Evaluating Influence of Inverter-Based Resources on System Strength

sustainability

Article Evaluating Inﬂuence of Inverter-based Resources on System Strength Considering Inverter Interaction Level

Dohyuk Kim, Hwanhee Cho , Bohyun Park and Byongjun Lee *

School of Electrical Engineering, Anam Campus, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Korea; [email protected] (D.K.); [email protected] (H.C.); [email protected] (B.P.) * Correspondence: [email protected]; Tel.: +82-10-9245-3242

Received: 17 March 2020; Accepted: 21 April 2020; Published: 24 April 2020

Abstract: The penetration of renewable energy sources (RESs) equipped with inverter-based control systems such as wind and solar plants are increasing. Therefore, the speed of the voltage controllers associated with inverter-based resources (IBRs) has a substantial impact on the stability of the interconnected grid. System strength evaluation is one of the important concerns in the integration of IBRs, and this strength is often evaluated in terms of the short circuit ratio (SCR) index. When IBRs are installed in an adjacent location, system strength can be weaker than evaluation by SCR. This study proposes an inverter interaction level short circuit ratio (IILSCR) method by tracing IBRs output flow. The IILSCR can accurately estimate system strength, wherein IBRs are connected in adjacent spots, by reflecting the interaction level between IBRs. The study also demonstrates the efficiency of IILSCR by applying this method to Institute of Electrical and Electronics Engineers (IEEE) 39 bus test system and future Korea power systems.

Keywords: inverter-based resources; inverter interaction level; renewable energy resources; system strength; voltage oscillation

1. Introduction Power systems are undergoing rapid changes mainly due to the increase of inverter-based resources (IBRs) supply, such as wind and solar power generation. This increase in IBRs lowers the inertia and system strength, which in turn affects frequency and voltage stability; therefore, it is necessary to pay attention to IBRs concentration areas. In addition, since IBRs are affected by the environment, it is installed in windy areas with abundant sunlight. Therefore, it is located far from the load center and there are few synchronous generators in such areas. In other words, IBRs are installed in areas where the system strength is relatively weak. When connected to systems with low system strength, the output sensitivity of IBRs has a direct impact on the output of the point of interconnection (POI). Wind and solar power control loops with inverter-based control schemes provide reactive/active power injections that react almost instantly to voltage changes at the POI. This dynamic response can lead to high voltage sensitivity to reactive power in weak power systems; small changes in reactive power can cause large fluctuations in voltage. When multiple IBRs are connected to weak power systems, power system stability issues related to voltage stability and quality can be exposed to serious consequences. In Korea, The Ministry of Trade, Industry, and Energy (MOTIE) has announced the “New Renewable 3020 Plan,” which aims to expand the proportion of renewable energy to 20% of the total generation by 2030 [1]. To achieve this goal, MOTIE plans to distribute 48.7 GW of renewable energy generation facilities from 2018 to 2030 and supply clean energy such as solar and wind power to more than 95% of renewable energy generation facilities. In order to accommodate

Sustainability 2020, 12, 3469; doi:10.3390/su12083469 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 3469 2 of 18 this large amount of renewable energy, it is necessary to evaluate the system strength beforehand and prepare measures to cope with any problems. In particular, large-capacity wind and solar generators are concentrated in certain areas and are likely to interact with renewable energy sources (RESs) in the vicinity. Therefore, when IBRs are concentrated in electrically connected areas, evaluation of system strength becomes necessary to reflect the interaction of IBRs. In the meantime, many studies have been undertaken to assess system strength as a means of accessing renewable energy and identify potential problems. Research has been focused on the case of output and voltage oscillation by renewable generators, specifically when connected to weak systems [2–4]. IEEE [5] first introduced the concept of short circuit ratio (SCR) to evaluate Active Current / Direct Current (AC/DC) system strength when IBR is connected to the grid. However, SCR do not reflect the interaction impact of IBRs in the vicinity. In the case of an integrated system based on inverters, in [6], Saad et al. evaluated system strength using the interaction factor. Researchers [7–9] overcame the disadvantage of solely considering IBR capacity connected to the bus, i.e., the SCR approach. Methods such as weighted short circuit ratio (WSCR) were developed by Electric Reliability Council of Texas (ERCOT), taking into account the interaction between IBRs. The study [10,11] considered the actual electrical interaction when IBRs are connected to nearby areas. Impedance metrics were used to estimate the interaction from IBRs installed in the vicinity and evaluate weak systems. Several researchers [12–15] have presented extensive research on the voltage stability issues that occur when large wind farms are connected to weak grids. The above methodology was mainly a measure of the system strength for renewable energy connections. Several studies [16–19] have proposed a system strength evaluation and design for linking high-voltage direct current (HVDC) and wind farms. Certain studies [20–22] have introduced inverter parameters and controls that affect the stability of inverter-based equipment connected to the grid. The existing methods for evaluating the system strength does not reflect the interaction of nearby IBRs, or assumed IBRs to have a 100% interaction within a boundary. However, it is very difficult to calculate the boundary within the actual system, and different results will be derived depending on the range of boundary. Therefore, to overcome these challenges, it is necessary to calculate the exact effect from nearby IBRs. In this paper, we propose a method to calculate the interaction level by tracking the output of IBRs. Power tracing method was used to reflect the impact of nearby IBRs. Thus, the interaction level of the IBRs can more accurately estimate the system strength when the renewable generator is connected to adjacent points. In addition, this study establishes a future system based on the power system of Southwest, the region where Korea’s renewable energy will be concentrated. Modeling of the connected IBRs adopts Western Electricity Coordinating Council (WECC) Type 4 to comply with grid codes. In this system, the proposed method to evaluate system strength has been derived. Thus, it can be quantitatively analyzed for system voltage stability. Based on the analysis results, the accuracy of the system strength evaluation limits the number of renewable connections at the POI. Therefore, the risk of the renewable energy at the POI can be minimized when planning the grid. Finally, the dynamic simulation results verify the performance of the proposed method. The rest of this paper is organized as follows. Section2 formulates a new methodology to overcome existing methodology limitations. Section3 evaluates and verifies the system strength in IEEE 39 bus test system and South West region of Korea. Section4 discusses the causes of reactive power oscillation in IBRs. Finally, this paper concludes with a brief explanation in Section5.

2. Techniques Pertaining to the Interactions among the Inverter-Based Resources

2.1. Relationship Between Inverter Interaction Level and System Strength This study aims to accurately evaluate the system strength when IBRs are connected to the system. When renewable power plants are installed in nearby areas, and if the system strength cannot be Sustainability 2020, 12, 3469 3 of 18

accurately identiﬁed, it may cause voltage problems such as control stability and control interaction. The general system strength evaluation method is based on the following formula.

