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Model‐free adaptive load frequency control for power systems with wind penetration under deregulation environment
Open accessAbstract
With the gradual deregulation of the power system by the power department, the power system has developed into a large‐scale and multiregional control system. Because of the power system internal complexity enhancing, the stable operation of power system becomes increasingly difficult. This paper analyzes the load frequency control problem of multiregional interconnected power system with wind energy. This study designs an improved model‐free adaptive control algorithm based on I/O data. It avoids model establishment of the multiregional power system. It also effectively solves the problem of frequency stability control under the influence of load change, introducing the generation participation matrix to simulate bilateral contracts under the power market. The dynamic evolution relationship of the system with the generation participation matrix is established, taking a three‐regional power system with wind energy as an example. Frequency fluctuations in all three regions are between . Convergence times of frequency deviation are all within 30 s, much less than the response time of load frequency control. The simulation results further demonstrate the effectiveness of the proposed algorithm, comparing the control algorithm proposed in this paper with other algorithms, which proves that the proposed algorithm has good control performance.
Overview
CoChat Summary
TL;DR
The paper proposes a model-free adaptive sliding mode control (MFASMC) algorithm for load frequency control (LFC) in multi-region power systems with wind penetration and deregulated bilateral contracts, using only input/output data and a generation participation matrix (GPM). Simulations on a three-region wind-integrated system show frequency fluctuations within ±0.1 Hz and frequency-deviation convergence within 30 s.
Key findings
- The proposed MFASMC avoids power-system model establishment and uses only I/O data; with GPM to simulate bilateral contracts, frequency fluctuations in all three regions are between ±0.1 Hz and convergence times of frequency deviation are all within 30 s, much less than LFC response time.
- In simulation case 1, after 5.7 s the frequency fluctuation amplitude and tie-line power deviation are obviously reduced and tend to 0; the system frequency fluctuation range is [-0.086, +0.043] Hz.
- In simulation case 2, with inter-regional contracts, the three-region wind power system frequency gradually converges to 0 after 6.3 s, with fluctuations much smaller than ±0.1 Hz.
- Under variable load demand, the total frequency fluctuation range in the three regions is always between [-0.05, +0.03] Hz and Δf converges to 0 in less than 30 s; under stochastic wind energy, Δf in the three regions is between [-0.0062, +0.0061].
- Comparison tests show faster convergence and smaller frequency fluctuation than classical MFAC; against a memory-based adaptive SMC from literature [38] under 0.02 p.u. load disturbances, the proposed algorithm makes Δf basically converge to 0 in 6 s versus 10 s.
Methods
- Design: a model-free adaptive sliding mode LFC algorithm (MFASMC) based on dynamic linearization, pseudo partial derivative (PPD) estimation, saturation function, and GPM for bilateral contracts; stability and tracking-error convergence are proved theoretically.
- Data/sample: simulation of a three-regional interconnected power system with wind penetration, where each region contains two thermal power generators and one wind power generator; area 1 links to areas 2 and 3, but area 2 is not linked to area 3; tie-line constants are T12 = 0.245, T13 = 0.212, T23 = 0, and sampling period T = 0.001 s.
- Analysis: simulation cases use GPM1, GPM2, and GPM3, load demands ΔP_L1 = 60 MW, ΔP_L2 = 80 MW, ΔP_L3 = 60 MW, wind powers ΔP_w1 = 10 MW, ΔP_w2 = 20 MW, ΔP_w3 = 10 MW, a 200 s variable-load test, a white-noise stochastic wind test, and comparisons with MFAC and SMC.
Limitations
- The paper does not state a dedicated limitations section.
- Evident from the text: validation is simulation-only on a three-region system, with no experimental or field validation reported.
- The method relies on assumptions including continuity of partial derivatives, a generalized Lipschitz condition, and a constant PPD sign; solar-energy applicability is discussed only as a theoretical remark, and stochastic wind is simulated using white noise.
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Claims the paper makes
0 Valid · 0 Not valid · 10 Not checked · 43 Own results and interpretations
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Frequency fluctuations in all three regions are between ±0.1Hz.”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > Abstract
plain- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The simulation results further demonstrate the effectiveness of the proposed algorithm, comparing the control algorithm proposed in this paper with other algorithms, which proves that the proposed algorithm has good control performance.”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > Abstract
boostedstates an association- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“It also effectively solves the problem of frequency stability control under the influence of load change, introducing the generation participation matrix to simulate bilateral contracts under the power market.”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > Abstract
plainstates a cause- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From Figure 6, the frequency of the three-regional wind power system gradually converges to 0 after 6.3 s”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 4.2 Simulation case 2
plainSingle case- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The simulation results further show that the proposed algorithm can effectively solve the problem of load demands.”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 1 INTRODUCTION
plainstates a cause- Asserted: passes — The authors put it forward as true.
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Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3.1 Algorithm design
“u i (k) = u i (k -1) + 1 𝜙 i (k) (Δ ACE i (k) -Δw i (k))(19)”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3 ALGORITHM DESIGN AND STABILITY ANALYSIS
“Δ ACE i (k + 1) = 𝜙 i (k)Δu i (k) + Δw i (k)(13)”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3.2 Main results
“e i (k + 1) -e i (k) = ACE d -ACE i (k + 1) -ACE d + ACE i (k) -Δw i (k) = ACE i (k) -ACE i (k + 1)”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3.1 Algorithm design
“e i (k) = ACE d -ACE i (k) (14”
Rated minor: it would not touch a result — a value no result rests on, a p-value that stays on the same side of the significance level, or a conflict that is clerical, resolved elsewhere in the paper, or outside its own findings.
