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In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular algebraic constraint. In contrast to the previous observer, the new one avoids the need of implementing an open loop integration that may stymie its practical application. We give two versions of this observer, one that ensures asymptotic convergence and the second one that achieves convergence in finite time. In both cases, the required excitation conditions are strictly weaker than the classical persistent of excitation assumption. It is shown that the proposed technique is applicable to the practically important examples of multimachine power systems and chemical–biological reactors.
We present the first solution to the problem of estimation of the state of multimachinepower systems with lossy transmission lines. We consider the classical three-dimensional “flux-decay” model of the power system and assume that the active and reactive power as wellas the rotor angle and excitation voltage at each generator is available for measurement—ascenario that is feasible with current technology. The design of the observer relies on two recentdevelopments proposed by the authors: a parameter estimation based approach to the problemof state estimation and the use of the dynamic regressor extension and mixing technique toestimate these parameters. Thanks to the combination of these techniques it is possible toovercome the problem of lack of persistent excitation that stymies the application of standardobserver designs. Simulation results illustrate the performance of the proposed observer.
The problem of effective use of phasor measurement units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use these new measurements to reconstruct the state of the system. In this article, we provide the first solution to the problem of (globally convergent) state estimation of multimachine power systems equipped with PMUs and described by the fourth-order flux-decay model. This article is a significant extension of our previous result, where this problem was solved for the simpler third-order model, for which it is possible to recover algebraically part of the unknown state. Unfortunately, this property is lost in the more accurate fourth-order model, and we are confronted with the problem of estimating the full state vector. The design of the observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the dynamic regressor extension and mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. Simulation results illustrate the latter fact and show the improved performance of the proposed observer with respect to a locally stable gradient-descent-based observer.
PMU-Based Decentralized Mixed Algebraic and Dynamic State Observation in Multi-Machine Power Systems
(2020)
We propose a novel decentralized mixed algebraic and dynamic state observation method for multi-machine power systems with unknown inputs and equipped with Phasor Measurement Units (PMUs). More specifically, we prove that for the third-order flux-decay model of a synchronous generator, the local PMU measurements give enough information to reconstruct algebraically the load angle and the quadrature-axis internal voltage. Due to the algebraic structure a high numerical efficiency is achieved, which makes the method applicable to large scale power systems. Also, we prove that the relative shaft speed can be globally estimated combining a classical Immersion and Invariance (I&I) observer with—the recently introduced—dynamic regressor and mixing (DREM) parameter estimator. This adaptive observer ensures global convergence under weak excitation assumptions that are verified in applications. The proposed method does not require the measurement of exogenous inputs signals such as the field voltage and the mechanical torque nor the knowledge of mechanical subsystem parameters.