Evaluating the Effect of Distributed Generation on Power Supply Capacity in Active Distribution System Based on Sensitivity Analysis

In active distribution system (ADS), the access of distributed generation (DG) can effectively improve the power supply capacity (PSC). In order to explore the effect of DG on the PSC, the influence of accessed DG on the power supply of ADS has been studied based on generalized sensitivity analysis (SA). On the basis of deriving and obtaining the sensitivity of the evaluation indexes of the PSC to the parameters of connected DG, seeking for the DG access instruction for the purpose of improving the PSC, PSC evaluation model with inserted DG is established based on SA. The change degrees and trends of the PSC and its evaluation indexes caused by the slight increase of DG are calculated rapidly, which provides reference for the planning and operation of ADS. Finally, the feasibility and validity of the proposed theory are validated via IEEE 14-node case study.


Introduction
The power supply capacity (PSC) of distribution network is the maximum load that the network can provide on the condition of meeting the branch power and node voltage constraints, which is determined by the operation mode of the distribution network and the growth mode of the load.Thus, the PSC is one of the most significant indexes that reflect the reliability and safety of active distribution system (ADS).The PSC evaluation is supposed to be performed in accurate and reliable system, which is not only able to provide the effective guidance for the grid optimization and economic operation, but also the feasible foundation for the system planning and construction [1][2][3][4][5][6].
ADS is assembled with the ability of active load control and power flow interaction.In ADS, with the progressive increase of the permeability of distributed generation (DG), flexible load, energy storage components and other distributed energy resources, the PSC of distribution network has been effectively improved [7][8][9].Among the DG connected to the grid, those which are installed on the user side are widely distributed and usually in small capacities, easy to install and take usage of.The widespread application of DG in the distribution network can not only promote the local consumption of electricity power and reduce the cost of purchase, but also can effectively alleviate the power shortage during peak load and improve the PSC.Nevertheless, in certain distribution networks, the flexibility of DG provides multiple options for its location distribution, type matching and capacity allocation.The possibility of DG real-time adjustment closely affects the assessment of the PSC.Moreover, the influence on the PSC which is exerted by randomness and volatility of DG output cannot be ignored [10][11][12][13][14]. Therefore, in the background of ADS, the quantitative study of DG changes on the PSC is significant and indispensable to the accurate assessment.
In the field of the PSC evaluation in ADS, plenty of research works have been completed by domestic and foreign scholars.In [15], in view of the interaction of main transformers and the N-1 guideline, the adjustment of PSC calculation is investigated on the condition of the tie-line capacity and the main transformer's overload.Considering the connection of DG and distributed storage system, an N-1 reconstruction model for calculating maximum PSC was mentioned in [16].Aiming for the characteristics of uncertainties of DG output and periodic fluctuation of grid load, [17] provided ADS with a real-time evaluation method of the PSC.
In all of the investments above, the access of DG is taken into consideration, implying its positive impact on PSC improvement.However, the development of the electricity market puts forward higher requirements for the accuracy and efficiency of the PSC evaluation.The PSC assessment provides real-time capacity and available capacity basis for the electricity market transactions of different time scales, which is an important guarantee for reliable power transaction.In the market environment, when the factors of accessed DG change, such as capacity, output and location, the accurate and rapid re-evaluation of PSC is required necessarily.In order to describe the change of the dependent variable caused by the fluctuation of the independent variable, the generalized sensitivity, one of the most significant means, has been widely used by scholars in multiple fields [18,19].Drawing on this idea, the PSC evaluation system in ADS is established in this paper.
In order to improve the accuracy of PSC evaluation and explore the DG distribution guidance to enhance the PSC level, and further put forward an evaluation system which is applicable to general situations, an investigation of PSC evaluation in ADS based on sensitivity analysis (SA) is developed.In the proposed model, aiming to analyze the impact on PSC by accessed DG, the SA of indexes to DG factors which includes type, output and location has been carried out referring to the existing PSC evaluation indexes based on the idea of generalized sensitivity.On that basis, the PSC evaluation model is established with DG taken into account.On the foundation of the sensitivity formulas achieved by SA, combined with the PSC evaluation model, the fluctuation of PSC upon the changes of DG can be calculated reliably and rapidly, providing vital reference for the dispatching and operation of ADS.
In the following papers, the PSC evaluation indexes are selected and the sensitivity formulas are deduced in Section 2; then PSC evaluation models are established in Section 3; on that basis, Section 4 is a generalization of the whole method and case study is carried out in Section 5.

