Voltage collapse diagnostic and ATC system

• US 20060030972A1
• Filed: 10/11/2005
• Published: 02/09/2006
• Est. Priority Date: 06/27/2003
• Status: Active Grant

• Current Assignee: Intelilcon Incorporated
• Original Assignee: Intelilcon Incorporated
• Inventors: Schlueter, Robert, Hunt, Ryan J., Minshall, Benjamin A.
• Granted Patent: US 8,024,076 B2
• Time in Patent Office: Days
• US Class Current: 700/292
• CPC Class Codes: H02J 2203/20 Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
• CPC Class Codes: H02J 3/00 Circuit arrangements for ac mains or ac distribution networks
• CPC Class Codes: H02J 3/0012 Contingency detection
• CPC Class Codes: Y02E 60/00 Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation
• CPC Class Codes: Y04S 40/20 Information technology specific aspects, e.g. CAD, simulation, modelling, system security

Abstract

The present invention provides an analysis method for an electrical power system whereby the plurality of buses are grouped into agents, family lines of agents and families of agents based on the reactive reserves depleted when the buses are loaded. Contingencies are then applied to the electrical power system and the reactive reserves are monitored and an exhaustion factor is determined for one or more family lines in one or more families. A method for selecting double outage that have no solution for each outage that has no solution when the outage is removed in small steps and an additional step has no solution. The boundary case solution is used to assess where, why, and how the contingency causes voltage instability, voltage collapse, and local blackout. Based on this information, the design of voltage rescheduling, active rescheduling, unit commitment, load shedding is determined that can be used as preventive, corrective, or emergency controls in applications such as system design and planning, operation planning, reactive and voltage management, real time control, and Special Protection System Control. Based on this information, solutions can then be applied to the political power system.

Claims

1. A voltage collapse diagnostic method for an electrical power system, comprising the steps of:

A) defining a network of a plurality of interconnected busses and reactive reserves,

B) defining groups of busses within said network such that when a load is applied to any bus within a first group of said groups of busses, a same at least one reactive reserve generally completely exhausts its reactive reserves.

2. The voltage collapse diagnostic method of claim 1, further including the step of:

applying load incrementally to the network.

3. The voltage collapse diagnostic method of claim 1, further including the step of:

C) for each at least one reactive reserve exhausted in step B), associating that at least one reactive reserve with every group within said groups of busses that cause the exhaustion of the at least one reactive reserve.

4. The voltage collapse diagnostic method according to claim 3, further including the steps of:

establishing each group of busses defined in step B) as a voltage instability region, which is represented by an agent; and

establishing each at least one reactive reserve associated in step C) as a reactive reserve zone, wherein the network includes a plurality of reactive reserve zones.

5. The voltage collapse diagnostic method according to claim 4, further including the step of:

identifying an exhaustion for each of the agents in response to applying at least one load to the network.

6. The voltage collapse diagnostic method according to claim 5, wherein the network is a mathematical model of an existing electrical power system and the load is a simulated electrical load.

7. The voltage collapse diagnostic method according to claim 4, further including the step of:

organizing the plurality of agents into a hierarchy based on the plurality of reactive reserve zones.

8. The voltage collapse diagnostic method according to claim 7, wherein agents at a higher level in the hierarchy include more reactive reserves than agents at a lower level in the hierarchy.

9. The voltage collapse diagnostic method according to claim 8, wherein agents at a higher level in the hierarchy are at a higher voltage level than agents at a lower level in the hierarchy.

10. The voltage collapse diagnostic method according to claim 9, further comprising the step of determining an available transfer capability for each single contingency that has no loadflow solution and a control region where Preventive Control is applied or load pocket.

11. The voltage collapse diagnostic method according to claim 10, wherein the step of determining an available transfer capability for the comprises:

identifying each single contingency that results in no loadflow solution;

performing Preventive load shedding in a control region until a loadflow solution exists for each single contingency;

determining the maximum amount of load that is shed over all single contingencies that utilize a specific control region for load shedding; and

defining of a remaining amount of reserves for that control region as a Incremental Transfer Capability for that control region.

12. The voltage collapse diagnostic of claim 11 where the maximum load shed over the single contingencies that have a specific control region is the Incremental Transfer Capability for that Control Region.

13. The voltage collapse diagnostic of claim 12 where the Incremental Transfer Capability is computed for control regions or load pockets where Preventive load shedding control is used for single and double contingencies is the value determined for single contingencies.

14. The voltage collapse diagnostic method according to claim 8, wherein agents at a higher level in the hierarchy are electrically proximate to a source of electrical power generation, and wherein agents at a lower level in the hierarchy are electrically distal to a source of electrical power generation.

15. The voltage collapse diagnostic method according to claim 8, wherein:

at least some of the agents at lower levels in the hierarchy have reactive reserve zones that are subsets of reactive reserves contained in reactive reserve zones for agents at higher levels in the hierarchy; and

wherein

family lines of agents are defined based on agents at lower levels in the hierarchy having subsets of reactive reserves contained in agents at higher levels in the hierarchy.

