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Modelling of Primary Frequency Control and
  Effect Analyses of Governing System
   Parameters on the Grid Frequency
                 Zhixin Sun
Outline


    Introduction
    Mathematical Model of Primary Frequency Control
    Dynamic Test & Parameter Identification
    Effects of Parameters of Governing System
         Effect of dead band
         Effect of speed droop




Page 2                           Institute of Turbomachinery,   Xi’an Jiaotong University
Introduction

                Power Plant         frequency
                                                                  Factory
                Power Plant                                       Machine
                Power Plant
                Power Plant                                      Home User



            Power Generation                                  load Demand

Frequency is an indicator of overall power imbalance.
  power increases, frequency rises
  load increases, frequency falls
Frequency deviation must be controlled within a certain range.
(±0.2Hz in China)
                               Primary frequency control
           Frequency
                               Secondary frequency control
 Page 3                                         Institute of Turbomachinery,   Xi’an Jiaotong University
Introduction

  Primary frequency control (speed droop control)                              load


      ref                             Servo-       Steam               -
            +
                -   1/Speed droop                 turbine
                                                                   +            Rotor
                                      motor




                                    Dead band
          load increases, frequency falls
          frequency deviation is greater than the dead band
          servo-motor increases governing valve opening of steam turbine
          power output increases to hold back the decrease of frequency
responses fast
utilizes the heat storage of boiler
has frequency error in steady state
 Page 4                                         Institute of Turbomachinery,      Xi’an Jiaotong University
Introduction



    Secondary frequency control

         balances the power and load through fuel regulation
         responses slowly
         can eliminate steady state frequency error




Page 5                                     Institute of Turbomachinery,   Xi’an Jiaotong University
Mathematical Model of Primary Frequency Control

                                       Boiler model

                                                                               load


     ref                             Servo-        Steam               -
           +
               -   1/Speed droop                  turbine
                                                                   +            Rotor
                                     motor




                                   Dead band
 Main steam pressure is the interface between steam turbine and
 boiler.
Governing valve opening rises                  Main Steam pressure falls
                              Boiler responses slowly


Page 6                                          Institute of Turbomachinery,      Xi’an Jiaotong University
Mathematical Model of Boiler


                                                      gD
                                                                                   gs
                                         pD                          pS
                  gQ             gw




                                                           pD              pS


                                                       1                     1
                                                                     K
                                                      sTD                   sTS

         PF                     gQ               gw             gD
                 1                       1
                       e −τ s
              TF s + 1                TW s + 1
         gs




Page 7                                           Institute of Turbomachinery,     Xi’an Jiaotong University
Mathematical Model of Steam Turbine

Steam Turbine: three cylinders, single reheat




 Page 8                                  Institute of Turbomachinery,   Xi’an Jiaotong University
Mathematical Model of Steam Turbine

Power is assumed to be proportional to the pressure before each cylinder




                           aH+aI+aL=1



Page 9                                  Institute of Turbomachinery,   Xi’an Jiaotong University
Mathematical Model of Steam Turbine

Power over-regulation of HP cylinder

  Power response of actual unit can reach 60% of regulation target
  in the first several seconds
  Power response of simulation only reach 38%




 Page 10                                Institute of Turbomachinery,   Xi’an Jiaotong University
Mathematical Model of Steam Turbine

    Improved model of Steam Turbine

Power over-regulation coefficient          1
                                         sTCH+1
                                                             1
                                                          sTRH+1
                                                                                 1
                                                                              sTCO+1
of HP cylinder:
λ=f( pressure ratio, adiabatic index )                       +-


                                                              λ
                                                    ++

              New model
power




                                                   αH                 αI                   αL
                    Classic model
                                                                         +                    +
                                                                     +                    +




        Page 11                            Institute of Turbomachinery,      Xi’an Jiaotong University
Mathematical Model of Steam Turbine

Single Unit




  Test of primary frequency control:
  1.static test of servo-motor for identification of Tact
  2.load dump test for identification of Ta
  3.dynamic test for identification of the time constants of steam turbine
     on line, increases or decreases the reference speed (by 25 rpm)

 Page 12                                         Institute of Turbomachinery,   Xi’an Jiaotong University
Dynamic Test & Parameter Identification


                                              1.0



                                              0.8       3
1                     4                                                                    2
                                                                        4
                                              0.6




                                      %
                                              0.4

    2                                                                                      1

                                              0.2



                                              0.0

                                                    0   10         20           30    40       50
                3                                                       t (s)




                                                             TCH
                                          2
          Pressure                                           TRH
                                          3
          Valve opening
          Power                           4
                                                         TCO

Page 13                            Institute of Turbomachinery,             Xi’an Jiaotong University
Effect of dead band