Selection of PSC Evaluation Indexes for SA
In order to evaluate the effect of accessed DG on the PSC of the distribution system comprehensively, [20] put forward a series of general evaluation indexes from the aspects of numerical size, fluctuation situation and contribution degree, including the expectation, the shortage and shortage rate of PSC, the contribution amount and the contribution rate of DG, etc.Here four indexes are chosen as follows: (1) Expectation of PSC (E PSC ): where M is the number of the total probabilistic scenario; S PSC (i) is the PSC of the i-th scenario, which is a discrete variable calculated using the parameters of the corresponding scenario; p(i) is the probability of occurrence of the i-th scenario.
Energies 2017, 10, 1473 3 of 14 (2) Dissatisfied Amount of PSC (DA PSC ), representing the value of E PSC that is less than its allowable value: where A is the allowed value of E PSC .
(3) Contribution Rate of DG to Expectation of PSC (CR DTE ), representing the relative promotion level of E PSC after the connection of DG: where E PSC,N (t) is the E PSC without the connection of DG.
(4) Contribution Rate of DG to Dissatisfied Amount of PSC (CR DTDA ), representing the relative decrease level of DA PSC after the connection of DG: where DA PSC,N is the DA PSC without the connection of DG.

Sensitivity of the Expectation of PSC to DG output
Calculate the sensitivity of E PSC to DG output at node j suitable for any distribution system, which is shown in Equation ( 5): where P DG (j) is the DG output at point j; N l is the sum of the quantities of the branches where loads locate in; f (•) is the empirical formula of the change amount of load carrying capacity on the change amount of the line capacity; P L (i,n) is the active power flow to the n-th load node in the i-th scenario.The solution of Equation ( 5) requires calculating the partial derivative of P L (i,n) to P DG (j), which is equivalent to the partial derivative of branch power to node injection power.When the grid is injected by unit power at node j, the active power of branch l can be deduced as follows [21].
Ignore the branch grounding impedance, and the branch power of the system can be presented as Equation ( 6): where P jk , G jk and B jk are active power, conductance and susceptance, respectively; U j and δ j are the amplitude and phase angle of node j.
The branch power flow is not only related to the amplitude and phase angle of the node voltage, but also to the size of the power injected at each node, so there is Equation (7): where P j and Q j are the active and reactive power injected at node j.
After performing the first-order Taylor series expansion on both sides, and combining with P jk (U j0 , δ j0 ) = P jk (P j0 , Q j0 ), the Equation ( 7) can be presented as: when the power flow is calculated using the Newton-Raphson method, the modified equation can be expressed as: where J is the Jacobi matrix in the modified equation of the Newton-Raphson method; H jk = ∂∆P j ∂δ k ; Substitute Equation (9) into Equation (8), and it gives: when ∆δ j and ∆U j /U j can be arbitrarily small, it gives: Transpose both sides of the equation at the same time, and Equation ( 12) can be obtained: Conduct further deduction of Equation ( 12) and it gives: Substitute Equation (13) into Equation ( 5), and the general sensitivity formula of E PSC to DG output at node j can be achieved:

Sensitivity of Other Evaluation Indexes of PSC to DG output
According to the main idea of the section above, the sensitivity formulas of other PSC evaluation indexes to DG output can be derived.
(1) Sensitivity formula of DA PSC to DG output Deduce the sensitivity of DA PSC to DG output at node j, which is shown in Equation (15): Energies 2017, 10, 1473 5 of 14 (2) Sensitivity formula of CR DTE to DG output Deduce the sensitivity of CR DTE to DG output at node j, which is shown in Equation ( 16): Because E PSC,N is irrelevant with P DG (j), and ∂E PSC,N /∂P DG (j) = 0, Equation ( 16) can be further simplified as: (3) Sensitivity formula of CR DTDA to DG output Deduce the sensitivity of CR DTDA to DG output at node j, which is shown in Equation ( 18): Likewise, ∂DA PSC,N /∂P DG (j) = 0, and Equation ( 18) can be further simplified as:

Sensitivity of Evaluation Indexes of PSC to DG type
The effects of different types of DG on the PSC upgrading mainly reflect on their corresponding output.Thus, the sensitivity of PSC evaluation indexes to DG type can be expressed as below: (1) Sensitivity formula of E PSC to DG type where S PV (j) and S WG (j) are the capacity of photovoltaic (PV) power and wind generation (WG) connected at node j, respectively; P PV (j) and P WG (j) are the output of PV and WG at node j, respectively.
(2) Sensitivity formula of DA PSC to DG type Energies 2017, 10, 1473 6 of 14 (3) Sensitivity formula of CR DTE to DG type (4) Sensitivity formula of CR DTDA to DG type

PSC Evaluation Model Based on the SA of DG
Due to the sensitivity formulas of PSC evaluation indexes to DG which is deduced above, the PSC evaluation model is established as follows.On the basis of this evaluation model, the PSC change degrees, change trends as well as evaluation indexes brought by the DG fluctuation can be derived quickly and accurately in the same topology.Moreover, the optimized distribution of DG is able to be obtained aiming to improve the PSC.

Calculation Model of PSC
(1) Objective function where P L is the maximum active load which is supplied by the distribution network; N is the number of the load node; P Li is the active load at load node i.
(2) Constraint condition where P Gi , P DGi and P Li are the active power of generator, DG and load at node i, respectively; Q Gi , Q DGi and Q Li are the reactive power of generator, DG and load at node i, respectively; G ij and B ij are the conductance and susceptance of branch i-j; θ ij is the power factor angle between node i and j; U i , U max i and U min i are the upper limit and lower limit of the voltage at node i; I l and I max l are the current and its upper limit at branch l; S T and S max T are the power and its upper limit of the transformer T.

The Non-Parametric Kernel Density Probability Model of DG
In this paper, the non-parametric kernel density probability model of DG is employed to establish the multiple-scenario of SA for PSC evaluation.Completely rooted from the data samples, non-parametric kernel density estimation method does not need any prior knowledge, which makes it one of the most effective methods to consider the characteristics of DG output.Furthermore, the method has been applied successfully in various areas, including load modeling, wind speed modeling and reliability index calculation [22,23].In the PSC evaluation based on SA, the non-parametric kernel density estimation method is adopted to model the output of the DG accessed to the system.
Let the n samples of DG output be p 1 , p 2 , . . ., p n , and the probability density function of DG output f k (p) can be obtained based on the theory, which is shown in Equation (34): where h is the bandwidth; n is the number of the sample; K(•) is the kernel function.
Select the commonly used Gaussian function as the kernel function, which is expressed in Equation (35).
On the foundation of the Latin hyper-cube sampling technique [24], the non-parametric probabilistic model of DG output is taken to extract samples with the length of M, and the multiple-scenario probability model of DG output is established.

PSC Reckoning Based on SA
Based on the deduction and solution of the sensitivity formulas of PSC evaluation indexes, the amount of PSC change is supposed to be calculated when the location, capacity or type of DG differs.According the change amount, the PSC is able to be reckoned when the connection situation of DG changes, which is shown in Equation (36).Similarly, the reckoning formula of other PSC evaluation indexes to DG is given in Equation (37).
where S' PSC,EI (t) is the reckoning value of the EI-th PSC evaluation index at time point t; S PSC,EI (t) is the evaluation value of the EI-th PSC evaluation index before the DG connection changes at time point t; SA EI (k) is the sensitivity of the EI-th PSC evaluation index to the k-th DG change.

Steps of PSC Evaluation Based on SA
The steps PSC evaluation based on SA can be summarized as follows and presented in Figure 1: (1) Base on the demands of PSC evaluation from various aspects, multiple PSC evaluation indexes are selected according to the consideration of numerical size, adequacy, and contribution degree of DG. (2) Based on the generalized sensitivity formulas, the sensitivity formulas of position, output and type of accessed DG are defined and deduced.
where S'PSC,EI(t) is the reckoning value of the EI-th PSC evaluation index at time point t; SPSC,EI(t) is the evaluation value of the EI-th PSC evaluation index before the DG connection changes at time point t; SAEI(k) is the sensitivity of the EI-th PSC evaluation index to the k-th DG change.