16. A voltage collapse diagnostic method of claim 15, further including the steps of:

observing that exhaustion of reactive reserve at a lower hierarchical level begins an accelerated exhaustion of the reactive reserves at a higher level in each family;

applying a reactive load at a bus in the voltage instability region of a patriarchal agent sequentially exhausts the reactive reserves of every agent in every family line in the family from the lowest hierarchical level to the highest hierarchical level which is the patriarchal agent;

applying active power load at buses in the vulnerability region of the family of the patriarchal agent that exhausts the reactive reserves of every agent in every family line in the family from the lowest hierarchical level to the highest hierarchical level which is the patriarchal agent;

applying a contingency incrementally such that the reserves exhaust sequentially from a lower hierarchical level to a higher hierarchical level in more than one family lines in one or more families;

exhaustion of reactive reserves in an agent can cause instability in that agent;

progressive exhaustion of reactive reserves in agents in a family line and family can cause progressive cascading instability in that family line and family;

the knowledge that the cascading exhaustion of reactive supply occurs can cause progressive cascading instability for applying active load and reactive load progressively and applying contingencies as a dimmer switch provides an understanding of how voltage instability, voltage collapse, and local blackout occur and how to prevent it by reducing active and reactive load and reducing reactive losses;

wherein a family of agents is defined as all agents in all family lines emanating from a patriarchal agent to which the family belongs;

wherein a vulnerability region of a patriarchal agent is defined as the busses belonging to the collection of voltage instability regions of all agents in the family.

17. The voltage collapse diagnostic method according to claim 15, further including the steps of:

applying to the network a single contingency that has a solution; and

monitoring a change in power output of the reactive reserves of at least one family line of agents.

18. The voltage collapse diagnostic method according to claim 17, further including the steps of:

calculating an exhaustion factor for each agent for each single contingency that has a solution; and

ranking each of the agents according to a respective exhaustion factor calculated in the calculating step.

19. The voltage collapse diagnostic method according to claim 18, wherein the exhaustion factor for each agent or groups of agents is calculated based on either:

$\begin{array}{c}\mathrm{exhaustion}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{factor}<br><br>\text{\hspace{1em}<br><br>}<br><br>1=\left(\frac{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenOutage}}{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenBase}}\right)·<br><br>100;<br><br>\mathrm{or}\\ \mathrm{exhaustion}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{factor}<br><br>\text{\hspace{1em}<br><br>}<br><br>2=\left(\frac{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenOutage}}{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenBase}}\right)·<br><br>100·<br><br>\langle <br><br>\mathrm{QgenOutage}-\mathrm{QgenBase}\rangle <br><br>\end{array}$

wherein;

Qmax is a maximum power that can be generated in the reactive reserve zone for each agent or groups of agents,

QgenOutage is power generated by the reactive reserve zone for each agent or groups of agents in response to the contingency, and

QgenBase is a base power output generated by the reactive reserve zone for each agent or groups of agents.

20. The voltage collapse diagnostic method according to claim 19, wherein the multiple contingency analysis comprises:

applying combinations of each single contingency identified in the identifying each single or multiple that had a solution via the contingency step to the electrical power system; and

monitoring a change in power output of the reactive reserves for each set of N agents.

21. The voltage collapse diagnostic method according to claim 19, wherein the step of determining an exhaustion of each agent further comprises:

calculating an exhaustion factor for each set of N agents for each of the combinations of each single or multiple contingency that have loadflow solution or where the maximum percentage remaining is zero; and

ranking each agent or of N agents according to the exhaustion factor calculated for each of the sets of agents for each single or multiple contingency and each of the combinations of each single contingency that have loadflow solution or the boundary case solution where the maximum percentage remaining is zero.

22. The voltage collapse diagnostic method according to claim 21, wherein the exhaustion factor for each agent or set of N agents is calculated based on:

$\begin{array}{c}\mathrm{exhaustion}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{factor}<br><br>\text{\hspace{1em}<br><br>}<br><br>1=\left(\frac{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenOutage}}{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenBase}}\right)·<br><br>100\\ \mathrm{exhaustion}<br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{factor}<br><br>\text{\hspace{1em}<br><br>}<br><br>2=\left(\frac{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenOutage}}{Q<br><br>\text{\hspace{1em}<br><br>}<br><br>\max -\mathrm{QgenBase}}\right)·<br><br>100·<br><br>\langle <br><br>\mathrm{QgenOutage}-\mathrm{QgenBase}\rangle <br><br>\end{array}$

wherein Qmax is a maximum power generated the reactive reserves for each agent or set of N agents, QgenOutage is power generated by the reactive reserves for each agent or set of N agents in response to the single or multiple contingency, and QgenBase is a base power output generated by the reactive reserves for each agent or set of N agents.

23. The voltage collapse diagnostic method according to claim 19, further comprising the step of determining an available transfer capability for each control region or load pocket and the single equipment outages that are components of the combinations that use Preventive Load Shedding Control in that control region or load pocket to obtain solutions.

24. The voltage collapse diagnostic method according to claim 23, wherein the step of determining an available transfer capability for the control region comprises:

identifying each of the combinations of each single contingencies that results in no loadflow solution and has a Preventive Control that sheds load in a particular control region;

determining a remaining amount of reserves for the control region available after single outages that in combinations have no loadflow solution but the Preventive Load Shedding Control in that control region obtains solutions; and

defining of a remaining amount of reserves as an incremental transfer capability or the maximum amount of load shed in the control region over all single contingencies that have no loadflow solution and that control region.