SCMVAi SCRi = (1) PIBRi

where SCMVAi is the short circuit capacity at the POI without the current contribution of the

inverter-based resource, and PIBRi is the nominal power rating of the IBR being connected at the POI. This system strength evaluation method is very useful when one IBR is connected to the system as shown in Figure1. When evaluating the system strength through SCR, only the connection capacity at the POI is considered. As shown in Figure2, it is easy to determine whether the system strength is strong through the PV curve. However, because this method does not reﬂect the interaction between the IBRs installed nearby, it may not provide an accurate evaluation of the system strength. In order to solve this problem, ERCOT has developed a WSCR method to evaluate the system strength reﬂecting the interaction between the wind farms in the Panhandle region.

PN SCMVAi PIBR WSCR = i ∗ i (2) PN 2 i PIBRi

where SCMVAi is the short circuit MVA at bus i before the connection of IBR and PRESi is the MW rating of IBRi to be connected. N is the number of IBRs fully interacting with each other and i is the IBR index. The proposed WSCR calculation method is based on the assumption of full interaction between the IBRs as shown in Figure3. This is equivalent to assuming all IBRs are connected at the Sustainabilitysame POI. 2020 The, 12 SCR, x FOR obtained PEER REVIEW with this method provides a more conservative estimate of the system3 of 18 strength. For a real power system, there is typically some electrical distance between POIs and all IBRs will not fully interact with each other. However, the other jurisdiction of ERCOT, South Texas, is not considered because application of this method is difficult in this area. It is also becoming increasingly difficult to apply this method in the Panhandle region due to the growing number of transmission lines, which is obscuring the boundaries requiredSCR = for calculating WSCR. Thus, the existing method(1) has two limitations, which are as follows: where is the short circuit capacity at the POI without the current contribution of the inverter-basedSCR, the resource, basic method, and can evaluate is the nominal the system power strength rating throughof the IBR a simplebeing connected method; however, at the POI. it is • This systemdifficult strength to apply evaluation due to the method large-scale, is very large-capacity, useful when andone powerIBR is electronics-basedconnected to the system facilities as of shownthe in renewableFigure 1. When generators evaluating that causethe system interaction strength effects. through SCR, only the connection capacity WSCR is the method wherein the connection buses are equalized and weighted to reflect the at• the POI is considered. As shown in Figure 2, it is easy to determine whether the system strength is strongfully through interaction the PV ecurve.ffects ofHowever, renewable because generators this method installed does in the not vicinity. reflect the However, interaction it is dibetweenfficult to the IBRsclearly installed calculate nearby, for it the may boundaries not provide being an equalized.accurate evaluation Moreover, of the the result system may strength. be very In di orderfferent to solvedepending this problem, on the ERCOT boundary has setting. developed a WSCR method to evaluate the system strength reflecting the interaction between the wind farms in the Panhandle region.

FigureFigure 1. 1.SimpleSimple AC AC System System with with single single inverter-based inverter-based resources resources (IBR). (IBR).

Figure 2. Voltage (point of interconnection (POI)) versus DC power curve.

SCR = (1) where is the short circuit capacity at the POI without the current contribution of the inverter-based resource, and is the nominal power rating of the IBR being connected at the POI. This system strength evaluation method is very useful when one IBR is connected to the system as shown in Figure 1. When evaluating the system strength through SCR, only the connection capacity at the POI is considered. As shown in Figure 2, it is easy to determine whether the system strength is strong through the PV curve. However, because this method does not reflect the interaction between Sustainabilitythe IBRs installed 2020, 12, x nearby, FOR PEER it REVIEWmay not provide an accurate evaluation of the system strength. In 4order of 18 to solve this problem, ERCOT has developed a WSCR method to evaluate the system strength reflecting the interaction between the wind farms in the Panhandle region.

• SCR, the basic method, can evaluate the system strength through a simple method; however, it is difficult to apply due to the large-scale, large-capacity, and power electronics-based facilities of the renewable generators that cause interaction effects. • WSCR is the method wherein the connection buses are equalized and weighted to reflect the fully interaction effects of renewable generators installed in the vicinity. However, it is difficult to clearly calculate for the boundaries being equalized. Moreover, the result may be very different depending on the boundary setting. SustainabilityThe IBRs2020 , 12such, 3469 as wind and solar plants are connected to power systems through power4 of 18 Figure 1. Simple AC System with single inverter-based resources (IBR). electronic controllers. The voltage/reactive power control loops within these IBRs are capable of providing almost instantaneous reactive power injections in response to the voltage change at the POI. Such rapid dynamic responses could result in high voltage sensitivity with respect to reactive power, i.e., a small change in reactive power will lead to a large oscillation in voltage. Therefore, the speed of the voltage controllers associated with IBR has a substantial impact on the stability of the interconnected grid. When a large amount of IBRs are connected to the weak points of a power system, undesirable system stability issues, especially those related to voltage stability and quality may be exposed and this may result in serious consequences. In the worst-case scenario, such system stability issues could be wide-spread and lead to loss of power generation and/or damage of IBR equipment if adequate protective measures are not implemented. Placing renewables at a distance from the main grid can result in problems when controlling the power injected to the grid. Moreover, the POIs of these IBRs are usually weak, hence voltage stability issues are more likely to occur in case of oscillation of reactive power. In the planning stage, therefore, it is important to evaluate the system strength that reflectsFigureFigure the 2.2. interaction VoltageVoltage (point(point of IBRs. ofof interconnectioninterconnection (POI)) (POI)) versus versus DC DC power power curve. curve.

∑ ∗ WSCR = (2) ∑ where is the short circuit MVA at bus i before the connection of IBR and is the MW rating of IBRi to be connected. N is the number of IBRs fully interacting with each other and i is the IBR index. The proposed WSCR calculation method is based on the assumption of full interaction between the IBRs as shown in Figure 3. This is equivalent to assuming all IBRs are connected at the same POI. The SCR obtained with this method provides a more conservative estimate of the system strength. For a real power system, there is typically some electrical distance between POIs and all IBRs will not fully interact with each other. However, the other jurisdiction of ERCOT, South Texas, is not considered because application of this method is difficult in this area. It is also becoming Figure 3. General system strength evaluation method for simple AC System with multiple IBRs. increasinglyFigure 3.difficult General to system apply strength this method evaluation in th methode Panhandle for simple region AC System due to with the multiplegrowing IBRs. number of transmissionThe IBRs suchlines, as which wind andis obscuring solar plants the are boundaries connected required to power systemsfor calculating through WSCR. power electronicThus, the 2.2. Techniques to Analyze the Inverter Interaction Level controllers.existing method The voltagehas two/ reactivelimitations, power which control are as loops follows: within these IBRs are capable of providing almostLine instantaneous power flow reactivetracing poweralgorithm injections is a useful in response method to to the determine voltage change the distributive at the POI. path Such of rapid the nodesdynamic from responses a specific could generator result into highthe final voltage consumption sensitivity of with the respectelectric toload. reactive Using power, this algorithm, i.e., a small it ischange possible in reactive to gain powerinformation will lead about to aan large IBR’s oscillation effect on in other voltage. buses. Therefore, Equation the (3) speed shows of the the amount voltage ofcontrollers MW inflow associated from another with IBR IBR. has The a substantial detailed impactderivation on theof stability(3) is presented of the interconnected in the Appendix. grid. Therefore,When a large it is amount feasible of to IBRs decompose are connected the effect to the of weak only points one IBR of a powerfrom those system, of other undesirable components. system Figurestability 4 describes issues, especially the mechanism those relatedof interaction to voltage between stability IBRs and at the quality power may systems. be exposed and this may result in serious consequences. In the worst-case scenario, such system stability issues could be wide-spread and lead to loss of power generation and/or damage of IBR equipment if adequate protective measures are not implemented. Placing renewables at a distance from the main grid can result in problems when controlling the power injected to the grid. Moreover, the POIs of these IBRs are usually weak, hence voltage stability issues are more likely to occur in case of oscillation of reactive power. In the planning stage, therefore, it is important to evaluate the system strength that reﬂects the interaction of IBRs.

