A Cost-effective Three-phase Grid-connected Inverter with Maximum Power Point Tracking

Solar energy is desirable due to its renewable and pollution-free properties. In order to utilize the present utility grid infrastructure for power transmission and distribution, grid connected dc-to-ac inverters are needed for solar power generation. However, previously proposed voltage source inverters with a two-power-stage structure or a cascaded structure increase the circuit complexity, power losses, and system cost. In addition, conventional maximum power point tracking (MPPT) methods usually need power calculation and complex logic judgment, so expensive multipliers and/or microprocessors are needed. This leads to high inverter capital cost, which becomes a major barrier for the wide use of solar power generation. A cost-effective MPPT method integrated within the one-cycle control (OCC) core is proposed in this paper. When integrated with a three-phase boost type inverter, the proposed method tracks MPP with good precision, and solar power is converted into three-phase ac power with a single power stage. There is no power calculation in the controller, which yields a simple and cost-effective solution. Experiments have been carried out with a photovoltaic source to verify good performance


INTRODUCTION
In recent years, many concerns have been raised regarding fossil fuel-electricity power generation, since it pollutes the environment and depletes limited energy supplies.On the other hand, alternative power sources, such as solar photo-voltaic energy, have gained a lot of attention because they are renewable, friendly to the environment, and flexible for installation.However, these types of sources supply dc power while the present power grid accepts 60Hz ac power, therefore dc-ac grid-connected inverters are necessary for power conversion.To avoid introducing additional distortions to the power grid, the generated currents from these inverters should have low harmonics.Furthermore, when the output currents are in phase with the grid voltages, the maximum active output power is achieved by minimizing the reactive output power.Thus inverters that have high power quality, high efficiency, high reliability, low cost, and simple circuitry are desired.
As far as the alternative source is concerned, each photovoltaic (PV) module or fuel cell stack usually supplies a dc voltage lower than the peak value of the grid voltage, and their output voltages vary in a wide range according to various operating conditions [1].Series connection of several modules or cells can be a simple way to increase output voltage so as to employ a buck type grid connected inverter [2] for power conversion.However, this method may reduce the overall efficiency [3] because no power will be collected through the inverter when its input dc voltage drops below the peak value of the ac output voltage.There are many publications dedicated to this problem.In article [4] and [5] a two-stage topology that first boosts the dc voltage by a dc-dc converter and then inverts it into ac is used.However, this method increases the complexity of the circuit and losses.In articles [3] and [6] a cascade structure is employed to increase the dc voltage, which needs more power switches and still results in a complex circuit.In article [7], a current source inverter (CSI) employing a large inductor is used for power conversion.However, this type of circuit could be bulky, heavy and expensive for a high power application.In paper [8], a One-Cycle Controlled (OCC) boost-type three-phase grid connected inverter was proposed.It has a single power stage, a low value dc side inductor and its input dc voltage can vary over a wide range.These key features of OCC are all desirable for low cost high efficiency PV power generation.
As far as maximum power point tracking (MPPT) methods are concerned, many methods have been addressed previously.The Perturb and Observe (P&O) method needs to calculate dP/dV to determine the maximum power point (MPP) [9] [10].Though the method is relatively simple, it can't track the MPP when the irradiance changes rapidly; and it oscillates around the MPP instead of directly tracking it.
The Incremental Conductance method tracks MPP rapidly but it has high algorithm complexity, which also employs the calculation of dI/dV [11].
Though this method can accurately determine MPPs, a digital signal processor (DSP) or a microprocessor is usually needed for these complex calculations.The Constant Voltage method [12], which uses 76% open circuit voltage as the MPP voltage, and the Short-Circuit Current method [13] are simple, but they do not always accurately track the real MPP.
In this paper, a cost-effective MPPT method integrated within the OCC controller is proposed.It features the following advantages:

II. REVIEW OF THREE-PHASE BOOST-TYPE GRID-CONNECTED IVERTER [8]
Figure 1 shows the power stage when a PV source is connected to the input side of a boost-type inverter [8], where  Additionally, their differential voltages are: where, V rms is the rms value of the line-to-neutral voltage. .Therefore, a boost converter operation is guaranteed as long as the dc voltage V g satisfies: At any given instant, one of the upper switches (S ap , S bp , S cp ) and one of the lower switches (S an , S bn , S cn ) are turned on.
For example, in Region I, S an and S cn are kept off and S bn is on for the entire region.S ap , S bp and S cp are controlled at the switching frequency.There are three stages for different switching patterns: 1) Stage I (Fig. 3 PWM signal Q p , Q n and Q t are distributed to the corresponding switches for driving IGBTs.
In a balanced three-phase system, the dc side current can be derived as: Simultaneously, three sinusoidal ac currents can be injected into grids.From the analysis in [8], the boost inverter allows input voltage to change as long as 6 ≤ is satisfied.The input power of the inverter can then be derived from (2): In order to make P in approach MPPs automatically, a cost-effective MPPT method is proposed in this paper.Figure 6 shows the diagram of the controller with the MPPT function integrated in the OCC core.Only V ref (in Fig. 4) is replaced by k g V g in order to achieve a better MPPT tracking capability.k g is the voltage sensing ratio and V g is the output voltage of the PV array.Thus: Fig. 6 OCC controller with MPPT function Substituting ( 5) into (4), the following can be obtained: Since R s , k g and k are constant for any particular circuit design and V rms is fixed, the input power of the inverter P in is only related to its input voltage V g .With the help of Matlab simulation of the proposed circuit design, the output power P g of the PV and the input power P in of the inverter can be drawn as shown in Fig. 7, where the solid lines indicate P g vs. V g at three different solar irradiance levels (as shown in Fig. 5) at 25ºC, and the dashed lines are the corresponding curves at 50ºC.The P in curve is superimposed onto the same graph versus V g in Fig. 7.At any time, when the input power of the inverter equals the output power of the PV, a temporary steady state of the system is achieved.These steady state operating conditions are represented by a series of intersection points between P in and P g in Fig. 7.These intersection points are the desired operating points for the circuit proposed in this paper.
When solar irradiance or temperature changes, the operation point can move up or down along the P in curve to satisfy the condition P in =P g .By this means, the inverter can adjust its input power automatically according to the variation of P g caused by operating circumstances.For any particular application case in which the output properties of the PV source are known, parameters R s , k g and k in (7) can be tuned to make the P in curve closely approach the MPPs.Thus, the MPPT function is achieved with an acceptable precision.).The bottom bar chart shows the relative error between P g and P max .The achieved power curve closely matches maximum power throughout the period.When P max hits its peak around 13:00 the relative error is only 3.8%.However, before 10:00 and after 16:00 when the temperature drops significantly from that of midday, the error increases up to almost 20%, because the proposed MPPT method does not account for temperature variations.Nonetheless, the proposed the MPPT method closely tracks MPPs (especially during the period of peak output) with an acceptable precision.In addition, the experimental results well match those predicted by the Matlab simulation.
i) A single power stage: MPPT and dc-to-ac power conversion can be achieved within a single power stage; ii) Simple control circuit: only the PV output voltage is sensed and used to achieve MPPT; the control circuit preserves the simplicity of OCC method; iii) No power calculation and no need for microprocessors or DSPs: the complexity of the control circuit is greatly reduced; iv) Good MPPT capability with acceptable precision: well tracks the real MPP.

V g is the
output voltage of the PV array, and meanwhile the input voltage of the inverter; I g is the output current from the PV and C in is the input dc capacitor of the inverter; L is the dc side inductor.S ap , S an , S bp , S bn , S cp and S cn are six switches in the bridge.Each switch is realized by an IGBT in series with a diode as shown in the dashed line box; and L fa , L fb , L fc and C a , C b , C c are output inductors and capacitors that form an output filter for the inverter.v a , v b and v c are three-phase grid voltages.

Fig. 1 Fig. 2 .
Fig.1 Power stage with PV array connection Each line cycle can be divided into six regions as shown in Fig.2.For example, in Region I (0~60º), v a >0, v c >0 and v b <0.

Fig. 2
Fig.2 Six regions in a line cycle Similarly, in other regions two independent phase voltages can always be selected so as to obtain the two differential voltages, which are referred to the third phase voltage, always greater than Fig.3 Three stages for different switching patterns Figure 4 shows the diagram of OCC core for the boost type inverter.It comprises an integrator with reset, two comparators, two flip-flops and other linear and logic components, where V ref is an adjustable constant and related to output power.R 1 and C 1 are integration components, and

Fig. 4
Fig.4 Diagram of the OCC core for the boost type inverter

Figure 5 Fig. 5
Figure 5 shows the typical output voltage V g vs. output current I g curves of a PV source.It can be seen that the MPPs vary with solar irradiance and the cell temperature.When the PV array is connected to the boost inverter, the actual operation point of the PV source is determined by the external circuit as well as the solar irradiance and cell temperature at --25ºC ------50ºC * MPPs

Fig. 7 Figure 8
Fig.7 Simulation results for Pg and Pin versus Vg

Fig. 8 Fig. 9
Fig.8The extracted power Pg, the maximum Pmax and relative error vs. time