25. The voltage collapse diagnostic method according to claim 24, wherein the step of determining a remaining amount of reserves for the control region comprises:

applying only one contingency of those combinations where Preventive Load Shedding Control is required to obtain solutions

placing a load on the control region to compensate for the application of only one contingency in the applying step where power factor and loading pattern are design parameters; and

determining an additional load that can be applied to the control region or load pocket after a specific contingency before no loadflow solution exists using a governor loadflow as the remaining amount of reserves available, where the set of generators that respond and the generation participation factors are design parameters;

taking the minimum of the additional load that can be applied as the Incremental Transfer Capability for the control region over all single contingencies that are components of double contingencies that have that control region.

26. The voltage collapse diagnostic method according to claim 25, where the incremental transfer capability for a load pocket belonging to several control regions for double contingencies is the minimum active load added over all control regions that contain that load pocket.

27. The voltage collapse diagnostic method according to claim 24, where the Incremental Transfer Capability for a load pocket belonging to several control regions for single contingencies is the maximum active load added over all control regions that contain that load pocket.

28. The voltage collapse diagnostic method according to claim 1, wherein the plurality of busses in said network define a region of interest and a buffer zone.

29. The voltage collapse diagnostic method according to claim 28, wherein at least one of the busses in the region of interest and buffer zone is associated with a load.

30. The voltage collapse diagnostic method according to claim 28, wherein at least one bus in the region of interest or in the buffer zone is located within a sub-transmission level or a distribution level of the network.

31. The voltage collapse diagnostic method according to claim 30 wherein the at least one bus of the network is at a voltage level of 34 KV or less.

32. The voltage collapse diagnostic method according to claim 31, wherein the step of identifying an exhaustion of the each of the agents further comprises:

applying a plurality of contingencies to the electrical power system; and

monitoring a change in power output of the reactive reserves for each of the agents.

33. The voltage collapse diagnostic method according to claim 32, further comprising the step of ranking the plurality of contingencies in order of most critical contingencies.

34. The voltage collapse diagnostic method according to claim 33, wherein the step of ranking the plurality of contingencies is calculated according to:

$C_i=\underset{j}{\sum <br><br>}<br><br>\frac{P_j<br><br>\left(-1+\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{reactivereservesremaining}}_{\mathrm{ij}}\right)}{1-\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{outageremaining}}_i}$

wherein contingency measure predicts the load that will experience blackout and the sum can be over the agents in the Blackout Region, Predicted Impact Region, or all agents, wherein contingency measure can be multiplied by the probability of the outage and/or the cost of power to produce an economic measure, a risk measure or an economic risk measure.

35. The voltage collapse diagnostic method according to claim 34, wherein the step of ranking each of the agents is calculated for contingencies that have no solution at the boundary case solution with nonzero percentage outage remaining or contingencies that solve or those that solve the boundary case solution with a zero percentage outage remaining according to:

$A_j=\underset{i}{\sum <br><br>}<br><br>\frac{P_j<br><br>\left(-1+\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{reactivereservesremaining}}_{\mathrm{ij}}\right)}{1-\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{outageremaining}}_i}$

wherein the term within the summation can be multiplied by the probability of the outage and/or the cost of power to provide an economic measure, a risk measure, or a economic risk measure.

36. The voltage collapse diagnostic method according to claim 32, further comprising the step of ranking the agents in order of most critical agents based on the plurality of contingencies.

37. The voltage collapse diagnostic method according to claim 1, wherein step B) further includes the substeps of:

A) establishing loadflow equations that define said network;

B) incrementally applying said load to a first bus within said network;

C) calculating a power output from each reactive reserve within said plurality of reactive reserves in response to the incrementally applied load;

D) computing a load curve at said first bus for each incremental load,

E) identifying a first reactive power minimum at said first bus, or if a first reactive power minimum cannot be identified due to lack of a solution to the loadflow equations, identifying a maximum load terminal point.

38. The voltage collapse diagnostic method according to claim 1, wherein step B) further includes the substeps of:

defining each group of busses as an agent such that each agent contains busses that either generally exhaust the same at least one reactive reserve in said set of reactive reserves or that bring about a first maximum terminal point as load is added to the busses of the respective agent.

39. The voltage collapse diagnosis method according to claim 1, further including the step of:

establishing loadflow equations that define said network,

applying said load in an incremental manner whenever the loadflow equations fail to solve.

40. The voltage collapse diagnostic method of claim 1, further including the step of:

subjecting the network to a plurality of single contingencies that can be simulated as a series of snapshots approximating a dynamic simulation or as a governor or AGC loadflow.

41. The voltage collapse diagnostic method of claim 40, wherein each single contingency in said series of single contingencies is applied incrementally.

42. The voltage collapse diagnostic method according to claim 40, further including the steps of:

a) selecting a count N of the number agents to be considered;

b) determining a threshold value X % for a reactive remaining exhaustion factor;

c) identifying each single contingency that results in the reactive remaining exhaustion factor for said N agents being less than threshold level X %; and

d) performing a multiple contingency analysis with each single contingency identified in step c).

