A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants
Abstract
:1. Introduction
- A novel STOA approach is proposed to compute the MPC optimum parameters-based nonlinear deregulated LFC combined with conventional, RESs, and energy storage systems (ESSs).
- Wind turbine (WT), photovoltaic (PV) model with maximum power point tracker (MPPT), hydropower, diesel generator, and thermal plant are presented and modeled in deregulated LFC.
- Practical case study of interconnected system comprising the Kuraymat solar thermal power station is analyzed based on actual recorded solar radiation.
- The proposed MPC-LFC optimized via STOA achieved robust performance under changing some parameters of the system and random load disturbance.
2. Mathematical Model of Deregulated LFC
3. Sooty Terns Optimizer Characteristics
4. The Proposed Approach
4.1. Model-Predictive Control (MPC)
4.2. Optimal Deregulated LFC Solving Problem
5. Simulation Results
5.1. Unilateral-Based Transaction
5.2. Bilateral Transaction
5.3. Contract Violation Transaction
5.4. Sensitivity Analysis
5.5. Practical Case Study
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
STOA | Sooty terns optimization algorithm | ST | Sooty terns |
LFC | Load frequency control | SBO | Stain bower braid algorithm |
MPC | Model predictive control | FA | Firefly algorithm |
TRANSCOs | Transmission companies | DE | Differential evolution |
DISCOs | Distribution companies | PUs | Peak undershoot |
GENCOs | Generation companies | POs | Peak overshoot |
SMES | Superconducting magnetic energy storage | Ts | Settling time |
DPM | DISCOs Participation Matrix | cpf | contract participation factor |
Symbols | |||
A, B, C and D | The system state space matrices | e | Normal logarithm |
dPLi | The load disturbance in area i | Radi | The radius of every spiral turn |
Tij | The coefficient of synchronizing between areas i and j | Rand | The random number in scale of [0, 1] |
CB | The random variable | dPDi | total load disturbance in area i |
The position of ST that does not conflict with ST another | x(k) | The system state | |
Cf | Controlling variable | y(k) | The system outputs |
The current position of sooty tern | z | The current iteration | |
The ST positions of other | u and v | The constant of spiral form | |
The disparity between the ST and excellent fittest ST | Kdies | The constant gain of diesel unit | |
So and Si | the output and input diagonal array | Kg | The gain of steam plant governor |
T | Sample time of MPC | Kgh | The gain of hydro plant governor |
M and P | The control and prediction horizons | Kp | The gain of generator and power system |
Q and R | Weighting factors | KPV1 and KPV2 | The gains of PV system |
t | Simulation time | Kpw1, Kpw2 and Kpw3 | Wind plant gains |
