Patent EA-000267-B1 (EA)
Title: Method and apparatus for load balancing among multiple compressors
Inventor: STAROSELSKY SERGE
IPC: F04D27/02
Filed: 1996-10-18
Abstract: 1. A method for controlling a compression system comprising at least two compressors, at least one driver, and a plurality of devices for varying the performance of said compressors, the method comprising the steps of: (a) defining a surge parameter, S, representing a distance between an operating point and a surge line for each compressor; (b) specifying a value, Sx, of said surge parameter for each compressor; (c) manipulating the performance of said compressors to maintain a predetermined relationship between all compressors and/or drivers when the operating points of all compressors are farther from surge than said specified value, sx and (d) manipulating the performance of said compressors in such a fashion that all compressors reach their surge lines simultaneously. 2. The method of Claim 1 wherein the step of defining a surge parameter, S, comprises the steps of: (a) constructing a surge control line of a compressor in two-dimensional space; (b) defining a function f1(x), which returns an abscissa value at surge for a given value of an ordinate variable; and (c) calculating a ratio of f1(x) to the abscissa value using actual values of the abscissa and ordinate variables. 3. The method of Claim 2 wherein the abscissa variable is a reduced flow, δpo / p, and the ordinate variable is a pressure ratio, Rc. 4. The method of Claim 2 wherein the abscissa variable is a reduced flow, δpo / p, and the ordinate variable is a reduced head, hr = (Rc<σ>-1) /σ 5. The method of Claim 2 wherein the abscissa variable is a differential pressure across a flow measurement device, δpo, and the ordinate variable is a pressure difference across the compressor δpc. 6. The method of Claim 1 wherein the step of maintaining a predetermined relationship between all compressors is accomplished by matching functions of pressure ratio, Rc. 7. The method of Claim 6 wherein a pressure ratio is calculated by the steps of: (a) sensing a pressure in a suction of said compressor; (b) sensing a pressure in a discharge of said compressor; (c) correcting said suction pressure and discharge pressure values to an absolute pressure scale; and (d) dividing said corrected discharge pressure by said corrected suction pressure to compute the pressure ratio. 8. The method of Claim 1 wherein the step of maintaining a predetermined relationship between all compressors is accomplished by matching functions of power, P. 9. The method of Claim 8 wherein the power is determined by sensing the power by a power measuring device and generating a power signal proportional to the power. 10. The method of Claim 8 wherein a value proportional to the power is calculated by the steps of:(a) sensing a value proportional to a suction pressure, Ps; (b) sensing a value proportional to a suction temperature, Ts; (c) sensing a value proportional to a discharge pressure, Pd; (d) sensing a value proportional to a discharge temperature, Td; (e) sensing a value proportional to a differential pressure across a flow measurement device, δpo. (f) calculating a value,   (g) constructing a first value by multiplying the values proportional to the temperature, pressure, and differential pressure, all in one of: the suction or discharge of said compressor, and taking a square root of said product; (h) calculating a pressure ratio, Rc, by dividing said discharge pressure by said suction pressure; (i) calculating a reduced head, hr., by raising said pressure ratio by a power equal to said o, subtracting one, and dividing the difference by said o; and (j) multiplying said first value by said reduced head. 11. The method of Claim 1 wherein the step of maintaining a predetermined relationship between all drivers is accomplished by balancing said drivers' distances to a limit. 12. The method of Claim 11 wherein said limit is a temperature limit of a gas turbine driver. 13. The method of Claim 11 wherein said limit is a maximum speed limit of said driver. 14. The method of Claim 11 wherein said limit is a minimum speed limit of said driver. 15. The method of Claim 11 wherein said limit is a maximum torque limit of said driver. 16. The method of Claim 11 wherein said limit is a maximum power limit of said driver. 17. The method of Claim 1 wherein the step of maintaining a predetermined relationship between all compressors is accomplished by matching functions of rotational speed, N. 18. The method of Claim 17 wherein the rotational speed is determined by sensing the rotational speed by a speed measuring device and generating a speed signal proportional to the speed. 