43. The voltage collapse diagnostic method according to claim 42, further including the steps of:

iteratively selecting the number of agents N, the threshold value Y=100-X, and the maximum number of double equipment outages that will be simulated to find the largest number of outages with no loadflow solution;

computing a matrix A for a discrete equally spaced values of the variable Y, which is the minimum percentage of the reserves of the agent exhausted (not the maximum reserves of the agent remaining X), and the number of agents N, wherein each cell of the matrix contains the number of single outages that satisfy the criteria of having at least one set of N agents experience at least Y % of their reactive reserves exhausted, the number of double outages that such a set of M(Y,N) single outages would produce M(M−

1)/2 double outages, the increase in the number of single outages Δ

M(Y,N) as Y is reduced and N is held fixed;

wherein the matrix includes number of double outages for cells on an exponentially declining curve of cells drawn on this matrix requires simulating approximately the same number of double outages;

wherein the matrix includes at least one exponentially declining set of cells Y_i(N);

wherein to simulate a maximum number of double outages (i), the options for values of Y and N are cells on approximate exponentially declining curve Y_i(N) drawn on the matrix;

wherein the outages simulated for any cell include all outages required to be simulated by all the cells in the upper off diagonal submatrix of cells with this cell as the corner.

44. The voltage collapse diagnostic according to claim 43, wherein if all the double outages for any specific cell are simulated, by way of at least one of a dynamic simulation approximation, governor loadflow, or AGC loadflow simulation, the number of double outages that have no solution for any cell of the matrix is given as part of the information contained for each cell.

45. the voltage collapse diagnostic according to claim 43, further including step of:

iteratively updating the A matrix to provide the number of outages that do not solve for simulation of all double outages for a cell designated for a particular value of Y and N can be used to maximize the number of double outages that do not solve as one moves along the exponential declining curve of cells Y_i(N) specified given a maximum number of double outages (i) that are willing to be simulated.

46. The voltage collapse diagnostic according to claim 45, including the steps of:

selecting the values of N and Y on a particular exponential declining curve, that will change the selected set of double outages but keep the total number of outages simulated approximately the same, will not significantly change the percentage of outages that have no loadflow solution;

that very small reductions in reserves exhausted Y with N fixed or sometimes small reduction in N with Y fixed are required to obtain additional outages with no solution;

showing that such a system will produce blackout by affecting different family lines in different families and that a very small affect on each of the family lines for single outages can cause very severe double outages.

47. The voltage collapse diagnostic method of claim 40, including the steps of:

A) subjecting the network to at least one double contingency which is defined as applying generally simultaneously, two single contingencies,

B) for all double contingencies applied in step A) that have no solution simulated via a dynamic simulation, approximation, a governor loadflow, or an AGC loadflow reapplying each double contingency incrementally.

48. The voltage collapse diagnostic method of claim 47, further including the step of:

utilizing loadflow equations that define said network;

interpreting all double outages that have a solution when the percentage of the remaining outage is zero as those outages that drive the network to, or close to, voltage instability, voltage collapse, or local blackout.

49. The voltage collapse diagnostic method according to claim 47, further including the step of:

determining the presence of a boundary operating condition for all double outages that lack a solution to the loadflow equations when the remaining reactive reserves is zero but that have a solution to the loadflow equations when the outage remaining reactive reserves affecting different family lines in one or more families is at a non-zero threshold percentage value.

50. The voltage collapse diagnostic method of claim 40, further including the step of:

determining preventive, corrective, and emergency measures to support power flow on the network based on each single contingency and combinations of two single contingencies at a boundary case solution where the percentage of the outage remaining in the network at the boundary case solution is at a threshold percentage value which is not equal to zero but a very slight increase in the percentage value of the outage has no solution.

51. The voltage collapse diagnostic method of claim 50, further including the step of:

determining preventive, corrective, or emergency measures to support power flow on the network based on each single contingencies and on combinations of the single contingencies that have a solution to loadflow equations that define the network when the percentage of the outage remaining in the system is zero or at the boundary case solution when the percentage of the outage is not equal to zero, in order to reduce severity and proximity to voltage collapse as measured by the contingency measure;

$C_i=\underset{j}{\sum <br><br>}<br><br>\frac{P_j<br><br>\left(-1+\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{reactivereservesremaining}}_{\mathrm{ij}}\right)}{1-\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{outageremaining}}_i},$

wherein the contingency measure is very negative for outages that blackout the largest region when P_j=1 and impact the largest load when P_j equals the load in an agent j,

wherein contingency measure is ranked based on absolute magnitude or on the most negative values.

52. The voltage collapse diagnostic method of claim 51, wherein the agents

$\frac{(-1+\%}{}$

 

⁢

reactivereservesremaining ij ) 1 - % ⁢

 

⁢

outageremaining i

with factors of −

1 or smaller for a contingency that has no solution at the boundary case solution with nonzero percentage remaining or those contingencies that solve or that solve at the boundary case solution with a zero percentage outage remaining are associated with the Predicted Blackout Region and with factors −

0.5 or smaller are associated with the Predicted Impact Region, wherein the agents that have values −

1 and smaller at the Base Case Solution are linearly projected to have no reactive reserve if the outage could be completely removed, wherein the reactive losses exhaust nonlinearly and thus the Predicted Blackout Region is a less conservative estimate of the region that is anticipated to experience blackout, wherein the contingency measure C_i is an estimate of the total load that would experience blackout for a contingency, wherein the agent measures with large negative measure are those agents with very little reactive reserves in the base case, that are significantly impacted by equipment outages so that they are frequently completely or significantly exhausted by equipment outages that do not solve, or both.

