Loss Evaluation of Distribution System Applying AC Utility and TAB Converter
4.1 Operation of Power Distribution with AC-DC Rectifier and TAB Converter Converter
4.1.1 AC-DC Rectifier Feedback Control Method
This section specifically discusses the power factor control and feedback DC voltage control in an AC-DC rectifier, which is one of the components in a power distribution system’s conversion stage.
First, the basic operation and principle of the AC-DC rectifier used in the proposed system is introduced, and the algorithm of the closed-loop control using d-q transformation is described in detail.
The circuit configuration of the AC-DC rectifier is shown in Fig. 4.1. The AC-DC rectifier used in this research is a three-phase H-bridge circuit, supplied by a three-phase AC utility power, and the parameters for frequency, voltage, and power are associate with pulse width modulation (PWM) control.
Fig.4.1. Configuration of AC-DC rectifier.
In this control technique, a modulating sinusoidal reference signal with amplitude proportional to the output AC voltage is compared with a triangular carrier-wave signal, and the gate pulse signals is generated at the intersection points between the modulating wave and the carrier wave. Fig.4.2 shows the principle of switching gate signal generation using SPWM method.
Fig.4.2 PWM gate signals for the switches.
When the modulation wave vo of each phase is larger than the carrier wave vt, the upper switch Q1 is turned on and the lower switch Q2 is turned off; in a small section where the 𝑣𝑜 is smaller than 𝑣𝑡, the upper switch Q1 is turned off and the lower switch Q2 is turned off.
As a result, when view on one cycle of individual carrier wave, the average value of the modulation wave magnitude and the positive and negative pulses of the interval is proportional.
Moreover, when view on the entire cycle of the modulated wave, it is possible to generate an AC voltage waveform that follows the modulation wave. In order to output the maximum voltage, when the modulation wave vo-peak is achieved with the peak value, the sinusoidal wave must be operated less than the amplitude of the carrier wave or equal to the carrier wave amplitude.
The modulation index (α) is defined as:
α =𝑣𝑜−𝑝𝑒𝑎𝑘
𝑣𝑡−𝑝𝑒𝑎𝑘 (4.1)
Where vo-peak is the peak of the modulating wave, and vt-peak is the peak value of the carrier wave.
Ideally, the range modulation index is varied from 0 to 1 to express a linear relationship between the modulating wave and the output wave magnitudes.
The modulation index reveals that the three-phase rectifier acts as a linear amplifier basically, and the specific gain of rectifier is decided by the modulating/reference wave signal and the output voltage.
In addition, the amplitude of the harmonics is not depend on the carrier frequency. When operate under higher carrier frequency, the output harmonics of rectifier will be automatically debilitated with using an output filter, and the output current and voltage waveforms could be closer to sinusoid waves with better shape. The decision of carrier frequency is depend on the resolution between the rectifier loss and the output waveforms’ quality, it is because the higher carrier frequency would increase rectifier’ switching loss, but eliminate the size and cost of output filter which reduces the distortion of output waveform.
Fig.4.3. The abc-dq transform diagram.
Since the current and voltage magnitude of the AC side is time-domain and fluctuates in periods, the reference values and the control system are often complicated to obtain when directly dealing with difference values of current and voltage. In order to avoid control complexity, the d-q transform method is used. The d-q transform, also called as the Park transform, is a transformation using space vector of three-phase time-domain signals, and could transform stationary three-phase coordinate system (abc) to a two-phase rotating coordinate system (dq).
By using this method, it is possible to convert an AC difference value to a DC amount, the closed-loop control system is feasible to construct. In this research, the equation for constructing the closed loop current control system is analyze by performing d-q conversion for the three-phase inverter.
Fig.4.3 shows an abc-dq transform with space vector.
Fig.4.4 The abc-dq transform with space vector.
Therefore, using the d-q transform, the relation between three-phase AC current ia, ib, ic and two-phases current value iα and iβ omitting the zero-phase alternating current, can be expressed as Eqn.4.2, excluding the zero-phase AC current.
[𝑖𝛼 𝑖𝛽] = √2
3[cos 0 cos2𝜋
3 cos4𝜋
3
sin 0 sin2𝜋
3 sin4𝜋
3
] [ 𝑖𝑎 𝑖𝑏 𝑖𝑐
] (4.2)
Next, transform from the two-phase stationary coordinate system to the two-phase rotational coordinate system is performed. The transform is shown in Fig.4.4. Assuming that the angular velocity is ω, the rotation angle θ = ωt is an angle when the d axis is viewed from the α axis.
As apparent from Fig.4.3, the rotating two-phase direct current id, iq on the d-q axis can be converted as following equations using the two-phase AC current iα, iβ on the α-β axis.
