer energy to another country when the surplus energy is produced. The existence of such connections significantly increases the energy security of the power system. This is the key future of plans related to the energy independence and energetic security in different countries of the EU (European Union). However, in order to assume that the whole system will be stable one of the key aspects is the quality of the supplied energy. The fluctuations in RMS (root mean square) of voltage value, high harmonic content, or frequency fluctuations [8] should be as low as possible. Moreover, the supply reliability and continuity shown by SAIDI parameter (System Average Interruption Duration Index) or SAIFI (System Average Interruption Frequency Index) parameter are of great importance [8]. If the topology of power networks nodes connections is resistant to the net damages caused by different random events then the country economy is attractive for investors [9,10]. In Poland the PSE as the National System Operator, is responsible for the reliability of the highest voltages energy networks, while the local Distribution System Operators (DSO) are responsible for the remaining high-, medium-, and low-voltage lines. Currently, the HVDC bridges are used as interconnections, such as the connection of Poland and Sweden via the Swe-Pol Link sea line, and the HVDC Back-to-Back solution in the connection of the Polish and Lithuanian systems (LitPol Link). These are expensive and often difficult to implement, but they replace traditional solutions (direct AC connections). It turns out, however, that under certain conditions such a transmission is much more advantageous and provides an acceptable return on investment. The HVDC SwePol Link HVDC line, launched in year 2000, provides a combination of Polish and Swedish systems. It is implemented as an undersea cable line that connects two converter stations connected to the Polish and Swedish systems. The connection between the Polish and Lithuanian systems is not a typical HVDC bridge. This connection consists of only one converter station, which connects the systems. This connection has most of the advantages of a typical HVDC bridge and is used when the systems between which the energy exchange is to take place are not synchronized (as in this case). Figure 1 shows the annual energy exchange balance from the European Network of Transmission System Operators for Electricity report and the graph of all energy exchanges in Europe [11].