dFi | The frequency deviation of i area | Kr | The gain of reheater |
dPtie,i | The power deviation of tie-line in area i | Kt | The gain of steam turbine |
Tg | Time constant of governor (sec.) | Tr | Time constant of reheater (sec.) |
Tgh | Time constant of hydro governor (sec.) | Trh | Reset time constants of hydro governor (sec.) |
Tp | Time constant of generator and power system (sec.) | Trs | Hydro governor transient droop |
TPV1 and TPV2 | Time constants of PV system (sec.) | Tt | Time constant of steam turbine (sec.) |
Tpw1, Tpw2 and Tpw3 | Time constants of wind plant (sec.) | Tw | Nominal start time of the water in penstock (sec.) |
Appendix A
Parameter | Value | Parameter | Value | Parameter | Value | |
---|---|---|---|---|---|---|
Tg | 0.08 s | Kpv1 | −18 | Kdiesel | 16.5 | |
Tr | 10 s | Tpv1 | 100 s | R | 0.425 pu MW/Hz | |
Kr | 0.33 Hz/pu MW | Kpv2 | 900 | B | 2.4 Hz/pu MW | |
Tt | 0.3 s | Tpv2 | 50 s | apf1 | 0.65 | |
Kp | 120 Hz/pu MW | Kwp1 | 1.25 | apf2 | 0.35 | |
Tp | 20 s | Kwp2 | 1.4 | Twp1 | 6 s | |
TW1 | 1 s | Twp2 | 0.041 s | Trs | 0.513 s | |
Trh | 10 s | Tgh | 48.7 s | Ks | 1.8 | |
Ts | 1.8 | Tgs | 1.0 | Tts | 3.0 | |
Ksmes | T1 | T2 | T3 | T4 | Tsmes | |
SMES1 | 0.8550 | 0.1279 | 0.1057 | 0.1000 | 0.6131 | 0.0144 |
SMES2 | 0.8181 | 0.1377 | 0.5205 | 0.1030 | 0.4241 | 0.0849 |
SMES3 | 0.5336 | 0.6088 | 0.1169 | 0.3597 | 0.2014 | 0.4638 |
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Author | Year | Deregulated/ Conventional | Type of Controller | Optimization Approach | System Construction | Has RESs?/Type | Has ESs?/Type | Defects |
---|---|---|---|---|---|---|---|---|
Panwar, A. et al. [3] | 2018 | Conventional | PID | BFOA | 2 areas | √ (Fuel cell) | × |
|
Shiva, C.K. et al. [17,18,19] | 2016–2017 | Deregulated | PID | QOHS | 2, 3 and 5 areas, multisources | × | × | |
Mohanty, B. et al. [20] | 2015 | Deregulated | PIDD | FOA | 2-areas, multisources | × | × | |
Dhundhara, S. et al. [23] | 2018 | Deregulated | PI | SCA | 2 areas, multisources | × | √ (CES) | |
Ghasemi-marzbali, A. [24] | 2020 | Deregulated | PID | MVCS | 4 areas, multisources | × | × | |
Selvaraju, R.K. et al. [25] | 2016 | Deregulated | PI | ACSA | 2 areas, multisources | × | √ (SMES and RFB) | |
Kumar, R. et al. [30] | 2020 | Deregulated | PI | Wahle algorithm | 2 areas, multisources | × | √ (CES) | |
Shankar, R. et al. [22] | 2019 | Deregulated | PID | FOA | 2 areas, multisources | × | × | |
Kumar, A. et al. [34] | 2021 | Deregulated | PIDN | QOLOA | 2 areas, multisources | √ (WT and PV) | √ (SMES and RFB) | |
Morsali, J. et al. [9] | 2018 | Deregulated | FOPID | MGSO | 2 areas, multisources | × | × |
|
Prakash, A. et al. [21] | 2020 | Deregulated | PIDN(1+FOD) | SSA | 2 areas, multisources | √ (WT) | × | |
