Grid Connected Thirteen Level Inverter for PV System Using PI Controller

Grid Connected Thirteen Level Inverter for PV System Using PI Controller

Grid Connected Thirteen Level Inverter for PV System Using PI Controller

K N S Durga Prakash PG Scholar

Sri Vasavi Engineering College Tadepalligudem

Ch Narendra Kumar Senior Asst Prof

Sri Vasavi Engineering College Tadepalligudem

Abstract

Grid connected solar system uses to have converters Circuits followed by two levels: A DC/DC boosters and PWM Inverter. This combination of converters leads to decrement of Quality and efficiency of electric power, In this paper the author Propose a single phase 13- level photo voltaic (PV) inverter for Grid connected solar system with A novel pulse width-modulated (PWM) control scheme. The fast variations of solar radiation can be compensated by Digital proportional-integral controller. The inverter offers less total harmonic distortion and good power factor. The proposed system offers improved performance over five level inverters and is verified through simulation

Index TermsGrid connected, photovoltaic (PV), proportionalintegral (PI) current control.

1. The importance for sustainable energy sources has been increasing for the past two decades because of scarcities of fossil fuel and global warming. Nowadays the most admirable energy sources out all renewable energy sources are wind energy and solar energy because of advancement in power electronics techniques. Especially Solar electric

   Fig.1 Carrier and Reference Signals.

   In addition, several modulation and control strategies have been developed or adopted for multilevel inverters, including the following: multilevel sinusoidal (PWM), multilevel selective harmonic elimination, and space-vector modulation [3], [18].

   A typical single-phase five-level inverter adopts full-bridge configuration by using approximate sinusoidal modulation technique as the power circuits. The output voltage then has the following five values: zero, +1/2Vdc, Vdc,-1/2Vdc and Vdc (assuming that Vdc is the supply voltage). The harmonic components of the output voltage are determined by the carrier frequency and switching functions. Therefore, their harmonic reduction is limited to a certain degree [25].

   To overcome this limitation, this paper presents a 13 level PWM inverter whose output voltage can be represented in the following 13 levels: zero, +1/12

   Vdc, +1/6 Vdc, +1/4 Vdc, +1/3 Vdc, +5/12 Vdc, +1/2

   energy became most popular because of advisement in manufacturing technologies and cost advantages

   Vdc

   , -1/2V

   dc, -5/12V

   dc, -1/3V

   dc, -1/4V

   dc, -1/6Vdc

   and –

   [1] In solar energy system inverter is the main part which converts DC power obtained from solar cells in to AC power to fed in to the Grid. Nowadays Multilevel inverters are drawing attention from researchers and manufacturers due to their more benefits over conventional three level pulse width modulated inverter [PWM] inverters. They offer improved output waveforms, smaller filter size, lower EMI, lower total harmonic distortion (THD), and others [3]-[8].

   The three common topologies for multilevel inverters are as follows: 1) diode clamped (neutral clamped) [9][11]; 2) capacitor clamped (flying

   capacitors) [12][14] and 3) cascaded H-bridge

   inverter [15][17].

   1/12Vdc. As the number of output levels increases,

   the harmonic content can be reduced. This inverter topology uses two reference signals, instead of one reference signal, to generate PWM signals for the switches. Both the reference signals Vref1 and Vref2 are identical to each other, except for an offset value equivalent to the amplitude of the carrier signal Vcarrier, as shown in Fig.1. Because the inverter is used in a PV system, a proportionalintegral (PI) current control scheme is employed to keep the output current sinusoidal and to have high dynamic performance under rapidly changing atmospheric conditions and to maintain the power factor at near

   unity. Simulation and experimental results are presented to validate the proposed inverter configuration.

   DC-DC Auxiliary Full Bridge Boost Converter Circuit Inverter

   Fig.2 Single phase Internal Inverter Topology

   DC-DC Boost 13 level- Inverter Boost Converter

   Fig.3 single-phase 13 level- inverter topology

2. The proposed single-phase 13-level inverter topology is shown in Fig. 3. The inverter adopts a full-bridge configuration with an auxiliary circuit [4]. PV arrays are connected to the inverter via a dcdc boost converter. Because the proposed inverter is used in a grid-connected PV system, utility grid is used instead of load. The DCDC boost converter is used to step up inverter output voltage Vinv to be more than 1.414 of grid voltage Vg to ensure power flow from the PV arrays into the grid [19]. A filtering inductance Lf is used to filter the current injected into the grid. The injected current must be sinusoidal with low harmonic distortion. In order to generate sinusoidal current, sinusoidal PWM is used because it is one of the most effective methods. Sinusoidal PWM is obtained by comparing a high-frequency carrier with a low-frequency sinusoid, which is the modulating or reference signal. The carrier has a constant period; therefore, the switches have constant switching frequency. The switching instant is determined from the crossing of the carrier and the modulating signal.