53. The voltage collapse diagnostic method of claim 52, wherein the Base Case Blackout Region is defined by agents in family lines and entire families where the reactive reserves are completely exhausted in the base solution and cause a region to be vulnerable to voltage instability, voltage collapse and local blackout because there is no reactive supply available to the family since it can not obtain reactive supply from ancestral agents that cover a larger region because the additional agents in the families of the ancestral agents are all completely exhausted and the agents in the family lines and families that have large negative A_j measures often have very little reactive reserves in the base case and thus can be easily exhausted, wherein the family lines that are in the Base Case Blackout Region can also channel the blackout once the exhaustion of reactive reserves due to a contingency reach this family line of agents.

54. The voltage collapse diagnostic method of claim 50, further including:

developing a posturing control wherein one control change is used to prevent voltage collapse for a set of contingencies that affect the same control regions and for contingencies that affect approximately the same control regions that include or exclude agents in the same families or different families, this cluster of control regions can be considered a load pocket, wherein posturing control eliminates that Base Case Blackout region containing family lines and families of agents with no reactive reserves in the base case;

posturing for set of single contingencies associated with clusters of control regions with agents from similar family lines and families;

posturing for sets of double equipment outages associated with clusters of control regions containing agents from similar family lines and families.

55. The voltage collapse diagnostic method of claim 50, wherein:

load bearing agents or load pockets are ranked according to exhaustion factor;

wherein a predicted control region includes all load bearing agents where the exhaustion at the boundary case solution for the outage is less than a predetermined threshold;

wherein the load bearing agents are selected for load shedding control and placed in the control set in the order based on the agent ranking or ordering decided above,

wherein active and reactive load is shed at all buses in the same increasing percentages until consecutive solutions are obtained, active generation response would cause generation decrease on generators via governor loadflow or AGC loadflow or from a swing bus;

wherein control is chosen near the center of the set of consecutive solutions or when reactive reserves on generators or control devices in the control set or control region exceed a given percentage of their reactive supply capability;

wherein consecutive solutions are not obtained or reactive reserves on generators or control devices in the control set or control region do not increase or do not exceed the given percentage as the percentage of load shed is increased to 50% or some other predetermined percentage, then another load bearing agent is added based on the ranking decided above and load shedding is performed on all load bearing agents in the control set simultaneously in increasing percentages;

wherein if no control is found that produces consecutive loadflow solutions and all agents from the predicted control region are added to the control region, there is no preventive, corrective, or emergency load shedding control for this contingency;

wherein if a robust Preventive Load Shedding Control was computed it can be implemented,

wherein the Preventive Control could be implemented by tripping large motors or industrial loads by tripping lines out of a substation if voltage at buses in the Control Set drops below a certain level, the first of a double contingency that has no solution occurs, or if the system is known to be vulnerable to voltage collapse for a single contingency, wherein other methods of implementation are possible as would be obvious to an artisan in the field.

56. The voltage collapse diagnostic method of claim 50, wherein:

the load bearing agents or load pockets are ranked according to exhaustion factor;

wherein a predicted control region includes all load bearing agents where the exhaustion factor at the boundary case solution for the outage is less than a threshold that is selected based on judgment of one skilled in the art;

selecting agents for load shedding control based on the agent ranking or ordering decided above;

shedding reactive load in the same increasing percentages until consecutive solutions are obtained, wherein;

control is chosen near the center of the set of consecutive solutions or when the reactive reserves on generators or control devices in the control set or control region exceed a given percentage of their reactive supply capability;

wherein if consecutive solutions are not obtained as the percentage of reactive load shed is increased to 90% or some other predetermined percentage, then another load bearing agent is added based on the ranking decided above and load shedding is performed on all load bearing agents in the control set simultaneously in increasing percentages, wherein this process could represent the use of FACTS devices distributed in load pockets, wherein no control is found that produces consecutive loadflow solutions and all agents from the predicted control region are added to the control region, there is no emergency reactive load shedding control for this contingency.

57. The voltage collapse diagnostic and method of claim 50, further including the steps of:

ranking the load bearing agents or load pockets according to exhaustion factor, wherein a predicted control region is all load bearing agents where the exhaustion factor at the boundary case solution for the outage is less than a threshold that is selected based on judgment of one skilled in the art;

selecting the agents for load shedding control based on the agent ranking;

shedding active load in the same increasing percentages until consecutive solutions are obtained, wherein control is chosen near the center of the set of consecutive solutions or when the reactive reserves on generators or control devices exceed a given percentage of their reactive supply capability;

wherein if consecutive solutions are not obtained as the percentage of active load shed is increased to 90% or some other predetermined percentage, then another load bearing agent is added based on the ranking decided above and load shedding is performed on all load bearing agents in the predicted control set simultaneously in increasing percentages, wherein this process could represent the use of Distributed Generation devices distributed in load pockets where the devices are assumed to have no voltage control and reactive supply, wherein if there is no control that produces consecutive loadflow solutions and all agents from the predicted control region are added to the control region, there is no preventive or corrective Distributed Generation Control for this contingency.

58. The voltage collapse diagnostic method of claim 1, comprising the steps of:

A) subjecting the network to a series of single contingencies;

simulated via a dynamic simulation approximation, a governor loadflow, or an AGC loadflow.

B) for all single contingencies in step A) that have no solution to loadflow equations when simulated via a dynamic simulation approximation, governor loadflow, or AGC loadflow that define said network, reapplying the contingencies in incremental steps.

59. The voltage collapse diagnostic method according to claim 58, further including the step of:

C) for all single contingencies that have no solution when step B) is performed, determining if the percentage of the outage remaining is zero and interpreting an outage remaining of zero as responsible for causing or nearly causing voltage instability, voltage collapse, or local blackout.