[𝑖𝑑
𝑖𝑞] = [cos 𝜃 sin 𝜃
−sin 𝜃 cos 𝜃] [𝑖𝛼
𝑖𝛽] (4.3)
From the above Eqn. (4.3), using the conversion, the two-phase DC current id, iq from the three-phase AC current ia, ib, ic can be written as:
[𝑖𝑑
𝑖𝑞] = [cos 𝜃 sin 𝜃
−sin 𝜃 cos 𝜃] × [𝑖𝛼 𝑖𝛽] = √2
3[
cos 0 cos2𝜋
3 cos4𝜋 3 sin 0 sin2𝜋
3 sin4𝜋 3
] [ 𝑖𝑎 𝑖𝑏 𝑖𝑐 ]
= √2
3[cos 𝜃 cos(𝜃 −2𝜋
3) cos(𝜃 −4𝜋
3)
−sin 𝜃 − sin (𝜃 −2𝜋3) − sin (𝜃 −4𝜋3)] [ 𝑖𝑎 𝑖𝑏 𝑖𝑐
] (4.4)
= [𝐶𝑑𝑞] [ 𝑖𝑎 𝑖𝑏 𝑖𝑐 ]
From the derived Eqns. (4.2) to (4.4), the AC current magnitude can be transformed into DC current magnitude by the transformational matrix [Cdq]. In addition, as a feature of transformation, it is understandable that the inverse matrix [CdqT
] of the transformational matrix [Cdq] is the inverse from two-phase DC current to a three-phase AC current, with calculated DC current value, it is also feasible to transform to AC current value, by multiplying the inverse matrix.
Therefore, by applying d-q transform to the circuit equation of the AC -DC rectifier, the relationship between input and output including the DC current id, iq is derived. Therefore, the following relations of the line current and phase voltage from Fig. 4.1 in each phase can be presented as:
[
𝑣𝑖𝑢− 𝑣𝑠𝑢 𝑣𝑖𝑣− 𝑣𝑠𝑣
𝑣𝑖𝑤− 𝑣𝑠𝑤] = (𝑅 + 𝐿𝑑𝑡𝑑) [ 𝑖𝑠𝑢 𝑖𝑠𝑣 𝑖𝑠𝑤
] (4.5)
For the AC currents isu, isv, isw in each of the three-phase, the following can be obtained by using the inverse transformation matrix [CdqT
].
[𝐶𝑑𝑞 𝑇] [𝑣𝑖𝑑− 𝑣𝑠𝑑
𝑣𝑖𝑞 − 𝑣𝑠𝑞] = (𝑅 + 𝐿𝑠)[𝐶𝑑𝑞 𝑇] [𝑖𝑑
𝑖𝑞] (4.6)
[𝑣𝑖𝑑− 𝑣𝑠𝑑
𝑣𝑖𝑞− 𝑣𝑠𝑞] = [𝑅 + 𝐿 𝑑
𝑑𝑡 𝜔𝐿
𝜔𝐿 𝑅 + 𝐿𝑑
𝑑𝑡
] [𝑖𝑑
𝑖𝑞] (4.7)
Eqn. (4.7) shows the relationship between input and output of the AC-DC rectifier simplified by d-q transform. This equation is the basis and utilized to determine the configuration of the closed-loop control system for phase current and the control system for the DC voltage.
Non-interference current control method
As comprehended from the Eqn. (4.7), by controlling the pair of the active current id, and the reactive current iq, the control for the three-phase AC current isu, isv, isw can be realized equivalent. For this purpose of construct a control system in which the currents id, iq has no interference and would not affect each other, the non-interference current control of the AC-DC rectifier is realized by algorithm of the non-diagonal component from the reverse matrix in Eqn.(4.6) becomes zero.
Therefore, the control method where non-interference control can be realized is expressed as:
[𝑣𝑖𝑑
𝑣𝑖𝑞] = [𝑣𝑑
𝑣𝑞] + [ 𝑅 −𝜔𝐿
−𝜔𝐿 𝑅 ] [𝑖𝑑
𝑖𝑞] + [𝐺𝑐𝑢1(𝑠) 0
0 𝐺𝑐𝑢2(𝑠)] [𝑖𝑑∗ − 𝑖𝑑
𝑖𝑞∗− 𝑖𝑞] (4.8)
In which, Gcu1(s) and Gcu2(s) indicate the controllers of the current id and iq in closed-loop control system respectively. The control system derived by the Eqn. (4.8) is shown in a block diagram in Fig.4.5.
Therefore, the current loop for feedback decoupled control is achieved.
Fig.4.5 Closed-loop control for the AC-DC rectifier.
4.1.2 Simulation of the Power Distribution System using the AC-DC Rectifier and TAB