Mishra, D.K. et al. [26] | 2020 | Deregulated | FOPID | Bat Algorithm | 2 areas, multisources | × | √ (SMES) | |
Arya, Y. [2] | 2019 | Deregulated | FO-fuzzy PID | BFOA | 2 and 3 areas, multisources | × | √ (RFB) | |
Mishra, A.K. et al. [28] | 2021 | Deregulated | FO-fuzzy PID | SSA | 3 areas, multisources | √ (WT, STPP and GTPP) | √ (RFB) | |
Fathy, A. et al. [6] | 2020 | Conventional/deregulated | Fuzzy PID | MBA | 2 and 3 areas | × | × |
|
Arya, Y. et al. [12] | 2017 | Conventional/deregulated | Fuzzy PI/PID | BFOA | 2 area/2 areas, multisources | × | × | |
Sharma, M. et al. [27] | 2020 | Deregulated | Fuzzy PIDN | SSA | 2 areas, multisources | × | √ (RFB) | |
Veerasamy, V. et al. [1] | 2020 | Conventional | Cascade PI-PD | PSO-GSA | 2 areas, multisources | √ (WT, Fuel cell) | √ (Battery) |
|
Tasnin, W. et al. [7] | 2019 | Deregulated | Cascade FOI-FOPD | SCA | 3 areas, multisources | √ (WT, STPP and GTPP) | × | |
Tasnin, W. et al. [10] | 2018 | Deregulated | Cascade FOPI-FOPID | SCA | 2 areas, multisources | √ (DSTS and GTPP) | × | |
Kumari, S. et al. [14] | 2020 | Deregulated | Calculus-based cascade TI-TID | WCA | 4 areas, multisources | × | × | |
Prakash, A. et al. [16] | 2019 | Deregulated | Cascade 2-DOF-PI-FOPDN | VPL | 2 areas, multisources | × | × | |
Babu, N.R. et al. [29] | 2021 | Deregulated | Cascade FOPDN-FOPIDN | CA | 3 areas, multisources | √ (Realistic DSTS) | × | |
Raj, U. et al. [33] | 2020 | Deregulated | Cascade 2DOF-PIDN-FOID | OISA | 3 areas, multisources | √ (WT and PV) | × | |
Pappachen, A. et al. [8] | 2016 | Deregulated | ANFIS | × | 2 areas, multisources | × | √ (SMES) |
|
Khamari, D. et al. [11] | 2020 | Deregulated | TID | hTLBO-PS | 2 areas, multisources | √ (Solar thermal) | √ (SMES) | |
Mohanty, B. [13] | 2020 | Deregulated | Output feedback SMC | hFPA-PS | 2 areas, multisources | × | × | |
Nosratabadi, S.M. et al. [15] | 2019 | Deregulated | Modified PID | GOA | 3 areas, multisources | √ (WT) | √ (RFB) | |
Das, M.K. et al. [31] | 2021 | Deregulated | PID-RLNN | GOA | 3 areas, multisources | √ (WT) | √ (SMES) | |
Das, S. et al. [32] | 2021 | Deregulated | TIDN-(1+PI) | MBA | 3 areas, multisources | √ (WT, GTPP and wave energy) | × | |
Present study | Deregulated | Optimal MPC | STOA | 3 areas, multisources | √ (WT, PV and STPP) | √ (SMES) |
Author | Year | Type of Controller | Optimization Approach | Linear/Nonlinear | Type of Generator | Has RESs?/Type | Cases Study | Has ESs?/Type | ||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | ||||||||
Arya, Y. [2] | 2019 | FO-fuzzy PID | BFOA | Linear | Thermal‒hydro | × | √ | √ | × | × | × | √ (RFB) |
Tasnin, W. et al. [7] | 2019 | Cascade FOI-FOPD | SCA | Linear | Thermal | √ (WT, STPP and GTPP) | √ | √ | √ | × | × | × |