2.2. Techniques to Analyze the Inverter Interaction Level Line power flow tracing algorithm is a useful method to determine the distributive path of the nodes from a specific generator to the final consumption of the electric load. Using this algorithm, it is possible to gain information about an IBR’s effect on other buses. Equation (3) shows the amount of MW inflow from another IBR. The detailed derivation of (3) is presented in the AppendixA. Therefore, it is Sustainability 2020, 12, 3469 5 of 18 feasible to decompose the effect of only one IBR from those of other components. Figure4 describes the mechanism of interaction between IBRs at the power systems.

N Pm i Pm i P 1 Pm i = d P − e Pi = d P − e Au− imPGm d − e i i d e m=1 (3) Sustainability 2020, 12, x FOR PEER REVIEW= α P + α P + + α P 5 of 18 i1 G1 i2 G3 ······ im Gm Sustainability 2020, 12, x FOR PEER REVIEWwhere 0 αim 1 f or m = 1, 2, , N 5 of 18 ··· ··· ······

FigureFigure 4. ConceptConcept of of inverter-based inverter-based resource resource interaction. 2.3. Inverter Interaction LevelFigure Short 4. CircuitConcept Ratio of inverter-based resource interaction. Interaction level short circuit ratio (IILSCR) tracks the amount of power output from the IBRs = = (3) to reflect the interactions between the IBRs. The output of the IBR is divided based on a matrix that = = (3) reflects the system’s lines and loads, allowing for accurate mutual impacts. Therefore, as shown in = + + ∙∙∙∙∙ + Figure5, it is possible to reflect the output of IBRs flowing from nearby as well as the amount of = + + ∙∙∙∙∙ + renewable connections connectedℎ 0 to the bus.1 Therefore, = 1,2,∙∙∙∙∙, equalization of renewable energy resources installed in the vicinity and calculation of the boundaries are not required. Equation (4) shows a new ℎ 0 1 = 1,2,∙∙∙∙∙, system strength method that reflects the interaction between IBRs. 2.3. Inverter Interaction Level Short Circuit Ratio 2.3. InverterInteraction Interaction level short Level circuit Short ratioCircuit (IILSCR) Ratio tracksSCMVA the amounti of power output from the IBRs to IILSCRi = (4) + PN reflect the interactions between the IBRs. ThePIBR outputi m =of1, mthe,i PIBRIBRm isi divided based on a matrix that Interaction level short circuit ratio (IILSCR) tracks the amount− of power output from the IBRs to reflectsreflect thethe interactionssystem’s lines between and loads, the IBRs.allowing The foroutput accurate of the mutual IBR is impacts. divided Therefore,based on aas matrix shown that in where SCMVAi is the short-circuit capacity connected to IBR on bus i, PIBR is the capacity of the IBR Figurereflects 5, the it issystem’s possible lines to reflect and loads, the output allowing of IBRsfor accurate flowing mutual from nearby impacts. ias Therefore,well as the as amount shown of in installed on bus i, and P is the inflow from the nearby IBR. In the power system, the system renewable connections connectedIBRm i to the bus. Therefore, equalization of renewable energy resources Figure 5, it is possible to reflect− the output of IBRs flowing from nearby as well as the amount of is generally considered weak if the SCR is less than 3 and weak if the WSCR is less than 1.5. Since installedrenewable in theconnections vicinity and connected calculation to the of bus.the boundaries Therefore, equalizationare not required. of renewable Equation energy(4) shows resources a new IILSCR does not equalize buses like WSCR, the system strength can be determined by individual bus systeminstalled strength in the vicinitymethod and that calculation reflects the of interaction the boundaries between are IBRs. not required. Equation (4) shows a new evaluation method such as SCR as shown in Figure6. system strength method that reflects the interaction between IBRs.

Figure 5. Equivalent diagram at POI considering between multiple IBRs. Figure 5. Equivalent diagram at POI considering between multiple IBRs. Figure 5. Equivalent diagram at POI considering between multiple IBRs. IILSCR = (4) + ∑, IILSCR = (4) + ∑, where SCMVAi is the short-circuit capacity connected to IBR on bus i, is the capacity of the IBR installed on bus i, and is the inflow from the nearby IBR. In the power system, the system is where SCMVAi is the short-circuit capacity connected to IBR on bus i, is the capacity of the IBR generally considered weak if the SCR is less than 3 and weak if the WSCR is less than 1.5. Since IILSCR installed on bus i, and is the inflow from the nearby IBR. In the power system, the system is doesgenerally not equalizeconsidered buses weak like if the WSCR, SCR is the less system than 3 andstrength weak ifcan the be WSCR determined is less than by 1.5.individual Since IILSCR bus evaluationdoes not equalizemethod suchbuses as likeSCR WSCR, as shown the in system Figure 6.strength can be determined by individual bus evaluation method such as SCR as shown in Figure 6. Sustainability 2020, 12, x FOR PEER REVIEW 6 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 6 of 18

