Power System Stabilizer as a Part of a Generator MPC Adaptive Predictive Control System
Abstract
:1. Introduction
1.1. Power Generation Problem at Large
- replacing the capacity of withdrawn sources in the power system,
- taking over the role of sources working as a base load power plant,
- covering the expected increase in demand, and
- consistent reduction in the energy sector of the impact on the environment.
1.2. Generator-Related Control Problem
1.3. Existing Methods to Control Generators
1.4. Motivation
1.5. The Proposed Solution
1.6. Contribution and Structure of the Paper
- adding adaptation features to a continuous monitoring framework,
- MPC approach to obtain optimal interplay between actions exerted on a plant and on a generator due to the introduction of the auxiliary signal, to minimize oscillations in the system, and
- detailed analysis of the behavior of the generator controller and an additional system stabilizer module proposed as a single model predictive controller with an additional input.
2. Problem Description
3. Model & Methods
3.1. Classical Generator Control
3.2. Recursive Least Squares Method
- 1.
- Flexibility, that is, extending the model in such a way that it is able to describe the largest possible family of objects, i.e., the model has a sufficient number of parameters to describe the complex dynamics of identified objects.
- 2.
- Economy, the greatest possible simplification of the model and the number of parameters in order to avoid a situation in which several models with a given structure can describe the considered object, which leads to ambiguity, and also affects the extension of the calculation time.
- 3.
- Algorithm complexity, which has a significant impact on the time of its implementation.
- 0—no additional external auxiliary input is used,
- —generator’s rotational speed,
- —generator’s active power, and
- —turbine’s control valve opening degree (this signal can be exchanged between turbine’s and generator’s controllers without any additional measurements).
3.3. Model Predictive Control
- 1.
- Determining the structure of the discrete input-output model (6).
- 2.
- Identification of model parameters at each step of the algorithm operation (RLS, Section 3.2).
- 3.
- Calculation of the step response model based on the current discrete model at each step of the algorithm operation.
- 4.
- The use of the step response model in the algorithm of the MPC controller.
- (1)
- obtain ;
- (2)
- solve;
- (3)
- if , proceed to the last step; otherwise, proceed to the next step;
- (4)
- calculate the step length
- (5)
- improve the solution
- (6)
- check the sign of the Lagrange multipliers for inequality constraints: stop the algorithm if no multiplier is nonnegative; otherwise, remove the constraint corresponding to the largest positive multiplier and proceed to Step 2.
4. Simulation Test Results
- —an MPC controller with turbine’s control valve opening as an external auxiliary input,
- —an MPC controller with rotational speed as an external auxiliary input,
- —an MPC controller with active power as an external auxiliary input,
- —an MPC controller without any external auxiliary input, and
- —a simple controller based on PID and a simple system stabilizer.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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outputs | power, voltage, frequency | |
set values | reference power, constant set voltage and frequency values | |
control signals | control valve opening, excitation voltage | |
constraints | , | minimum/maximum: valve opening (0–100%), excitation system voltage ( |
40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | |
---|---|---|---|---|---|---|---|---|
10 | 2.4387 | 2.3790 | 2.4315 | 2.5688 | 2.7062 | 2.9677 | 3.2324 | 3.7393 |
11 | 2.0458 | 1.9942 | 2.0383 | 2.1829 | 2.3395 | 2.5497 | 2.8270 | 3.1587 |
12 | 1.0768 | 0.9138 | 1.6176 | 1.8004 | 1.9839 | 2.2141 | 2.4476 | 2.7803 |
13 | 0.9638 | 0.7808 | 0.6702 | 0.6220 | 1.6392 | 1.8816 | 2.1633 | 2.4560 |
14 | 0.9500 | 0.7409 | 0.6182 | 0.5472 | 0.5179 | 0.5505 | 1.8418 | 2.1968 |
15 | 0.9486 | 0.7307 | 0.5993 | 0.5207 | 0.4783 | 0.4673 | 0.5076 | 1.9037 |
16 | 0.9495 | 0.7288 | 0.5900 | 0.5067 | 0.4619 | 0.4432 | 0.4552 | 0.5451 |
17 | 0.9509 | 0.7288 | 0.5867 | 0.4990 | 0.4517 | 0.4308 | 0.4383 | 0.4871 |
18 | 0.9534 | 0.7300 | 0.5862 | 0.4956 | 0.4446 | 0.4231 | 0.4287 | 0.4721 |
19 | 0.9571 | 0.7320 | 0.5870 | 0.4940 | 0.4401 | 0.4173 | 0.4226 | 0.4646 |
20 | 0.9614 | 0.7346 | 0.5886 | 0.4942 | 0.4380 | 0.4137 | 0.4186 | 0.4604 |
21 | 0.9659 | 0.7375 | 0.5905 | 0.4951 | 0.4373 | 0.4116 | 0.4162 | 0.4584 |
22 | 0.9705 | 0.7404 | 0.5927 | 0.4967 | 0.4377 | 0.4107 | 0.4156 | 0.4583 |
23 | 0.9750 | 0.7435 | 0.5951 | 0.4987 | 0.4389 | 0.4112 | 0.4159 | 0.4596 |
ISE\ | 21 | 22 | 23 |
---|---|---|---|
3.4 | 3.4 | 3.4 | |
3.5 | 3.5 | 3.5 | |
3.5 | 3.5 | 3.5 | |
3.5 | 3.5 | 3.5 |
ITSE \ | 21 | 22 | 23 |
---|---|---|---|
0.999 | 1.001 | 1.003 | |
1.086 | 1.086 | 1.086 | |
1.098 | 1.098 | 1.098 | |
1.087 | 1.087 | 1.087 |
PID + PSS [57] | 12.82 | 29.03 | 0 | 0.65 | 1.74 | ||
T | |||||||
MPC | 22 | 1 | 1 | 0.01 | 1;1;1 | 0 |
ISE | ITSE | |
---|---|---|
33.76 | 10.01 | |
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Sokólski, P.; Rutkowski, T.A.; Ceran, B.; Horla, D.; Złotecka, D. Power System Stabilizer as a Part of a Generator MPC Adaptive Predictive Control System. Energies 2021, 14, 6631. https://doi.org/10.3390/en14206631
Sokólski P, Rutkowski TA, Ceran B, Horla D, Złotecka D. Power System Stabilizer as a Part of a Generator MPC Adaptive Predictive Control System. Energies. 2021; 14(20):6631. https://doi.org/10.3390/en14206631
Chicago/Turabian StyleSokólski, Paweł, Tomasz A. Rutkowski, Bartosz Ceran, Dariusz Horla, and Daria Złotecka. 2021. "Power System Stabilizer as a Part of a Generator MPC Adaptive Predictive Control System" Energies 14, no. 20: 6631. https://doi.org/10.3390/en14206631