Sun , D. A more streamlined modeling procedure is proposed which serves as a general framework for comparing different models. A duty ratio constraint that defines the diode conduction interval is identified to be the key to accurate prediction of high-frequency behavior. A new duty-ratio constraint is proposed that leads to full-order averaged… Expand. View via Publisher.
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Engineering, Computer Science. View 1 excerpt, cites methods. State-space averaged modeling of PWM converters in discontinuous conduction mode DCM has received significant attention in the literature and several models have been developed. These models are … Expand. Highly Influenced. View 10 excerpts, cites background and methods. When the switch is on, the voltage across the inductor in boost converter where is a constant.
The approximation in the above expres- is. Hence the new duty-ratio constraint for boost converter is sion holds under the assumption that 21 which will hold under conditions of low output ripple. Notice that this expression balances both flux and charge as the converter operates.
Substituting this into 10 gives the fol- D. New Full-Order Model for Other Basic Topologies lowing full-order averaged model for boost converter in DCM: Based on 5 and 19 , new duty-ratio constraints and, con- sequently, new full-order averaged models can also be derived for other topologies. The results for buck, boost, and buck-boost 22 converters are given below for easy reference. DC Analysis 27 The dc operating point of the boost converter with a constant duty ratio can be determined by letting the right-hand 2 Boost sides of differential equations 22 and 23 equal to zero and solving the two resulting algebraic equations for and.
Let 28 the scalar value of be the intended output—input voltage ratio. The results can be expressed as 29 3 Buck-Boost 30 31 It can be verified that this represents the same dc operating point The discussion so far has focused on DCM operation as that predicted by the conventional reduced-order model [3], involving the inductor.
The proposed modeling procedure is [4] as well as by the previous full-order model [5], [6]. As an example, consider the Using standard linearization techniques, a small-signal model Cuk converter depicted in Fig. Three different discontinuous can be derived from 22 and 23 as follows: conduction modes can occur in this converter: 1 is discontinuous during the off period of the switch ; 24 2 both and are discontinuous; 3 is discontinuous in which case the switch and the diode are on simultaneously.
The third case would occur when the internal transfer capacitor is small. Cuk converter topology. Boost converter with resistive load. For comparison, the corre- sponding responses predicted by the new and the two previous Note the duality between 32 and Detailed analysis of models are also shown.
As the figure shows, the new averaged DCM in high-order topologies will be addressed in future work. The response is almost identical to that of the detailed IV.
Model Comparison switching frequency. The improvement of the new model over previous models is significant, especially in the phase response. In this section, the new full-order averaged models are com- Simulated frequency responses above one third of the pared with the reduced-order models and the full-order averaged switching frequency are not included in Fig. This is because models presented in [5] and [6].
For the boost converter, the the converter response is dependent on the phase of the dis- full-order averaged model derived using the method presented turbance, and this sensitivity cannot be picked up with any in [5] and [6] is average-based LTI model.
A cosine disturbance at the same The comparison is made at the small-signal level. Table II frequency produces a phase angle of and magnitude of summarizes the poles and the zero in the control-to-output The reduced-order verter at is compared in Fig. The losses of the converter RHP zero.
There is also a significant difference between the were addressed in the model by a 0. Table III shows the poles and pared to the simulation results. As the figure shows, the new zeros of the control-to-output transfer function for buck and model predicts almost exactly the same response as the experi- buck-boost converters predicted by the new model. Model Verification V. The converter was first simulated with over previous models. Control-to-output frequency responses of the DCM boost converter Fig.
Measured control-to-output frequency responses of the DCM boost predicted by a model 15 , b model 33 and 34 , and c the new model converter in comparison with predictions by the new averaged model. Dashed 22 , The dots represent switching model simulation results obtained using lines a measurements; solid lines and b model predictions. Previous models failed to accurately capture First, we want to point out that averaged modeling of PWM these fast dynamics, hence are unable to predict converter re- converters in DCM involves two steps at which approximations sponses at high frequencies.
This is in contrast to the CCM case, A. The Fast Dynamics in which only averaging is involved. It is possible to quantify the error introduced by averaging. In the CCM case, it is generally To understand the origin of the fast dynamics associated believed that averaging does not introduce significant error as with the inductor current, we assume that input and output long as the switching frequency is sufficiently higher than the voltages are kept constant.
Under this assumption, the inductor natural frequency of the converter, and the averaged model can current has a constant slope in both subintervals and be expected to be accurate up to one third of the switching fre-. The steady-state waveform of the current quency. The degree of error can be analyzed more explicitly [7], is shown in Fig. In the DCM case, we would of the two subintervals.
