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Fast power tracking control of PV power plants for frequency support

  • Horst Schulte

    Horst Schulte heads the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW), is head of the European Master Program in Dynamics of Renewables-based Power Systems, is the Chairman of the Federation of German Windpower and Other Renewable Energies (FGW e.V.). His research interests are Computational Intelligence in Automatic Control; Modeling, Stability Analysis, and Control of Nonlinear Dynamic Systems; Robust and Fault-tolerant Control; Applications in Power Systems, Wind and PV Power Plants, Power Electronics and Protection in Renewables-based Power Systems.

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    and Stephan Kusche

    Stephan Kusche received his diploma in physical engineering from the Technische Universität Berlin (TUB) in 2012 and his PhD in friction physics from TUB in 2017. From 2017 to 2022, he worked on various research projects on control engineering at HTW Berlin that were publicly funded. Since 2022, he has been supporting interdisciplinary research at HTW in the field of modeling and simulation.

Abstract

A power tracking controller for frequency support by photovoltaic power plants without battery storage is presented. Due to the decreasing inertia, regenerative systems such as wind turbines and photovoltaic power plants must provide an instantaneous reserve for fast frequency support in power systems. To provide grid support by PV power plants, a control scheme, and a design procedure are introduced to ensure power reserve by leaving the optimal operating point. A model-based generalized design procedure in the Takagi-Sugeno fuzzy framework for PV system with switched-mode DC-DC converter is presented to achieve the specified control objectives. Simulation studies show the applicability of the control scheme.

Zusammenfassung

Vorgestellt wird ein Regelungskonzept für Photovoltaik Kraftwerken zur Bereitstellung von positiver und negativer Regelleistung ohne Batteriespeicher. Aufgrund der abnehmenden Trägheit in elektrischen Energienetzen müssen zukünftig regenerative Energiesysteme wie Windturbinen und Photovoltaikanlagen eine Momentanreserve zur schnellen Frequenzstützung in Stromsystemen bereitstellen können. Um die Leistungsreserve ohne zusätzliche Batteriesysteme aufbringen zu können, wird bei der Betriebsführung der optimale Betriebspunkt von PV-Modulen verlassen. Dadurch muss die Regelung für einen größeren Betriebsbereich als bisher üblich ausgelegt werden. Um die Regelziele wie Stabilität, Führungs- und Störverhalten erreichen zu können, wird ein modellbasiertes Entwurfsverfahren im Takagi-Sugeno Fuzzy Rahmen für PV Systeme mit geschalteten DC-DC Wandlern vorgestellt.


Corresponding author: Horst Schulte, Department of Engineering I, Control Engineering Group, University of Applied Sciences Berlin (HTW), Wilhelminenhofstr. 75A, 12459 Berlin, Germany, E-mail: .

About the authors

Horst Schulte

Horst Schulte heads the Control Engineering Group at the Department of Engineering I (Energy and Information), University of Applied Sciences Berlin (HTW), is head of the European Master Program in Dynamics of Renewables-based Power Systems, is the Chairman of the Federation of German Windpower and Other Renewable Energies (FGW e.V.). His research interests are Computational Intelligence in Automatic Control; Modeling, Stability Analysis, and Control of Nonlinear Dynamic Systems; Robust and Fault-tolerant Control; Applications in Power Systems, Wind and PV Power Plants, Power Electronics and Protection in Renewables-based Power Systems.

Stephan Kusche

Stephan Kusche received his diploma in physical engineering from the Technische Universität Berlin (TUB) in 2012 and his PhD in friction physics from TUB in 2017. From 2017 to 2022, he worked on various research projects on control engineering at HTW Berlin that were publicly funded. Since 2022, he has been supporting interdisciplinary research at HTW in the field of modeling and simulation.

  1. Research ethics: Not applicable.

  2. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: The authors state no conflict of interest.

