Distributed Load Shedding considering the Multicriteria Decision-Making Based on the Application of the Analytic Hierarchy Process

This paper shows an analytic hierarchy process (AHP) algorithm-based approach for load shedding based on the coordination of the load importance factor (LIF), the reciprocal phase angle sensitivity (RPAS), and the voltage electrical distance (VED) to rank the load buses. This problem is important from a power system point of view, and the AHP method is able to support the decision-making process in a simple and intuitive way in a three-criterion environment. This satisﬁes the multicriteria decision-making to meet economic-technical aspects. The ranking and distributed shedding power at each demand load bus are based on this combined weight. The smaller overall weights of the load buses show the lesser importance of the load bus, the smaller reciprocal phase angle sensitivity, and the closer voltage electrical distance. Therefore, these load buses cut a larger amount of capacity, and vice versa. By considering the generator control, the load shedding consists of the primary and secondary control features of the generators to minimize the load shedding capacity and restore the system frequency value back to the allowable range. The eﬃciency of the suggested load-shedding scheme was veriﬁed via the comparison with the under-frequency load shedding (UFLS). The latter result is that the load shedding power of the suggested approach is 22.64% lower than the UFLS method. The case studies are experienced on the IEEE 9-generator; the 37-bus system has proven its eﬀectiveness.