2 MATEC Web of Conferences 336, 05020 (2021) https://doi.org/10.1051/matecconf/202133605020 CSCNS2020

Complex systems show many interesting features in both: spatial and temporal domains. Among them there are complex networks of nodes and relations (edges) based on graphs G = {V, E} with n nodes (vertices V = {v1, v2, …, vn}) connected by m edges E = {e1, e2, …, em}. Such graphs are usually characterized by special features. The length of the shortest path dij calculated as the sum of the ℓij distances (paths) between all possible paths in the graph between the nodes i and j, dij ≥ ℓij, i ≠ j is usually quite low even then the size of network (its diameter) is big. It can be used to measure the scattering of the network [6]. The parameter defined as ɛij = 1/dij, i ≠ j∀ can represent the network efficiency (if dij = ∞, then ɛij = 0). The high network efficiency is high means low costs of its operation (e.g. costs of energy transmission during the interconnection∀ exchange). If network of vertices has ki edges that connect each vertex to other ki nodes then the ratio between the number Ei of edges that exist among these ki nodes and the number of total possible vertices connections, give the clustering coefficient Ci of node i. For clique Ci = 1, for random graphs Ci → 0, but Fig. 1. Electricity exchange between Poland and neighboring countries in GWh (left) and power for complex networks this parameter can vary [7]. Graphs with high value of C are called system interconnection in Europe as a graph of a complex network (right). small worlds. Table 1. Shows the energy exchange balance between Poland and neighbouring countries in GWh per year [11]. 3 The interconnection exchange between systems Table 1. Interconnection system exchange balance data for Poland and its neighbors. The interconnection exchange is an inseparable element of the power system operation. A [GWh] Total Germany Czech Republic Slovakia Ukraine Lithuania Sweden From the system point of view, it allows, during the high demand, to import energy from Year balance another county in order to provide electricity supply to consumers, and to transfer energy to 2009 -5483 6737 2274 -199 - -1140 2189 2010 -5167 5364 1415 0 - -267 1345 another country when the surplus energy is produced. The existence of such connections 2011 -4705 8208 3028 -59 - -1236 5236 significantly increases the energy security of the power system. This is the key future of 2012 -5877 8754 3498 -1005 - -2545 2825 plans related to the energy independence and energetic security in different countries of the 2013 -4909 7663 3051 -1029 - -253 4523 EU (European Union). However, in order to assume that the whole system will be stable 2014 -9153 7158 3496 -685 - -2984 -2168 one of the key aspects is the quality of the supplied energy. The fluctuations in RMS (root 2015 -10644 9549 4926 -67 50 -3491 323 mean square) of voltage value, high harmonic content, or frequency fluctuations [8] should 2016 -8740 6693 4185 -957 -596 -2587 -2002 2017 -7319 5571 4372 -895 -1042 -2974 -2287 be as low as possible. Moreover, the supply reliability and continuity shown by SAIDI 2018 -7033 3128 3209 -1410 -897 -2724 -5727 parameter (System Average Interruption Duration Index) or SAIFI (System Average 2019 -7541 -1810 1916 -658 -1401 -1043 -10537 Interruption Frequency Index) parameter are of great importance [8]. If the topology of power networks nodes connections is resistant to the net damages caused by different random events then the country economy is attractive for investors [9,10]. In Poland the 4 Case study PSE as the National System Operator, is responsible for the reliability of the highest In this Section, the power grid based on PSE data is analyzed (see Fig. 2). All data has been voltages energy networks, while the local Distribution System Operators (DSO) are entered into the Gephi software package and the real network consists of 124 vertices and responsible for the remaining high-, medium-, and low-voltage lines. 175 edges. Because of security reasons we are not able to show all details relating to node’s Currently, the HVDC bridges are used as interconnections, such as the connection of physical location. But this graph is enough to examine the complex network features Poland and Sweden via the Swe-Pol Link sea line, and the HVDC Back-to-Back solution in presented in Section 2. The nodes and edges in the graph refer to the physical objects in the the connection of the Polish and Lithuanian systems (LitPol Link). These are expensive and transmission network: the nodes are transformers or power distribution stations, the edges often difficult to implement, but they replace traditional solutions (direct AC connections). are transmission lines. It turns out, however, that under certain conditions such a transmission is much more Figure 3 shows the graphical analysis of the network (from Fig. 2) degree centrality. advantageous and provides an acceptable return on investment. The HVDC SwePol Link The count of the number of node connections is converted into a 0...1 scale (the node with HVDC line, launched in year 2000, provides a combination of Polish and Swedish systems. the highest number has the value 1 whereas the other ones as the ratio of the largest one). It is implemented as an undersea cable line that connects two converter stations connected The more blue is the node’s color, the more important is the node. to the Polish and Swedish systems. The connection between the Polish and Lithuanian Now we are going to remove some nodes from the network starting from the nodes with systems is not a typical HVDC bridge. This connection consists of only one converter the highest degrees. We assume that when it is done this could cause the major negative station, which connects the systems. This connection has most of the advantages of a effects (for example after the terroristic attack). After each removal the graph properties are typical HVDC bridge and is used when the systems between which the energy exchange is shown in Table 2. to take place are not synchronized (as in this case). Figure 1 shows the annual energy exchange balance from the European Network of Transmission System Operators for Electricity report and the graph of all energy exchanges in Europe [11].