60. The voltage collapse diagnostic method according to claim 58, further including the step of:

D) determining the presence of a boundary operating region for all single outages that have no solution when the percentage of the outage remaining in the system is zero but that do have a solution when the percentage of the outage remaining in the system is non-zero.

61. The voltage collapse diagnostic method of claim 58, further including employing a divide and conquer technique, including the steps of:

grouping agents into families,

wherein single outages are selected based on small effects on agents in the same family;

or

wherein single outages are selected based on small effects on agents in one or more family;

or

wherein combinations of single outages from a collection of single outages produce a double equipment outage that have no loadflow solution to equations that define the network.

62. The voltage collapse diagnostic method of claim 61, further including the steps of:

A) determining a class of double contingencies that

i) have no loadflow solution when the double contingency is applied in a single step, but that

ii) have a loadflow solution when the double contingency is applied incrementally,

B) interpreting the class defined in step A) as those double contingencies that will place the network in, or close to, a state of voltage instability, voltage collapse, or blackout.

63. A voltage collapse diagnostic and preventive or corrective voltage rescheduling control system, comprising the steps of:

A) defining a network of interconnected busses and reactive reserves,

B) defining groups of busses within said network such that when a load is placed on any bus within a first group of said groups of busses, a same at least one reactive reserve generally completely exhausts its reactive reserves,

C) establishing each group of busses defined in step B) as an agent,

D) ranking agents according to an exhaustion factor for an outage,

E) grouping agents into one or more predicted control regions wherein an exhaustion factor at a boundary case solution for an outage is less than a predetermined threshold.

64. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 63, further including the steps of:

F) placing agents and reactive reserves in a predicted control region for rescheduling control based on the agent ranking established in step D).

65. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 64, wherein the reactive reserves associated with any agent are added to a control set of reactive reserves in an order based on active or reactive capacity, loading factor, or reactive reserve losses incurred due to a small change of voltage set point or active generation set point, wherein the order of reactive reserves added to the control region and reactive reserves previously added to the control set are maintained, wherein the order can also be determined based on methods obvious to a skilled artisan.

66. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 65, including the steps of:

increasing the voltage set point on a reactive reserve within a control set, one reactive reserve at a time, in small percentage increasing steps while concurrently, seeking consecutive loadflow solutions to equations that define the network,

if consecutive solutions are found then, selecting the control to be at a point where the reactive reserve level on the reactive reserves in the control region or control set exceed a certain percentage of their reactive capability or at the approximate a center of the consecutive set of solutions, which is termed a robust solution;

increasing the voltage set point on any reactive reserve until reactive reserve in the control set no longer increases or until one or more of the reactive reserve in the control set reach its control limits,

holding at its control limit a reactive reserve that has reached its control limit,

continuing the process set out above for all reactive reserve associated with agents in the control region until consecutive loadflow solutions are found, a robust solution is found, or until all reactive reserve associated with agents in the control region have been used.

67. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 66, further including the steps of:

for an agent that was last added to the control region, if a selection of loadflow solutions are not found using all generators, continuing the process of selecting additional generators in agents to be included in the control set and then selecting additional agents to be in the control region until all agents in the predicted control region are used in which case there is no preventative voltage rescheduling possible by way of increasing voltage set points.

68. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 63, further including the step of:

Implementing a Preventive Control either by modifying the voltage setpoints on the control devices or by adding shunt capacitors close to the generators that experience reactive reserve increases predicted via the Preventive Voltage Rescheduling Control, wherein the Preventive Voltage Rescheduling Control is implemented if the voltage decreases sufficiently in the Control Region of agents, if the contingency occurs, or if the system is known to be vulnerable to voltage collapse for this single contingency or if the first contingency component of a double contingency occurs, wherein other criteria for implementation of the Preventive Control is possible, and wherein other methods of implementation are possible as would be obvious to an artisan in the field.

69. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 63, wherein all of the generators in the control set are increased simultaneously and wherein voltage is increased in small percentage steps until any given generator reaches it voltage rating limit, thereafter, any generator that has reached its voltage rating limit is held at its voltage rating limit.

70. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 63, wherein all generators in an agent are added to the control set simultaneously.

71. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system, of claim 63 wherein the voltage is decreased on generators that have high loading factors and increased on generators with small loading factors wherein the voltage increase setpoint never exceeds the voltage rating of its respective generator and wherein voltage decrease on any generator not be reduced when the reactive generation in total or on those generators with the largest reactive generation levels or loading factors in the control set is not be being reduced due to reducing reactive losses on the paths from those generators by voltage reduction, wherein if there is no control found after all agents in the predicted control region have been used progressively with this voltage increase and voltage decrease rescheduling, there is no preventive and corrective voltage rescheduling control using a combination of voltage increase and voltage decrease.

72. The voltage collapse diagnostic and preventive or corrective voltage rescheduling control system of claim 71, wherein decrease and generation decrease will occur on the same generators and voltage increase and generation increase will occur on the same generators based on the variables used to decide whether voltage is increased or decreased and active power is increased or decrease, wherein transfer of active power between generators in the control set will occur, wherein voltage and active power generation limits on all generators are used to limit control action, wherein control action is taken on a particular control set of generators as long as the reactive reserves on the generators in the control set is increased, wherein additional generators in the predicted control region based on an exhaustion factor ranking are added to the control set if no consecutive set of solutions is found or reactive reserves on the control set or control region do not increase, wherein if no control is found that produced consecutive loadflow solutions or reactive reserve levels on generators in the control set or control region exceed a percentage of the reactive supply capability and all the agents from the predicted control region have been added to the control region, there is no preventive and corrective voltage and active rescheduling control for this contingency.