Multi-units




Tab.1 The responses of units under
      different load disturbance

       Dead band        Power percentage
  1        2 r/min            38.0%
  2        3 r/min            41.2%
  3        4 r/min            11.0%
  4        5 r/min            9.8%

 Page 14                                   Institute of Turbomachinery,   Xi’an Jiaotong University
Effect of dead band

              Dead band =2 rpm                              Dead band =3 rpm




              Dead band =4 rpm                              Dead band =5 rpm




                        Simulation results
Page 15                                Institute of Turbomachinery,   Xi’an Jiaotong University
Effect of dead band

                    Tab.2 The responses of units under different load disturbance

    Load disturbance                      5%                                   7.6%                                 10%


   Dead band /r·min-1      2          3          4     5        2          3          4        5           2    3         4         5


 Freq variation max /Hz   -0.22      -0.21     -0.3   -0.31    -0.31   -0.30      -0.44       -0.45   -0.39    -0.38    -0.56    -0.57

  Freq variation Steady
                          -0.15      -0.15   -0.15    -0.15    -0.2     -0.2      -0.2        -0.2    -0.25    -0.25    -0.25    -0.25
        state /Hz


Steady State Frequency deviations<0.2 Hz

     Tab.3 The relationship between different dead band combination and allowed load disturbance
                               a             b             c           d                  e            f            g           h
      2 r/min capacity      0.25             0.5         0.7           0.9                1           0             0           0
      3 r/min capacity      0.25             0.2         0.1           0.1                0           1             0           0
      4 r/min capacity      0.25             0.2         0.1           0                  0           0             1           0
      5 r/min capacity      0.25             0.1         0.1           0                  0           0             0           1
        Allowed load
                               7.1           7.6         7.9           8.3            8.4             7.6        6.8            5.9
       disturbance/%

Page 16                                                                 Institute of Turbomachinery,             Xi’an Jiaotong University
Effect of speed droop




                                                  speed
speed droop
          n max − n N
  δ =                 × 100 %
               nN                                                                                         10% capacity with constant
   nmax —— no-load speed                                                                                  speed droop of 4%
   nN —— full-load speed
                                        unit with speed droop of 4%
                                        unit with speed droop of 6%
                                        unit with speed droop of 8%
                                        unit with speed droop of 10%




                                                                       Frequency /Hz
                              Load increases by 10%




                    Time /s

              90% capacity                                                                              10% capacity
Page 17                                                                                Institute of Turbomachinery,   Xi’an Jiaotong University
Xi'an Jiaotong University is a top10 university in China,and was founded in
1896. Today, Xi'an Jiaotong University is a comprehensive research
university offering programs in nine areas with a major emphasis on
science and engineering.




 Page 18                                 Institute of Turbomachinery,   Xi’an Jiaotong University
Page 19   Institute of Turbomachinery,   Xi’an Jiaotong University

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Zhixin Workshop on Modelling and Simulation of Coal-fired Power Generation and CCS Process