   1. Sinusoidal PWM Law

      A fundamental period in Fig. 3 consists of p pulses whose widths vary sinusoidal throughout the cycle to give the fundamental component of frequency. The basis of equivalence between the desired sinusoid and the actual pulsed waveform

      is taken to be voltseconds, as shown in Fig.4, i.e., As1=Ap1 and As2 = Ap2. One of these pulses, the general kth pulse, is characterized in detail in Fig.5. where M is the modulation index and

      M = Vm/Vs (21)

      Equation (21) can be expressed in terms of amplitude of carrier signal Vc by replacing Vs with Vc. Because, in this topology, two identical reference signals are used, Vs=2Vc and Vm =Vref1 = Vref2.

      If M >1, higher harmonics in the phase waveform are obtained. Therefore, M is maintained between zero and one. If the amplitude of the reference signal is increased to be higher

      than the amplitude of the carrier signal, i.e., M >1, this will lead to over modulation. Large values of M in sinusoidal PWM techniques lead to full over modulation [20]. Fig.4 shows the carrier and reference signals for different values of M. Equations

      (19) and (20) define the modulation law, which is more

      Fig. 4. Carrier and reference signals for different values of modulation index M >1

      Commonly expressed in terms of 1k and 2k, by substituting from (7) and (9) to give

      1k =0 [1 +M sin(k – 0)] (22)

      2k =0 [1 +M sin(k + 0)] (23)

      Thus, the switching angles 1k and 2k for the kth pulse can be calculated from (22) and (23) in terms of modulation index M and angles k and 0 which depend upon the fundamental frequency and frequency ratio.

   2. Harmonic Spectrum of Sinusoidal PWM Waveform The voltage harmonics produced by the sinusoidal PWM can be computed by first calculating the harmonics due to the kth pulse alone, Ank, and then summating the harmonic contributions of all p

      pulses

      Fig.5. Ideal 13-level inverter output voltage Vinv.

3. Because PV arrays are used as input voltage sources, the voltage produced by the arrays is known as Varrays. Varrays is boosted by a DCDC boost converter to exceed 2Vg. The voltage across the DC-bus capaciors is known as Vpv. The operational principle of the proposed inverter is to generate 13- level output voltage, i.e., zero, +1/12 Vdc, +1/6 Vdc,

   +1/4 Vdc, +1/3 Vdc, +5/12 Vdc, +1/2 Vdc, -1/2Vdc, – 5/12Vdc, -1/3Vdc, -1/4Vdc, -1/6Vdc, and -1/12Vdc- supply dc voltage as in Fig.5. As shown in Fig.2, an auxiliary circuit which consists of four diodes and a switch S1 is used between the dc-bus capacitors and the full-bridge inverter. Proper switching control of the auxiliary circuit can generate half level of PV supply voltage, i.e., +Vpv/2 and -Vpv/2 [4]. Two reference signals Vref1 and Vref2 will take turns to be compared with the carrier signal at a time. If Vref1 exceeds the peak amplitude of the carrier signal Vcarrier, Vref2 will be compared with the carrier signal until it reaches zero. At this point onward, Vref1 takes over the comparison process until it exceeds Vcarrier. This will lead to a switching pattern. Switches S1S7 will be switching at the rate of the carrier signal frequency, whereas S4 and S9 will operate at a frequency equivalent to the fundamental frequency.

4. The feedback controller used in this application utilizes the PI controller. As shown in Fig. 6. the current injected into the grid, also known as grid current Ig, is sensed and fed back to a comparator which compares it with the reference current Iref . Iref is obtained by sensing the grid voltage and converting it to reference current and multiplying it with constant m. This is to ensure that Ig is in phase with grid voltage Vg and always at near-unity power factor.

   One of the problems in the PV generation systems is the amount of the electric power generated by solar arrays always changing with weather conditions, i.e., the intensity of the solar radiation. A maximum power point tracking (MPPT) method which has quick-response characteristics and is able to make good use of the electric power generated in any weather, is needed to solve the aforementioned

   problem [21]. Various MPPT control methods have been discussed in detail in [22]. Constant m is derived from the MPPT algorithm. The perturb-and- observe algorithm is used to extract maximum power from PV arrays and deliver it to the inverter [23],[24]. The instantaneous current error is fed to a PI controller. The integral term in the PI controller improves the tracking by reducing the instantaneous error between the reference and the actual current. The resulting error signal u which forms Vref1 and Vref2 is compared with a triangular carrier signal, and intersections are sought to produce PWM signals for the inverter switches.