73. The voltage collapse diagnostic and preventive and corrective control of active rescheduling of claim 72, wherein decrease and generation decrease will occur on the same generators and voltage increase and generation increase will occur on the same generators based on the variables used to decide whether voltage is increased or decreased and active power is increased or decrease, wherein transfer of active power between generators in the control set will occur, wherein voltage and active power generation limits on all generators are used to limit control action, wherein control action is taken on a particular control set of generators as long as the reactive reserves on the generators in the control set is increased, wherein additional generators in the predicted control region based on an exhaustion factor ranking are added to the control set if no consecutive set of solutions is found or reactive reserves on the control set or control region do not increase, wherein if no control is found that produced consecutive loadflow solutions or reactive reserve levels on generators in the control set or control region exceed a percentage of the reactive supply capability and all the agents from the predicted control region have been added to the control region, there is no preventive and corrective voltage and active rescheduling control for this contingency.

74. The voltage collapse diagnostic and preventive and corrective control of active rescheduling of claim 73 further including:

applying preventive load shedding if there is no preventive voltage and active rescheduling control for a specific contingency.

75. The voltage collapse diagnostic and preventive, corrective, and emergency control of voltage rescheduling of claim 71, including the steps of:

decreasing voltage and power generation on a first set of generators and increasing voltage and power generation on a second set of generators, wherein if consecutive solutions are not obtained on all agents in the predicted control region for a contingency, then other measures are taken.

76. The voltage collapse diagnostic method according to claim 63, further comprising:

determining preventive, corrective, or emergency measures to support power flow on the electrical power system on the set of N agents with the largest ranking based on the ranking of each single or multiple contingency and each of the combinations of each single contingency that have solution or boundary case solution where the maximum percentage of the outage remaining is zero or is at the boundary case when the percentage of the outage is not equal to zero.

77. The voltage collapse diagnostic method according to claim 76, further comprising a means for determining and executing the preventive, corrective, and emergency measures.

78. The voltage collapse diagnostic method according to claim 77, wherein the preventive measures include shifting load, adding new generation within unit commitment or construction of new generation, rescheduling active power on existing reactive reserves or rescheduling voltage for strengthening the electrical power system in critical locations.

79. The voltage collapse diagnostic and preventive and corrective control of active rescheduling comprising the steps of:

A) ranking agents according to an exhaustion factor for a boundary case solution for that outage;

B) defining a predicted control region which includes all agents that experience an exhaustion factor less than a predetermined threshold;

C) selecting associated generators defined in step B),—

belonging to the predicted control region and placing said generators in the control set for active rescheduling control based on a generator or control device ranking of an exhaustion factor;

D) adding the generators associated with any agent selected to be added to the control region to the generators or control devices in the control set simultaneously;

wherein the generators with the largest exhaustion factor in the control set will generate less power by a participation factor proportional to the variable such as reactive and active loading factor or reactive losses incurred for a slight increase in active generation or voltage setpoint and the generators with the smallest variables will increase power using a participation factor that is inversely proportional to this variable such that the sum of the amount of power increased and decreased on generators in the control set is always zero or equal to the change in active losses incurred by the control change, wherein transfer of power is produced within the control set of generators that is progressively increased;

wherein the active power setpoint on any generator is changed as part of the transfer level increase until reactive reserves on the generators in the control set no longer increase or until they reach the (maximum or minimum) active power capability limit on the generator and then they are held at that (maximum or minimum) active power capability limit;

wherein the transfer of power within the set generators in the control set using the participation factors is progressively increased until reactive generation levels on generators in the control set or control region exceed a certain percentage of their reactive supply capability by increase in transfer or until a consecutive set of solutions is obtained, wherein no solution is found then another generator or control device is added to the control set based on the ranking of generators and control devices in the predicted control region are added to the control set, wherein process of increasing transfer within the control set of generators in an attempt to find consecutive loadflow solutions and increasing reactive reserves on generators or control devices in the control set or control region by increasing transfer levels on generators in the control set and if unsuccessful then adding an additional generator or control device to the control set is continued until there are no more generators or control devices in the predicted control region, wherein consecutive solutions are found, the control is selected to be nearer the centered of the consecutive set of solutions or where the reactive reserves on the generators and control devices exceed a certain percentage of their reactive supply capability, wherein no control is found after all agents in the predicted control region are placed in the control region, there is no preventive and corrective active rescheduling control for this contingency, wherein the Preventive Control could be implemented by modifying the active power generation setpoints if the first of a double contingency occurs with no solution, or if the system is known to be vulnerable to voltage collapse for this single contingency before it actually occurs on the system.

80. A method of posturing control for a Base Case Blackout Region comprising the steps of:

adding generators to agents in the Base Case Blackout Region in order to add reactive reserve to these agents;

adding generators to agents in the Base Case Blackout Region when there are generators in the vulnerability region at the same generating station as the added generators;

performing Preventive Voltage and Reactive Rescheduling to add reactive reserves to the agents in the Base Case Blackout Region;

performing Preventive Active Rescheduling to add reactive reserves to agents in the Base Case Blackout Region;

wherein if the system has experienced a contingency that makes blackout imminent, perform Preventive or Emergency load shedding to add reactive reserves to agents in the Base Case Blackout Region and the Predicted Control Region for that outage.