Introduction
In the load-shedding issue, the ranking of loads according to the priority of shedding is essential for adjusting the power balance, restoring frequency to bring economic, technical efficiency to customers. erefore, it is necessary to determine which loads need to be classified in the list of loads to be shed and their priority order. e ranking of these loads should satisfy many aspects that require an analysis of the economic and technical consequences. However, the calculation of economic and technical analysis is very complicated, and most power companies in the world still base on the evaluation of electrical system experts. However, it is very difficult for experts to prioritize these loads, especially when a load needs to be considered in many different criteria.
Studies on optimizing load shedding considering multiobjective constraints are mainly to solve the problem of minimizing the load shedding power. e proposal of a multiobjective optimization model considering load-shedding risk [1] is of interest to many researchers operating power systems. e multiobjective constraints are mostly technical constraints, such as conditions for power constraints of generating sets, power carrying capacity of the line, and the voltage at the nodes. However, in current times, the load shedding must meet many different goals, including achieving the technical requirements and economic goals including restoring frequency, load importance factor, the damage caused by power shedding, and priority level. e distributed shedding power at each demand load buses so that it is optimal and reduces the damage to the power supplier as well, such as customer power consumption. Solving this multicriteria load-shedding problem needs the application of algorithms for system experts.
e calculation of the load-shedding power is an essential factor to return the frequency back to the value within the permissible range and prevent the frequency degradation in the power system [2,3]. e load-shedding power is usually calculated based on frequency degradation [4], calculating the amount of load-shedding power; if the calculation is insufficient, it will not be possible to restore the frequency to the permissible value, and vice versa will cause excessive load shedding. Studies on load shedding mainly calculate it based on the rotation motion of the rotor [5]. However, these methods do not consider the actual operating conditions such as primary and secondary controls of generating sets. e techniques of load shedding are distributed into three fundamental areas of study [6]: conventional load shedding, adaptive load shedding, and intelligent load shedding techniques. Conventional load shedding is a method of load shedding by using underfrequency loadshedding (UFLS) or under-voltage load-shedding (UVLS) relays. is is the most common method used for frequency control and voltage stabilization of the power grid. According to the IEEE standard, UFLS must be implemented quickly to prevent the electrical system frequency attenuation and power system blackout [7]. Many works used UFLS and UVLS [8][9][10][11]. ese studies have the advantage of a low-cost, simple working principle. However, they have the main disadvantage that they do not estimate the amount of unbalanced power in the system. is result causes excessive load shedding, affects the quality of electricity, or leads to the discontinuation of electricity services or consumers [12]. In [13,14], the high-priority loads were considered during load shedding, but the secondary frequency control was not added. Reference [15] showed the UFLS using decision trees to decide whether the load needs to be cut or not and the amount of load capacity to be cut. e decision tree was built based on the frequency derivative, the load demand, and the system's reserve capacity. However, this method has not considered the important factor of the load in the electricity system. e adaptive loadshedding method uses the swing rotor equation to calculate the amount of load shedding [5]. Rate of change of frequency (ROCOF) relay is used to perform load shedding [16]. e method proposed in [12] used both frequency deviation and voltage parameters to improve the accuracy of the frequency and voltage stability. In [17], a semi-adaptive multistage UFLS plan with ROCOF element and AHP method is proposed. e AHP method is based on two main criteria including the total amount of load shed and the minimum point of frequency response to rank the importance of load shedding. However, assessing the importance of loads based on the AHP algorithm has not been considered. In [18], the artificial neural network (ANN) and power flow tracing were used to evaluate the total active power imbalance. e load priority was considered in this study. However, the 0-1 variable is introduced to represent. e load priority of the load at bus k was allowed to be shed; the value of a is set to 1. Otherwise, the value of a was set to 0. is shows that the baseload and the ranking of load shedding priority have not been considered in this situation. e intelligent load-shedding methods include the application of intelligent algorithms such as artificial neural network (ANN) [19][20][21], adaptive neural-fuzzy inference system (ANFIS) [22,23], fuzzy logic control (FLC) [24], genetic algorithm (GA) [25], and particle swarm optimization (PSO) [26,27] to calculate and select the shed load. ese approaches can easily solve nonlinear, multiobjective problems in power systems that conventional methods cannot solve with the desired speed and acceptable accuracy [19,28]. For ANN, the output is the total quantity of active power that needs to be cut. is output is not an actual signal because it does not determine the number of loads and the load capacity to be shed in each step. Multiobjective optimization methods using GA or PSO algorithms only have constraints on technical conditions. ese methods do not have a combination of multiple methods including economic technical parameters when studying the load ranking. In [29], the weight coefficient in the load shedding objective equation was adjusted to satisfy the actual needs. Furthermore, reference [30] coordinated the optimization loadshedding method based on sensitivity analysis. e weighted sum of economic expense and equilibrium index was taken as the objective function to establish the load-shedding optimization model. However, this model has not considered the important factor of the load and has not yet ranked the load in the order of priority load. is paper focuses on the coordination of various objectives during the load-ranking process. In this paper, a new load shedding method is presented based on the calculation of primary and secondary control of the generator to determine the minimum amount of shedding power. It coordinates criteria to consider the aspects to respond to load shedding in the direction of decision-making multicriteria.
is satisfies the technical and economic factors to optimize the distribution of the power shedding at each load bus.
ere is an easier method for experts to approach the critical issues of load shedding criteria. When giving opinions, they often rely on technology characteristics and operating realities to be able to make verbal comments. Experts make it easy for a comparison of pairs and common languages like Load 1 is more important than Load 2, or Criterion 1 is more important than Criterion 2. In addition, the evaluation of the important rank of the load in the frequency control problem is also considered under many criteria with different importance levels. e paper proposes an approach based on consultation with experts when expressed in words. Each load will be considered under many criteria. e efficiency of the suggested load-shedding technique was proved through the test on the 9-generator, 37-bus system. e calculations are evaluated with a traditional underfrequency load-shedding method.
e results have shown that the suggested approach has a lower amount of load shedding capacity than the UFLS method. erefore, the proposed method can minimize the damage and inconvenience caused to electricity customers. e recuperation time and rotor deviation angle are still guaranteed within the permissible values and sustained the power system stability. In addition, the proposed method demonstrates the combination of multimethod taking into account both technical and economic criteria that have not been carried out by previous studies. erefore, in large disturbance situations such as large outage generators, this proposed method can be used to teach operators and improve their skills.

Calculate the Overall Weights and Rank the Load Buses to
Load Shedding Based on the AHP Algorithm. It is supposed that there are m loads to be shed in the electrical system diagram. ese loads need to be ranked for load shedding based on coordination of three criteria including LIF, RPAS, and VED. e problem is that in the case of outage generators and load shedding is required, ranking and distributing the amount of load-shedding power to these loads require the satisfaction of multiple criteria simultaneously. To achieve that, it requires technical and economic consequences analysis. However, these calculations and analysis are very complicated and time-consuming. erefore, it is necessary to collect reviews of power system experts in this regard. Experts easily give a verbal comment when comparing each pair of criteria and using common language, such as Criterion 1 is more important than Criterion 2. In this section, the AHP method is able to support the decision-making process in a simple and intuitive way in a three-criterion environment to calculate the overall weights of criteria and rank the load buses to load shedding. e ranking of the load buses is based on the AHP method which includes three stages: establishing the hierarchical structure, determining the weights of criteria, and calculating the overall weights.