Nosratabadi, S.M. et al. [15] | 2019 | Modified PID | GOA | Nonlinear (GRC-GDB) | Thermal‒hydro-gas‒diesel | √ (WT) | √ | √ | √ | √ | × | √ (RFB) |
Shiva, C.K. et al. [17] | 2016 | PID | QOHS | Linear | Thermal | × | √ | √ | √ | × | × | × |
Mishra, A.K. et al. [28] | 2021 | FO-fuzzy PID | SSA | Nonlinear (GRC-GDB) | Thermal | √ (WT, STPP and GTPP) | √ | √ | √ | √ | × | √ (RFB) |
Babu, N.R. et al. [29] | 2021 | Cascade FOPDN-FOPIDN | CA | Nonlinear (GRC) | Thermal | √ (Realistic DSTS) | √ | √ | √ | × | × | × |
Das, M.K. et al. [31] | 2021 | PID-RLNN | GOA | Linear | Thermal‒hydro‒diesel | √ (WT) | × | √ | √ | √ | × | √ (SMES) |
Das, S. et al. [32] | 2021 | TIDN-(1 + PI) | MBA | Linear | Thermal‒hydro | √ (WT, GTPP and wave energy) | × | √ | × | × | × | × |
Raj, U. et al. [33] | 2020 | Cascade 2DOF-PIDN-FOID | OISA | Linear | Thermal‒hydro‒gas‒diesel | √ (WT and PV) | √ | × | √ | × | × | × |
Present study | Optimal MPC | STOA | Nonlinear (GRC-GDB) | Thermal‒hydro‒diesel | √ (WT, PV and STPP) | √ | √ | √ | √ | √ | √ (SMES) |
Algorithm | ITAE | IAE | ITSE | ISE |
---|---|---|---|---|
GOA [31] | 1.5881 | 0.1035 | 0.00064 | 0.00012 |
IWD | 1.6434 | 0.1796 | 0.0022 | 0.0006 |
FA | 1.5204 | 0.2097 | 0.0036 | 0.00099 |
DE | 0.7078 | 0.1176 | 0.00096 | 0.00041 |
SBO | 0.9502 | 0.1573 | 0.0020 | 0.00073 |
STOA | 0.3736 | 0.0862 | 0.00057 | 0.00036 |
STOA with SMES | 0.1302 | 0.0357 | 0.00011 | 0.00011 |
Algorithm | Cont. | Parameter | ||||
---|---|---|---|---|---|---|
T | P | M | R | Q | ||
IWD | MPC1 | 1.0188 | 4.0000 | 3.6313 | 8.0187 | 9.4088 |
MPC2 | 1.4835 | 7.0000 | 3.0423 | 1.2121 | 4.1062 | |
MPC3 | 1.7736 | 9.0000 | 2.3223 | 5.8237 | 2.5449 | |
FA | MPC1 | 4.5778 | 7.0000 | 2.9508 | 7.1024 | 4.9171 |
MPC2 | 7.9330 | 7.0000 | 2.8788 | 6.8717 | 2.1063 | |
MPC3 | 4.1919 | 7.0000 | 2.5025 | 6.3966 | 6.1616 | |
DE | MPC1 | 0.1058 | 10.000 | 1.0000 | 9.5576 | 1.8960 |
MPC2 | 0.1714 | 10.000 | 1.0316 | 1.0000 | 9.9312 | |
MPC3 | 8.0646 | 4.0000 | 1.0000 | 9.7133 | 7.2729 | |
SBO | MPC1 | 2.2503 | 7.0000 | 3.4737 | 4.2343 | 8.6914 |
MPC2 | 7.2548 | 7.0000 | 2.0266 | 7.2507 | 1.9411 | |
MPC3 | 6.6740 | 8.0000 | 3.2194 | 8.8556 | 9.1734 | |
STOA | MPC1 | 0.1015 | 10.000 | 1.6962 | 1.0000 | 4.7993 |
MPC2 | 0.1425 | 5.0000 | 1.0000 | 1.0098 | 10.000 | |
MPC3 | 0.1000 | 5.0000 | 2.1788 | 1.0037 | 10.000 | |
STOA with SMES | MPC1 | 0.9897 | 6.0000 | 3.0211 | 1.0000 | 10.000 |
MPC2 | 0.1114 | 9.0000 | 1.0329 | 1.0000 | 3.6893 | |
MPC3 | 0.1163 | 7.0000 | 3.7377 | 9.3049 | 1.0792 |
Sig. | MPC via IWD | MPC via FA | MPC via DE | ||||||
---|---|---|---|---|---|---|---|---|---|
Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | |
dF1 | 27.0376 | −0.0086 | 0.0168 | 19.0569 | −0.0067 | 0.0179 | 14.6580 | −0.0066 | 0.0164 |
