Review on Energy Resilience

Optimal Grid Reconfiguration Algorithm for Improving System Resilience under Extreme Weather Events

Victor Widiputra, Jaesung Jung* Department of Energy Systems Research

Ajou University Suwon, South Korea

e-mail: [email protected], [email protected]

Abstract—Due to global warming, the number of extreme weather events has increased in the last ten years. Consequently, the number of power system blackouts has also increased in this period. The reliability index is incapable of analyzing the power system behavior during these events because it does not account for extreme weather events for its calculation. Therefore, the resilience index is proposed for measuring the system functionality during extreme weather events. To increase the resilience value of the system, its functionality during such events must be increased. One way to achieve this is through the reconfiguration of the power system, to ensure that the parts of the power system which do not experience failure remain operational even during the extreme weather events. This paper proposes an algorithm to determine the optimal reconfiguration of the power system to increase the grid resilience. First, it applies the actual condition of the system during the extreme weather events. Then, the algorithm finds the islanded buses in the power system using bus injection to bus current (BIBC) matrix. Finally, the algorithm utilizes a genetic algorithm to find the optimal reconfiguration for the system. The results show that the reconfiguration strategy can be utilized to increase the system resilience under similar extreme weather events.

Keywords-bus injection to bus current; extreme weather; grid resilience; power system reconfiguration

I. INTRODUCTION

The IPCC has warned governments worldwide to prepare for an increase in extreme weather events due to global warming [1]. Power systems are fundamental aspects that require special attention due to their vulnerability to extreme weather events. As per a survey conducted in [2], the number of extreme weather events with power outages in the USA has increased by 64% between 2008-2015. The IPCC suggests the implementation of a thorough disaster risk management system for damage prevention during extreme weather events. However, the calculation of the reliability index herein eliminates extreme weather events that have a low probability of occurrence [3]. Therefore, it does not provide information regarding the system’s response to extreme weather events. Therefore, to evaluate the system’s ability to withstand the extreme weather, resilience index is introduced [4].

The resilience index enables evaluation of how well prepared the system is, and can respond and adapt to an

extreme weather event [5]. A resilient system can effectively minimize the impact of an extreme weather event, and hence minimize the time required for restoration; furthermore, it can also determine preventive actions required to ensure that the system can withstand a similar event in the future. One approach to minimize the damage to the system is by reconfiguring the system during the extreme weather events, because it enables the system to supply an undamaged islanded load.

The framework in [6] is shown for the genetic reconfiguration algorithm, which is used for the restoration of the power system; moreover, this reconfiguration algorithm was proposed considering the load priority and the connection between interdependent buses in the power system. Another approach proposed in [7] utilized Prim’s algorithm to convert the power system into a graph to find the candidates that require reconfiguration. An application for the reconfiguration of a radial distribution system is proposed in [8]. Their work formulated new network constraints by analyzing the voltage angle of the buses. However, none of these works are specifically aimed at increasing the resilience index of the power system.

This paper proposes an algorithm to improve the grid resilience index for reconfiguration of the grid by operating the sectionalizing switch to supply the undamaged bus during an extreme weather event. The bus injection to bus current (BIBC) matrix was utilized to analyze the topology of the system. Such an analysis shows the current flow to each bus in the system, which is useful for finding the islanded buses. The algorithm then searches for the nearest switch that can be operated to supply the islanded buses without violating the operational constraints. The actual data available for extreme weather events is applied to the system. Subsequently, the genetic algorithm is applied to determine the optimal reconfiguration for the system to increase the resilience index.

The remainder of this paper is organized as follows: Section II presents the concept of the grid resiliency and its possible improvement through reconfiguration of the power system. Then, Section III presents the proposed reconfiguration algorithm by applying the actual condition of the system during an extreme weather event. Section IV presents a case study to verify the proposed algorithm. Finally, the findings of the study are summarized in Section V.

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II. GRID RESILIENCY IMPROVEMENT BY RECONFIGURING THE POWER SYSTEM

A. Grid Resilience Index There are multiple ways to quantify the system’s

resilience. One of the most popular ways is by using the system’s functionality [5], which shows its performance at a specific time. This functionality can be calculated as the ratio between the current active customers and the total customers in the power system. At a given analysis time t, a system has a functionality which can be defined as:

where, ( ) and active totaln t n are the number of active customers at time t and total customers in the system, respectively. An extreme weather event would damage the system, which would then need repair accordingly. However, this process will affect its functionality, with the value of its functionality following the curve shown in Fig. 1. The three major analysis points in the grid resilience quantification represent the times when: First, an extreme weather occurs ( ), second, the system is at its worst condition ( ), and third, the system is fully restored ( ). , , and are the corresponding grid functionality values at , , and , respectively. The three points form a resilience triangle. A better system performance will result in a smaller area of the resilience triangle.

Figure 1. Grid functionality under an extreme weather event.

