# Determination of Parameters of Adaptive Law for the Control of an Off-grid Power System

### Konstantin Suslov, Svetlana Solodusha, Dmitry Gerasimov

#### Abstract

The paper presents the results of a study of an off-grid electric power system that contains typical generation and load devices. The aim of the study is to develop an algorithm for selecting the optimal parameters of adaptive control law of the energy characteristics in the off-grid power system at the connection point of a varied load. To this end a simulation experiment was carried out and its results were used to numerically model the off-grid power system. The authors apply a known method of modelling the complex multi-parametric systems represented by the Volterra integro-power series. Standard approaches to the measurement of dynamic performance were applied to identify a transient response of the system.

#### References

- Voropai, N.I., Suslov, K.V., Sokolnikova, T.V., Styczynski, Z.A., Lombardi, P., 2012. Development of power supply to isolated territories in Russia on the bases of microgrid concept, in Proc. 2012 IEEE Power and Energy Society General Meeting.
- Suslov, K.V., 2013. Development of isolated systems in Russia, in Proc. 2013 IEEE PowerTech.
- He, Z., Xu, J., Xiaoyu, W., 2009. The dynamic characteristics numerical simulation of the wind turbine generators tower based on the turbulence model, in Proc. 2009 4th IEEE Conference on Industrial Electronics and Applications (ICIEA).
- Li, J., Chen, J., Chen, X., 2011. Dynamic Characteristics Analysis of the Offshore Wind Turbine Blades, Journal Marine Sci., vol.10, pp. 82-87.
- Manyonge, A.W., Ochieng, R.M., Onyango, F.N., Shichikha, J.M., 2012. Mathematical Modelling of Wind Turbine in a Wind Energy Conversion System: Power Coefficient Analysis, Applied Mathematical Sciences, vol.6. No. 91, pp. 4527-4536.
- Bhandari, B., Poudel, S., Lee, K., Ahn, S.,2014. Mathematical Modelling of Hybrid Renewable Energy System: A Review on Small Hydro-Solar-Wind Power Generation, International Journal of Precision Engineering and Manufacturing-Green Technology, vol.1, No. 2, pp.157-173.
- Saadat, H., 2010. Power System Analysis. 2rd Edition, New York: The McGraw-Hill Primis, pp. 528-562.
- Ogata, K., 2010. Modern Control Systems, 5th Edition, United States: Prentice Hall Publications, pp. 669-674.
- Kabanikhin, S.I., 2011. Inverse and Ill-posed problems. Theory and applications, Germany: De Gruyter.
- Salamanca, J.M., Rodriguez, O.O., 2010. LMI's control using a system of three power generators based on differential algebraic model, in Proc 2010 IEEE ANDESCON.
- Chenx, L., Jiang, J.N., Choon, Y.T., Runolfsson, T., 2011. A study on the impact of control on PV curve associated with doubly fed induction generators, in Proc 2011 IEEE PES Power Systems Conference and Exposition (PSCE).
- Al-Jufout, S.A., 2010. Differential-algebraic model of ring electric power systems for simulation of both transient and steady-state conditions, in Proc. 2010 15th IEEE MELECON.
- Wang, X., Chiang, H.D., 2014. Quasi steady-state model for power system stability: Limitations, analysis and a remedy, in Proc 2014 Power Systems Computation Conference (PSCC).
- Wang, X. Z., Chiang, H. D., 2013. Analytical Studies of Quasi Steady-State Model in Power System Longterm Stability Analysis, IEEE Transactions on Circuits and Systems I: Regular Papers.
- Volterra, V., 1959. A Theory of Functionals, Integral and Integro-Differential Equations, New York: Dover Publ.
- Doyle III, F., Pearson, R., Ogunnaike, B., 2002. Identification and Control Using Volterra Models, Springer-Verlag.
- Rugh, W.J., 1981. Nonlinear System Theory: The Volterra/Wiener Approach, Johns Hopkins University Press, Baltimore.
- Venikov, V.A., Sukhanov, O.A., 1982. Cybernetic models of electric power systems, Moscow: Energoizdat, (in Russian).
- Pupkov, K.A., Kapalin, V.I., Yushenko, A.S., 1976. Functional Series in the Theory of Non-Linear Systems, Moscow: Nauka (in Russian).
- Giannakis, G.B., Serpedin, E., 2001. A bibliography on nonlinear system identification and its applications in signal processing, communications and biomedical engineering, Signal Processing - EURASIP, vol. 81, No. 3, pp. 533-580.
- Apartsyn, A.S., Solodusha, S.V., Spiryaev, V.A., 2013. Modeling of Nonlinear Dynamic Systems with Volterra Polynomials: Elements of Theory and Applications, IJEOE, vol. 2, No. 4, pp. 16-43.
- Suslov K.V., Gerasimov D.O., Solodusha S.V., 2015. Smart Grid: Algorithms for Control of ActiveAdaptive Network Components, PowerTech.
- Solodusha, S.V., Suslov, K.V., Gerasimov, D.O., 2015. A New Algorithm for Construction of Quadratic Volterra Model for a Non-Stationary Dynamic System, IFACPapers Online, vol. 48, No. 11, pp. 992-997.
- Gerasimov, D.O., Suslov, K.V. A simulation model of a horizontal-axis wind turbine. State registration certificate for the computer software No. 2016610203, 11.01.2016 (in Russian).

#### Paper Citation

#### in Harvard Style

Suslov K., Solodusha S. and Gerasimov D. (2016). **Determination of Parameters of Adaptive Law for the Control of an Off-grid Power System** . In *Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,* ISBN 978-989-758-184-7, pages 129-135. DOI: 10.5220/0005759401290135

#### in Bibtex Style

@conference{smartgreens16,

author={Konstantin Suslov and Svetlana Solodusha and Dmitry Gerasimov},

title={Determination of Parameters of Adaptive Law for the Control of an Off-grid Power System},

booktitle={Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,},

year={2016},

pages={129-135},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005759401290135},

isbn={978-989-758-184-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Conference on Smart Cities and Green ICT Systems - Volume 1: SMARTGREENS,

TI - Determination of Parameters of Adaptive Law for the Control of an Off-grid Power System

SN - 978-989-758-184-7

AU - Suslov K.

AU - Solodusha S.

AU - Gerasimov D.

PY - 2016

SP - 129

EP - 135

DO - 10.5220/0005759401290135