dF2 | 31.1874 | −0.0056 | 0.0052 | 31.7522 | −0.0004 | 0.0007 | 20.7756 | −0.0019 | 0.0066 |
dF3 | 33.0361 | −0.0048 | 0.0080 | 32.3542 | −0.0058 | 0.0090 | 26.9215 | −0.0039 | 0.0081 |
dPtie1 | 25.2028 | −0.0048 | 0.0062 | 25.3927 | −0.0016 | 0.0102 | 21.6732 | −0.0029 | 0.0061 |
dPtie2 | 28.6876 | −0.0049 | 0.0033 | 26.9591 | −0.0092 | 0.0018 | 22.6277 | −0.0047 | 0.0023 |
dPtie3 | 49.6124 | −0.0032 | 0.0024 | 35.4933 | −0.0034 | 0.0021 | 31.1791 | −0.0031 | 0.0015 |
MPC via SBO | MPC via STOA | MPC via STOA with SMES | |||||||
dF1 | 19.7260 | −0.0075 | 0.0187 | 10.0692 | −0.0064 | 0.0178 | 10.9544 | −0.0055 | 0.0133 |
dF2 | 29.1531 | −0.0004 | 0.0007 | 15.7320 | −0.0020 | 0.0053 | 7.8413 | −0.0003 | 0.0022 |
dF3 | 28.6542 | −0.0062 | 0.0093 | 11.3257 | −0.0078 | 0.0119 | 10.3924 | −0.0006 | 0.0024 |
dPtie1 | 21.2646 | −0.0016 | 0.0083 | 10.9328 | −0.0028 | 0.0069 | 10.2124 | −0.0012 | 0.0045 |
dPtie2 | 20.5120 | −0.0097 | 0.0010 | 10.9060 | −0.0046 | 0.0026 | 9.3023 | −0.0024 | 0.0006 |
dPtie3 | 33.0939 | −0.0035 | 0.0022 | 10.7960 | −0.0032 | 0.0022 | 10.2997 | −0.0021 | 0.0006 |
Algorithm | ITAE | IAE | ITSE | ISE |
---|---|---|---|---|
IWD | 35.6750 | 2.1620 | 0.2921 | 0.0385 |
FA | 33.2202 | 2.4408 | 0.4506 | 0.0499 |
DE | 30.1369 | 2.3571 | 0.4204 | 0.0493 |
SBO | 32.1007 | 2.3821 | 0.4301 | 0.0487 |
STOA | 3.2369 | 0.3996 | 0.0102 | 0.0028 |
STOA with SMES | 0.6619 | 0.1343 | 0.0011 | 0.00055 |
Algorithm | Cont. | Parameter | ||||
---|---|---|---|---|---|---|
T | P | M | R | Q | ||
IWD | MPC1 | 6.1667 | 8.0000 | 3.7863 | 8.2602 | 6.2492 |
MPC2 | 2.0503 | 5.0000 | 3.8281 | 1.4377 | 5.5301 | |
MPC3 | 1.8900 | 10.000 | 3.5589 | 5.8544 | 5.7842 | |
FA | MPC1 | 6.8705 | 6.0000 | 2.5811 | 6.4681 | 3.3892 |
MPC2 | 2.3363 | 7.0000 | 2.5216 | 5.2274 | 5.8524 | |
MPC3 | 9.3026 | 8.0000 | 1.6665 | 7.1737 | 4.7571 | |
DE | MPC1 | 2.5035 | 4.0000 | 2.2353 | 7.0311 | 1.8310 |
MPC2 | 2.6587 | 6.0000 | 3.6384 | 2.6987 | 9.4498 | |
MPC3 | 9.4381 | 4.0000 | 1.6674 | 10.000 | 6.0715 | |
SBO | MPC1 | 2.9720 | 7.0000 | 1.2831 | 9.6783 | 2.6398 |
MPC2 | 1.1842 | 6.0000 | 1.6785 | 4.3008 | 4.5068 | |
MPC3 | 9.3530 | 10.000 | 1.1492 | 6.9536 | 5.1313 | |
STOA | MPC1 | 0.3460 | 10.000 | 3.1737 | 1.0000 | 1.1277 |
MPC2 | 5.4724 | 6.0000 | 3.3661 | 1.0000 | 7.1087 | |
MPC3 | 0.1000 | 4.2887 | 4.0000 | 1.0000 | 10.000 | |
STOA with SMES | MPC1 | 0.1068 | 4.0000 | 3.1802 | 1.2149 | 7.1680 |
MPC2 | 0.1051 | 4.0000 | 1.8494 | 1.1014 | 7.6772 | |
MPC3 | 0.1000 | 5.0000 | 3.2439 | 1.0000 | 10.000 |
Sig. | MPC via IWD | MPC via FA | MPC via DE | ||||||
---|---|---|---|---|---|---|---|---|---|
Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | |
dF1 | 63.9004 | −0.0072 | 0.0306 | 53.6476 | −0.0074 | 0.0349 | 43.7017 | −0.0078 | 0.0319 |