3 MATEC Web of Conferences 336, 05020 (2021) https://doi.org/10.1051/matecconf/202133605020 CSCNS2020

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PLE OST LMS WIE PPD CZE MOS KRM ZRC ZDK PPD KRM ANI WLA PLO LSN PAT OSR ROK CZT NAR PDE GDA JAS PAT JOA WRZ KON WYS KON PAB KOP LES BYD KAT MSK ADA LIS PRB SOC OLT STN PDE ADA WTO ROG ZUK MOR GRU HCZ LAG HAL MIL SDU GBL ZGI PIA POL PLO JAM JAN ZGI BUJ CRN WLA PAB KOZ BEK PAS SOC BYC OSR PUL JAN KOM LSY TEL PIO OLT KHK HAG MIK ROZ OLM TCN ABR CHS OLS ROG PIO BIR MSK BEK TRE KIE KPK OSC WYS SIE CPC SWI WRC ZAM LOS MKR MIL RAD OST WTO KPK SKA STW ELK LUA DOB KIE CHM PEL DBN STN RAD BOG MOR KLA LUA WAN ANI RZE LMS ZBK KLA ROZ ATA GRO ATA CHA WAN BGC JOA TAW NAR SDU HCZ KOZ KRI PEL TAW ALY EKB WRZ PIA OSC LEM LEM KRI BLA PUL RZE LOS SKA KED ROK LAG TCN LSY CHM CHS HAL KAT JAM KHK WIE BGC KOP ABR CHA BYC SIE STW BIR ZAM MOS MKR ALB CZT PRB NOS KOM DOB LIS BUJ Fig. 2. Graph based on PSE power grid network: organic layout (left) and physical (geographical) layout (right).

0.22 ZRC 0.22 SLK 0.33 0.11 0.22 REC DUN GDA 0.33 GBL

0.33 0.22 PLC ZDK 0.22 0.33 0.11 GLN VIE 0.44 ZYD 0.44 KRA MON 0.11 ALY 0.33 0.44 0.33 OLMOLS GRU 0.22 0.11 0.22 ELK 0.33 0.33 EKB PKW GOR JAS 0.11 0.22 0.22 BYD TEL 0.78CZE 0.56 0.33 0.22 PLE 0.44 OST LMS PPD 0.33 KRM 0.33 0.33 0.56 WLA PLO 0.22 LSN PAT 0.22 NAR 0.44 PDE 0.22 0.11 LES KON 0.22WYS MSK0.67 0.22 0.44 0.33 SOC OLT 0.22 0.22 0.33 STN0.56 ADA WTO 0.22 ZUK MOR MIL 0.22 0.22 SDU 0.56 ZGI 0.44 PIA POL 0.22 0.67 0.22JAN CRN 0.22 0.33 PAB KOZ 0.44 PAS OSR 0.22 0.56 PUL 1.00 0.22 0.33 0.11 LSY0.33 PIO ROZ 0.22 HAG MIK ABR ROG CHS 0.11 0.56 0.33BEK 0.11 0.22 0.44 0.22 0.33 0.22 TRE KPK OSC WRC KIE 0.22ZAM CPC SWI 0.22 MKR RAD 0.22 0.33 0.11 0.67STW DOB 0.56 CHM 0.22 PEL 0.33 0.56 BOG DBN 0.11 0.22 0.33 ANI LUA 0.33 0.22 RZE 0.11 ZBK 0.78 0.22 GRO KLA0.22 ATA0.33 CHA 0.11 WAN BGC0.33 HCZ JOA TAW 0.11 KRI WRZ 0.11 0.22 LEM

BLA 0.44 0.56 0.33 0.11 0.44 0.33 LOS SKA KED ROK LAG TCN 0.22 0.22 0.22 0.22 0.78 HAL KAT JAM KHK 0.44 0.89 WIE 0.33 0.22 KOP BYC SIE 0.22 BIR 0.22 0.11 MOS 0.22 ALB 0.11 0.22CZT PRB NOS 0.22 KOM 0.33 LIS BUJ Fig. 3. The graph nodes centrality for Fig. 2 (right). The description of parameters given in Table 2 can be found in literature, see for example [12]. It can be seen that after the removal of 3 nodes the average network efficiency falls more than 25%. Table 2. Averaged data from the analysis of the modified graphs. Number of Removed Nodes 0 1 2 3 (avg.) Nodes in graph 124 123 122 121 Edges in graph 175 166 158 151 Average vertex degree 2.823 2.699 2.59 2.5 Graph density 0.023 0.022 0.021 0.021 Local efficiency 0.114 0.1 0.101 0.097 Average efficiency 0.216 0.156 0.191 0.171 Average clustering coefficient 0.131 0.117 0.124 0.121 Average path length 5.984 6.8 6.93 7.92 Graph diameter 16 17 17 20.67