  • 1. Modelling of Primary Frequency Control and Effect Analyses of Governing System Parameters on the Grid Frequency Zhixin Sun
  • 2. Outline Introduction Mathematical Model of Primary Frequency Control Dynamic Test & Parameter Identification Effects of Parameters of Governing System Effect of dead band Effect of speed droop Page 2 Institute of Turbomachinery, Xi’an Jiaotong University
  • 3. Introduction Power Plant frequency Factory Power Plant Machine Power Plant Power Plant Home User Power Generation load Demand Frequency is an indicator of overall power imbalance. power increases, frequency rises load increases, frequency falls Frequency deviation must be controlled within a certain range. (±0.2Hz in China) Primary frequency control Frequency Secondary frequency control Page 3 Institute of Turbomachinery, Xi’an Jiaotong University
  • 4. Introduction Primary frequency control (speed droop control) load ref Servo- Steam - + - 1/Speed droop turbine + Rotor motor Dead band load increases, frequency falls frequency deviation is greater than the dead band servo-motor increases governing valve opening of steam turbine power output increases to hold back the decrease of frequency responses fast utilizes the heat storage of boiler has frequency error in steady state Page 4 Institute of Turbomachinery, Xi’an Jiaotong University
  • 5. Introduction Secondary frequency control balances the power and load through fuel regulation responses slowly can eliminate steady state frequency error Page 5 Institute of Turbomachinery, Xi’an Jiaotong University
  • 6. Mathematical Model of Primary Frequency Control Boiler model load ref Servo- Steam - + - 1/Speed droop turbine + Rotor motor Dead band Main steam pressure is the interface between steam turbine and boiler. Governing valve opening rises Main Steam pressure falls Boiler responses slowly Page 6 Institute of Turbomachinery, Xi’an Jiaotong University
  • 7. Mathematical Model of Boiler gD gs pD pS gQ gw pD pS 1 1 K sTD sTS PF gQ gw gD 1 1 e −τ s TF s + 1 TW s + 1 gs Page 7 Institute of Turbomachinery, Xi’an Jiaotong University
  • 8. Mathematical Model of Steam Turbine Steam Turbine: three cylinders, single reheat Page 8 Institute of Turbomachinery, Xi’an Jiaotong University
  • 9. Mathematical Model of Steam Turbine Power is assumed to be proportional to the pressure before each cylinder aH+aI+aL=1 Page 9 Institute of Turbomachinery, Xi’an Jiaotong University
  • 10. Mathematical Model of Steam Turbine Power over-regulation of HP cylinder Power response of actual unit can reach 60% of regulation target in the first several seconds Power response of simulation only reach 38% Page 10 Institute of Turbomachinery, Xi’an Jiaotong University
  • 11. Mathematical Model of Steam Turbine Improved model of Steam Turbine Power over-regulation coefficient 1 sTCH+1 1 sTRH+1 1 sTCO+1 of HP cylinder: λ=f( pressure ratio, adiabatic index ) +- λ ++ New model power αH αI αL Classic model + + + + Page 11 Institute of Turbomachinery, Xi’an Jiaotong University
  • 12. Mathematical Model of Steam Turbine Single Unit Test of primary frequency control: 1.static test of servo-motor for identification of Tact 2.load dump test for identification of Ta 3.dynamic test for identification of the time constants of steam turbine on line, increases or decreases the reference speed (by 25 rpm) Page 12 Institute of Turbomachinery, Xi’an Jiaotong University
  • 13. Dynamic Test & Parameter Identification 1.0 0.8 3 1 4 2 4 0.6 % 0.4 2 1 0.2 0.0 0 10 20 30 40 50 3 t (s) TCH 2 Pressure TRH 3 Valve opening Power 4 TCO Page 13 Institute of Turbomachinery, Xi’an Jiaotong University
  • 14. Effect of dead band Multi-units Tab.1 The responses of units under different load disturbance Dead band Power percentage 1 2 r/min 38.0% 2 3 r/min 41.2% 3 4 r/min 11.0% 4 5 r/min 9.8% Page 14 Institute of Turbomachinery, Xi’an Jiaotong University
  • 15. Effect of dead band Dead band =2 rpm Dead band =3 rpm Dead band =4 rpm Dead band =5 rpm Simulation results Page 15 Institute of Turbomachinery, Xi’an Jiaotong University
  • 16. Effect of dead band Tab.2 The responses of units under different load disturbance Load disturbance 5% 7.6% 10% Dead band /r·min-1 2 3 4 5 2 3 4 5 2 3 4 5 Freq variation max /Hz -0.22 -0.21 -0.3 -0.31 -0.31 -0.30 -0.44 -0.45 -0.39 -0.38 -0.56 -0.57 Freq variation Steady -0.15 -0.15 -0.15 -0.15 -0.2 -0.2 -0.2 -0.2 -0.25 -0.25 -0.25 -0.25 state /Hz Steady State Frequency deviations<0.2 Hz Tab.3 The relationship between different dead band combination and allowed load disturbance a b c d e f g h 2 r/min capacity 0.25 0.5 0.7 0.9 1 0 0 0 3 r/min capacity 0.25 0.2 0.1 0.1 0 1 0 0 4 r/min capacity 0.25 0.2 0.1 0 0 0 1 0 5 r/min capacity 0.25 0.1 0.1 0 0 0 0 1 Allowed load 7.1 7.6 7.9 8.3 8.4 7.6 6.8 5.9 disturbance/% Page 16 Institute of Turbomachinery, Xi’an Jiaotong University
  • 17. Effect of speed droop speed speed droop n max − n N δ = × 100 % nN 10% capacity with constant nmax —— no-load speed speed droop of 4% nN —— full-load speed unit with speed droop of 4% unit with speed droop of 6% unit with speed droop of 8% unit with speed droop of 10% Frequency /Hz Load increases by 10% Time /s 90% capacity 10% capacity Page 17 Institute of Turbomachinery, Xi’an Jiaotong University
  • 18. Xi'an Jiaotong University is a top10 university in China,and was founded in 1896. Today, Xi'an Jiaotong University is a comprehensive research university offering programs in nine areas with a major emphasis on science and engineering. Page 18 Institute of Turbomachinery, Xi’an Jiaotong University
  • 19. Page 19 Institute of Turbomachinery, Xi’an Jiaotong University