Steps of PSC Evaluation Based on SA
The steps PSC evaluation based on SA can be summarized as follows and presented in Figure 1  Energies 2017, 10, 1473 9 of 14

General Situation of the System
The modified IEEE 14-node system is employed to the PSC evaluation in ADS based on SA as in Figure 2, which is simulated in the platform of MATLAB.
In Figure 2, node 1 is the balance node and the rest are all load nodes.The reference capacity of the system is 100 MVA, and the reference voltage of the system is 23 kV.Set the power limit of the branches as its thermal stability limit capacity, and voltage allowable range as 1 ± 5%.
accessed DG are of the same type.(8) Based on the SA results of step 6, the PSC evaluation results in ADS can be reckoned and compared when the types of the accessed DG are different.(9) Comparing with the PSC evaluation results in step 5, and the PSC reckoning results based on SA in steps 7 and 8, the feasibility and effectiveness of the PSC evaluation based upon the SA can be verified.

General Situation of the System
The modified IEEE 14-node system is employed to the PSC evaluation in ADS based on SA as in Figure 2, which is simulated in the platform of MATLAB.
In Figure 2, node 1 is the balance node and the rest are all load nodes.The reference capacity of the system is 100 MVA, and the reference voltage of the system is 23 kV.Set the power limit of the branches as its thermal stability limit capacity, and voltage allowable range as 1 ± 5%.

General Situation of the Distribution System
Based on the principle of non-parametric kernel density estimation, the probability model of DG output is established.On that basis, applying the Latin hyper-cube technology, the probability samples at the length of 10 are extracted from the output intervals of PV power and WG with the rated power of 1 MW, which is shown in Table 1.Due to the non-sequential sampling results, the weighted sums of the corresponding DG samples are taken as their probabilistic output.

General Situation of the Distribution System
Based on the principle of non-parametric kernel density estimation, the probability model of DG output is established.On that basis, applying the Latin hyper-cube technology, the probability samples at the length of 10 are extracted from the output intervals of PV power and WG with the rated power of 1 MW, which is shown in Table 1.Due to the non-sequential sampling results, the weighted sums of the corresponding DG samples are taken as their probabilistic output.

Sensitivity Calculation of PSC Evaluation
Based on the sensitivity formulas of PSC evaluation indexes to DG, which is derived from the previous theory, the evaluation indexes and the sensitivity values of the case are calculated, taking node 3 as an example.The results are expressed in Table 2. On the condition of single type of DG (take PV power for instance) accessed to the system, let the capacity of DG increase at the speed of 1 MW/time.The E PSC values were reckoned and the comparison of reckoning and evaluation values are completed based on sensitivity, which are illustrated in Figures 3 and 4, respectively.According to Figure 3, the smaller the DG capacity accessed to the grid, the more concise the SA can be.In Figure 4, it is obvious that the relative error increases as the DG capacity grows.It can be seen that, in order to ensure the accuracy of the results obtained, the reckoning of E PSC according to SA is preferably within a small range.