4 MATEC Web of Conferences 336, 05020 (2021) https://doi.org/10.1051/matecconf/202133605020 CSCNS2020

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KRA GLN VIE ZYD LSN MIK VIE SWI KRA ZBK MON This paper shows the data about the energy interconnection exchange and the analysis of GOR ALB GRO ALY ZUK WRC BLA OLM OLS LES PAS GRU POL ELK DBN NOS KED EKB complex network parameters of real data obtained from PSE network. The removal of some PKW DUN PKW GOR JAS PLE CRN SLK TRE BYD TEL ZYD CZE

PLE nodes in analyzed network caused the drop of network average efficiency by more than OST LMS WIE PPD CZE MOS KRM ZRC ZDK PPD KRM ANI WLA PLO LSN PAT OSR ROK CZT NAR PDE 25%. The efficiency is related to the cost of whole network operation: high efficiency GDA JAS PAT JOA WRZ KON WYS KON PAB KOP LES BYD KAT MSK ADA LIS PRB SOC OLT STN PDE ADA WTO ZUK MOR means low costs. In turn the breakdown, damage or accidents in the nodes of the highest ROG GRU HCZ LAG HAL MIL SDU GBL ZGI PIA POL PLO JAM JAN ZGI BUJ CRN WLA PAB KOZ BEK PAS OSR degree can significantly increase the cost of whole network operation. We show that it is SOC BYC PUL JAN KOM LSY TEL PIO OLT KHK HAG MIK ROZ OLM TCN ABR CHS OLS ROG PIO BIR MSK BEK enough to break 3 vertices to cause such a situation. TRE KIE KPK OSC WYS SIE CPC SWI WRC ZAM LOS MKR MIL RAD OST WTO KPK SKA STW ELK DOB LUA CHM KIE PEL DBN STN RAD BOG MOR KLA LUA WAN ANI RZE ZBK KLA LMS ROZ GRO ATA CHA ATA BGC Authors' alphabetical order means equal contribution. WAN JOA TAW NAR SDU HCZ KOZ KRI PEL TAW ALY EKB WRZ PIA OSC LEM LEM KRI BLA PUL RZE LOS SKA KED ROK LAG TCN LSY CHM CHS HAL KAT JAM KHK WIE BGC KOP ABR CHA BYC SIE STW BIR ZAM MOS MKR ALB CZT PRB References NOS KOM DOB LIS BUJ Fig. 2. Graph based on PSE power grid network: organic layout (left) and physical (geographical) 1. Newman, M.; Networks: An Introduction; Oxford University Press, Inc.: New York, layout (right). NY, USA, 2010.

0.22 ZRC 2. Wu, L.; Anderson, R.N.; Boulanger, A.; Rudin, C.; Kaiser, G.E. Failure Analysis of the 0.22 SLK 0.33 0.11 0.22 REC DUN GDA 0.33 New York City Power Grid; CU CS Technical Report CUCS-025-14; Department of GBL

