Electrical Energy Processing and Conditioning

SCOPE

In this paper, we are going to study about the various techniques used for processing and conditioning DC electrical energy to AC.

A qualitative approach is used to describe various concepts with the help of Simulink.

COMPONENTS & SYSTEMS

The fundamental components and systems that are required to carry out Energy processing can be listed as follows:

1) DC to AC inversion ----------------> Using PWM(Pulse Width Modulation)

2) Frequency regulation of the solar array ------------> Using PLL(Phase Locked Loop)

3) d-q Transformations and its applications.

I) PWM INVERTER

For all practical purposes, a solar array can be considered as a DC battery even though it has NON-LINEAR characteristics but for our purposes, we can assume it to be a simple DC source.

In order to connect a DC source to an AC utility, we will need to invert it to AC.

A simple square wave can be realised using an SPDT switch, while the frequency of the square wave can be controlled by controlling the rate of switching between the two poles.

For a 60hz square wave, the switch needs to be operated every 8.33ms

Now to convert the Square wave to an equivalent sin wave we need to modulate the pulse width of the switching "Duty Cycle" hence the name PULSE WIDTH MODULATION.

To approximate a sin wave from a square wave the Pulse widths are modulated as shown above.

The peaks of the sin wave can correspond to the maximum Duty cycle of the pulses as shown above.

While the troughs of the sin wave correspond to the minimum Duty cycle of the pulses.

So, in effect, the value of the sin wave can be "Encoded" in this pulse width modulated wave.

Now if we run Sin modulated square wave through a low pass RLC filter it will give us the average value which looks like a sin wave.

A single-phase PWM generator is shown which converts Dc input into a 1-Phase is shown. To realise the system in MATLAB open the example power_PWMGenerator2Level.

The example is for a complex 3-phase system, make the following changes to make the model look like the above. In principle, a Reference wave is used to generate a gating signal as shown which then drives the Semiconductor switch.

UREF GENERATION BLOCK

PWM GENERATOR(2-LEVEL) BLOCK

UNIVERSAL BRIDGE BLOCK

The neutral node in the original example connected to the 2 DC sources has to be replaced by ground as shown in the schematic.

The filter circuit can be parameterized as follows

SERIES RLC BRANCH BLOCK

PARALLEL RLC BRANCH BLOCK.

One can use a Single output Demux and a Voltage Measurement block as shown and feed the outputs of both of them to a scope to view the Pulse Width Modulation and the Output Voltage.

Run the simulation for about 0.1 sec to view the results. It's pretty clear from the plot how the peaks of the sin wave correspond to a higher value of duty cycle where the width of the pulse is more and troughs correspond to a lower value of duty cycle where the Pulse width is thin.

RESULT

II) FREQUENCY CONTROL USING PHASE LOCKED LOOP(PLL)

Now that we have a Sin wave output we need to match the frequency with the grid and "lock on" to that frequency before feeding it to the Utility.

A common way to match the frequency to a standard is to use a Phase-Locked Loop(PLL) feedback system.

In principle, it's a system which monitors the Grid frequency and generates a feedback signal to match with the reference frequency.

We take a system reference and pass it into a Phase-locked loop which gives us a reference frequency that we can then use to generate the gating signal for the Inverter.

In principle, phase-locking between two waves can only be maintained if the frequencies of the concerned waves are the same. Therefore, if we are able to match the phase of the output wave with the reference signal we can achieve frequency regulation.

The above diagram shows the schematic of a PLL frequency control arrangement.

A reference is fed to the Phase detector and is compared with the final output of the system.

Error signal thus generated will indicate the phase or frequency difference between the two waveforms.

Error is fed through a Low Pass filter which then generates a proportional Dc signal. If the error is 0 then the LP filter will generate 0volts.

The VCO outputs an AC signal for a given DC input much like an inverter. The Quiescent frequency of the system is 60Hz i.e for 0v input to the VCO the output waveform will have 60Hz output.

