CN116454873A - Average frequency obtaining method and related device for power system - Google Patents

Abstract

The invention discloses a method for calculating the average frequency of a power system and related devices. The invention divides the power system into regions, determines the centers of inertia of each region, and calculates the average frequency of the power system based on the frequencies of the centers of inertia of each region. The method only The frequency of the center of inertia needs to be monitored. While ensuring accuracy, the number of monitoring points is greatly reduced, the efficiency of calculating the average frequency of the system is improved, and it can provide technical support for fault area positioning and real-time power gap calculation.

Description

A method and related device for calculating the average frequency of a power system

technical field

The invention relates to a method for calculating the average frequency of a power system and related devices, belonging to the technical field of power systems and automation thereof.

Background technique

The frequency stability of the power system refers to the ability of the system frequency to maintain or return to the allowable range without frequency collapse when the power system is severely disturbed and there is a large imbalance between power generation and load demand. When the system is disturbed and there is a shortage of active power, before the system returns to a steady state, its frequency will experience a transient process of oscillation, which is the dynamic frequency response of the system. This process is a multi-stage oscillation process, and the disturbance energy Due to the difference in grid structure and inertia distribution, different regions and different nodes are affected by disturbances in different degrees, and the frequency response characteristics are different, which has the characteristics of time and space distribution.

With the gradual increase of the grid-connected scale of new energy, the proportion of output continues to increase, and its inertia-free characteristics have an impact on the frequency response of the system. First of all, due to the reduction of the equivalent inertial time constant of the system, the frequency response of the same proportion of power imbalance in a high proportion of new energy connected to the grid is more severe, and the decline speed is faster and deeper; secondly, after the new energy replaces the conventional unit, the change The original inertia distribution in the system is eliminated, making the inertia difference of each partition more obvious, and aggravating the temporal and spatial distribution characteristics of the transient frequency of the power grid.

Since the establishment of the "three lines of defense" of the power system, they have played an important role in ensuring the safe and stable operation of the power system and preventing major blackouts. Low-frequency load shedding is an important part of the third line of defense. When there is a large power shortage in the system and the frequency drops, some loads can be selectively cut off according to design needs and real-time data to compensate for the power shortage and restore the grid frequency to Within the safe range, it is the main means of the third line of defense.

At present, the adaptive low-frequency load shedding algorithm needs to obtain the frequency and frequency change rate of the system, and use the frequency change rate of the system at the beginning of the fault to determine the real-time power shortage of the system. Based on this, the load shedding amount, location and rounds are determined according to the design plan. distribute. The adaptive low-frequency load shedding algorithm has a good response to accidents with different power shortages, but its actual operation effect depends on the calculation accuracy of the power shortage. It is necessary to calculate the real-time average frequency change rate of the system, that is, to obtain the average frequency of the system .

Obtaining the accurate average frequency of the system requires measuring the angular frequency of each generator and weighting it according to its inertia, and sampling the angular frequency values of all generators in the system. There are too many nodes to be monitored and the complexity is high.

Contents of the invention

The invention provides a method for calculating the average frequency of a power system and a related device, which solves the problem that the existing average frequency calculation needs too many monitoring nodes.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is:

A method for calculating the average frequency of a power system, comprising:

According to the grid structure and operation mode of the power system, the power system is divided into regions;

Determine the inertia center of each area according to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator;

The frequency of the center of inertia of each area is collected, and the average frequency of the power system is calculated according to the frequency of the center of inertia of each area.

According to the grid structure and operation mode of the power system, the power system is divided into regions, including:

According to the grid structure and operation mode of the power system, determine the expected fault set;

Simulate the predicted faults in the predicted fault set, and determine the grouping combination of generator sets under all transient instability predicted faults based on the extended equal area criterion; among them, the transient instability predicted fault is the relative Predicted faults of transient power angle instability of other generator sets;

According to the grouping combination of generator sets, clustering generates a coherent grouping set that may be excited by the power system;

According to the coherent grouping set, the power system is divided into regions.