dF2 | 63.5724 | −0.0199 | 0.0376 | 53.3038 | 0.0026 | 0.028 | 45.2208 | −0.0057 | 0.0284 |
dF3 | 60.1116 | −0.0442 | 0.0680 | 56.1535 | −0.0142 | 0.0566 | 52.0592 | −0.0143 | 0.0558 |
dPtie1 | 68.2425 | −0.0306 | 0.0075 | 45.1001 | −0.0292 | 0.0070 | 42.9730 | −0.0317 | 0.0092 |
dPtie2 | 61.5340 | −0.0246 | 0.0236 | 54.0869 | −0.0219 | 0.0048 | 51.4809 | −0.0189 | 0.0042 |
dPtie3 | 54.8649 | −0.0039 | 0.0463 | 49.0363 | −0.0092 | 0.0469 | 46.4990 | −0.0085 | 0.0480 |
MPC via SBO | MPC via STOA | MPC via STOA with SMES | |||||||
dF1 | 50.5606 | −0.0077 | 0.0328 | 21.8899 | −0.0069 | 0.0187 | 11.4348 | −0.0053 | 0.0146 |
dF2 | 49.7371 | −0.0046 | 0.0315 | 41.6452 | −0.0004 | 0.0105 | 10.6745 | −0.0001 | 0.0117 |
dF3 | 55.3097 | −0.0188 | 0.0553 | 18.4991 | −0.0048 | 0.0242 | 9.9298 | −0.0044 | 0.0146 |
dPtie1 | 42.3331 | −0.0306 | 0.0061 | 24.2308 | −0.0076 | 0.0016 | 14.1611 | −0.0030 | 0.0007 |
dPtie2 | 51.1851 | −0.0211 | 0.0044 | 46.4254 | −0.0062 | 0.0023 | 9.5737 | −0.0037 | 7.3 × 10−5 |
dPtie3 | 45.8561 | −0.0089 | 0.0487 | 41.7109 | −0.0002 | 0.0078 | 11.7334 | −9.9 × 10−5 | 0.0066 |
Algorithm | ITAE | IAE | ITSE | ISE |
---|---|---|---|---|
IWD | 53.9881 | 3.1885 | 0.6218 | 0.0785 |
FA | 49.0131 | 3.7460 | 1.1571 | 0.1293 |
DE | 46.3893 | 3.6482 | 1.0186 | 0.1222 |
SBO | 47.0683 | 3.5857 | 1.0208 | 0.1184 |
STOA | 5.1892 | 0.6027 | 0.0210 | 0.0056 |
STOA with SMES | 1.0106 | 0.2071 | 0.0025 | 0.0012 |
Algorithm | Cont. | Parameter | ||||
---|---|---|---|---|---|---|
T | P | M | R | Q | ||
IWD | MPC1 | 6.1667 | 8.0000 | 3.7863 | 8.2602 | 6.2492 |
MPC2 | 2.0503 | 5.0000 | 3.8281 | 1.4377 | 5.5301 | |
MPC3 | 1.8900 | 10.000 | 3.5589 | 5.8544 | 5.7842 | |
FA | MPC1 | 5.2872 | 6.0000 | 2.9868 | 6.3122 | 4.0850 |
MPC2 | 1.2944 | 8.0000 | 1.7920 | 5.3635 | 6.3384 | |
MPC3 | 9.3368 | 9.0000 | 1.5967 | 4.5315 | 3.9342 | |
DE | MPC1 | 10.000 | 6.0000 | 1.0000 | 10.000 | 4.1331 |
MPC2 | 2.3147 | 9.0000 | 2.3905 | 1.0000 | 3.4827 | |
MPC3 | 9.2692 | 10.000 | 1.3768 | 7.5380 | 8.5526 | |
SBO | MPC1 | 2.8428 | 7.0000 | 1.0952 | 9.8400 | 2.6615 |
MPC2 | 1.3013 | 6.0000 | 1.6362 | 3.7066 | 5.3726 | |
MPC3 | 9.3763 | 10.000 | 1.3055 | 7.5704 | 3.4958 | |
STOA | MPC1 | 0.3863 | 6.0000 | 1.3697 | 1.0000 | 10.000 |
MPC2 | 1.3889 | 10.000 | 1.7762 | 1.0000 | 10.000 | |
MPC3 | 0.1000 | 4.0000 | 4.0000 | 1.0000 | 10.000 | |
STOA with SMES | MPC1 | 0.1061 | 8.0000 | 1.1080 | 1.1258 | 8.9523 |
MPC2 | 0.1092 | 4.0000 | 1.2645 | 2.1158 | 8.0565 | |
MPC3 | 0.1000 | 7.0000 | 2.4561 | 1.0000 | 10.000 |
Sig. | MPC via IWD | MPC via FA | MPC via DE | ||||||
---|---|---|---|---|---|---|---|---|---|
Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | |
dF1 | 63.9340 | −0.0165 | 0.0454 | 47.9268 | −0.0166 | 0.0557 | 51.4054 | −0.0167 | 0.0507 |