There are several resilience indexes that can be used to evaluate the system [5]. However, grid reconfiguration does not guarantee an improved restoration time of the system. Therefore, in this study, only two resilience indexes are considered. The first index is the capacity resilience ( ) [9], and the second is the operational resilience ( ). The index is used to compare the system’s performance with its original performance. The recovery time and the system states are considered for calculation of . The damaged and restored states of the system are first normalized by its stable state and, then, multiplied by a recovery speed index. Subsequently, a comparison can show the ability of the system to minimize the damage relative to its normal condition as follows:

, (2)

where, are the grid functionality at damaged, restored, and normal conditions, respectively, and

is the recovery speed index, which compares the time before the beginning of the restoration with the time required to fully restore its functionality after an extreme weather event. It can be expressed using the following equation:ggg

The operational resilience ( ) shows the amount of grid functionality that can be restored within a given restoration time. It provides an average value of the grid functionality that can be restored within a given restoration time. It can be stated as:

(4)

Figure 2. The effect of grid reconfiguration in an extreme weather event.

B. Resiliency Improvement by Reconfiguration Power system reconfiguration can help us operate the

system even in an extreme weather event. Fig. 2 illustrates the effect of the microgrid operation on the grid functionality during an extreme weather event. The blue triangle shows the grid functionality before the reconfiguration, and the green triangle shows the grid functionality after the formation of the microgrid during an extreme weather event.

At the beginning of an extreme weather event (time tE), the functionality is reduced to Q(tD) without any reconfiguration. The system must wait until it can be repaired, i.e., until time tR, to restore its full functionality. In contrast, the green triangle shows the effect of grid reconfiguration. The sectionalizing switches can be operated to supply the undamaged island in the system; thus, the grid functionality can be increased from Q(tD) to Q′(tD). As shown in Fig. 2, this results in a reduced area of the resilience triangle, and thus, into an increased value of the resilience index.

III. OPTIMUM POWER SYSTEM RECONFIGURATION ALGORITHM

To determine the optimum reconfiguration for the system, the proposed algorithm encodes the switch into a combination of binary numbers. A value of 1 shows that the

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switch is closed, and 0 shows that the switch is open. For example, a system with 16 switches can be represented as

(5)

Using the encoded switch, the optimization can be done by using a genetic algorithm [10], for using which, an objective function is required. With the aim to improve the resilience index, the objective function can be stated as:

(6)

where and are the capacity resilience index before and after the reconfiguration, respectively;

and are the operational resilience index before and after the reconfiguration, respectively; and are the power loss on the system before and after the reconfiguration, respectively; and , , are the weight for the capacity resilience index, operational resilience index, and power losses, respectively. If there are no islanded buses during an extreme weather, the proposed algorithm minimizes the power loss of the system; therefore, the power loss objective needs to be added.

During the extreme weather event, the system will be in the damaged state (from tE to tR). In this period, the buses can be categorized as: normal buses which do not experience failure (type 1); damaged buses which experience failure (type 2); and islanded buses which do not experience failure but are not supplied by any generator (type 3).

To increase the resilience index, the reconfiguration must supply the type 3 bus. Furthermore, to identify the bus type 3, the system is converted into its bus injection to branch current (BIBC) matrix. The BIBC matrix shows the current flow in each branch in the system and can be represented as follows:

(7)

The columns and rows of the T matrix represent the bus current injection in the system. Each element of the BIBC(n,m) shows whether a current is injected from bus n into bus m bus through a branch where n and m are the row and column of the BIBC matrix, respectively. The value of each element can be expressed as:

(8)

When there is an islanded bus, there is no current injection to the bus. Consequently, every element in that row of the BIBC is 0. As a result, the sum of every element in that row is 0. This can be stated as:

1

( , ) 0 j

m BIBC n m

�

�� (9) where j is the maximum number of the columns in the BIBC matrix.

To improve the result of the optimization and make sure the result is viable from the point of view of system

operation, the optimization considers some constraints as below: � The number of islanded buses must be reduced after the

reconfiguration. If there are i islanded bus before the reconfiguration, then the system must fulfil below condition

, (9)after beforei i i� � (10) where and after beforei i are the number of islanded buses

after and before the reconfiguration, respectively. � The operating voltage of each active bus must be within

the permissible range (11)

where are the minimum and maximum permissible voltages of the system which is 0.95 and 1.05 p.u., respectively, and is the voltage at bus h.

Figure 3. The proposed optimal grid reconfiguration algorithm.

The proposed algorithm for the grid reconfiguration is shown in Fig. 3 and can be explained as follows: � Step 1: Determine the failure probability of each bus when

an extreme weather event strikes the system by analyzing the historical data

� Step 2: Generate the extreme weather event � Step 3: Create the BIBC matrix for the damaged system. � Step 4: Check the presence of islanded buses in the system

using equation (7). If no island is formed during the extreme weather event, the system is not restored until all failures have been cleared from the system, after which, proceed to Step 8. Otherwise, we need to go back to Step 5, i.e., if one or more islands are formed.