0.33 0.22 PLC ZDK 0.22 0.33 0.11 Computer Science, Columbia University: Columbia, 2014. GLN VIE 0.44 ZYD 0.44 KRA MON 0.11 ALY 3. Klir, G.J. ; Wiley Interscience: New York, NY, USA, 0.33 Trends in General Systems Theory 0.44 0.33 OLMOLS GRU 0.22 0.11 0.22 ELK 0.33 0.33 EKB 1972 PKW GOR JAS 0.11 0.22 0.22 BYD TEL 0.78CZE 0.56 0.33 0.22 PLE 0.44 OST LMS 4. von Bertalanffy, L. ; George PPD 0.33 0.33 General System Theory: Foundations, Development KRM 0.33 0.56 WLA PLO 0.22 LSN PAT 0.22 NAR 0.44 PDE Braziller: New York, NY, USA, 1968. 0.22 0.11 LES KON 0.22WYS MSK0.67 0.22 0.44 0.33 SOC OLT 0.22 0.22 0.33 STN0.56 ADA WTO 0.22 ZUK MOR 5. Upton, J.; Janeka, I.; Ferraro, N. MIL SDU 0.22 0.22 The whole is more than the sum of its parts: Aristotle, 0.56 ZGI 0.44 PIA POL 0.22 0.67 0.22JAN CRN 0.22 0.33 PAB KOZ 0.44 . J Craniofacial Surg. 2014, 25, 59–63. PAS 0.22 metaphysical OSR 0.56 PUL 1.00 0.22 0.33 0.11 LSY0.33 PIO ROZ 0.22 HAG MIK ABR ROG CHS 0.11 0.56 0.33BEK 0.11 0.22 6. Å. J. Holmgren, 0.44 0.22 0.33 0.22 Using Graph Models to Analyze the Vulnerability of Electric Power TRE KPK OSC WRC KIE 0.22ZAM CPC SWI 0.22 MKR RAD 0.22 0.11 STW0.33 0.67 DOB , an International Journal 2006, 26, 955-969. CHM Networks, Risk Analysis 0.56 0.22 PEL 0.33 0.56 BOG DBN 0.11 0.22 0.33 ANI LUA 0.33 0.22 RZE 0.11 ZBK 0.78 0.22 GRO KLA0.22 ATA0.33 CHA 0.11 BGC 7. Latora, V.; Marchiori, M. . Phys. Rev. Lett. WAN 0.33 JOA TAW Efficient behavior of small-world networks HCZ 0.11 KRI WRZ 0.11 0.22 LEM 2001, 87, 198701. BLA 0.44 0.56 0.33 0.11 0.44 0.33 LOS SKA KED ROK LAG TCN 0.22 0.22 0.22 0.22 0.78 HAL KAT JAM KHK 0.44 0.89 8. . WIE 0.33 Łatka, M.; Nowak, M Analysis of Electrical Power Quality Parameters at the High 0.22 KOP BYC SIE 0.22 BIR 0.22 0.11 MOS 0.22 ALB 0.11 0.22CZT PRB . In Proceedings of the 2018 Conference on Progress in Applied NOS 0.22 KOM 0.33 Voltage Level LIS BUJ Electrical Engineering (PAEE), Kościelisko, Poland, 18-22th June 2018. Fig. 3. The graph nodes centrality for Fig. 2 (right). 9. Markovskii, P.; Merkushev, A. Investigation into high voltage network reliability The description of parameters given in Table 2 can be found in literature, see for predictive calculation. In Proceedings of the 2018 19th International Scientific example [12]. It can be seen that after the removal of 3 nodes the average network Conference on Electric Power Engineering (EPE), Brno, Czech Republic, 16-18th May efficiency falls more than 25%. 2018. 10. Polish Ministry of Energy, . ver. Table 2. Averaged data from the analysis of the modified graphs. Polityka Energetyczna Polski do 2040 Roku (PEP2040) 1.2 2018. Available online: https://www.gov.pl/web/aktywa- Number of Removed Nodes 0 1 2 3 (avg.) panstwowe/zaktualizowany-projekt-polityki-energetycznej-polski-do-2040-r (accessed Nodes in graph 124 123 122 121 on 9 May 2020). Edges in graph 175 166 158 151 2.823 2.699 2.59 2.5 11. European Network of Transmission System Operators for Electricity statistical reports: Average vertex degree https://www.entsoe.eu/publications/statistics-and-data/#statistical-factsheet (accessed Graph density 0.023 0.022 0.021 0.021 on 15 May 2020). Local efficiency 0.114 0.1 0.101 0.097 Average efficiency 0.216 0.156 0.191 0.171 12. Hadaj, P.; Strzałka D.: Modelling Selected Parameters of Power Grid Network in the Average clustering coefficient 0.131 0.117 0.124 0.121 South-Eastern Part of Poland: The Case Study, Energies, 2020,13 (1), 239 Average path length 5.984 6.8 6.93 7.92 Graph diameter 16 17 17 20.67