Main components of harmonic solutions of nonlinear oscillations

Binghua, Huang; Huang, Xin; Li, Hui

doi:10.1109/iceice.2011.5778295

Cited by 8 publications

(6 citation statements)

References 2 publications

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“…The currents of branches L and C from difference frequency component are equal in size and opposite in direction. The consumed reactive power totals zero, as shown in (9). 12 12…”

Section: Results Verified By Power Balance Theoremmentioning

confidence: 99%

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Power Balance of Multi-Harmonic Components in Nonlinear Network

Binghua¹,

He²

2014

JMP

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The main harmonic components in nonlinear differential equations can be solved by using the harmonic balance principle. The nonlinear coupling relation among various harmonics can be found by balance theorem of frequency domain. The superhet receiver circuits which are described by nonlinear differential equation of comprising even degree terms include three main harmonic components: the difference frequency and two signal frequencies. Based on the nonlinear coupling relation, taking superhet circuit as an example, this paper demonstrates that the every one of three main harmonics in networks must individually observe conservation of complex power. The power of difference frequency is from variable-frequency device. And total dissipative power of each harmonic is equal to zero. These conclusions can also be verified by the traditional harmonic analysis. The oscillation solutions which consist of the mixture of three main harmonics possess very long oscillation period, the spectral distribution are very tight, similar to evolution from doubling period leading to chaos. It can be illustrated that the chaos is sufficient or infinite extension of the oscillation period. In fact, the oscillation solutions plotted by numerical simulation all are certainly a periodic function of discrete spectrum. When phase portrait plotted hasn't finished one cycle, it is shown as aperiodic chaos.

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“…The currents of branches L and C from difference frequency component are equal in size and opposite in direction. The consumed reactive power totals zero, as shown in (9). 12 12…”

Section: Results Verified By Power Balance Theoremmentioning

confidence: 99%

“…Note that the self-excited oscillation is inhibited and disappears due to nonlinear coupling interaction when the combination strength of the F u is strong enough [9]- [12]. At this time, setting the Table 2.…”

Section: Three Main Harmonic Solved By Harmonic Analysismentioning

confidence: 99%

Power Balance of Multi-Harmonic Components in Nonlinear Network

Binghua¹,

He²

2014

JMP

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“…Supposing the voltage a u of nonlinear branch-a as shown in (11) includes two harmonics ha u and pa u .…”

Section: Coupling Relation Among Various Harmonic Must Be Commonly Obmentioning

confidence: 99%

“…where ω h denotes the frequency of ha u , while ω p denotes the frequency of pa u . The current a i includes various harmonics, among these harmonics, the ha i and pa i are two main components denoted by 1a i as shown in (11). The program Twoωhp.nb proves the branch current ( ) ha i t of h th -harmonic is related to the p thharmonic voltage pam U as shown in (12), where the eqh g is defined as equivalent h-harmonic conductance.…”

Section: Coupling Relation Among Various Harmonic Must Be Commonly Obmentioning

confidence: 99%

“…The first harmonic can correctly be obtained from the complex power balance theory of the frequency domain [1]- [10]. The main harmonic component in non-autonomous circuits can further be solved by extending the balance theory [11]- [14]. The literatures [15] put forward that this is a new research topic in the nonlinear circuit and chaos field.…”

Section: Introductionmentioning

confidence: 99%

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Power Balance Theorem of Frequency Domain and Its Application

Binghua¹,

Li²,

Liu³

2014

JMP

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This paper proves a power balance theorem of frequency domain. It becomes another circuit law concerning power conservation after Tellegen's theorem. Moreover the universality and importance worth of application of the theorem are introduced in this paper. Various calculation of frequency domain in nonlinear circuit possess fixed intrinsic rule. There exists the mutual influence of nonlinear coupling among various harmonics. But every harmonic component must observe individually KCL, KVL and conservation of complex power in nonlinear circuit. It is a lossless network that the nonlinear conservative system with excited source has not dissipative element. The theorem proved by this paper can directly be used to find the main harmonic solutions of the lossless circuit. The results of solution are consistent with the balancing condition of reactive power, and accord with the traditional harmonic analysis method. This paper demonstrates that the lossless network can universally produce chaos. The phase portrait is related closely to the initial conditions, thus it is not an attractor. Furthermore it also reveals the difference between the attractiveness and boundedness for chaos.

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Solving the Main Harmonic of Lossless System Using the Reactive Power Balance Principle

炳华¹

2012

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In the nonautonomous circuit which contains the dissipative element, the existence of self excited oscillation depends upon whether or not active power can maintain balance. The nonautonomous circuit with excited source has no dissipative element. It is a lossless system. The forced and self-excited oscillation components can simultaneously coexist unconditionally. The excited source export only reactive power. The resonant circuit does not consume any active power. The energy stored in this resonant circuit varies at all time; but after a cycle, the energy stored maintains original quantity. The relation between self-oscillation frequency and two voltage amplitude of oscillation can be found from the condition for reactive power balance. The main harmonic solutions are relative to both excited source and the initial condition. Taking the resonant circuit which contains the voltage-controlled nonlinear inductor as example, this paper demonstrates that the chaos can be produced by nonlinear coupling of forced and self-excited oscillation components.

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Main components of harmonic solutions of nonlinear oscillations

Cited by 8 publications

References 2 publications

Power Balance of Multi-Harmonic Components in Nonlinear Network

Power Balance of Multi-Harmonic Components in Nonlinear Network

Power Balance Theorem of Frequency Domain and Its Application

Solving the Main Harmonic of Lossless System Using the Reactive Power Balance Principle

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