In the paper
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3 ALGORITHM DESIGN AND STABILITY ANALYSIS
“ACE i (k + 1) = C i H i x i (k) + C i G i u i (k) + C i I i v i (k) -v 3i (k) (8)”
§ Model-free adaptive load frequency control for power systems with wind penetration under deregulation environment > 3 ALGORITHM DESIGN AND STABILITY ANALYSIS
“ACE i (k) = C i x i (k) -v 3i (k)(7)”
Citations
Cites
Yan, Z., & Xu, Y. H. (2020) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2020.2999890 · Cited by 410
Yan, Z., & Xu, Y. H. (2018) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2018.2881359 · Cited by 393
Alhelou, H. H., Hamedani-Golshan, M.-E., Zamani, R., Heydarian-Forushani, E., & Siano, P. (2018) · Energies · doi:10.3390/en11102497 · Cited by 349
Robust Load Frequency Control for Power System Considering Transmission Delay and Sampling Period
Shangguan, X., Zhang, C., He, Y. M., Jin, L., Jiang, L., Spencer, J. W., & Wu, M. (2020) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2020.3026336 · Cited by 305
Area load frequency control using fuzzy gain scheduling of PI controllers
Chang, C. S., & Fu, W. (1997) · Electric Power Systems Research · doi:10.1016/s0378-7796(96)01199-6 · Cited by 304
Robust Fixed-Time Stability: Application to Sliding-Mode Control
Moulay, E., Léchappé, V., Bernuau, E., & Plestan, F. (2021) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2021.3069667 · Cited by 275
Faster Fixed-Time Control of Flexible Spacecraft Attitude Stabilization
Cao, L., Xiao, B., Golestani, M., & Ran, D. (2019) · IEEE Transactions on Industrial Informatics · doi:10.1109/tii.2019.2949588 · Cited by 251
Bagheri, A., Jabbari, A., & Mobayen, S. (2020) · Sustainable Cities and Society · doi:10.1016/j.scs.2020.102544 · Cited by 157
Sobhy, M. A., Abdelaziz, A. Y., Hasanien, H. M., & Ezzat, M. (2021) · Ain Shams Engineering Journal · doi:10.1016/j.asej.2021.04.031 · Cited by 154
Sampled-data based discrete and fast load frequency control for power systems with wind power
Shangguan, X., He, Y. M., Zhang, C., Jiang, L., Spencer, J. W., & Wu, M. (2019) · Applied Energy · doi:10.1016/j.apenergy.2019.114202 · Cited by 148
Research works printed but not linked: 2
- Jianwu Z., 2008, New load frequency control method in power market, I Grid Technol., 281, 64
- Zhao L., 2021, Distributed model predictive load frequency control in power market, J. Electr. Power Sci. Technol., 36, 109
Cited by
Bakeer, M., Magdy, G., Nosrati, K., & Petlenkov, E. (2026) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2026.111864 · Cited by 3
Optimal Frequency Control of Multi Area Power System Under Restructured Environment
Kumar, S. A., Lakshmi, V. A., Reddy, G. V. S., Mohan, Y. R., & Reddy, A. V. K. (2025) · International Journal of Electrical and Electronics Research · doi:10.37391/ijeer.130320 · Cited by 1
Chen, Y., Zhao, H., Ogura, M., Gao, Y., & Peng, L. (2025) · Energy Science & Engineering · doi:10.1002/ese3.70381 · Cited by 1
Su, L., Li, Y., Li, F., & Wang, J. (2025) · Asian Journal of Control · doi:10.1002/asjc.3787
Ma, L., Zhao, H., Chen, Y., Xie, L., & Yu, H. (2026) · Nonlinear Dynamics · doi:10.1007/s11071-026-12333-x
PI Iterative Feedback Tuning for Load Frequency Control in Wind-Integrated Power Systems
Zeng, Y., Xu, D., Ji, X., Pei, J., Hu, G., Hua, F., & Zhang, W. (2026) · IEEE Data Driven Control and Learning Systems Conference (DDCLS) · doi:10.1109/ddcls71227.2026.11610053
Self-citationZhao, J., Zhang, H., Li, X., & Wang, C. (2026) · Asian Journal of Control · doi:10.1002/asjc.70263
Metadata
- Authors
- Zeng, Y., Bu, X., & Yin, Y.
- Affiliations
- Henan Polytechnic University (CN)
- Corresponding author
- Bu, Xuhui
- Venue
- Asian Journal of Control
- Publisher
- Wiley
- Published
- 2024-09-06
- Volume
- 27
- Issue
- 2
- Pages
- 948-961
- ISSN
- 1561-8625 (ISSN-L)
- 1934-6093
- OpenAlex
- W4402315251
- Cited by
- 7
- References
- 36
- Citations by year
- 2026: 4 · 2025: 3
- FWCI
- 0.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Asian Journal of Control (publishedVersion)
- Funders
- National Natural Science Foundation of China (62273133)
- Henan Provincial Science and Technology Research Project (242102210036)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Frequency Control in Power Systems
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Wind Turbine Control Systems
- Physical Sciences › Energy › Energy Engineering and Power Technology › Power Systems and Renewable Energy
- Keywords
- load frequency control, model-free adaptive control, wind power integration, power system deregulation, bilateral contracts, frequency stability, electricity market
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