81. A method of posturing control for a set of equipment outage that have no solution, comprising the steps of:

finding a Preventive Voltage Rescheduling and Preventive Active Rescheduling Control for each contingency that obtains robust solutions;

finding the set of contingencies with nearly identical control regions;

utilizing a coordinated voltage control for finding a posturing control for all contingencies for a control region by utilizing different control sets and different levels of voltage control to obtain solutions for all contingencies for that set of clustered control regions.

82. The method of claim 81, further including the step of:

utilizing a coordinated active power control for finding a posturing control for all contingencies for a set of clustered control region by utilizing different control sets and different levels of active power control to obtain solutions for all contingencies for that set of clustered control regions.

83. The method of claim 81, further including the step of:

utilizing a coordinated voltage and active power control that finds a posturing control for all contingencies for a set of clustered control regions by utilizing different control sets and different levels of voltage and active power control change to obtain solutions for all contingencies for that set of clustered control regions.

84. The method of claim 81, further including the step of:

adding agents in families and family lines belonging to the control region that are not currently in that set of clustered control regions but exhaust a significant percentage of their reactive reserves and retry coordinated voltage control, coordinated active power control, and voltage and active power control if an effective postured control could not be obtained without these additional agents.

85. The method of claim 81, further including the step of:

locating groups of possibly modified control region clusters (load pockets) that have postured control once postured control has been found for all control regions clusters.

86. The method of claim 81, further including the step of:

selecting a prototype postured control for the largest control region in the group of control region clusters (load pockets).

87. The method of claim 81, further including the step of:

utilizing a coordinated voltage and active power control that attempts to find a posturing control for all contingencies for all control region clusters in the group by utilizing different control sets and different levels of voltage and active power control change to obtain solutions for all contingencies for that group of control region clusters.

88. The method of claim 81, further including the step of:

adding additional agents for family lines and families if needed to obtain a postured control for each group of control region clusters.

89. The method of claim 81, further including the step of:

implementing and coordinating postured controls for different groups of control region clusters.

90. The method of claim 81, wherein,

if no postured control is found for all of the contingencies for all control regions in the cluster of control regions (load pockets) or groups of clustered control regions using a postured voltage and active rescheduling, a postured coordinated voltage and active and load shedding would be attempted utilizing different control sets, different levels of voltage and active power control change and load reduction change to obtain solutions for all contingencies for that group of control region clusters.

91. The method of claim 81, wherein,

if no postured control is found for all contingencies for all control regions in the group of control region clusters;

preventive control can be applied individually to those contingencies for which the postured control is not effective in obtaining robust solutions.

92. A method for determining criticality of a plurality of contingencies, comprising:

applying a voltage collapse diagnostic to an electrical power system, wherein a plurality of contingencies are applied to the electrical power system and responses from a plurality of agents are monitored; and

ranking the plurality of contingencies according to criticality.

93. The method according to claim 92, wherein the step of ranking is performed according to:

$C_i=\mathrm{\Sigma <br><br>}<br><br>\text{\hspace{1em}<br><br>}<br><br>j<br><br>\text{\hspace{1em}<br><br>}<br><br>\frac{P_j<br><br>\left(-1+\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{reactivereservesremaining}}_{\mathrm{ij}}\right)}{1-\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{outageremaining}}_i}$

wherein contingency can be ranked for outages that have a solution, the percentage of the outage remaining is zero, or the percentage of the outage is not zero and is at the boundary case solution or some combination or all such contingencies.

94. The method according to claim 92, wherein the step of ranking is performed according to:

$A_j=\underset{i}{\sum <br><br>}<br><br>\frac{P_j<br><br>\left(-1+\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{reactivereservesremaining}}_{\mathrm{ij}}\right)}{1-\%<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{outageremaining}}_i}$

wherein the outages used can be all outages that have no solution and are evaluated at the boundary case solution, all outages that that solution when the percentage of the outage is zero, or all outages that have loadflow solution or some combination or all such contingencies.

95. A method for determining criticality of a plurality of agents, comprising:

applying a voltage collapse diagnostic to an electrical power system, wherein a plurality of contingencies are applied to the electrical power system and responses from a plurality of agents are monitored; and

ranking the plurality of agents according to criticality.

96. A method for determining an available transfer capability, comprising:

determining an amount of power that is available for transfer into or out of a load pocket or control area where the set of importing and the set of exporting generators and their participation factors are design parameters.

97. The method according to claim 96, wherein the determining step is a function of firm and non-firm transfer into the load pocket, a Transmission Reliability Margin (TRM) and a Capacity Benefit Margin (CBM) for a load pocket. NERC specifies the methodology for computing TRM and CBM.

98. The method of claim 97, wherein:

TTC=ITC+net power flow into the control region

NATC=TTC−

TRM−

NRES

RATC=TTC−

a TRM−

NRES-RRES a<

1,

wherein NRES is the non-recallable or firm transmission reservation for the control region or load pocket, RRES, is the recallable or non firm reservation for the control region or load pocket,

wherein NATC is the Non Recallable Available Transfer Capability and RATC is the Recallable Transfer Capability.