Sustainability 2020, 12, 3469 6 of 18

FigureFigure 6. 6.Weak Weak system system criteria criteria for for various various indexes. indexes. Figure 6. Weak system criteria for various indexes. 3. Numerical Studies 3. Numerical3. Numerical Studies Studies In this section, the proposed method is validated. The wind and solar generator to be installed In this section, the proposed method is validated. The wind and solar generator to be installed is aIn WECC this section, Type 4 (fullythe proposed rated converter) method is generator validated. model. The wind According and solar to thegenerator Korean to grid be installed code [23], is a WECC Type 4 (fully rated converter) generator model. According to the Korean grid code [23], isthe a WECC power factorType 4 is (fully modeled rated as aconverter) power factor generato of 0.95r model. for wind According generators to andthe Korean as 1 for solargrid code generators. [23], the power factor is modeled as a power factor± of ± 0.95 for wind generators and as 1 for solar theThe power detailed factor Korean is modeled grid code as abouta power reactive factor powerof ± 0.95 requirements for wind generators are presented and inas Appendix1 for solarB. generators. The detailed Korean grid code about reactive power requirements are presented in generators.Applied to theThe IEEE detailed 39 bus Korean test system grid andcode the about Korean reacti powerve power system, requirements vulnerable buses are presented were selected in Appendix B. Applied to the IEEE 39 bus test system and the Korean power system, vulnerable buses Appendixin each system B. Applied by comparing to the IEEE SCR, 39 WSCR,bus test and syst IILSCR.em and the Korean power system, vulnerable buses werewere selected selected in ineach each system system by by comparing comparing SCR, SCR, WSCR, WSCR, and and IILSCR. IILSCR. 3.1. Analysis of the IEEE 39 Bus Test System 3.1.3.1. Analysis Analysis of theof the IEEE IEEE 39 39Bus Bus Test Test System System In order to verify the effectiveness of IILSCR, we applied it to the IEEE 39 bus test system [24] as shownIn Inorder order in to the toverify Figure verify the7 the. effectiveness Conventional effectiveness of generators ofIILSCR, IILSCR, we installedwe applied applied atit to it buses tothe the IEEE 35 IEEE and 39 39 36bus bus have test test system been system replaced [24] [24] as as shownbyshown WECC in inthe Type the Figure Figure 4 generator 7. Conventional7. Conventional model. As generators showngenerators in in Table stalledinstalled1, theat atbuses IBR buses output 35 35and and was 36 36 limitedhave have been sobeen thatreplaced replaced the SCR by by WECCvalueWECC ofType theType buses4 generator4 generator to be connected model. model. As wasAs shown shown 5, 4, 3.in Bus inTable Table 36 is1, notthe1, the aIBRff ectedIBR output output by IBR was was output limited limited connected so sothat that the at the bus SCR SCR 35. valueHowever,value of ofthe busthe buses buses 35 is to a fftobeected beconnected connected by IBR was output was 5, 4,5, connected 3.4, Bu3. Bus 36s at 36is bus notis not 36.affected affected All three by by IBR cases IBR output areoutput considered connected connected strong at busat bus in 35.SCR35. However, (aboveHowever, 3) bus and bus 35 WSCR 35is affectedis affected (above by 1.5),by IBR IBR but output inoutput case connected ofconnected IILSCR, at riskatbus bus is36. indicated36. All All three three in cases CASE3. cases are are considered considered strongstrong in inSCR SCR (above (above 3) and3) and WSCR WSCR (above (above 1.5), 1.5), but but in incase case of ofIILSCR, IILSCR, risk risk is indicatedis indicated in inCASE3. CASE3.

Figure 7. A Single-line diagram of IEEE 39Bus Test System. Figure 7. A Single-line diagram of IEEE 39Bus Test System. Figure 7. A Single-line diagram of IEEE 39Bus Test System. Figures8–10 show active power output, reactive power output, and voltage magnitude in detailed

time-domain dynamic simulation following a fault in system. As can be seen in the case of Case 2, IILSCR 3.33, it recovers stably after fault. However, in the case of CASE3 where IILSCR becomes 2.24,

it can be seen that oscillation occurs after fault. Sustainability 2020, 12, x FOR PEER REVIEW 7 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 7 of 18

Table 1. Comparison among various indices for IEEE 39 bus test system. Table 1. Comparison among various indices for IEEE 39 bus test system. IBR Sustainability 2020, 12, 3469 IBR Inflow from nearby Total IBRs 7 of 18 Year Bus No. SCC (MVA) Capacity SCR WSCR Inflow from nearby Total IBRs IILSCR Year Bus No. SCC (MVA) Capacity SCR WSCR IBRs (MW) Inflow (MW) IILSCR (MW) IBRs (MW) Inflow (MW) 35 2,127 452.61(MW) 5 - 452.61 5 CASE1 Table 1. Comparison among various2.2 indices for IEEE 39 bus test system. 3635 1,6242,127 382.76452.61 5 86.26- 469.02452.61 3.955 CASE1 IBR 2.2 36 1,624 SCC 382.76 5 Inﬂow 86.26 from Total IBRs 469.02 3.95 35 Year Bus2,127 No. 531.64Capacity 4SCR WSCR - 531.64IILSCR 4 (MVA) Nearby IBRs (MW) Inﬂow (MW) CASE2 35 2,127 531.64(MW) 4 2.0 - 531.64 4 CASE2 36 1,624 405.93 4 2.0 81.51 487.44 3.33 35 2127 452.61 5 - 452.61 5 3536CASE1 2,1271,624 708.85405.93 34 2.2 81.51- 708.85 487.44 3.333 CASE3 36 1624 382.76 51.6 86.26 469.02 3.95 3635 1,6242,127 541.24708.85 3 73.66- 614.90708.85 2.643 CASE3 35 2127 531.64 4 1.6 - 531.64 4 36CASE2 1,624 541.24 3 2.0 73.66 614.90 2.64 Figures 8–1036 show 1624active power 405.93 output, 4 reactive power output, 81.51 and voltage 487.44 magnitude 3.33 in Figures 8–10 show active power output, reactive power output, and voltage magnitude in detailed time-domain35 dynamic 2127 simulation 708.85 following 3 a fault in system.- As can 708.85be seen in the 3 case of detailedCASE3 time-domain dynamic simulation following1.6 a fault in system. As can be seen in the case of Case 2, IILSCR 3.33,36 it recovers 1624 stably 541.24 after 3 fault. However, in 73.66 the case of CASE3 614.90 where 2.64 IILSCR becomesCase 2, IILSCR 2.24, it can3.33, be it seen recovers that oscillationstably after occurs fault. after However, fault. in the case of CASE3 where IILSCR becomes 2.24, it can be seen that oscillation occurs after fault.

Figure 8. Active power response at bus 36 after fault for IEEE 39 bus test system. Figure 8. Active power response at bus 36 after fault for IEEE 39 bus test system. Figure 8. Active power response at bus 36 after fault for IEEE 39 bus test system.

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Figure 9. Reactive power response at bus 36 after fault for IEEE 39 bus test system. Figure 9. Reactive power response at bus 36 after fault for IEEE 39 bus test system. Figure 9. Reactive power response at bus 36 after fault for IEEE 39 bus test system.

Figure 10. Voltage response at bus 2 after fault for IEEE 39 bus test system. Figure 10. Voltage response at bus 2 after fault for IEEE 39 bus test system.