dF2 | 63.5803 | −0.0238 | 0.0497 | 49.1896 | −0.0074 | 0.0511 | 53.2465 | −0.0033 | 0.0450 |
dF3 | 60.3591 | −0.0558 | 0.0901 | 55.4846 | −0.0242 | 0.0882 | 53.9884 | −0.0259 | 0.0826 |
dPtie1 | 68.2835 | −0.0448 | 0.0054 | 47.3875 | −0.0447 | 0.0081 | 47.4371 | −0.0558 | 0.0080 |
dPtie2 | 61.5780 | −0.0344 | 0.0305 | 53.6804 | −0.0333 | 0.0107 | 54.8810 | −0.0256 | 0.0115 |
dPtie3 | 55.0195 | −0.0047 | 0.0649 | 48.6736 | −0.0102 | 0.0747 | 49.5926 | −0.0066 | 0.0706 |
MPC via SBO | MPC via STOA | MPC via STOA with SMES | |||||||
dF1 | 53.5217 | −0.0168 | 0.0516 | 20.5473 | −0.0142 | 0.0331 | 11.4963 | −0.0125 | 0.0176 |
dF2 | 56.2937 | −0.0047 | 0.0450 | 37.5205 | −0.0004 | 0.0203 | 11.8392 | −0.0002 | 0.0170 |
dF3 | 53.2066 | −0.0240 | 0.0817 | 19.9847 | −0.0073 | 0.0388 | 10.6878 | −0.0040 | 0.0214 |
dPtie1 | 42.3381 | −0.0482 | 0.0058 | 22.3325 | −0.0124 | 0.0003 | 12.8129 | −0.0059 | 0.0005 |
dPtie2 | 53.7500 | −0.0287 | 0.0120 | 35.5661 | −0.0088 | 0.0063 | 21.0063 | −0.0042 | 0.0041 |
dPtie3 | 46.4073 | −0.0083 | 0.0751 | 41.1126 | −0.0003 | 0.0122 | 11.7787 | −0.0002 | 0.0099 |
Parameter | Bilateral Transaction | Contract Violation | ||||||
---|---|---|---|---|---|---|---|---|
ITAE (0.6619) | ITAE (1.0106) | |||||||
−50% | −25% | +25% | +50% | −50% | −25% | +25% | +50% | |
Tg | 0.6619 | 0.6619 | 0.6619 | 0.6618 | 1.0106 | 1.0106 | 1.0106 | 1.0106 |
Kr | 0.6619 | 0.6619 | 0.6619 | 0.6618 | 1.0106 | 1.0106 | 1.0106 | 1.0106 |
Tr | 0.6619 | 0.6619 | 0.6619 | 0.6618 | 1.0106 | 1.0106 | 1.0106 | 1.0106 |
Tt | 0.6619 | 0.6619 | 0.6619 | 0.6618 | 1.0106 | 1.0106 | 1.0106 | 1.0106 |
Kp | 0.7049 | 0.6651 | 0.6607 | 0.6606 | 1.1089 | 1.0157 | 1.0094 | 1.0090 |
Tp | 0.6826 | 0.6606 | 0.6640 | 0.6678 | 1.0105 | 1.0094 | 1.0137 | 1.0195 |
Algorithm | ITAE | IAE | ITSE | ISE |
---|---|---|---|---|
IWD | 8.1699 | 0.7598 | 0.0419 | 0.0074 |
FA | 5.7623 | 0.5724 | 0.0253 | 0.0052 |
DE | 2.7636 | 0.2837 | 0.0054 | 0.0012 |
SBO | 6.0784 | 0.5965 | 0.0230 | 0.0055 |
STOA | 1.9642 | 0.2347 | 0.0036 | 9.74 × 10−4 |
STOA with SMES | 0.7647 | 0.1092 | 6.65 × 10−4 | 3.03 × 10−4 |
Algorithm | Cont. | Parameter | ||||
---|---|---|---|---|---|---|
T | P | M | R | Q | ||
IWD | MPC1 | 2.2386 | 6.0000 | 2.7958 | 3.1128 | 8.6028 |
MPC2 | 2.0960 | 5.0000 | 1.7696 | 3.0907 | 5.4609 | |
MPC3 | 3.2193 | 10.000 | 2.8946 | 2.7096 | 9.1469 | |
FA | MPC1 | 2.3419 | 5.0000 | 2.5255 | 3.8603 | 7.9511 |
MPC2 | 1.1804 | 5.0000 | 1.6602 | 2.6835 | 5.7731 | |
MPC3 | 2.6442 | 9.0000 | 2.1220 | 2.1650 | 9.2610 | |
DE | MPC1 | 0.1000 | 7.0000 | 2.6028 | 1.1892 | 9.7307 |
MPC2 | 0.1003 | 8.0000 | 1.0000 | 1.0010 | 9.8950 | |
MPC3 | 0.1000 | 10.000 | 4.0000 | 1.0007 | 9.9993 | |
SBO | MPC1 | 2.2841 | 6.0000 | 2.5856 | 3.1844 | 8.4974 |