According to the coherent grouping set, the power system is divided into regions, including:

According to the preset increase and decrease rules, the coherence grouping set is increased or decreased;

According to the grid structure of the power system, the equivalent impedance between each load node and each generator node is calculated, and each load node is assigned to the corresponding generator node with the smallest equivalent impedance. All the generator nodes of a cluster, the load nodes assigned by the generator nodes, and the connection lines between the generator nodes and the assigned load nodes are divided into an area.

The default increase and decrease rules are:

Delete duplicate clusters in the homology cluster set;

For the case where the group S _n contains another group S _m , if there is no group S _l = S _n - S _m , then add the group S _l ;

For the case that the group S _a and the group S _b intersect and do not overlap, add the group S _a ∪ S _b -S _a ∩ S _b .

According to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator, determine the inertia center of each area, including:

According to the inertia of the generators in each area and the equivalent impedance between the busbar and the generator, calculate the inertia center criterion index of all generators in each area, and use the generator with the smallest inertia center criterion index as the inertia of the corresponding area center.

Calculate the inertia center criterion index of all generators in each area, the formula is:

Among them, η _j is the inertia center criterion index of the jth generator in the area, n is the number of buses in the area, Z _ij is the equivalent impedance between the jth busbar and the jth generator in the area, E _{MWs .j} is the inertia of the jth generator in the area.

To calculate the average frequency of the power system, the formula is:

Among them, f _COI is the average frequency of the power system, K is the number of areas, f _COIk is the frequency of the kth area inertia center, γ _k is the weight of the kth area inertia, E _MWs.kj is the inertia of the jth generator in the kth area, and J is the number of generators in the kth area.

A device for calculating the average frequency of a power system, comprising:

The area division module divides the power system into areas according to the grid structure and operation mode of the power system;

The inertia center determination module determines the inertia center of each area according to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator;

The average frequency calculation module collects the frequency of the center of inertia of each area, and calculates the average frequency of the power system according to the frequency of the center of inertia of each area.

The area division module divides the power system into areas according to the grid structure and operation mode of the power system, including:

According to the grid structure and operation mode of the power system, determine the expected fault set;

Simulate the predicted faults in the predicted fault set, and determine the grouping combination of generator sets under all transient instability predicted faults based on the extended equal area criterion; among them, the transient instability predicted fault is the relative Predicted faults of transient power angle instability of other generator sets;

According to the grouping combination of generator sets, clustering generates a coherent grouping set that may be excited by the power system;

According to the coherent grouping set, the power system is divided into regions.

In the area division module, the area division of the power system is carried out according to the coherent grouping set, including:

According to the preset increase and decrease rules, the coherence grouping set is increased or decreased;

According to the grid structure of the power system, the equivalent impedance between each load node and each generator node is calculated, and each load node is assigned to the corresponding generator node with the smallest equivalent impedance. All the generator nodes of a cluster, the load nodes assigned by the generator nodes, and the connection lines between the generator nodes and the assigned load nodes are divided into an area.

In the area division module, the preset increase and decrease rules are:

Delete duplicate clusters in the homology cluster set;

For the case where the group S _n contains another group S _m , if there is no group S _l = S _n - S _m , then add the group S _l ;

For the case that the group S _a and the group S _b intersect and do not overlap, add the group S _a ∪ S _b -S _a ∩ S _b .

The inertia center determination module determines the inertia center of each area according to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator, including:

According to the inertia of the generators in each area and the equivalent impedance between the busbar and the generator, calculate the inertia center criterion index of all generators in each area, and use the generator with the smallest inertia center criterion index as the inertia of the corresponding area center.

In the inertia center determination module, calculate the inertia center criterion index of all generators in each area, the formula is:

Among them, η _j is the inertia center criterion index of the jth generator in the area, n is the number of buses in the area, Z _ij is the equivalent impedance between the jth busbar and the jth generator in the area, E _{MWs .j} is the inertia of the jth generator in the area.

In the average frequency calculation module, the average frequency of the power system is calculated, and the formula is:

Among them, f _COI is the average frequency of the power system, K is the number of areas, f _COIk is the frequency of the kth area inertia center, γ _k is the weight of the kth area inertia, E _MWs.kj is the inertia of the jth generator in the kth area, and J is the number of generators in the kth area.