Stage 1: Establishing the Hierarchical Structure.
is step targets to solve the problem of the ranking of load buses into a hierarchical structure [31][32][33][34]. Accordingly, a three-level hierarchical structure is proposed for calculating the overall weights, as shown in Figure 1. In this study, three types of criteria are proposed: LIF, RPSA, and VED. e three criteria are described in detail in the following sections.
(1) First Criterion: e Reciprocal Phase Angle Sensitivity (RPAS) from the Load Buses to the Outage Generator. e concept of the RPAS between two buses is defined as follows [35][36][37][38][39]: In the power system, the goal is to concentration on the priority of load shedding at the nearby outage generator location. To do this, the idea of the RPAS between two buses is applied. Two buses close to each other always have exceptionally little RPAS. e smaller the RPAS between the load buses and the outage generator, the closer the load bus is to the outage generator. erefore, when a disturbance occurs in an area on the grid, adjusting the grid in the disturbance area will achieve the best effect.
us, minimizing the control errors in the disturbance area will have little effect on other areas in the system. Additionally, in load shedding, the delineation of a serious disturbance and load shedding around the disturbance area make the impact of the disturbance on a smaller system a more effective loadshedding method. e following steps show the calculation of the reciprocal phase angle sensitivity: Step 1: Extract the Jacobian matrix [J Pθ ] Step 2: Inverse elements in the Jacobian matrix [J Pθ ], calculate the elements in the matrix [J − 1 Pθ ] Step 3: Apply formula (1) to calculate D p(i, j) e weight of the load bus based on the RPAS between the load bus and the outage generator is calculated by the following formula: where W D P (i,j) is the weight of the RPAS from the i-bus to the outage generator and D P (i, j)is the RPAS from the i-load bus to the outage generator.
Step 2: Calculate [zV/zQ]in all buses. is value is the inverse of the Jacobian matrix that indicates the effect on a voltage variation at neighboring buses of reactive power injection at a bus. where Step 3: Calculate α ij using the sensitivity matrix of step 2. e voltage changes in the bus i due to voltage change in bus j are as follows: where α ij is defined as Step 4: Calculate the VED using (α ij × α ji ), which is reflected by the symmetrical distance.
where α ji is defined as

Mathematical Problems in Engineering
After calculating the VED, the weight of the load buses based on the VED between the load buses and the outage generator is calculated by the following formula: where W D P (i,j) is the weight of the VED from the i-load bus to the outage generator and D V (i, j) is the VED from the iload bus to the outage generator. e VED is the physical relationship between two buses in the power system. Formula (5) shows that the closer the distance, the smaller D V or the largerα ij . On the other hand, formula (4) evaluates the voltage interactions between bus i and bus j. e bigger α ij is, the greater the voltage attenuation at bus i when a disturbance occurs at bus j. us, when an outage generator occurs, the amplitude of the voltage fluctuation near this generator is large, leading to an attenuation voltage at nodes with a small VED also increasing. To ensure the voltage profile returns to its stability margin, the amount of load shedding at each bus can be calculated on the principle that the smaller the VED, the larger the load shedding power, and vice versa. e relationship between the generator and the loads is shown in Figure 2. With: (3) ird Criterion: e Load Importance Factor (LIF). e parameters of the LIF weight, W LIF , were calculated by the fuzzy AHP algorithm and suggested to be in [34]. e LIF shows how important the loads are to each other when the assessor considers mainly the economic aspect. In other words, the larger the W LIF is, the more damage when load shedding is.

