Power Electronics-Enabled Autonomous Power Systems. Qing-Chang Zhong

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but also should be synchronized. This leads to the concept of synchronized and democratized (in short, SYNDEM) smart grids (Zhong 2017f). For such a SYNDEM grid, all active players, large or small, conventional or renewable, supplying or consuming, would follow the same rule of law and play the same equal role to achieve the same common goal, that is to maintain grid stability.

      It is shown in (Zhong 2013b) that the synchronization mechanism of synchronous machines, which has underpinned the organic growth and stable operation of power systems for over 100 years, can continue serving as the rule of law for SYNDEM smart grids. Moreover, the power electronic converters that are adopted to integrate different players can be equipped with the synchronization mechanism through control to achieve legal equality.

2.2 SYNDEM Rule of Law – Synchronization Mechanism of Synchronous Machines

      There are different power plants, such as coal‐fired, nuclear, and hydro power plants, in existing power systems. However, electricity generation is dominated by only one type of electrical machine – synchronous machines. The reason why the industry has decided to adopt synchronous machines while there are different types of electric machines is because synchronous machines have an inherent synchronization capability. This can be understood by looking at the mathematical model of synchronous machines.

      A synchronous generator, which is a synchronous machine operated as a generator, is governed by the swing equation

(2.1)

where is the rotor angle; is the angular speed of the machine; is the mechanical torque applied to the rotor; is the moment of inertia of all the parts rotating with the rotor; is the friction coefficient; and is the electromagnetic torque

(2.2)

      Here, is the number of pole pairs of the magnetic field and can be assumed to be 1 without loss of generality; is the stator current; is the field excitation current; is the maximum mutual inductance between the stator windings and the field winding; and denotes the conventional inner product. The vectors and are defined, respectively, as

      The three‐phase generated voltage and the reactive power are, respectively,

      (2.3)

      (2.4)

      with being the amplitude of the voltage. Assume that the terminal voltage is . Then the stator current is

(2.5)

      where is the impedance of the stator windings. Note that , and in (2.5) are the Laplace transforms of the corresponding signals. It should be clear whether a signal is in the time domain or in the frequency domain from the context.

The mathematical model of a synchronous machine described in (2.1)–(2.5) for the single‐phase case is shown in Figure 2.2, after adding one integrator to zero the output of the block and two low‐pass filters to remove the ripples in the torque and the reactive power. This is actually an enhanced phase‐locked loop called the sinusoid‐locked loop (Zhong and Hornik 2013; Zhong and Nguyen 2012). The core of the upper part of Figure 2.2 represents the swing (equation 2.1) and the torque (2.2), which is a conventional phase‐locked loop that can synchronize the frequency and the phase with those of the terminal voltage. The lower part is an amplitude channel to synchronize the amplitude of with the terminal voltage. In the steady state, when and the reference for is 0, there are and , which means and , achieving frequency, phase and amplitude synchronization. In other words, synchronous machines have the inherent mechanism of synchronization, which allows them to synchronize with each other or the grid autonomously.

Figure 2.2 The sinusoid‐locked loop (SLL) that explains the inherent synchronization mechanism

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