A computer-readable storage medium storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to execute a method for finding an average frequency of a power system.

A computing device comprising one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more Executed by multiple processors, the one or more programs include instructions for executing the method for calculating the average frequency of the power system.

The beneficial effects achieved by the present invention: the present invention divides the power system into regions, determines the centers of inertia of each region, and calculates the average frequency of the power system based on the frequencies passing through the centers of inertia of each region, only needing to monitor the frequency of the centers of inertia, and then While ensuring the accuracy, the number of monitoring points is greatly reduced, the efficiency and accuracy of calculating the average frequency of the system are improved, and at the same time, it can provide technical support for fault area positioning and real-time power gap calculation.

Description of drawings

Fig. 1 is a flowchart of a method for calculating the average frequency of a power system.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solution of the present invention more clearly, but not to limit the protection scope of the present invention.

As shown in Figure 1, a method for calculating the average frequency of a power system includes the following steps:

Step 1, according to the grid structure and operation mode of the power system, divide the power system into regions;

Step 2, according to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator, determine the inertia center of each area;

Step 3: Collect the frequency of the center of inertia in each area, and calculate the average frequency of the power system according to the frequency of the center of inertia in each area.

The above method divides the power system into regions, determines the inertia center of each region, calculates the average frequency of the power system based on the frequency of the inertia center of each region, and only needs to monitor the frequency of the inertia center, which greatly reduces the accuracy while ensuring the accuracy. The number of monitoring points is increased, the efficiency and accuracy of calculating the average frequency of the system are improved, and at the same time, it can provide technical support for fault area location and real-time power gap calculation.

As an embodiment of the present invention, in step 1 of the above method, expected faults can be set, and area division can be performed through offline time domain simulation. The specific process can be as follows:

1) According to the grid structure and operation mode of the power system, determine the expected fault set.

Concentrated expected faults The expected faults select all combined faults of two double-circuit or single-circuit lines with the highest voltage level inside the power grid, including N-4 faults of double-circuit lines combined in pairs, and N-3 faults of double-circuit lines and single-circuit lines combined , and the N-4 fault of the single-channel 4-circuit line, and eliminate the fault of the generator outlet line.

2) Simulate the predicted faults in the predicted fault set, and determine the grouping combination of all generator sets under the predicted faults of transient instability based on the extended equal area rule EEAC; where the predicted faults of transient instability are those that cause more than two generators in the system The expected failure of the transient power angle instability of the unit relative to other units.

3) According to the grouping combination of the generator sets, the coherent grouping set {S ₁ , S ₂ ,...S _z } that the power system may be excited is generated by clustering.

4) According to the homology grouping set {S ₁ , S ₂ ,...S _z }, the power system is divided into regions.

As an embodiment of the present invention, the specific process of 3) in the above-mentioned method can be:

31) According to the preset increase and decrease rules, the coherence grouping set is increased or decreased.

The preset increase and decrease rules can be: delete the repeated groups in the homology group set, and only keep one; for the case where the group S _n contains another group S _m , that is If there is no group S _l =S _n -S _m , add the group S _l ; for the case where the group S _a and the group S _b intersect and do not overlap, add the group S _a ∪ S _b -S _a ∩ S _b .

32) According to the grid structure of the power system, determine the generator with the electrical distance closest to each load, and distribute each load to the corresponding group where the generator with the electrical distance closest is located.

Specifically, the equivalent impedance between each load node and each generator node can be calculated according to the grid structure of the power system, and each load node can be assigned to the corresponding generator node with the smallest equivalent impedance.

33) Divide all the generator nodes of each group in the coherent grouping set after the increase and decrease, the load nodes assigned by the generator nodes, and the contact lines between the generator nodes and the assigned load nodes into one area to ensure that no isolation occurs load node.

As an embodiment of the present invention, in step 2 of the above-mentioned method, on the basis of the above-mentioned division of regions, it is further possible to calculate all the The criterion index of the center of inertia of the generator can be expressed as:

Among them, η _j is the inertia center criterion index of the jth generator in the area, n is the number of buses in the area, Z _ij is the equivalent impedance between the jth busbar and the jth generator in the area, E _{MWs .j} is the inertia of the jth generator in the area;

Furthermore, the generator with the smallest criterion index of the center of inertia can be used as the center of inertia of the corresponding area.