Sensitivity Calculation of PSC Evaluation
Based on the sensitivity formulas of PSC evaluation indexes to DG, which is derived from the previous theory, the evaluation indexes and the sensitivity values of the case are calculated, taking node 3 as an example.The results are expressed in Table 2. On the condition of single type of DG (take PV power for instance) accessed to the system, let the capacity of DG increase at the speed of 1 MW/time.The EPSC values were reckoned and the comparison of reckoning and evaluation values are completed based on sensitivity, which are illustrated in Figures 3 and 4, respectively.According to Figure 3, the smaller the DG capacity accessed to the grid, the more concise the SA can be.In Figure 4, it is obvious that the relative error increases as the DG capacity grows.It can be seen that, in order to ensure the accuracy of the results obtained, the reckoning of EPSC according to SA is preferably within a small range.Based on the sensitivity formulas of PSC evaluation indexes to DG, which is derived from the previous theory, the evaluation indexes and the sensitivity values of the case are calculated, taking node 3 as an example.The results are expressed in Table 2. On the condition of single type of DG (take PV power for instance) accessed to the system, let the capacity of DG increase at the speed of 1 MW/time.The EPSC values were reckoned and the comparison of reckoning and evaluation values are completed based on sensitivity, which are illustrated in Figures 3 and 4, respectively.According to Figure 3, the smaller the DG capacity accessed to the grid, the more concise the SA can be.In Figure 4, it is obvious that the relative error increases as the DG capacity grows.It can be seen that, in order to ensure the accuracy of the results obtained, the reckoning of EPSC according to SA is preferably within a small range.(2) Reckoning of the other PSC evaluation indexes based on SA Except for E PSC , sensitivities of the rest of the PSC evaluation indexes to DG mainly contribute to calculate the corresponding evaluation indexes.Here, the sensitivity of each index to the DG output is calculated as an example.Figure 5 presents the comparison between the evaluation results and reckoning results of the four PSC indexes based on sensitivity.The contrast results show that the PSC evaluation indexes calculation can basically rely on the corresponding sensitivities, and the results of which can provide certain reference value.In addition, with the enlargement of the reckoning radius, the prediction accuracy is basically decreasing.It means that the application of SA is conditional, which is suitable for the calculation in a small range.
Energies 2017, 10, 1473 11 of 14 (2) Reckoning of the other PSC evaluation indexes based on SA Except for EPSC, sensitivities of the rest of the PSC evaluation indexes to DG mainly contribute to calculate the corresponding evaluation indexes.Here, the sensitivity of each index to the DG output is calculated as an example.Figure 5 presents the comparison between the evaluation results and reckoning results of the four PSC indexes based on sensitivity.The contrast results show that the PSC evaluation indexes calculation can basically rely on the corresponding sensitivities, and the results of which can provide certain reference value.In addition, with the enlargement of the reckoning radius, the prediction accuracy is basically decreasing.It means that the application of SA is conditional, which is suitable for the calculation in a small range.(3) Ratio selection of DG Based on SA In to investigate the influence of different types of DG on the PSC, the connection of pure PV, pure WG and the combination of PV and WG are considered, respectively.In each case, EPSC is reckoned using sensitivity index and compared with the evaluation results, as shown in Figure 6.The differences between PSC calculation results are mainly attributed to the type ratios of DG.The EPSC change is mostly due to the actual DG output, in this example, the output is represented by probabilistic average of sampling.(3) Ratio selection of DG Based on SA In order to investigate the influence of different types of DG on the PSC, the connection of pure PV, pure WG and the combination of PV and WG are considered, respectively.In each case, E PSC is reckoned using sensitivity index and compared with the evaluation results, as shown in Figure 6.The differences between PSC calculation results are mainly attributed to the type ratios of DG.The E PSC change is mostly due to the actual DG output, in this example, the output is represented by probabilistic average of sampling.
Figure 6 provides users the optimal choice of DG capacity ratio.In this case, it suggests that with the same capacity, the PSC value is the most satisfying when pure PV is accessed, and the one with the connection of PV and WG in a same-size ratio ranked second, which makes the third system all installed with WG the last choice.It follows that the PSC improvement and the increase of the load level of the ADS are more relevant to PV power than WG generation here.This phenomenon may be attributed to the significant contribution of PV power during the day time, which is capable of meeting the peak electricity demand better.
In order to investigate the influence of different types of DG on the PSC, the connection of pure PV, pure WG and the combination of PV and WG are considered, respectively.In each case, EPSC is reckoned using sensitivity index and compared with the evaluation results, as shown in Figure 6.The differences between PSC calculation results are mainly attributed to the type ratios of DG.The EPSC change is mostly due to the actual DG output, in this example, the output is represented by probabilistic average of sampling.

Conclusions
The PSC has a direct bearing on the load capacity of the ADS.For the sake of improving the accuracy of the PSC evaluation and exploring the optimal ratio of PSC to DG, the PSC evaluation indexes are selected and the sensitivity formulas are deduced in view of the idea of the generalized sensitivity.On that basis, the PSC and its evaluation indexes are reckoned precisely and rapidly, providing important references for the operation and dispatching of the ADS.The results of the case study indicate that: (1) On the foundation of the generalized sensitivity, the sensitivity formulas applicable to PSC evaluation are deduced and calculated, the analysis results of which are capable of providing the sensitivity of PSC evaluation indexes to the type, output and capacity of DG at specific node directly and effectively.(2) In view of the sensitivity results obtained above, the fluctuation of PSC and its evaluation indexes are supposed to be reckoned at specific node when the type and capacity of added DG varied, offering vigorous evidence for the PSC evaluation of multiple perspectives.(3) Considering the connection of various types of DG at the same node, the optimal DG proportion of type and capacity can be presented, as well as its corresponding PSC numerical result, which contributes to lowering the investigation costs and optimizing the PSC.(4) The application of the PSC evaluation based on SA is limited by the DG, the capacity of which is supposed to be within a certain small boundary.Furthermore, the calculation precision is in inverse proportion to the distance between reference point and reckoning point.On one hand, the PSC evaluation based on SA is supposed to meet the demand of the operation and scheduling of ADS basically; on the other hand, starting from the point of view of upgrading and planning, it may be necessary to build up a new sensitivity criteria to provide guidance for the component renewal and the further expansion of the power grid.
where S' PSC (t) is the reckoning value of PSC at time point t; S PSC (t) is the evaluation value of PSC before the DG connection changes at time point t; SA(k) is the sensitivity of PSC to the k-th DG change (when k = 1, SA(k) represents the change of DG output; when k = 2, SA(k) represents the change of DG type); C DG (j,k) is the parameter which represents the k-th DG change at node j.

