Lecture 2: Stability Criteria

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1 Lecture 2: Stability Criteria S.D. Sudhoff Energy Sources Analysis Consortium ESAC DC Stability Toolbox Tutorial January 4, 2002 Version 2.1 1

2 Lecture 2 Outline Comparison of Stability Criteria Design Specifications From Arbitrary Stability Criteria Generalized Impedance / Admittance Concepts 2

3 Stability Factoid The source load system is stable provided that the evaluation of along the Nyquist contour does not encircle -1 Z s Y l 3

4 Stability Criteria Imaginary Axis ESAC Criteria GMPM Criteria Unit Circle PM 1/GM Real Axis Opposing Argument Criteria Middlebrook Criteria [2] S.D. Sudhoff, Admittance Space Based Stability Specification, Proceedings of the 1998 ONR - Drexel-NSWC Workshop on Electric Shipboard System Modeling, Simulation and Control, June 22-23, 1998, Philadelphia, PA, USA 4

5 Purpose of Stability Criteria Primary Basis for calculating load admittance spec from source impedance; or source impedance spec from load admittance Secondary Check of stability 5

6 Comparison of Stability Criteria Cost of resulting design Amenability to arbitrary component grouping Amenability to formulation of design specification 6

7 Cost of Resulting Design Imaginary Axis ESAC Criteria GMPM Criteria Unit Circle PM 1/GM Real Axis Opposing Argument Criteria Middlebrook Criteria [2] S.D. Sudhoff, Admittance Space Based Stability Specification, Proceedings of the 1998 ONR - Drexel-NSWC Workshop on Electric Shipboard System Modeling, Simulation and Control, June 22-23, 1998, Philadelphia, PA, USA 7

8 Cost of Resulting Design Middlebrook (Highest) Opposing Argument Gain/Phase ESAC (Lowest) 8

9 Grouping: Case Study 1 9

10 Grouping: Case Study 1 - Lecture 2 Nyquist Plane Results GMPM Criiteria Imaginary Axis -1.5 ESAC Criteria -3 Real Axis Nyquist Contour Unstable Case Nyqusis Contour Stable Case

11 Grouping: Case Study 2 r L V s +_ C - R Source Load 11

12 Grouping: Case Study 2 Lecture 2 Nyquist Plane Results Imaginary Axis 3 Nyquist Contour, Stable Case ESAC Criteria Arcs at s = 400π 3 Real Axis -3 GMPM Criteria Nyquist Contour, Unstable Case -3 12

13 Grouping: Summary ESAC Criteria much less sensitive to grouping than other proposed criteria 13

14 Design Specification: Middlebrook Suppose Z s known Design specification on load becomes Y < l GM 1 Z s Alternately, could come up with specification on load impedance 14

15 Design Specification: Lecture 2 Gain and Phase Margin Criteria Design specification based on Y Z < l l 1 GM Y l ( s) + Z s ( s) ( o ) 180 PM and Y l ( s) + Z s ( s) ( o ) PM x angle(re( x) + j Im( x)) 15

16 Design Specification: ESAC Criteria Construction of a load admittance specification at a point 16

17 Design Specification: ESAC Criteria Construction of load admittance constraint at a frequency 17

18 Design Specification: ESAC Criteria magnitude, db D stability constraint in admittance space Stability Constraint in Admittance Space phase, degrees Load Admittance, Unstable Case Load Admittance, Stable Case Inflection 2 log of frequency, Hz 4 18

19 Comments on Stability Criteria Design Cost (Highest to Lowest) Middlebrook, Opposing Argument, GMPM, ESAC Component Grouping ESAC criteria much less sensitive to grouping Translation to Design Specification Middlebrook most readily used GMPM not bad ESAC requires toolbox 19

20 Dealing with Reality: Lecture 2 Example System * vdc s Vol. Reg./ Exciter T e,des IM Controls ω rm,im Turbine SM v r v dcs v dci i abcs IM Mechanical Loa d 3 - φ LC Tie Line C apacitiv e 3 - φ Uncontrolled Filter Filter Fully Controlled Rectifier Inverter 20

21 Generalized Source Impedance Speed: p.u. Power: p.u. Voltage: p.u. Number of Plants Considered:

22 Generalized Source Impedance 22

23 Generalized Load Admittance Lecture 2 and Load Admittance Constraint 23

24 Generalized Source Impedance Lecture 2 and Source Impedance Constraint 24

25 Measured Performance 25

26 Mitigation: The Nonlinear Stabilizing Lecture 2 Control Architecture (NSCA) [3] S.D. Sudhoff, K.A. Corzine, S.F. Glover, H.J. Hegner, and H.N. Robey, DC Link Stabilized Field Oriented Control of Electric Propulsion Systems, IEEE Transactions on Energy Conversion, Vol. 13, No. 1, March [4] S.D. Sudhoff, Control of Power Electronics Based Systems Proceedings of the 1998 ONR -Drexel-NSWC Workshop on Electric Shipboard System Modeling, Simulation and Control, June 22-23, 1998, Philadelphia, PA, USA [5] S.D. Sudhoff, S.F. Glover, Nonlinear Stabilizing Control for Power Electronic Based Systems, U.S. Patent No. 6,051,941, April 18, International Patents Applied For. 26

27 Generalized Load Admittance Lecture 2 and Constraint with NSCA 27

28 Generalized Source Impedance Lecture 2 and Constraint with NSCA 28

29 Measured Performance with NSCA 29

30 Conclusions ESAC Criteria Leads to Less Expensive / Higher Performance Designs Facilitates Modularity in Design Process 3-Dimensional Admittance/Impedance Space Approach Allows ESAC (and Arbitrary) Stability to Be Used Facilitates Specification of Source Given Load Facilitates Specification of Load Given Source 30

Figure 4-1. Naval Combat Survivability Testbed. 4.1 CLASSIFICATION OF SINGLE PORT POWER CONVERTERS

Figure 4-1. Naval Combat Survivability Testbed. 4.1 CLASSIFICATION OF SINGLE PORT POWER CONVERTERS 4 / System Analysis Thus far, our consideration of immittance based stability analysis has been limited to simple one source, one load, problems. In this chapter, we consider immittance based stability