As an embodiment of the present invention, in step 3 of the above method, on the basis of obtaining the center of inertia, the frequency of the center of inertia of each area is collected, and the average frequency of the power system is calculated according to the frequency of the center of inertia of each area, which can be expressed as:

Among them, f _COI is the average frequency of the power system, K is the number of areas, f _COIk is the frequency of the kth area inertia center, γ _k is the weight of the kth area inertia, E _MWs.kj is the inertia of the jth generator in the kth area, and J is the number of generators in the kth area.

The above method divides the power system into regions according to the network topology, operation mode, inertia of synchronous generator sets, real-time power balance, time section power flow and other information of a synchronous power grid, so that the synchronous generators in each region have similar Dynamic frequency characteristics are not prone to relative instability. In each area, the regional inertia center is determined according to the electrical distance and inertia information, and the influence of the uncertainty of the fault location on the calculation of the average frequency error is reduced while reducing the number of monitoring points. , improve the accuracy of calculating the average frequency of the system, and provide technical support for fault area location and real-time power gap calculation.

Based on the same technical solution, the present invention also discloses the software device of the above method, a device for calculating the average frequency of a power system, including:

The area division module divides the area of the power system according to the grid structure and operation mode of the power system.

The process of regional division of the power system by the area division module may include:

S1) According to the grid structure and operation mode of the power system, determine the expected fault set;

S2) Simulate the predicted faults in the predicted fault set, and determine the grouping combination of all generating units under the predicted faults of transient instability based on the extended equal area criterion; where the predicted faults of transient instability are those that cause more than two generators in the power system Predicted failure of the transient power angle instability of the unit relative to other generating units;

S3) According to the grouping combination of the generator sets, clustering generates a coherent grouping set that the power system may be excited;

S4) According to the preset increase and decrease rules, the coherence grouping set is increased or decreased;

The preset increase and decrease rules are: delete the repeated group in the homology group set; for the case where the group S _n contains another group S _m , if there is no group S _l =S _n -S _m , then increase the group S _l ; for In the case that group S _a and group S _b intersect and do not overlap, add group S _a ∪ S _b -S _a ∩ S _b ;

S5) According to the grid structure of the power system, calculate the equivalent impedance between each load node and each generator node, assign each load node to the corresponding generator node with the smallest equivalent impedance, and group the coherent group after the increase or decrease All the generator nodes, the load nodes allocated by the generator nodes, and the connection lines between the generator nodes and the allocated load nodes in each cluster are divided into an area. The inertia center determination module determines the inertia center of each area according to the inertia of the generator in each area and the equivalent impedance between the busbar and the generator.

The process of determining the inertia center of each area by the inertia center determination module may include: calculating the inertia center criterion index of all generators in each area according to the inertia of the generators in each area and the equivalent impedance between the busbar and the generator, The generator with the smallest criterion index of the center of inertia is taken as the center of inertia of the corresponding area;

Calculate the inertia center criterion index of all generators in each area, the formula can be:

Among them, η _j is the inertia center criterion index of the jth generator in the area, n is the number of buses in the area, Z _ij is the equivalent impedance between the jth busbar and the jth generator in the area, E _{MWs .j} is the inertia of the jth generator in the area.

The average frequency calculation module collects the frequency of the center of inertia of each area, and calculates the average frequency of the power system according to the frequency of the center of inertia of each area.

In the average frequency calculation module, the average frequency of the power system is calculated, and the formula can be:

Among them, f _COI is the average frequency of the power system, K is the number of areas, f _COIk is the frequency of the kth area inertia center, γ _k is the weight of the kth area inertia, E _MWs.kj is the inertia of the jth generator in the kth area, and J is the number of generators in the kth area.

Based on the same technical solution, the present invention also discloses a computer-readable storage medium that stores one or more programs, and the one or more programs include instructions that, when executed by a computing device, cause the computing The device implements the method for calculating the average frequency of the power system.