Energies 2017, 10 , 1473 8 of 14 ( 3 )
Taking constraint conditions into consideration, including the active and reactive power flow, branch capacity and node voltage, the basic model of PSC evaluation is established.(4) On the basis of the non-parametric kernel density estimation theory, the uncertainty of DG output is simulated and the probability model is established.The output samples are extracted from the model by Latin hyper-cube sampling technique to form multiple scenarios with different probabilities.(5) Due to the traditional PSC evaluation methods, the PSC values are calculated when the type and capacity of the connected DG differs.(6) Calculate the sensitivity value corresponding to the PSC and its evaluation indexes.(7)Based on the SA results of step 6, the PSC evaluation results in ADS can be reckoned when the accessed DG are of the same type.(8) Based on the SA results of step 6, the PSC evaluation results in ADS can be reckoned and compared when the types of the accessed DG are different.(9)Comparing with the PSC evaluation results in step 5, and the PSC reckoning results based on SA in steps 7 and 8, the feasibility and effectiveness of the PSC evaluation based upon the SA can be verified.Energies 2017, 10, 1473 8 of 14

:Figure 1 .
Figure 1.Flow chart of PSC evaluation based on SA.

Figure 1 .
Figure 1.Flow chart of PSC evaluation based on SA.

Figure 3 .
Figure 3.The fluctuation situation of the reckoning value and evaluation value of EPSC with single type of DG connected.

Figure 4 .
Figure 4.The fluctuation situation of the relative error of reckoning value to evaluation value of EPSC with single type of DG connected.

Figure 3 .
Figure 3.The fluctuation situation of the reckoning value and evaluation value of E PSC with single type of DG connected.

Figure 3 .
Figure 3.The fluctuation situation of the reckoning value and evaluation value of EPSC with single type of DG connected.

Figure 4 .
Figure 4.The fluctuation situation of the relative error of reckoning value to evaluation value of EPSC with single type of DG connected.Figure 4. The fluctuation situation of the relative error of reckoning value to evaluation value of E PSC with single type of DG connected.

Figure 4 .
Figure 4.The fluctuation situation of the relative error of reckoning value to evaluation value of EPSC with single type of DG connected.Figure 4. The fluctuation situation of the relative error of reckoning value to evaluation value of E PSC with single type of DG connected.

Figure 5 .
Figure 5. (a) Reckoning results of the EPSC based on SA; (b) Reckoning results of the DAPSC based on SA; (c) Reckoning results of the CRDTE based on SA; (d) Reckoning results of the CRDTDE based on SA.

Figure 6 .
Figure 6.The comparison of the reckoning value and the evaluation value of EPSC with different types

Figure 5 .
Figure 5. (a) Reckoning results of the E PSC based on SA; (b) Reckoning results of the DA PSC based on SA; (c) Reckoning results of the CR DTE based on SA; (d) Reckoning results of the CR DTDE based on SA.

Figure 6 .
Figure 6.The comparison of the reckoning value and the evaluation value of EPSC with different types of DG accessed.

Figure 6 .
Figure 6.The comparison of the reckoning value and the evaluation value of E PSC with different types of DG accessed.

Table 1 .
Sampling results of the probabilistic output of DG.

Table 1 .
Sampling results of the probabilistic output of DG.

Table 2 .
Calculation results of PSC evaluation indexes and corresponding sensitivities at node 3.

Table 2 .
Calculation results of PSC evaluation indexes and corresponding sensitivities at node 3.

Table 2 .
Calculation results of PSC evaluation indexes and corresponding sensitivities at node 3.