3.2.1. Validation through Dynamic Simulation In the previous section, a dynamic simulation was explained to verify the differences in the system strength evaluation that occurred in 2022. Dynamic simulation assumes a single line 7–8 fault of 154 kV, three levels away from 2 buses in 1 s, and the fault was eliminated in 1.1 s. Bus 1 flows through bus 2 so that all the power generated by bus 1 can reach the center of load. As a result, bus 2 is affected by the amount of renewable energy generated by bus 1. Therefore, IILSCR of bus 2 is calculated by adding 673 MW of renewable power connected to bus 1 as well as 268 MW of bus 2. This would cause the IILSCR to decrease to 2.24, resulting in a very weak bus 2. In order for the IILSCR result to be greater than or equal to 3, it is necessary to limit the number of renewable Sustainability 2020, 12, 3469 8 of 18

3.2. Analysis of the Korea Power System Korea’s MOTIE has announced the ‘New Renewable 3020 Plan’ to increase the share of renewable energy to 20% of total generation by 2030. To this end, MOTIE plans to supply 48.7 GW of renewable energy generation facilities. More than 95% of the renewable energy power generation facilities, which will be installed from 2018 to 2030, will be sourced by clean energy such as solar and wind Sustainability 2020power., 12 The, x FOR southwest PEER REVIEW region, in which most of the installation is expected, is the region farthest from 9 of 18 the load center and without any synchronous generators. Figure 11 shows the southwest regional system one-line diagram (345 kV, 154 kV) in Korea and shows the highest concentration of IBRs in the southwest. To verify the effectiveness of IILSCR, the system strength of IBRs, which will be installed in the southwest region, is evaluated. Figure 12 is a schematic of the Southwest region where the renewable energy resources are installed. The buses 1 to 10 were selected in study areas. Table2 and connectionsFigure on buses 13 show 1 theand results 2. In of this the system study, strength we limit evaluation the number based on the of amount IBRs connected of renewable powerto bus 1 because we proposegeneration a method to be for installed evaluating in the study the area. system The Short stre Circuitngth Capacitythat reflects (SCC) value, intera whichction. represents Therefore, bus 1 connection thewas strength limited of the from AC system, 673 MW gradually to 400 increases MW. overIf the the 273 years; MW this isconnection the result of the is systemrestricted, being the IILSCR reinforced gradually. However, the system reinforcement does not occur, and the connection amount value for busof IBRs2 will is observed be 3.12. to Figures increase. 14–16 From 2019 show to 2021, dynamic SCR, WSCR, simulation and IILSCR result weres allfor higher the IILSCR than of bus 2 with 2.24 andthe weak3.12. criteria.As shown However, in the when figures, comparing if the results IILSCR of 2022, is 3 SCR or less, and WSCR the original were evaluated equilibrium as point cannot be foundsystem strengthafter the at busfailure 2, while and IILSCR the wasvoltage, less than reactive 3. The di ffpower,erent results and regarding active IILSCRpower from are oscillated. the previous two methods can be attributed to the difference between how these circuit ratios reflect Renewable generators based on inverters respond quickly to faults in the system using fast switching interactions. In the case of the SCR, it only reflected the amount connected to its bus, which resulted in devices. If therelatively renewable positive results.connection The second bus cause is not is the stro effectng, of the the boundariesreactive ofpower the buses injected being equalized by the renewable generator canin the cause WSCR. large In this changes, study, the WSCRcausing calculation causes is oscillations. equalized only whenHowever, a renewable when generator the IILSCR is is 3 or higher, the connectedinfluence within of the one renewable level away from generators the bus. If equalizedhas less within influence three levels, on the the AC results system. would be As shown in different. In the case of IILSCR, equalization is not required; hence, the system strength on each bus Figures 14–16,can beif assessedIILSCR and is 3 consistent or more, results after obtained. the fault, oscillation does not occur and a new equilibrium point is reached.

Figure 11. FigureThe configuration 11. The conﬁguration of southwest of southwest side side ofof Korea Korea power power systems systems transmission transmission grid. grid.

Figure 12. A Single-line diagram of the studied area for future renewable energy source (RES) connection. Sustainability 2020, 12, x FOR PEER REVIEW 9 of 18

connections on buses 1 and 2. In this study, we limit the number of IBRs connected to bus 1 because we propose a method for evaluating the system strength that reflects interaction. Therefore, bus 1 connection was limited from 673 MW to 400 MW. If the 273 MW connection is restricted, the IILSCR value for bus 2 will be 3.12. Figures 14–16 show dynamic simulation results for the IILSCR of bus 2 with 2.24 and 3.12. As shown in the figures, if the IILSCR is 3 or less, the original equilibrium point cannot be found after the failure and the voltage, reactive power, and active power are oscillated. Renewable generators based on inverters respond quickly to faults in the system using fast switching devices. If the renewable connection bus is not strong, the reactive power injected by the renewable generator can cause large changes, causing causes oscillations. However, when the IILSCR is 3 or higher, the influence of the renewable generators has less influence on the AC system. As shown in Figures 14–16, if IILSCR is 3 or more, after the fault, oscillation does not occur and a new equilibrium point is reached.

Sustainability 2020, 12, 3469 9 of 18 Figure 11. The configuration of southwest side of Korea power systems transmission grid.

Figure 12. A Single-line diagram of the studied area for future renewable energy source (RES) connection. Figure 12. A Single-line diagram of the studied area for future renewable energy source (RES) Table 2. Comparison among various indicesconnection. for southwest side of Korea power systems.

IBR Inﬂow from Total IBRs SCC Year Bus No. Capacity SCR WSCR Nearby Inﬂow IILSCR (MVA) (MW) IBRs (MW) (MW) 1 2090 150.0 13.93 - 150.0 13.93 2019 10.81 2 2101 43.5 48.30 150.0 193.5 10.86 1 2090 400.0 5.23 - 400.0 5.23 2020 4.39 2 2101 76.0 27.65 400.0 476.0 4.41 1 2094 400.0 5.24 - 400.0 5.24 4.40 2 2106 76.0 27.71 400.0 476.0 4.42 2021 4 3576 60.0 59.60 - 239.3 299.3 11.95 6 2917 37.5 77.79 - 239.3 276.8 10.54 1 2101 673.0 3.12 - 673.0 3.12 2.63 2 2112 268.0 7.88 673.0 941.0 2.24 2022 4 3574 60.0 59.56 - 612.1 672.1 5.32 6 2920 37.5 77.88 - 289.5 327.0 8.93 9 2980 50.0 59.60 - 175.5 225.5 13.22 1 2124 1112.5 1.91 - 1112.5 1.91 1.78 2 2136 268.0 7.97 1112.5 1380.5 1.54 2023 4 3776 60.0 62.93 - 1009.8 1069.8 3.53 6 2984 37.5 79.57 - 371.2 408.7 7.30 9 3466 50.0 69.33 - 356.0 406.0 8.54 Sustainability 2020, 12, x FOR PEER REVIEW 10 of 18

Table 2. Comparison among various indices for southwest side of Korea power systems.