Stage 2:
Determining the Weights of Criteria. Based on the established hierarchy structure, there are three steps to determine the weights of criteria. Firstly, pair-wise comparison or judgment matrices are formed to measure the relative importance of each two criteria.
e pair-wise comparison scale proposed by Saaty [44] is applied, as showed in Table 1. A pair-wise comparison matrix is described by the following equation. e value of p ij is equal to the reciprocal of p ij in the pair-wise comparison matrix.
where P is a pair-wise comparison matrix and p ij is the importance of the i-th criteria relative to the j-th criteria. Secondly, the largest eigenvalue and the eigenvector of a pair-wise comparison matrix are calculated. e relation among the largest eigenvalue, eigenvector, and pair-wise comparison matrix is defined by the following equation. e eigenvector is then normalized to obtain the weight vector of corresponding criteria.
where P is a pair-wise comparison matrix, λ max is the largest eigenvalue of the pair-wise comparison matrix, and ω is the corresponding eigenvector. irdly, the consistency index and consistency ratio of a pair-wise comparison matrix are evaluated, as the inconsistency may happen due to subjective expert judgment. ey are defined by the following equations. A pair-wise comparison matrix is satisfied if the stochastic consistency ratio, CR < 0.10.
where CI is the consistency index of a pair-wise comparison matrix, CR is the consistency ratio of the matrix, RI is the random index of the matrix, λ max is the largest eigenvalue of the matrix, and n is the number of criteria in the matrix.

Stage 3: Calculating the Overall Scores.
e overall score of each load bus is calculated by using equation (11). e higher the overall score of load bus is, the more important the load bus is. It means that the higher the load is ranked, the less the load shedding distributed power to that load bus is done.
where μ A ∼ i is the overall score of each load bus, W i is the weight of the i-th criterion, and W D,j are the values rep-

Calculate the Minimum Load-Shedding Power and Distribute Load-Shedding Power at the Load Buses.
After the overall weights are calculated for each load bus, the distributed shedding power at each demand load bus can be implemented according to the following flow chart in Figure 3.
Distributing the shedding power at the load buses requires two processes. In the first process, from the grid configuration and the location of the outage generator, the overall weights are calculated with the support of the AHP algorithm; the results are presented in equation (11). In the second process, when there is an outage generator and load shedding has to be implemented; the calculation of the load shedding power taking into account the process of primary and secondary frequency controls reduces the amount of shedding. is minimizes damages to customers due to power outages.

Primary and Secondary Frequency Controls in Power
System. e process of frequency control when there is a disturbance in the power system consists of stages: level 1 control or primary frequency control and level 2 control or secondary frequency control [45]. In case after performing the level 2 control, the frequency has not returned to the allowable value, the load shedding control must be implemented to restore the frequency to the allowable value. e generator frequency control process includes primary and secondary frequency controls described in [46,47]. e process of this control is shown in Figure 4.
In summary, in the case of an outage of the generator or a power imbalance between the load and the generator, the power system implements primary and secondary frequency controls. After the implementation of the secondary frequency control adjustment process, the electrical system's frequency has not yet recovered to the permissible value, the load shedding will be implemented to restore the frequency.
is is the last mandatory solution to avoid grid blackout and power system collapse.

Establish the Minimum Load-Shedding Power.
e calculation of the minimum load shedding power ensures the minimum amount of power is shed while restoring the power system frequency to the permissible value and minimize damage to electricity users. e computation takes into account the primary control and the secondary control of the generator group in accordance with the actual operation. e relationship between the load power variations with frequency variation is determined by the following equation: where P L is the active power of the load, ∆P D is the change of load power according to frequency change, and D is the percentage characteristic of the change of load according to the percentage change of frequency, D value ranges from 1% to 2%. It is determined experimentally in power systems [48]. For example, a value of D � 2% means that a 1% change in frequency will cause a 2% change in load. In the power system with n generators and m loads, when the power system has an outage of the generator, the primary frequency control of (n − 1) remaining generators is  performed with the amount of power adjustment according to the following expression: where ΔP Primary control is the primary control power of the i-th generator, P Gn,i is the rated power of the i-th generator, Δf 1 � f 1 − f 0 is the frequency attenuation, and f 0 is the rated frequency of the power system. When an outage of the generator occurs, the difference between the generator power and the P L load power results in a frequency difference; in particular, the frequency is attenuated. e amount of load power depending on the frequency will be reduced by the amount of ∆P D , and the value of ∆P D is presented in formula (12). e status of power balance is presented in the following formulas: Set ΔP L � P L − n− 1 i�1 P G i and β � P L .D + n− 1 i�1 P G n,i /R i . From formula (17) In the case of considering the power of the secondary control to restore the frequency, the new status of power balance with the new frequency value f 2 , equation (14) becomes: where ΔP Secondary control max is the maximum amount of secondary control power generated by the power system. is amount of secondary control power is determined by the following equation: ΔP Secondary control max � m j�1 P Gm,j − ΔP Primary control, j , (20) where P Gm,j is the maximum generating power of the secondary frequency control generator j and ΔP Primary control, j is the primary control power of the secondary control generator j.
After including the secondary control process and the system frequency has not yet restored to the fallow the allowable value, then load shedding is required to recover the frequency; the minimum amount of load shedding power P LSmin is calculated by the following equations: (H) where Δf allow � f 0 − f allow is the allowable frequency attenuation.
Formula (22) is abbreviated into the following formula:

Distribute Load-Shedding Power at the Load Buses.
After calculating the overall weights and the P LS min , the load-shedding power at each load bus can be distributed in the same way as the principle of load sharing in the parallel circuit as follows: with where P LSi is the amount load shedding power at the buses, μ eq is the equivalent weight of all load buses, μ A ∼ i is the overall weights at the i-th bus, and P LSmin is the total minimum load shedding power.

Case Studies.
e efficiency of the suggested approach is experienced on the IEEE 37-bus 9-generator system [47,49], which is shown in Figure 5. All test cases are simulated using PowerWorld GSO 19 software. e calculations are compared with the traditional load shedding method using an underfrequency load-shedding relay.
In the studied case, the generator JO345 # 1 (bus 28) is facing an outage and disconnected from the grid. Using formula (18), the established frequency value is calculated when the JO345 # 1 generator (bus 28) faces an outage at 59.6 Hz. e frequency value after the outage of generator JO345 # 1 (bus 28) is less than the allowed value. erefore, it is important to execute the process of the generator control and re-establish frequency. e primary frequency control is performed automatically. e reaction of the governor is performed immediately after the generator JO345 # 1 (bus 28) has been outage. e primary control power values for each generator turbine are shown in Table 2.
Because the recovery frequency is less than the allowed value, the secondary frequency control process should be implemented after the primary control. Secondary standby generator control power will be mobilized to perform secondary control. In the IEEE 37-bus 9-generator power system diagram, the SLACK 345 (SLACK bus) was chosen as the secondary frequency control generator. In this case, using equation (20), the amount of secondary control power calculated is 10.72 MW. A graphical simulation of the frequency of the system after the implementation of the secondary control is illustrated in Figure 6.
us, after carrying out the secondary control process, the recovery frequency is 59.66 Hz and has not been back to the allowed value. erefore, the ultimate solution is load shedding to restore the frequency to the allowable value. Application of formula (24) calculates the minimum amount of load shedding power to restore the frequency to the permissible value.
In a 60 Hz power system, the permissible frequency attenuation ∆fallow is 0.3 Hz.
In summary, the minimum load shedding power P LSmin is 17.64 MW.
We implemented the same calculation steps above for a few other case studies. We calculated the value of the system frequency, the amount of primary and secondary control power and the load power to be reduced. Calculation results for these case studies are shown in Table 3. e results of these calculations are the basis for the distribution of the amount of load-shedding power at the load buses based on the overall weights of the criteria.
After computing the minimum amount of load-shedding power, the next step calculates the load importance factor (LIF), the reciprocal phase angle sensitivity (RPAS), and the voltage electrical distance (VED). Using formulas (2) and (6), calculate the reciprocal phase angle sensitivity (RPAS) and the voltage electrical distance (VED). e parameters of the load importance factor (LIF) were calculated by fuzzy AHP algorithm and published by the authors in [34]. e overall weights for multimethod coordination criteria will be calculated using theory at stage 2: determining the weights of criteria section and expert opinion, obtaining P matrix as follows: e eigenvector is calculated based on the matrix P; its value is shown below: Equations (8)-(10) are used to calculate the largest eigenvalues (λ max ), the consistency index (CI), and the stochastic consistency ratio (CR), respectively. e calculation results are presented as follows: e above results show that the values of stochastic consistency ratio CR � 0.00775 < 0.1, so the proposed judgment matrix is reasonable.
After obtaining the weighted values of the criteria, the next step applies formula (11) to determine the values of the overall weights of each load bus and applies formula (25) to calculate the amount of power needed to be shed at each busload; the values are shown in Table 4 and Figure 7. e smaller overall weights of the load bus indicate that the load bus is of minor LIF, the RPAS is small, and the VED is small and, therefore, that the load will prioritize the shedding load with a large amount of load shedding power, and vice versa. e suggested approach is compared to an underfrequency load-shedding relay approach. ese values are shown in Table 5 [34].
It can be seen that the proposed load-shedding method has less amount of shedding (65.19 MW) than the UFLS, thereby minimizing the damage caused by power outages a lot. Simultaneously, satisfying the goal of combining a variety of economic and technical methods: e Load Importance Factor 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48