   Fig. 6 . 13-level inverter with PI controller

   where

   u(t) control signal;

   e(t) error signal;

   t continuous-time-domain time variable;

   calculus variable of integration; Kp proportional-mode control gain; Ki integral-mode control gain.

   Implementing this algorithm using a DSP requires one to transform it into the discrete-time domain. Trapezoidal sum approximation is used to transform the integral term into the discrete-time domain because it is the most straightforward technique. The proportional term is directly used without approximation.

   Fig.7 Block Diagram of PI controller

   To eliminate the need to calculate the full summation at each time step (which would require an

   ever-increasing amount of computation as time goes on), the summation is expressed as a running sum

   sum(k) =sum(k – 1) + [e(k) + e(k – 1)] (33)

   u(k) =Kpe(k) + K_isum(k). (34)

   These two equations, which represent the discrete-time PI control law, are implemented in control the overall operation of the inverter.

   Control signal saturation and integral-mode anti windup limiting are easily implemented.. In this work, the control signal itself takes the form of PWM outputs from the Pi controller. Therefore, the control signal is saturated at the value that corresponds to 100% duty cycle for the PWM. An undesirable side effect of saturating the controller output is the integral-mode windup. When the control output saturates, the integral-mode control term (i.e., the summation) will continue to increase but will not produce a corresponding increase in controller output (and hence will not produce any additional increase in plant response). The integral can become quite large, and it can take a long time before the controller is able to reduce it once the error signal changes sign. The effects of windup on the closed-loop output are larger transient overshoot and undershoot and longer settling times. One approach for overcoming the integral-mode windup is to simply limit in pi controller the maximum absolute value allowed for the integral, independent of the controller output saturation [25], as shown in Fig.4.

   Fig.8. PWM switching strategy

5. Fig.9. Inverter 13-level output voltage for M=0.2

   Fig.10. Inverter 13-level output voltage for M=0.8

   Fig.11. Inverter 13-level output voltage for M=1.2

   Fig.12. Inverter 13-level output current for M=0.2

   Fig.13. Inverter 13-level output current for M=0.8

   Fig.14. Inverter 13-level output current for M=1.2

   1. Simulation Results

In order to verify that the proposed inverter simulations were performed by using MATLAB SIMULINK. Fig. 8 shows the PWM switching strategy used in this paper. It consists of two reference signals and a triangular carrier signal. Both the reference signals are compared with the triangular carrier signal to produce PWM switching signals for switches S1-S5 of inverter circuit. Note that one leg of the inverter is operating at a high switching rate equivalent to the frequency of the carrier signal, whereas the other leg is operating at the rate of fundamental frequency (i.e., 50 Hz). The switch at the auxiliary circuit S1 also operates at the rate of the carrier signal. As mentioned earlier, the modulation index M will determine the shape of the inverter output voltage Vinv and the grid current Ig. Figures 9 – 14 shows Vinv and Ig for different values of M. The dc-bus voltage is set at 400 V (> 2Vg; in this case, Vg is 240 V) in order to inject current into the grid. Fig. 9 shows that Vinv is less than 2Vg due toM being less than 0.5.

Fig.15. THD of 5-level output voltage

Fig.16. THD of 13-level output voltage for M=0.8

The inverter should not operate at this condition because the current will be injected from the grid into the inverter, rather than the PV system injecting the current into the grid, as shown in Fig.

12. Over modulation condition, which happens when M >1.0, is shown in Fig. 11. It has a flat top at the peak of the positive and negative cycles because both the reference signals exceed the maximum amplitude of the carrier signal. This will cause Ig to have a flat portion at the peak of the sine waveform, as shown in Fig. 14. To optimize the power transferred from PV arrays to the grid, it is recommended to operate at 0.5

< M < 1.0. Vinv and Ig for optimal operating condition. As shown in fig.10,13. Ig is almost a pure sine wave, the THD can be reduced compared with that under other values of M. To analyze the performance of the PI current control scheme, a sudden step change is applied to the simulation process. This step change is similar to real-time environment condition (for example, the sun is emerging from the clouds).

level	THD
5-level	38.56%
13-level	26.41%

1. This paper presented a single-phase 13 level inverter for synchronized grid pv system. It utilizes two reference signals and a carrier signals to generate PWM switching signals. The circuit topology, modulation law, and operational principle of the proposed inverter were analyzed in detail. The pi controller Is to optimize the operation of inverter. Simulation results indicate that the THD of the 13- level inverter is much lesser than that of the onventional 5- level never. Furthermore, both the grid voltage and the grid current are in phase at near- unity power factor.

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