Inflow from Bus SCC IBR Capacity Total IBRs Year SCR WSCR nearby IBRs IILSCR No. (MVA) (MW) Inflow (MW) (MW) 1 2090 150.0 13.93 - 150.0 13.93 2019 10.81 2 2101 43.5 48.30 150.0 193.5 10.86 1 2090 400.0 5.23 - 400.0 5.23 2020 4.39 2 2101 76.0 27.65 400.0 476.0 4.41 1 2094 400.0 5.24 - 400.0 5.24 4.40 2 2106 76.0 27.71 400.0 476.0 4.42 2021 4 3576 60.0 59.60 - 239.3 299.3 11.95 6 2917 37.5 77.79 - 239.3 276.8 10.54 1 2101 673.0 3.12 - 673.0 3.12 2.63 2 2112 268.0 7.88 673.0 941.0 2.24 2022 4 3574 60.0 59.56 - 612.1 672.1 5.32 6 2920 37.5 77.88 - 289.5 327.0 8.93 9 2980 50.0 59.60 - 175.5 225.5 13.22 1 2124 1112.5 1.91 - 1112.5 1.91 1.78 2 2136 268.0 7.97 1112.5 1380.5 1.54 2023 4 3776 60.0 62.93 - 1009.8 1069.8 3.53 Sustainability6 20202984, 12, 3469 37.5 79.57 - 371.2 408.7 10 of 18 7.30 9 3466 50.0 69.33 - 356.0 406.0 8.54

(a) (b)

Figure 13. Annual values values (IBR (IBR Capacity, Capacity, SCC, short circ circuituit ratio (SCR), weighted short circuit ratio (WSCR), and proposed interaction level short circuit ratio (IILSCR)) for the southwest side of future Korea power systemsystem (a(a)) IBR IBR capacity capacity of of point point of of interconnection interconnection (POI). (POI). (b) (b) Short Short circuit circuit capacity capacity of POI. of POI.(c) Calculation (c) Calculation of SCR of andSCR WSCR.and WSCR. (d) Calculation (d) Calculation of the of proposed the proposed IILSCR. IILSCR.

3.2.1. Validation through Dynamic Simulation In the previous section, a dynamic simulation was explained to verify the differences in the system strength evaluation that occurred in 2022. Dynamic simulation assumes a single line 7–8 fault of 154 kV, three levels away from 2 buses in 1 s, and the fault was eliminated in 1.1 s. Bus 1 flows through bus 2 so that all the power generated by bus 1 can reach the center of load. As a result, bus 2 is affected by the amount of renewable energy generated by bus 1. Therefore, IILSCR of bus 2 is calculated by adding 673 MW of renewable power connected to bus 1 as well as 268 MW of bus 2. This would cause the IILSCR to decrease to 2.24, resulting in a very weak bus 2. In order for the IILSCR result to be greater than or equal to 3, it is necessary to limit the number of renewable connections on buses 1 and 2. In this study, we limit the number of IBRs connected to bus 1 because we propose a method for evaluating the system strength that reflects interaction. Therefore, bus 1 connection was limited from 673 MW to 400 MW. If the 273 MW connection is restricted, the IILSCR value for bus 2 will be 3.12. Figures 14–16 show dynamic simulation results for the IILSCR of bus 2 with 2.24 and 3.12. As shown in the figures, if the IILSCR is 3 or less, the original equilibrium point cannot be found after the failure and the voltage, reactive power, and active power are oscillated. Renewable generators based on inverters respond quickly to faults in the system using fast switching devices. If the renewable connection bus is not strong, the reactive power injected by the renewable generator can cause large changes, causing causes oscillations. However, when the IILSCR is 3 or higher, the influence of the renewable generators has less influence on the AC system. As shown in Figures 14–16, if IILSCR is 3 or more, after the fault, oscillation does not occur and a new equilibrium point is reached. Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18

Sustainability 2020, 12, 3469 11 of 18

Figure 14. Active power response at bus 2 after fault for southwest side of Korea power systems. Figure 14. Active power response at bus 2 after fault for southwest side of Korea power systems. Figure 14. Active power response at bus 2 after fault for southwest side of Korea power systems. Figure 14. Active power response at bus 2 after fault for southwest side of Korea power systems.

Figure 15. Reactive power response at bus 2 after fault for southwest side of Korea power systems. Figure 15. Reactive power response at bus 2 after fault for southwest side of Korea power systems. Figure 15. Reactive power response at bus 2 after fault for southwest side of Korea power systems. Figure 15. Reactive power response at bus 2 after fault for southwest side of Korea power systems.

Figure 16. Voltage response at bus 2 after fault forfor southwestsouthwest sideside ofof KoreaKorea powerpower systems.systems.

3.2.2. OscillationFigure 16. Source Voltage Tracking response at bus 2 after fault for southwest side of Korea power systems. 3.2.2. OscillationFigure 16. Source Voltage Tracking response at bus 2 after fault for southwest side of Korea power systems. 3.2.2.With Oscillation dynamic Source simulation, Tracking if oscillation occurs on bus 2 after a fault, the oscillation will flow With dynamic simulation, if oscillation occurs on bus 2 after a fault, the oscillation will flow 3.2.2.through Oscillation the system. Source If oscillation Tracking occurs from the point of view of the system operator, the source of throughWith the dynamic system. simulation, If oscillation if occursoscilla fromtion occurs the po inton ofbus view 2 after of the a fasystemult, the operator, oscillation the willsource flow of the oscillation should be identified to eliminate the cause and facilitate stable operation. Therefore, it is throughWith the dynamic system. simulation,If oscillation if occursoscilla fromtion occurs the po inton ofbus view 2 after of the a fasystemult, the operator, oscillation the willsource flow of necessary to confirm whether the source of the generated oscillation, IILSCR, is from the lowest rated through the system. If oscillation occurs from the point of view of the system operator, the source of bus 2. To confirm this, the DEF (dissipating energy flow) method was applied. Using the DEF method Sustainability 2020, 12, x FOR PEER REVIEW 12 of 18

the oscillation should be identified to eliminate the cause and facilitate stable operation. Therefore, it isSustainability necessary2020 to, 12confirm, 3469 whether the source of the generated oscillation, IILSCR, is from the lowest12 of 18 rated bus 2. To confirm this, the DEF (dissipating energy flow) method was applied. Using the DEF methodbased on based the energy on the approach, energy approach, we can ﬁnd we sources can find of sources weakly dampedof weakly natural damped or forcednatural oscillations or forced oscillationsin the power in system.the power After system. obtaining After theobtaining values the of voltage, values of frequency, voltage, frequency, reactive power, reactive and power, active andpower active in the power bus through in the bus dynamic through simulation, dynamic thesimula sourcetion, of the oscillation source of was osci tracedllation using was thetraced following using theequations following [25, 26equations]. From [[25,26].25], an energyFrom [25], function an ener formgy function in the network form in has the been network derived has as been Equation derived (5) as Equation (5) to express that the energy dissipates at the network by the damping torque. to express that the energy dissipates at the network by the damping torque. =∆Z ∆ +∆∆ ln (5) D Wij = (∆Pijd∆θij + ∆Qijd(∆ ln Vi)) (5) where ∆ and ∆ are deviations from the steady-state values of the active and reactive power flowwhere in∆ branchPij and i-j;∆Q ∆ij are and deviations ∆ are fromdeviations the steady-state from the steady-state values of the values active of and bus reactive voltage power angle ﬂowand frequencyin branch i -atj; ∆busθi andi; ∆ isfi arethe deviationsbus voltage from magnitude. the steady-state ∆ln values= ln of−ln bus, voltage, where angle , andis the frequency steady- stateat bus voltagei; V is magnitude. the bus voltage Equation magnitude. (6) is an∆ approxln V = imatedln V lnformV ,of where EquationV is (5) the for steady-state the computational voltage i i i − i,s i,s purposemagnitude. [24]. Equation (6) is an approximated form of Equation (5) for the computational purpose [24].

