1. A method of validating a calibration factor for a material flow, comprising the steps of:
defining at least one density at a reference temperature of said material flow;
determining a compensated line density and a line temperature of said material flow, wherein the step of determining the compensated line density includes temperature compensating a line density by determining the line density when said line temperature corresponds to said reference temperature; and
detecting an error condition, wherein the step of detecting an error condition includes comparing said compensated line density to the at least one density.
2. The method according to claim 1, wherein said at least one density includes upper and lower limits for said compensated line density.
3. The method according to claim 2, wherein said upper and lower limits are determined by determining a reference density for said material flow at said reference temperature and selecting said upper and lower limits so that the reference density is between said upper and lower limits.
4. The method according to claim 1, wherein said at least one density is a reference density for said material flow that is determined at the reference temperature.
5. The method according to claim I, further comprising the steps of:
measuring the line pressure of said material flow;
determining a pressure compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature compensated line density using said pressure compensation factor.
6. The method according to claim 5, wherein said step of determining the pressure compensation factor includes the steps of:
determining the ratio of changes in density to changes in pressure;
determining a pressure difference between said line pressure and a reference pressure; and
multiplying said ratio by said pressure difference to obtain said pressure compensation factor.
7. The method according to claim 5, further comprises the steps of:
measuring the material composition of said material flow;
determining a material composition compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature and pressure compensated line density using said material composition compensation factor.
8. The method according to claim 1, further comprising the steps of:
measuring the material composition of said material flow;
determining a material composition compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature compensated line density using said material composition compensation factor.
9. The method according to claim 8, further comprising the steps of:
measuring the line pressure of said material flow;
determining a pressure compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said material composition and temperature compensated line density using said pressure compensation factor.
10. A computer program product comprising computer usable medium including executable code for executing a process comprising the steps of:
defining at least one density at a reference temperature of a material flow;
determining a compensated line density and line temperature of said material flow, wherein the step of determining the compensated line density includes temperature compensating a line density by determining the line density when said line temperature corresponds to said reference temperature; and
detecting an error condition, wherein the step of detecting an error condition includes comparing said compensated line density to the at least one density.
11. The computer program product according to claim 10 wherein said at least one density includes upper and lower limits for said compensated line density.
12. The computer program product according to claim 11 wherein said upper and lower limits are determined by determining a reference density for said material flow at said reference temperature and selecting said upper and lower limits so that the reference density is between said upper and lower limits.
13. The computer program product according to claim 10 wherein said at least one density is a reference density for said material flow that is determined at the reference temperature.
14. The computer program product according to claim 10, wherein said process further comprises the steps of:
measuring the line pressure of said material flow;
determining a pressure compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature compensated line density using said pressure compensation factor.
15. The computer program product according to claim 14 wherein said pressure compensation factor is formed by the steps of:
determining the ratio of changes in density to changes in pressure;
determining a pressure difference between said line pressure and a reference pressure; and
multiplying said ratio by said pressure difference to obtain said pressure compensation factor.
16. The computer program product according to claim 14, wherein said process further comprises the steps of:
measuring the material composition of said material flow;
determining a material composition compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature and pressure compensated line density using said material composition compensation factor.
17. The computer program product according to claim 10 characterised in that said method further comprises the steps of:
measuring the material composition of said material flow;
determining a material composition compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said temperature compensated line density said material composition compensation factor.
18. The computer program product according to claim 17, wherein said process further comprises the steps of:
measuring the line pressure of said material flow;
determining a pressure compensation factor for said material flow; and
wherein the step of determining the compensated line density includes the step of compensating said material composition and temperature compensated line density using said pressure compensation factor to derive the compensated line density that has been compensated for material composition, pressure, and temperature.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
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.