Now consider that a small-signal expect similar accuracy of the averaged model if we could find disturbance, , is added to , as shown in Fig. In other words, the unusually large result, the inductor current will also be perturbed, as shown in discrepancies compared to CCM case exhibited by previous Fig.
The current perturbation, , starts DCM models can largely be attributed to the use of inaccurate from zero at , reaches the peak at , constraints that define. Based on the waveform, the shift, , of the trailing predict the same dc as well as low-frequency responses. The dif- edge of the second subinterval, and the peak of the perturbation ferences and discrepancies exist only at high frequencies. Since can be calculated as follows: the inductor current in DCM resets to zero or a constant in every switching cycle, the energy flow in the inductor is inde- pendent from cycle to cycle, i.
Delay Effect As Fig. Therefore, the total change in as a result of is 40 However, this expression does not take into account the se- quence of changes: As can be seen from Fig. Taking this delay into account, shall be written as , where is a unit step function, and its Laplace transform 41 This relation can also be approximated as follows by using the Pade expansion Fig. Small-signal dynamics of inductor current.
For this or the diode conducts the current, respectively. Their reference purpose, note that the averaged model of the inductor can be directions are taken such that both are positive. In contrast, substituting 40 into 43 yields Therefore, the transfer function from a perturbation in to the , which corresponds to the conventional re- corresponding perturbation in is duced-order model and does not correctly predict the dynamics of.
Duty-Ratio Constraints 38 Now we turn back to our original question of why the new duty-ratio constraint 20 would result in more accurate models. Note that the small-signal relations 41 and 42 do not provide a large- signal constraint on. But the large-signal constraint should simplify to 41 or 42 upon linearization under the assump- 39 tion of constant input and output voltages.
The new model as well as the models presented in [3] and It can be concluded from 39 that the effect of the fast dynamics [5] have been reexamined by comparing the corresponding associated with the inductor current in DCM is to introduce duty-ratio constraint against The analysis was done by a high-frequency pole at.
It can be verified assuming constant input and output voltages and calculating that this is the same high-frequency pole predicted by the new both transfer functions and. It was full-order model for the three basic converter topologies. The constraint used in deriving the reduced-order model is which effectively eliminates the fast dynamics, as can be seen from the last subsection.
For the averaged switch model presented in [6], the transfer function under constant terminal voltage condition is found to be This is again different from 42 which explains why the re- Fig.
In ad- operation. Therefore, we can expect the model presented in [14] also to predict inaccurate response Fig. Terminal current waveform of the switch cell defined in Fig. In summary, PWM converters operating in DCM exhibit fast dynamics due to the transient behavior of the inductor current includes the switch, the diode, and the inductor, as shown in within a switching cycle.
The constraint defining is the key Fig. It is suitable for converters with current-based discon- to accurate prediction of these fast dynamics with averaged tinuous modes. The constraint 20 proposed in this paper results three terminals of this cell when the inductor current is in DCM. All values of the terminal voltages and currents over a switching averaged models have limited utility above about one third of cycle: the switching frequency, since the response above that value depends on the specific timing of the disturbance and is not 46 captured with a conventional frequency-domain model.
From these the following equations relating average terminal For example, large-signal stability analysis of a distributed voltages and currents can be deduced: power system usually relies on averaged model simulation of the system.
To serve those applications, the averaged circuit 48 counterpart of the new full-order averaged model is developed These relations can be represented by the circuit shown in in this section. The model is completed by the duty-ratio constraint The idea of averaged circuit modeling is to identify a switch 20 which is rewritten using variables defined for the switch cell that is common in different topologies and to develop an cell equivalent circuit that, when inserted in place of the original switch cell, results in an electrical circuit that has the same av- erage behavior as the converter.
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More Filters. Averaged modeling and analysis of resonant converters. An averaged modeling and analysis method for resonant power converters is described. The method is based on the slowly varying amplitude and phase transformation. Application of such a transformation … Expand. Modeling of PWM converters in discontinuous conduction mode. A reexamination. Engineering, Computer Science.
PESC 98 Record. Averaged modeling of PWM converters operating in discontinuous conduction mode. Various aspects of averaged modeling of hard-switching pulse-width modulated PWM converters operating in the discontinuous conduction mode DCM are studied. A more streamlined modeling procedure … Expand.
View 1 excerpt, cites background. An accurate average modeling technique for power converters is important in order to be able to analyze the converters and design proper control laws. The classical technique works well under the … Expand. View 1 excerpt, cites methods.
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