∆ ∆R ∆ +∆ d(∆V ) D + ∗ i Wij ∆Pijd∆θij ∆Qij V ≈ i∗ (6) R d(∆Vi) = 2π∆Pij∆ fijdt + ∆Qij V ∆i∗ = 2∆ ∆ + ∆ ∗ ) (6) From this stage, there are no need to take steady-state quantities, but a mean value for the studiedFrom frequency this stage, or periodthere are by no applying need to fast take Fourier steady-state transformation quantities, (FFT) but doesa mean work value suffi forciently. the studiedFrom Equation frequency (6), valuesor period with by∆ applyingmeans that fast the Fourier deviation transformation between each (FFT) of the meandoes work values sufficiently. for studied = e + e Fromperiod. Equation Additionally, (6), valuesVi∗ Vwithi ∆ ΔV i meansand V i thatis the the average deviation voltage between in this each studied of the period. mean Furthermore, values for ∗ studiedEquation period. (6) is modified Additionally, to consider = discrete +∆ inputsand and is the dissipating averageenergy voltage outputs in this for studied each step period. [26], Furthermore,by constructing Equation a recurrence (6) is modi relationshipfied to consider as follows, discrete inputs and dissipating energy outputs for each step [26], by constructing a recurrence relationship as follows,   ∆Vi,k+1 ∆Vi,k 1  WD = WD + 2π∆P ∆ f t + ∆Q ∆ −∆− −  (7) i,j,k+1 i,j,k  ij,k i,k s ij,k , V ,  ,, =,, +2π∆,∆, · +∆, 2 ∗ i∗,k (7) 2, where ts isis the the time time step step between between samplings samplings for thefor dynamicthe dynamic simulation simulation and index and kindexfor each for quantity each quantityreflects the reflects time samplethe time number sample for number the time for instant. the time Figure instant. 17 shows Figure the 17 magnitudeshows the andmagnitude direction and of directionoscillation of energy oscillation after failure.energy Asafter with failure. the IILSCR As wi results,th the itIILSCR can be seenresults, that it the can oscillation be seen energythat the is oscillationhighest on energy bus 2. Figuresis highest 18 andon bus 19 show2. Figures the energy 18 and of 19 increasing show the oscillationsenergy of increasing that occur oscillations after in the thatstudy occur area after over time.in the Therefore, study area IILSCR over time. shows Theref that itore, is possibleIILSCR shows to evaluate that theit is system possible strength to evaluate more theaccurately system whenstrength connecting more accurately renewable when sources. connecting renewable sources.

Figure 17. Oscillation energy ﬂow. Sustainability 2020, 12, x FOR PEER REVIEW 13 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 13 of 18

Sustainability 2020, 12, 3469 Figure 17. Oscillation energy flow. 13 of 18 Figure 17. Oscillation energy flow.

FigureFigure 18. 18. LastLast value value of of oscillation oscillation dissipating dissipating energy energy flow ﬂow for for 10 10 s s of of time time interval. interval. Figure 18. Last value of oscillation dissipating energy flow for 10 s of time interval.

Figure 19. Calculation of oscillation dissipating energy after the fault. Figure 19. Calculation of oscillation dissipating energy after the fault. 4. Discussion Figure 19. Calculation of oscillation dissipating energy after the fault. 4. Discussion 4. DiscussionIn the previous section, we introduced the proposed method to detect interaction phenomena includingIn the oscillation previous andsection, veriﬁed we introduced the origin source. the prop Inosed this section, method we to discuss detect theinteraction relationship phenomena between In the previous section, we introduced the proposed method to detect interaction phenomena includingvoltage regulation oscillation deadband and verified and the the inﬂuence origin ofsource. interactions In this by changingsection, we deadband discuss range. the relationship The Korean including oscillation and verified the origin source. In this section, we discuss the relationship betweengrid code voltage for IBR regulation contributes deadband to voltage and stability the influenc by supplyinge of interactions or absorbing by changing reactive deadband power when range. the between voltage regulation deadband and the influence of interactions by changing deadband range. ThePOI Korean voltage grid is out code of the for 0.95–1.05 IBR contributes pu range. to Figurevoltage 20 stability shows theby voltagesupplying sensitivity or absorbing at the reactive 2 bus in The Korean grid code for IBR contributes to voltage stability by supplying or absorbing reactive powerdynamic when simulation. the POI voltage IBRs supply is out reactive of the 0.95–1.05 power to pu recover range. the Figure voltage 20 shows in the transientthe voltage period sensitivity after a power when the POI voltage is out of the 0.95–1.05 pu range. Figure 20 shows the voltage sensitivity atfault. the 2 When bus in the dynamic system simulation. strength is low,IBRs the supply voltage reactive sensitivity power is to increased, recover the and voltage oscillation in the is generated.transient at the 2 bus in dynamic simulation. IBRs supply reactive power to recover the voltage in the transient periodThis is becauseafter a fault. the reactive When powerthe system absorption strength and is supply low, ofthe all voltage nearby sensitivity IBRs is beyond is increased, the deadband and period after a fault. When the system strength is low, the voltage sensitivity is increased, and oscillationrange. In orderis generated. to prevent This the is because oscillation, the ifreactive the deadband power absorption is increased and to supply 0.9 to 1.0 of all pu nearby as shown IBRs in oscillation is generated. This is because the reactive power absorption and supply of all nearby IBRs isFigure beyond 21 ,the the deadband oscillation range. may beIn order eliminated. to prevent As mentioned the oscillation, earlier, if the increasing deadband the is deadbandincreased to range 0.9 is beyond the deadband range. In order to prevent the oscillation, if the deadband is increased to 0.9 tomay 1.0 causepu as voltageshown oscillationin Figure 21, problems, the oscillation so it is necessarymay be eliminated. to accurately As evaluatementioned the earlier, system increasing strength at to 1.0 pu as shown in Figure 21, the oscillation may be eliminated. As mentioned earlier, increasing thethe deadband planning stage.range Tomay apply cause the voltage proposed oscillation method proble to realms, power so it systems,is necessary the to exact accurately system evaluate topology the deadband range may cause voltage oscillation problems, so it is necessary to accurately evaluate theis important. system strength at the planning stage. To apply the proposed method to real power systems, the exactthe system system strength topology at is the important. planning stage. To apply the proposed method to real power systems, the exact system topology is important. Sustainability 2020, 12, x FOR PEER REVIEW 14 of 18

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Figure 20. Voltage sensitivity at bus 2 during dynamic simulation for southwest side of Korea power systems. Figure 20. Voltage sensitivity at bus 2 during dynamic simulation for southwest side of Korea Figure 20. Voltage sensitivity at bus 2 during dynamic simulation for southwest side of Korea power power systems. systems.