Now if the reference frequency of the utility is greater than the output of the PLL then the error will be positive and the LP filter will give a DC output signal which is greater than 0 and hence the output of the VCO will be greater than 60Hz which will match the reference frequency requirements.

To illustrate the above concept a Simulink model is realized using the same Schematic.

The reference frequency is 65Hz i.e the required frequency is 65HZ in Quiescent frequency of the VCO is 60HZ with a sensitivity of 10Hz/volt i.e for 1 volt DC output from the LP filter the output of the VCO will increase by 10HZ this means for the system to match the required reference frequency the output of the LP filter must be 0.5 Hz.

CONTINUOUS-TIME VCO BLOCK

ANALOG-FILTER DESIGN BLOCK

RESULT

The results are as expected, the frequency is corrected to the required 65 Hz and a DC "correction" signal of 0.5V is generated.

Initially, we can see a phase shift between the Reference and the Actual waveforms which ultimately vanishes as the waveforms overlap indicating that frequency regulation has been achieved.

III) PARK-CLARKE d-q -Zero TRANSFORMATIONS

In this paper, we are going to use a qualitative approach to understand d-q transformations, its importance and various applications

In principle, the d-q transformation is used(one of the most popular) to represent a 3-phase sinusoidally varying current/voltage by using only 2-values i.e a vector.

XY coordinates of a simple vector are referred to as d-q coordinates or direct and quadrature axis.

Essentially, the direct-quadrature-zero transformation is a tensor that rotates the reference frame of a three-element vector or a 3x3 element matrix in an effort to simplify analysis.

If we consider the arms a,b and c to be the stator of an induction motor then we, know that when energised by 3-phase AC current a rotating magnetic field is formed. This rotating magnetic field can be further represented by a single vector rotating in space, That single vector can be decomposed into its components aka d and q components. Thus in effect, a three-phase sinusoidally varying current can be represented as a vector with components d-q and vice-versa.

This allows us to execute complex control loops and algorithms on a mathematical vector and convert it back into a physical quantity like current/voltage.

So now we have a conceptual idea of how we can fully describe a balanced set of 3-phase sinusoidal sin waves by a single vector using magnitude and angle. We can convert back and forth between the two. Which can be demonstrated using a Simulink model.

In the first part of the model, we build a vector from the d-q components.

These d-q components are nothing but the cos and sin components respectively. In the simulation, we assume that we have a machine rotating at a constant speed at 60Hz or 377 rad/sec. With constant stator vector magnitude and angle relative to the rotor.

Let the constant angle be 45deg which is then converted to radians.

Next, we extract a vector with the sin and cos components and the multiplication by 1 signifies the magnitude of the vector.

We take the d-q-zero components and feed them to the multiplexer(mux) the out is then fed to the "dq0 to abc2" converter block. The function of this block is to simply convert the d-q vector to its 3-phase quantities.

the inputs to the block are the d-q-0 components and w*t(omega*time) of the vector which in our case is 60Hz or 377rad/sec. This information is fed through a ramp using goto and from blocks.

The ramp can be parameterized in the following way.

This means that in the output scope we should see a value of 60Hz as the frequency.

I've also made a phase detector block so that we can compare a sin wave at with 0 phase and 1 magnitude with the output wave which should have a 45-degree phase shift.

RESULT

3-Phase output

The other scope gives information about the Frequency, Phase-difference and the radians/sec information.

As we can see the phase difference is at about 45deg and the frequency is also stable at 60Hz.

We can clearly see the phase difference between the reference and output wave of the dq0 and abc converter block and it is 45 degrees.

From this, we can conclude that we can convert a vector into a 3-phase sinusoidal wave.

As stated earlier the importance of this technique is the ease of analysis, Complex control systems and algorithms can be realised using this technique of transforming 3-phase voltages and currents.

One of the most famous applications of this technique is the Vector or Field oriented control of induction motors.

It is also applied for Power system Harmonics Identification and Measurements and many such applications.