� Step 5: Determine the optimum reconfiguration for the power system using the genetic algorithm by using equation (8) as the objective function.

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� Step 6: Run a 48-hour simulation of an extreme weather event using the scenario formed in Step 2.

� Step 7: Determine the resilience indexes using equations (2)-(4).

IV. CASE STUDY

A. Simulation Parameters This paper used the actual power grid damage from

Korea Electric Power Corporation (KEPCO) and local weather data from Korea Meteorological Administration (KMA) [11] from January–March 2018 in South Korea to determine the optimal reconfiguration. The test circuit used for the simulation is a modified IEEE 30-bus system. Each bus has different number of customers. The circuit is modified by adding a sectionalizing switch in some lines in the system; the red switches indicate the switch in open condition, as shown in Fig. 4, and those in green indicate the switch in closed condition, as shown in Figs. 5 and 6. The switches are assumed to be open during normal operation. The reconfiguration, in the simulation, is performed by isolating the failures in the system and reconnecting the islanded buses through one of the sectionalizing switches. The system is shown in Fig. 4 and the number of customers in each bus is provided in Table 1.

TABLE I. CUSTOMER DATA ON EACH BUS OF THE POWER SYSTEM

Bus Number Total Customer Bus Number Total

Customer

1 0 16 214,602

2 189,877 17 144,443

3 230,059 18 110,056

4 291.027 19 102,896

5 293,207 20 59,943

6 282,561 21 41,251

7 291,720 22 268,541

8 302,034 23 0

9 298,553 24 226,689

10 930,303 25 168,722

11 0 26 101,733

12 197,128 27 0

13 0 28 0

14 747,72 29 123,043

15 27,773 30 87,075

TABLE II. OPERATIONAL RESILIENCE OF THE SYSTEM

Case ROP, Before ROP, After Improvement 1 0.308 0.396 28.3%

2 0.333 0.337 1.3%

TABLE III. CAPACITY RESILIENCE OF THE SYSTEM

Case RC, Before RC, After Improvement 1 0.849 0.973 14.6%

2 0.819 0.849 3.68%

Figure 4. The modified IEEE 30 bus system.

Two storms are simulated according to the recorded data. The damages are normalized into a 48-hour period to directly compare the resilience index between the storms. The timing of the damage caused by the storm in the simulation is matched to its actual time. For instance, if storm A starts to damage bus 1 at 2 P.M., then the simulation considers a damage to bus 1 at 2 P.M. The storms that are included in the simulations are:

1) Case 1

Figure 5. System condition after reconfiguration in Case 1.

In Case 1, Typhoon Halong, which lasted from August 14, 2014 until August 15, 2014 is simulated. The damaged

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buses are bus 5, 6, 7, 8, and 28. In this case, buses 27, 29, and 30 will be islanded if the switch stays in its original condition. However, the grid can be reconfigured to supply the islanded buses. The proposed algorithm manages to find the switch combination which ensures that the supply to the islanded bus is fulfilled while maintaining the required operating performance. The system condition after the reconfiguration is shown in Fig. 5. The red crosses show the buses that experience failure. The resilience improvement for both cases is summarized in Table 2 and Table 3. It can be seen that the algorithm manages to improve both the resilience indexes that are used to evaluate the system.

2) Case 2 In Case 2, Typhoon Nanmadol, which lasted from July

3rd, 2017 until July 4th, 2017 is simulated. The damaged buses are 5, 7, 8, 20, and 22. In this case, buses 21, 27, 28, 29, and 30 will be islanded if the switch stays in its original condition. However, the grid can be reconfigured to supply the islanded buses. In this case, two islands are formed. The first island consists of bus 21, and the second island consists of bus 27, 28, 29 and 30. The system condition after the reconfiguration is shown in Fig. 6. The red crosses represent the buses that experienced failure. It can be seen that, in this case as well, the algorithm manages to improve both the resilience indexes that are used to evaluate the system. The improvement of the resilience index is not as significant as the previous case. From Table 1, it can be seen that the damaged buses in case 2 has low number of customers compared with the damaged buses in case 1. Therefore, the damages caused by the typhoon does not reduce the grid functionality significantly. However, the proposed algorithm can still improve the grid resilience index.

V. CONCLUSION

An optimum reconfiguration algorithm was developed to increase the resilience index of the system. The proposed algorithm utilizes BIBC matrix to find the islanded buses and uses it as a constraint to limit the search space of the optimization. The algorithm was tested on a modified IEEE 30 bus system. Two cases of actual extreme weather events were applied to the test system. The proposed algorithm managed to increase the operational and capacity resilience values of the system. Therefore, the algorithm has performed satisfactorily to find the optimum reconfiguration of the power system. However, a further development is required for the proposed algorithm to be applied for an online analysis on a real-time basis under extreme weather event.

ACKNOWLEDGMENT

This research was supported by Korea Electric Power Corporation. (Grant number: R17XA05-37).

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