Figure 21. Reactive power voltage response capability for type-4 wind power plant. Figure 21. Reactive power voltage response capability for type-4 wind power plant. 5. Conclusions 5. Conclusion In this study,Figure a 21. system Reactive strength power evaluationvoltage response method capability is derived for type-4 that wind reflects power the interactionplant. effects betweenIn this IBRs. study, This a system method strength was developed evaluation by tracingmethod the is derived output ofthat IBR reflects to accurately the interaction assess systemeffects betweenstrength.5. Conclusion IBRs. Subsequently, This method this was method developed was applied by tracing to IEEEthe output 39bus of test IBR system to accurately and the assess future system Korea strength.systemsIn this toSubsequently, comparestudy, a system the this di ffstrength erencesmethod evaluation withwas applied the existing method to IEEE methodology. is derived 39bus test that system Thereflects energy and the interactionthe decision future method Koreaeffects systemswasbetween used to IBRs. to compare analyze This methodthe the differences oscillation was developed with source. the Asexistiby atracing resultng methodology. ofthe simulations, output of The IBR the energy to following accurately decision conclusions assess method system was can usedbestrength. drawn. to analyze Subsequently, the oscillation this method source. was As aapplied result ofto simulations,IEEE 39bus testthe followingsystem and conclusions the future can Korea be drawn. 1.systemsThe to system compare strength the differences evaluation with by the the proposed existing methodology. method is shown The toenergy correspond decision to themethod dynamic was 1. The system strength evaluation by the proposed method is shown to correspond to the used simulationto analyze results.the oscillation It has been source. shown As that a result if the of IBRs simulations, are concentrated the following in areas conclusions with weak systems, can be dynamic simulation results. It has been shown that if the IBRs are concentrated in areas with drawn.oscillation problems representing voltage instability may occur. weak systems, oscillation problems representing voltage instability may occur. 2. 1.The The energy system dissipation strength methodevaluation showed by the that prop theosed source method of oscillation is shown was to consistentcorrespond with to the weakestdynamic bus simulation of IILSCR. Aresults. bus can It has be the been weakest shown bus that since if the the IBRs bus are is influenced concentrated by bothin areas the IBRswith installedweak systems, on its bus oscillation and nearby problems the bus. representing voltage instability may occur. 3. When the IBRs are concentrated in weak area, the deadband range can be selected to eliminate voltage instability such as voltage oscillation. However, this method can cause power quality problems. Therefore, the system strength must be accurately evaluated for areas in which Sustainability 2020, 12, 3469 15 of 18

IBRs are concentrated. Therefore, the methodology proposed in this paper can serve as an adequate preliminary review to assess the system strength before adopting a detailed approach to system planning.

Author Contributions: D.K. conceived and designed the research methodology, performed the system simulations, and wrote this paper. B.L. supervised the research, improved the system simulation, and made suggestions regarding this research. H.C. and B.P. discussed the results and contributed to the writing of the paper. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by Korea Electric Power Corporation [Grant no. R17XA05–4] and Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), financed by the Ministry of Trade, Industry & Energy, Republic of Korea [Grant no. 20174030201540]. Conflicts of Interest: No conflicts of interest relevant to this article are reported.

Appendix A Derivation of (3) The active power ﬂow of bus i is composed of the sum of MW generated from IBR at bus i and MWs delivered from other IBR near bus i. P Pi = Pi j + PGi (u)d − e j α ∈ i P Pi j (A1) = d − e P + P f or i = 1, 2, , n Pj j Gi (u) ······ j α ∈ i Aﬀected by interaction at bus i with bus j can be expressed mathematically as follows [27,28]:

The active power ﬂows into the bus i can be simply expressed as PGi . By multiplying the inverse matrix of distribution Au matrix and Pg vec0.tor, which describes the generation of each bus, gives P, the active power supplied from individual buses.

X Pi j P = P d − eP P = AuP. (A2) Gi i − P j ⇒ G (u) j j α ∈ i Au matrix is an n n square upstream matrix for power distribution for all buses; individual × elements are given as follows,   1 f or i = j   Pj i (u) Au ij = d − e f or j α (A3)  Pj i d e  − ∈  0 f or otherwise

Assuming that Au matrix is nonsingular, a vector representing the active power supplied at each bus P and the supplied MWs at each bus Pi are shown as,

1 P = Au− PG (A4)

Xn 1 P = A− P (A5) i d u eik Gk k=1 Additionally, the result of Equation (A6) is an inﬂow MWs at bus i, which decides how much of generation component is composed of that bus as a multiple of Au upstream matrix and generated Sustainability 2020, 12, x FOR PEER REVIEW 16 of 18

Additionally, the result of Equation (13) is an inflow MWs at bus i, which decides how much of generation component is composed of that bus as a multiple of Au upstream matrix and generated power. Using the approaches above, we can describe the inflow from the transmission line i-j to bus Sustainability 2020, 12, 3469 16 of 18 i by proportional sharing rule as, power. Using the approaches above, we can describe the inﬂow from the transmission line i-j to bus i by proportional sharing rule as, = = n Pi j Pi j P = d − e = d − e 1 Pi j P Pi P Au− ikPGk d − e i i = d e k 1 (A6) = α P + α P + + α P Z =i1 G1 +i2 G3 + ∙∙∙∙∙······ +inGn (13) where 0 α 1 f or i = 1, 2, , n ≤ ik ≤ ······

Hence, the method is appliedℎ 0 as a tracing method 1 among = 1,2,∙∙∙∙∙, the interaction buses with respect to the transmission lines. Moreover, Equation (A6) decides the contribution of k-th generator for the amount of MWsHence, supplied the method to the transmissionis applied as linea tracingi-j. method among the interaction buses with respect to the transmission lines. Moreover, Equation (13) decides the contribution of k-th generator for the amountAppendix of MWs B supplied to the transmission line i-j. Criteria for Reliability and Quality of Electricity System of Korea Appendix B Reactive power capability requirements: Criteria for Reliability and Quality of Electricity System of Korea Wind generator: lag 0.95–lead 0.95, • Reactive power capability requirements: Tidal energy generator: lag 0.95–lead 0.95, • • Wind generator: lag 0.95–lead 0.95, •Photovoltaic generator: none. • Tidal energy generator: lag 0.95–lead 0.95, • Low Photovoltaic Voltage Ride generator: Through none. standard is shown in Figure A1. Low Voltage Ride Through standard is shown in Figure 22.

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