19. A method for controlling a compression system comprising at least two compressors, at least one driver, and a plurality of devices for varying the performance of said compressors, relief means, and instrumentation, the method comprising the steps of: (a) defining a surge parameter, S, representing a distance between an operating point and a surge line for each compressor; (b) calculating a value of S for each compressor based on signals from said instrumentation; (c) determining a maximum value, S max, of all values of S for all compressors; (d) specifying a value, Sx,., of said surge parameter for each compressor; (e) specifying a value, sδ, of said surge parameter as close or closer to surge than Sx, for each compressor; (f) constructing a function, f 2(x), of pressure ratio, Rc, for each compressor; (g) computing a value for the pressure ratio, for each compressor; (h) calculating a value of a scaling factor, x, (0 <= x <= 1); (i) calculating a value which is a function of the state of said relief means, f v (v) (j) calculating a value of a balancing parameter, B = (1-x)f2c(Rc) + x[l -β(1-S)][1 + f v (v)] for each compressor; (k) defining a value of a set point for said balancing parameter for each compressor; and (1) manipulating the performance of said compressors to match said balancing parameters to said set point for each compressor. 20. The method of Claim 19 wherein said scaling factor is x = min {1, max [(Smax -S)/( Sσ - S )]}   21. The method of Claim 19, wherein v is taken to be a set point, OUT, for the relief means, obtained from an antisurge controller. 22. The method of Claim 19, wherein said function, f v (x), is also a function of a pressure ratio, R c across the compressor. 23. The method of Claim 19, wherein said function, f v (x) is a function of a mass flow rate,  , through said relief means. 24. The method of Claim 23 wherein calculating a value proportional to said mass flow rate,   through said relief means comprises the steps of: (a) constructing a function of a set point, f 5(OUT), to represent a flow coefficient, C v, of the relief means; (b) constructing a function of the pressure ratio across the valve in accordance with ISA (Instrument Society of America) or a valve manufacturer; (c) calculating a first product by multiplying said function of said set point by said function of pressure ratio; (d) calculating a second product by multiplying said first product by an absolute pressure, P1, at an inlet to said relief means; and (e) dividing said second product by a square root of an absolute temperature, T 1, at said inlet to said relief means. 25. The method of Claim 24 wherein the function of pressure ratio across the valve is calculated as   26. The method of Claim 24 wherein the absolute pressure, P 1, is assumed constant. 27. The method of Claim 24 wherein the absolute temperature, T 1, is assumed constant. 28. The method of Claim 25 wherein calculating a value proportional to said mass flow rate,   through said relief means comprises the steps of: (a) sensing a differential pressure across a flow measurement device; (b) sensing a pressure in the neighborhood of said flow measurement device; (c) sensing a temperature in the neighborhood of said flow measurement device; (d) calculating a product by multiplying the values of said differential pressure and said pressure; and (e) dividing said product by the value of said temperature and taking the square root of the entire quantity. 29. An apparatus for controlling a compression system comprising at least two compressors, at least one driver, and a plurality of devices for varying the performance of said compressors, the apparatus comprising: (a) means for defining a surge parameter, S, representing a distance between an operating point and a surge line for each compressor; (b) means for specifying a value, Sx,., of said surge parameter for each compressor; (c) means for manipulating the performance of said compressors to maintain a predetermined relationship between all compressors and/or drivers when the operating points of all compressors are farther from surge than said specified value, sx and (d) manipulating the performance of said compressors in such a fashion that all compressors reach their surge lines simultaneously. 30. An apparatus of Claim 29 wherein the means of defining a surge parameter, S, comprises the steps of: (a) constructing a surge control line of a compressor in two-dimensional space; (b) defining a function f1(x), which returns an abscissa value at surge for a given value of an ordinate variable; and (c) calculating a ratio of f1(x) to the abscissa value using actual values of the abscissa and ordinate variables. 31. An apparatus of Claim 30, wherein the abscissa variable is a reduced flow, δpo / p, and the ordinate variable is a pressure ratio, Rc. 32. An apparatus of Claim 30, wherein the abscissa variable is a reduced flow, δpo / p, and the ordinate variable is a reduced head, hr = (Rc<σ>-1) /σ 33. An apparatus of Claim 30 wherein the abscissa variable is a differential pressure across a flow measurement device, δpo, and the ordinate variable is a pressure difference across the compressor δpc. 34. An apparatus of Claim 29, wherein the means the step of maintaining a predetermined relationship between all compressors is accom