System and method for monitoring and managing electrical power transmission and distribution networks

1. A computer implemented method for determining a state of stability of an electrical grid having n nodes, comprising the steps of:

a. embedding load flow equations (L) representing the electrical grid in a holomorphic embedding (L(s)) where s is a variable in a complex domain that includes a value s=0 corresponding to a no load case (L(0)), in which all voltages are equal to a normal or designed voltage level and there is no energy flow in links of the electrical grid and the value s=1 corresponding to an objective case (L(1)) representative of the electrical grid in a condition for which stability is to be determined, wherein each variable of the load flow equations (L) is contained in L(s) as a function of the complex variable s by said holomorphic embedding, and transcribing the holomorphic embedding into software for use in a computer processor adapted to execute said software;

b. developing in power series, values of unknowns in parameters of the holomorphic embedding (L(s)), using said computer processor, wherein the values of s are in a neighborhood of the value for the no load case of each parameter of the load flow equations;

c. using said computer processor to compute an n-order algebraic approximant to the power series produced in step b;

d. said computer processor evaluating the n-order algebraic approximant produced in step c for the power series produced in step b to provide a solution to the load flow equations (L); and

e. displaying the solution to the load flow equations as a measure of a state of stability of the electrical grid.

2. The method of claim 1 , further comprising the steps of:

prior to said embedding step, receiving data from a supervisory and data acquisition system representative of conditions of the electrical grid, and forming said load flow equations (L) from said data.

3. The method of claim 2 , further comprising the steps of repeating said receiving step and steps a through e continuously to provide a continuous, real time estimation of the state of stability of the electrical grid.

4. The method of claim 3 , further comprising the steps of confirming that a set of voltages and flows contained in said solution to said load flow equations (L) are representative of a physical electrical state.

5. A computer implemented method of measuring load flow in a power generating system having an electrical grid comprised of n nodes, comprising the steps of:

a. embedding load flow equations (L) representing the electrical grid in a holomorphic embedding (L(s)) where s is a variable in a complex domain that includes a value s=0 corresponding to a no load case (L(0)), in which all voltages are equal to a normal or designed voltage level, and there is no energy flow in links of the electrical grid and the value s=1 corresponding to an objective case (L(1)) representative of the electrical grid in a condition for which stability is to be determined, wherein each variable of the load flow equations (L) is contained in L(s) as a function of the complex variable s by said holomorphic embedding, and transcribing the holomorphic embedding into software for use in a computer processor adapted to execute said software;

b. developing in power series, values of unknowns in parameters of the holomorphic embedding (L(s)), using said computer processor, wherein the values of s are in a neighborhood of the value for the no load case of each parameter of the load flow equations;

c. using said computer processor to compute an n-order algebraic approximant to the power series produced in step b;

d. said computer processor evaluating the n-order algebraic approximant produced in step c for the power series produced in step b to provide a solution to the load flow equations (L); and

e. displaying the solution to the load flow equations as a measure of the load flow in the power generating system.

6. The method of claim 5 , further comprising the steps of:

prior to said embedding step, receiving data from a supervisory and data acquisition system representative of conditions of the electrical grid, and forming said load flow equations (L) from said data.

7. The method of claim 6 , further comprising the steps of repeating said receiving step and steps a through e continuously to provide a continuous, real time measure of the load flow in the power generating system.

8. A system for measuring load flow in a power generating system having an electrical grid having n nodes, said system comprising:

a supervisory control and data acquisition system adapted to collect data from said electrical grid indicative of electrical conditions in said electrical grid, said supervisory control and data acquisition system being in communication with a microprocessor-controlled energy management system, said energy management system further comprising executable computer instructions to:

a. process said data received from said supervisory control and data acquisition system into load flow equations (L) representing the electrical grid;

b. embed said load flow equations (L) representing the electrical grid in a holomorphic embedding (L(s)) where s is a variable in a complex domain that includes a value s=0 corresponding to a no load case (L(0)), in which all voltages are equal to a normal or designed voltage level and there is no energy flow in links of the electrical grid and the value s=1 corresponding to an objective case (L(1)) representative of the electrical grid in a condition for which stability is to be determined, wherein each variable of the load flow equations (L) is contained in L(s) as a function of the complex variable s by said holomorphic embedding;

c. develop in power series, values of unknowns in parameters of the holomorphic embedding (L(s)) wherein the values of s are in a neighborhood of the value for the no load case of each parameter of the load flow equations;

d. compute an n-order algebraic approximant to the power series produced in step c;

e. evaluate the n-order algebraic approximant produced in step d for the power series produced in step c to provide a solution to the load flow equations (L); and

f. display the solution to the load flow equations as a measure of a state of stability of the electrical grid.