Based on the same technical solution, the present invention also discloses a computing device, including one or more processors, one or more memories, and one or more programs, wherein one or more programs are stored in the one or more In the memory and configured to be executed by the one or more processors, the one or more programs include instructions for executing the method for calculating the average frequency of the power system.

Those skilled in the art should understand that the embodiments of the present invention may be provided as methods, systems, or computer program products. Accordingly, the present invention can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.

The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each procedure and/or block in the flowchart and/or block diagram, and a combination of procedures and/or blocks in the flowchart and/or block diagram can be realized by computer program instructions. These computer program instructions may be provided to a general purpose computer, special purpose computer, embedded processor, or processor of other programmable data processing equipment to produce a machine such that the instructions executed by the processor of the computer or other programmable data processing equipment produce a An apparatus for realizing the functions specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing apparatus to operate in a specific manner, such that the instructions stored in the computer-readable memory produce an article of manufacture comprising instruction means, the instructions The device realizes the function specified in one or more procedures of the flowchart and/or one or more blocks of the block diagram.

These computer program instructions can also be loaded onto a computer or other programmable data processing device, causing a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby The instructions provide steps for implementing the functions specified in the flow chart or blocks of the flowchart and/or the block or blocks of the block diagrams.

The above is only an embodiment of the present invention, and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the pending application of the present invention. within the scope of the claims.

Claims (16)

1. A method for obtaining an average frequency of an electric power system, comprising:

dividing the area of the power system according to the grid structure and the operation mode of the power system;

determining inertia centers of all areas according to inertia of the generators in all areas and equivalent impedance between the bus and the generators;

and acquiring the frequency of the inertia center of each area, and calculating the average frequency of the power system according to the frequency of the inertia center of each area.

2. The method for determining the average frequency of an electric power system according to claim 1, wherein the dividing the electric power system into regions according to the grid structure and the operation mode of the electric power system comprises:

determining an expected fault set according to a grid structure and an operation mode of the power system;

simulating the expected faults in the expected fault set, and determining grouping combination of the generator sets under all transient instability expected faults based on area criteria such as expansion; the transient state instability expected faults are expected faults which cause transient state power angle instability of more than two generator sets relative to other generator sets in the power system;

clustering to generate coherent clustering sets possibly excited by the power system according to clustering combinations of the generator sets;

and according to the coherent grouping set, carrying out regional division on the power system.

3. The method for determining an average frequency of an electric power system according to claim 2, wherein the dividing the electric power system into regions according to the coherent group set comprises:

increasing and decreasing the coherent group set according to a preset increasing and decreasing rule;

according to the grid structure of the power system, the equivalent impedance between each load node and each generator node is calculated, each load node is distributed to the corresponding generator node with the minimum equivalent impedance, and all generator nodes in each group in the same-modulation group set after increase and decrease, the load nodes distributed by the generator nodes and the communication lines between the generator nodes and the distributed load nodes are divided into a region.

4. A method for determining an average frequency of an electrical power system according to claim 3, wherein the preset increasing and decreasing rule is:

deleting repeated clusters in the coherent cluster set;

for group S _n Comprising another subgroup S _m If there is no cluster S _l ＝S _n -S _m Then increase the cluster S _l ；

For group S _a And grouping S _b In the case of intersecting and non-overlapping, the cluster S is increased _a ∪S _b -S _a ∩S _b 。

5. The method of claim 1, wherein determining the center of inertia of each region based on the inertia of the generator in each region and the equivalent impedance between the bus and the generator comprises:

according to the inertia of the generators in each area and the equivalent impedance between the bus and the generators, calculating inertia center criterion indexes of all the generators in each area, and taking the generator with the smallest inertia center criterion index as the inertia center of the corresponding area.

6. The method for determining the average frequency of an electric power system according to claim 5, wherein the inertia center criterion index of all generators in each region is calculated, and the formula is:

wherein eta _j Is the criterion index of the inertia center of the jth generator in the area, n is the number of buses in the area, Z _ij Is equivalent impedance between the jth busbar and the jth generator in the region, E _MWs.j Is the inertia of the j-th generator in the area.