Discussion
e AHP method is quite simple and intuitive in a threecriterion environment. It easily supports the calculation of the overall weights of the criteria. In this study, the pair-wise comparison matrixes are formed by one expert. If there are many experts, some group decision-making methods can be accepted to aggregate the pair-wise comparison matrixes determined by these experts [50]. For example, a weighted geometric mean method can be used as a tool to do this aggregation. In addition, if the value of the pair-wise comparison is uncertain, the combined use of AHP with fuzzy methods is also one of the possible solutions [34].
For a very large power system, when there is a failure of one generator, the space of influence on the technical parameters of the entire grid is negligible. It is only significant when very serious problems occur and the large-power system is divided into smaller systems or islands. In particular, in the larger power grid, areas far from the outage generator are not affected much. It only affects the areas near and around the outage generator. erefore, this situation does not need to take the entire grid into consideration. In  [44] e W RPSA between the load buses and the outage generator is calculated by formula (24) e W VED between the load buses and the outage generator is calculated by formula (29) e IEEE 37-bus 9 generator system Grid configuration and the Generator outage location  this case, the problem should only be considered in a range around the "observation area" that is affected by the outage generator. e determination of RPAS and VED will support determining this influence gap. However, the RPAS and VED values for each grid configuration need to be studied further. At this time, the opinion of the power system expert will support limiting "observation areas" and "inter-observation areas".

Conclusions
e calculation of overall weights includes the following criteria: Reciprocal Phase Angle Sensitivity (RPAS), Voltage Electrical Distance (VED), and Load Importance Factor (LIF). It ensures multicriteria decision-making that meets economic and technical factors. e analytic hierarchy process algorithm is applied to calculate the weights of the criteria, thereby contributing to combining the weights of the criteria together to determine the combined weight. is weight is used to rank and distributed shedding power to the load buses. e computation of the amount of load shedding includes the generator control processes that makes the loadshedding power less than the UFLS method and restores the frequency to the allowed value. e distributed shedding power at each demand load bus based on the overall weights W ensures multimethod coordination of economic and technical criteria and reduces technical and economic losses to power companies and customers. e efficiency of the suggested approach has been verified on the 37-bus 9-generator system under case studies. is implementation is better than that of the traditional UFLS method.
e results proved that the suggested approaches solutions to reduce amount of shedding power while still meeting the technical and economic operating conditions of the network. In future work, the load-shedding scheme should reflect the following aspects minimizing the economic and technical losses of both power companies and customers. To solve this multiobjectives problem, we need to apply algorithms such as genetics algorithm and PSO. e feasibility of the proposed technique has been shown on the 37-bus system with 9 generators under various experiments.
is presentation is superior to that of the traditional UFLS method. e discoveries show that the proposed strategy brings about a decreased measure of load shedding while at the same time fulfilling the specialized technical-economic operating conditions of the network. Later in work, the load-shedding issue ought to consider the accompanying components minimizing the economic and technical losses of both influence organizations and clients. To resolve this multiobjective issue, we need to apply calculations like genetics algorithm and PSO.
Data Availability e data of expert opinion in the formulation of the judgment matrix and parameter values and primary control power of the generator used to support the findings of this study are included within the article. e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.

Authors' Contributions
All the authors contributed to the study's conception and design. Topical guidance was performed by Nghia T. Le. Material preparation, data collection, and analysis were performed by An T. Nguyen, Trang H. i, Vu Nguyen Hoang Minh, Anh H. Quyen, and Binh T. T. Phan. e first draft of the manuscript was written by Nghia T. Le, and all the authors commented on previous versions of the manuscript. All the authors read and approved the final manuscript.  4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29  Voltage in steady state before the load rejection Voltage in steady state a er the load rejection