Designing Structure-Dependent MPC-Based AGC Schemes Considering Network Topology
Abstract
:1. Introduction
2. Generator and Power Network Dynamics
2.1. Generator Dynamic Model
2.2. Power Network Model
2.3. Generator and Network Coupling Model
2.4. Line Power Flow Model
3. MPC-Based AGC
3.1. Centralized MPC-Based AGC
3.2. Line Flow Control in Centralized Structure
3.3. Distributed MPC-Based AGC
3.4. Bulk-Area Partitioning for MPC-Based AGC
4. Illustrative Example
Generator Bus | M | D | Tg | Ta | Kt | r | () | () |
---|---|---|---|---|---|---|---|---|
# 30 (Gen1) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 31 (Gen2) | 3 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 32 (Gen3) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 2 | −2 |
# 33 (Gen4) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 2 | −2 |
# 34 (Gen5) | 3 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 35 (Gen6) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 36 (Gen7) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 37 (Gen8) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 3 | −3 |
# 38 (Gen9) | 3 | 5 | 0.25 | 0.2 | 250 | 19 | 2 | −2 |
# 39 (Gen10) | 2 | 5 | 0.25 | 0.2 | 250 | 19 | 2 | −2 |
Event time [s] | Bus number | Magnitude [pu] |
---|---|---|
1 | 28 | 0.2 |
50 | 13 | -0.1 |
100 | 22 | 0.15 |
4.1. Centralized MPC-Based AGC Systems
Description | Parameter | Value |
---|---|---|
Discretized Minimum Step Time [s] | Tf | 1 |
AGC Update Time [s] | Tu | 2 |
Line Control Update Time [s] | Tline | 6 |
Weighting Matrix | Q | 102I |
QN | 102I | |
R | I | |
Qf | Iline | |
Rf | I | |
Prediction Horizon | N | 20 |
Frequency Bias Factor | 200 |
4.2. Distributed MPC-based AGC Systems
Description | Parameter | BA1 | BA2 |
---|---|---|---|
Discretized Minimum Step Time [s] | Tf | 1 | 1 |
AGC Update Time [s] | Tu | 3 | 2 |
Weighting Matrix | Q | 102I1 | 102 I2 |
QN | 102 I1 | 102 I2 | |
R | I1 | I2 | |
Prediction Horizon | 20 | 20 | |
Frequency Bias Factor | 120 | 80 |
Description | Parameter | SB1 | SB2 |
---|---|---|---|
Mechanical power sampling time [s] | Tm | 4 | |
Q | 102Isb1 | 102 Isb2 | |
Weighting Matrix | QN | 102 Isb1 | 102 Isb2 |
R | Isb1 | Isb2 |
4.3. Discussion on Structure-Dependent AGC Scheme
Considerations for implementation | Centralized structure | Distributed structure | ||
---|---|---|---|---|
Original | Proposed | Original | Proposed | |
Wheeling | Χ | Χ | Χ | |
Computation Time | Χ | Χ | ∆ | |
Practicality | Χ | Χ | ||
Settling time (Tst) [s] | 7.60 | 24.60 | 15.05 | 16.01 |
5. Conclusions
Nomenclature
Constants:
V | Bus voltage [pu] |
Bus voltage angle [radian] | |
P | Initial bus power generation or demand [pu/100 MW] |
Ta | Time constant of the turbine [s] |
Tg | Time constant of governor [s] |
Tf | Discretized minimum time step [s] |
Tu | Discretized automatic generation control update time [s] |
Tm | Discretized mechanical power sampling time step [s] |
Tline | Discretized line power flow control update time step [s] |
Tst | Frequency settling time [s] |
D | Damping constant |
M | Moment of inertia of the generator [s] |
Kt | Parameter in linearization for turbine characteristics |
r | Parameter in linearization for governor droop characteristics |
J | Jacobian matrix of power evaluated at angle |
Frequency bias factor in i-balancing area | |
Maximum generation control ramp rate [pu/s] | |
Minimum generation control ramp rate [pu/s] |
Variables:
Load reference [pu] | |
Load frequency set point [pu] | |
Generator frequency [pu] | |
Pm | Turbine mechanical power [pu] |
Governor-controlled valve opening [pu] | |
F | Mapped injected-power [pu] |
Pf | Tie-line power flow [pu] |
y | Concatenated state variables in full-scale dynamic model |
Indices:
k | Discretized minimum time step [k = kTf] |
ku | Discretized frequency control update time step [ku = kuTu] |
Kline | Discretized tie-line flow control update time step [kline = klineTline] |
km | Discretized mechanical power sampling time step [km = kmTm] |
Author Contributions
Conflicts of Interest
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Jang, Y.-S.; Park, J.; Yoon, Y.T. Designing Structure-Dependent MPC-Based AGC Schemes Considering Network Topology. Energies 2015, 8, 3437-3454. https://doi.org/10.3390/en8053437
Jang Y-S, Park J, Yoon YT. Designing Structure-Dependent MPC-Based AGC Schemes Considering Network Topology. Energies. 2015; 8(5):3437-3454. https://doi.org/10.3390/en8053437
Chicago/Turabian StyleJang, Young-Sik, JoonHyung Park, and Yong Tae Yoon. 2015. "Designing Structure-Dependent MPC-Based AGC Schemes Considering Network Topology" Energies 8, no. 5: 3437-3454. https://doi.org/10.3390/en8053437