7. The method for determining an average frequency of an electrical power system according to claim 1, wherein the average frequency of the electrical power system is calculated by the formula:

wherein,, f (f) _COI Is the average frequency of the power system, K is the number of areas, f _COIk Frequency of inertia center of kth region, gamma _k Is the weight of the inertia of the kth region,E _MWs.kj the inertia of the J-th generator in the k-th region, and J is the number of generators in the k-th region.

8. An average frequency calculation device for an electric power system, comprising:

the regional division module is used for dividing the region of the power system according to the grid structure and the operation mode of the power system;

the inertia center determining module is used for determining the inertia center of each region according to the inertia of the generator in each region and the equivalent impedance between the bus and the generator;

the average frequency calculation module is used for collecting the frequency of the inertia center of each area, and calculating the average frequency of the power system according to the frequency of the inertia center of each area.

9. The apparatus for determining an average frequency of an electric power system according to claim 8, wherein the area dividing module performs area division on the electric power system according to a grid structure and an operation mode of the electric power system, and comprises:

determining an expected fault set according to a grid structure and an operation mode of the power system;

simulating the expected faults in the expected fault set, and determining grouping combination of the generator sets under all transient instability expected faults based on area criteria such as expansion; the transient state instability expected faults are expected faults which cause transient state power angle instability of more than two generator sets relative to other generator sets in the power system;

clustering to generate coherent clustering sets possibly excited by the power system according to clustering combinations of the generator sets;

and according to the coherent grouping set, carrying out regional division on the power system.

10. The apparatus for determining an average frequency of an electric power system according to claim 9, wherein the area division module performs area division on the electric power system according to the coherent group set, comprising:

increasing and decreasing the coherent group set according to a preset increasing and decreasing rule;

according to the grid structure of the power system, the equivalent impedance between each load node and each generator node is calculated, each load node is distributed to the corresponding generator node with the minimum equivalent impedance, and all generator nodes in each group in the same-modulation group set after increase and decrease, the load nodes distributed by the generator nodes and the communication lines between the generator nodes and the distributed load nodes are divided into a region.

11. The power system average frequency obtaining apparatus according to claim 10, wherein in the area dividing module, a preset increasing and decreasing rule is:

deleting repeated clusters in the coherent cluster set;

for group S _n Comprising another subgroup S _m If there is no cluster S _l ＝S _n -S _m Then increase the cluster S _l ；

For group S _a And grouping S _b In the case of intersecting and non-overlapping, the cluster S is increased _a ∪S _b -S _a ∩S _b 。

12. The power system average frequency calculation apparatus according to claim 8, wherein the inertia center determination module determines the inertia center of each region based on the inertia of the generator in each region and the equivalent impedance between the bus and the generator, comprising:

according to the inertia of the generators in each area and the equivalent impedance between the bus and the generators, calculating inertia center criterion indexes of all the generators in each area, and taking the generator with the smallest inertia center criterion index as the inertia center of the corresponding area.

13. The power system average frequency calculation apparatus according to claim 12, wherein in the inertia center determination module, inertia center criterion indexes of all generators in each region are calculated, and the formula is:

wherein eta _j Is the criterion index of the inertia center of the jth generator in the area, n is the number of buses in the area, Z _ij Is equivalent impedance between the jth busbar and the jth generator in the region, E _MWs.j Is the inertia of the j-th generator in the area.

14. The power system average frequency calculation apparatus according to claim 8, wherein in the average frequency calculation module, the power system average frequency is calculated by the formula:

wherein f _COI Is the average frequency of the power system, K is the number of areas, f _COIk Frequency of inertia center of kth region, gamma _k Is the weight of the inertia of the kth region,E _MWs.kj the inertia of the J-th generator in the k-th region, and J is the number of generators in the k-th region.

15. A computer readable storage medium storing one or more programs, wherein the one or more programs comprise instructions, which when executed by a computing device, cause the computing device to perform any of the methods of claims 1-7.

16. A computing device, comprising:

one or more processors, one or more memories, and one or more programs, wherein the one or more programs are stored in the one or more memories and configured to be executed by the one or more processors, the one or more programs comprising instructions for performing any of the methods of claims 1-7.