MPC2 | 1.8531 | 6.0000 | 1.6108 | 3.1598 | 5.2159 | |
MPC3 | 3.03711 | 9.0000 | 2.3412 | 1.0113 | 9.2644 | |
STOA | MPC1 | 0.1306 | 6.0000 | 1.1957 | 1.6546 | 4.2269 |
MPC2 | 0.1072 | 10.000 | 1.4580 | 1.2117 | 4.0086 | |
MPC3 | 0.1000 | 4.0000 | 1.2055 | 1.0000 | 10.0000 | |
STOA with SMES | MPC1 | 0.1000 | 5.0000 | 3.2188 | 1.0000 | 10.000 |
MPC2 | 0.1000 | 10.000 | 1.9825 | 1.0000 | 8.5687 | |
MPC3 | 0.1000 | 5.0000 | 1.1332 | 1.0000 | 10.000 |
Sig. | MPC via IWD | MPC via FA | MPC via DE | ||||||
---|---|---|---|---|---|---|---|---|---|
Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | Ts (s) | PUs (Hz) | Pos (Hz) | |
dF1 | 38.2310 | −0.0157 | 0.0163 | 35.5070 | −0.0091 | 0.0124 | 29.0191 | −0.0079 | 0.0098 |
dF2 | 33.5896 | −0.0207 | 0.0106 | 33.0856 | −0.0178 | 0.0106 | 28.0973 | −0.0078 | 0.0117 |
dF3 | 34.2854 | −0.0273 | 0.0300 | 33.3888 | −0.0297 | 0.0240 | 38.2454 | −0.0132 | 0.0118 |
dPtie1 | 32.4268 | −0.0055 | 0.0172 | 31.6296 | −0.0011 | 0.0126 | 30.9189 | −0.0007 | 0.0047 |
dPtie2 | 30.0549 | −0.0077 | 0.0141 | 29.4559 | −0.0075 | 0.0089 | 30.1285 | −0.0014 | 0.0051 |
dPtie3 | 34.7497 | −0.0174 | 0.0020 | 31.8582 | −0.0187 | 0.0026 | 30.9790 | −0.0017 | 0.0011 |
MPC via SBO | MPC via STOA | MPC via STOA with SMES | |||||||
dF1 | 35.4207 | −0.016 | 0.0165 | 25.3660 | −0.0087 | 0.0117 | 15.3465 | −0.0073 | 0.0115 |
dF2 | 35.2094 | −0.0132 | 0.0106 | 25.7349 | −0.0068 | 0.0115 | 14.3275 | −0.0027 | 0.0115 |
dF3 | 32.4255 | −0.0308 | 0.0287 | 26.5229 | −0.0118 | 0.0103 | 14.9977 | −0.0082 | 0.0054 |
dPtie1 | 30.6435 | −0.0053 | 0.0170 | 27.0556 | −0.0012 | 0.0051 | 20.9348 | −0.0006 | 0.0034 |
dPtie2 | 32.5795 | −0.0121 | 0.0073 | 22.5349 | −0.0004 | 0.0045 | 13.8070 | −1.6 × 10−6 | 9.4805 |
dPtie3 | 32.9513 | −0.0173 | 0.0029 | 27.0283 | −0.0005 | 0.0006 | 11.7035 | −4.5 × 10−5 | 5.6 × 10−5 |
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Ali, H.H.; Fathy, A.; Al-Shaalan, A.M.; Kassem, A.M.; M. H. Farh, H.; Al-Shamma’a, A.A.; A. Gabbar, H. A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants. Energies 2021, 14, 5393. https://0-doi-org.brum.beds.ac.uk/10.3390/en14175393
Ali HH, Fathy A, Al-Shaalan AM, Kassem AM, M. H. Farh H, Al-Shamma’a AA, A. Gabbar H. A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants. Energies. 2021; 14(17):5393. https://0-doi-org.brum.beds.ac.uk/10.3390/en14175393
Chicago/Turabian StyleAli, Hossam Hassan, Ahmed Fathy, Abdullah M. Al-Shaalan, Ahmed M. Kassem, Hassan M. H. Farh, Abdullrahman A. Al-Shamma’a, and Hossam A. Gabbar. 2021. "A Novel Sooty Terns Algorithm for Deregulated MPC-LFC Installed in Multi-Interconnected System with Renewable Energy Plants" Energies 14, no. 17: 5393. https://0-doi-org.brum.beds.ac.uk/10.3390/en14175393