  4. Research funding: This research is part of the project EU-Project POSYTYF (POwering SYstem flexibiliTY in the Future through RES), https://posytyf-h2020.eu. The POSYTYF project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 883985.

  5. Data availability: Not applicable.

Appendix A: Input-to-state stability (ISS)

For a quadratic Lyapunov function candidate

(38) V ( x ̃ ) = x ̃ T P x ̃ > 0 , x ̃ 0

the following shows that V ̇ ( x ̃ ) satisfies the condition for ISS

(39) V ̇ ( x ̃ ) γ 1 ( x ̃ ) + γ 2 ( | y ref | )

for all x ̃ and a bounded y ref , where γ 1 ( x ̃ ) and γ 2(|y ref |) satisfying the properties of a K functions [18]. A continuous function γ(r) : [0, a) → [0, ∞) is said to belong to class K if it is strictly increasing, γ(0) = 0 and if a ≔ ∞ then γ(r) → ∞ for r → ∞ [27].

From the time derivative of (38) with (22) follows

V ̇ ( x ̃ ) = x ̃ ̇ T P x ̃ + x ̃ T P x ̃ ̇ = x ̃ T i = 1 N r j = 1 N r h i ( z ) h j ( z ) × A ̃ i b ̃ i k ̃ j T T P + P A ̃ i b ̃ i k ̃ j T x ̃ + 2 i = 1 N r j = 1 N r h i ( z ) h j ( z ) x ̃ T P a i j + 2 x ̃ T P e 3 y ref .

Due to convexity, an upper bound is given for the second double sum term

i = 1 N r j = 1 N r h i ( z ) h j ( z ) x ̃ T P a i j x ̃ T P max i j a i j

The eigenmotion is exponentially stable with a decay rate of α if a sufficient LMI criterion related to the double sum term is fulfilled:

(40) i = 1 N r j = 1 N r h i ( z ) h j ( z ) A ̃ i b ̃ i k ̃ j T T P + P A ̃ i b ̃ i k ̃ j T 2 α P .

for P ≻ 0 [13]. Thereby (40) is fulfilled if a common matrix P exists such that the LMI problem

(41) A ̃ i T P + P A ̃ i k ̃ j b ̃ i T P P b ̃ i k ̃ j T + 2 α P 0 , P 0

holds for all i, j = 1, , N r . This results in

V ̇ ( x ̃ ) 2 α x ̃ T P x ̃ + 2 x ̃ T P max i j a i j + 2 x ̃ T P e 3 y ref 2 α λ min ( P ) x 2 + 2 x P max i j a i j + 2 x P e 3 | y ref | λ x 2 + 2 x P max i j a i j + 2 x P | y ref | λ x 2 + 2 x P max i j a i j | y ref | min + 1 | y ref | = λ x 2 + 2 δ | y ref | x λ 2 x 2 + 2 δ 2 λ | y ref | 2

with λ ≔ 2αλ min(P), δ P max i j a i j | y ref | min + 1 and |y ref |min ≤ |y ref | ≤ |y ref |max, where λ min(P) denotes the smallest eigenvalue of P. Finally with γ 1 ( x ̃ ) λ 2 x 2 and γ 2 ( | y ref | ) 2 δ 2 λ | y ref | 2 the TS closed-loop system (22) fulfill the ISS property related to [18]. The above analysis shows that the eigenmotion of (22) without the reference value (y ref = 0) and affine vector (a ij = 0) must be exponentially stable so that the entire system with reference values and affine components is ISS. The proof of exponential stability results from a feasible solution of (41).

Appendix B: Model parameters

Model parameters of a generic 3 MW photovoltaic power plant consisting of a DC-DC buck converter and N = N p N s mono-crystalline silicon solar cells manufactured by JA-Solar, JACM6SR-3:

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Received: 2023-03-01
Accepted: 2023-09-20
Published Online: 2023-10-17
Published in Print: 2023-10-26

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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