Simple PCS for Photovoltaic Power Generation – optimum inverter switching –

Photovoltaic power generations have been accepted and spread widely. Various innovative power conditioning systems including inverters have been also studied. In domestic utilization, the actual application of such solar panels are almost installed on top of the roof of the detached house. Some residents living in the apartment house, however, have fairly strong desires to contribute for energy saving due to natural energy generation. The generating power in such case is fairly reduced, so the system construction should balance the reduced power. Thus, it is necessary to improve the construction toward simple one. In this paper, in order to give a reply, simple and concise power conditioners (PCS), especially inverter waveforms are examined. Considering fairly reduced generating power and narrow space of installation, the system constructions should be compact. The circuits which gratifies their wishes are presented and examined the effectiveness.


Introduction
Preserving the developments of economy, science and technology with conquering the problems against environmental conservation is an important assignment for humanity of the world.The usage of the renewable energies is expected to be able to mitigate such problem, which is an important means [1,2].Among them, photovoltaic power generation have various advantages such as usage of inexhaustible and unpolluted sunlight, which is advantageous for maintenances, easily construction from small power to large one, and can be installed in various location including city center.In such a way, this power generation system is a promising one with bright future.
As a utilization form, utility interactive power generation system has been accepted and widely spread.In such system, it is necessary to install the chopper, where the lower voltage of solar cell should be boosted to suitable voltage, and inverter where the dc power of boosted voltage should be converted to ac power in the power system [3,4].
The power conditioners-PCS including inverter have been presented in various systems so far [5,6].However, it is necessary to reduce the cost even more.It is said that the system is approaching to an ideal ones with respect to efficiency and construction strategy, but that cost would prevent wide spread if there is no public financial support.
In such discussions, there are many subjects to be solved to utilize the PV power in utility interactive power generation.Even more, various safeguard equipment required according to regulations make the cost increase Thus, it is required to obtain even lower cost PCS.In an extremely lower capacity PCS as discussed in this paper, a way of handling would be different compared to typical power range.In such case of reduced generating power, quantities of reversed power to the power system would be small, where another mitigated regulation or deregulation would be approved.Thus, in such PV power generation systems, there are so many subjects to be resolved [7].Under such circumstances accepted by electrical utility industry as recognitions and assessments for renewable energy, spread of application is strongly sustained by financial supports of public organizations, and a lot of consumers are hoping to install such PV power generation system.For ordinary homes, installation of solar panel is restricted to house having roofs.However, a lot of residents living in the apartment house also wish to install the PV panel under considering resource conservation and such public financial support.In the present situation, however, there is no scheme to perform these requirements.The authors have been studied in a series of the small power PV system [8,9].In this paper, some simple PCS systems, especially the components like inverters including control strategies are presented and discussed.

Pursuit of compact construction using
half-bridge circuit.

Optimum waveform-single switching of α 1
In general, in utility-interactive operation, it is necessary to inject a sinusoidal wave if possible.Consequently, standard full-bridge circuit is generally adopted.Firstly, instead of such full-bridge, half-bridge circuit in Fig. 1 is used.Some switching strategies are examined from single switching per a quarter cycle [14].The purpose is to obtain a satisfactory wave having minimum harmonics by using optimum switching pattern.In general, the full bridge circuit is well-known to be utilized in PCS, but the circuit construction is a little sophisticated due to increased number of switching devices followed by increased control strategies.The increased number of control circuits makes the cost high.In order to attain satisfactory harmonic characteristics, the suitable control strategy would be utilized in simple half bridge construction.The discussion is to begin with a case of single switching notch of α 1 .The harmonic amplitudes are varied according to variation of timings of notches.The employed example waveform is presented in Fig. 3 discussed later, where a type of waveform having thrice notches per a quarter cycle is presented.In order to make control strategy simple, the maximum number of notch is decided as presented thrice in this paper.Some such switching strategies are examined.At α 1 =π/9 in firstly started single notch, the third order harmonic becomes zero, that is V 3 = 0.In this case of single switching notch of α 1, each harmonic is represented in uppermost row in Table 1.
Each value is calculated relative to the fundamental amplitude.Though V 3 is zero, other harmonic remains in a fairly quantity.In order to improve these characteristics, the optimum waveform would be pursued in the next stage.By means of using an evaluation function, the optimum value is resolved where the harmonic effective value is given by minimum one.The obtained harmonics are examined and evaluated using a weighting function.
Such evaluation function is defined as follows; where n is natural number.
………….(1) The minimum value of Eq.( 1) is solved by varying α 1 .V h is the objective value calculated in weighting function which is divided by each order like V 5 / 5, etc.In practical applications of this method, the flowing load current is suppressed mainly by inductance in accordance to harmonic order.Consequently, it can be seen that the evaluation function is significantly related to evaluating the effective value of current.From such reasons, evaluation function V h is sometimes called harmonic effective value in this paper.The minimum or optimum value of V h is described in V h * by relative value.Let the minimum value of evaluation function be termed the optimum one.It can be seen that the optimum value V h * is given at α 1 = 0.253 in second row in Table 1, whose resolving procedure is shown in Fig. 2.
It is given at smaller switching angle than α =π/9 = 0.349 where the 3 rd order harmonic is zero.Except V 3 = 0, harmonic characteristic can be much improved compared with results in upper row.The evaluation function V h is improved by more than 40 %. 5 th and 7 th orders can be improved by 50 to 70 %.

Optimum waveform -double switching of α 1 and α 2
In this section, further attempt by increasing the number of notches is performed.Let the number of the switching notch be twice, that is α 1 and α 2 .Under this condition, the optimum waveform can also be solved.The similar procedure described above is executed.The evaluation function is used to pursue the optimum value.At first, the method of specific lower order harmonics elimination, that is, V 3 = V 5 = 0, where α 1 and α 2 are presented in uppermost row in Table 2. Though 3 rd and 5 th order harmonics are zero, the other harmonics fairly remain.According to the evaluation function of Eq.( 1), α 1 and α 2 can be solved for the optimum value, which are represented in second row in Table 2.The optimum value is given in this table.Relative optimum value is V h * = 0.045.In general, the harmonics in upper row are fairly large except V 3 = V 5 = 0. On the other hand, in optimum wave, the harmonics are totally much reduced by about 30 to 80 %.

Optimum waveformthree switching times in α 1 , α 2 and α 3
In this section, by using three switching notches, the optimum waveform is solved and examined.The results are in Table 3, where the uppermost row is of V 3 = V 5 = V 7 = 0 and the second row is of the optimum switching.In upper row, V 3 , V 5 and V 7 are eliminated, however, the other order harmonics fairly remain.In order to improve such characteristics, the optimum waveform method is performed.Fig. 4 shows the method how to obtain the optimum value.Firstly, after α 1 is arbitrarily given and fixed, a minimum value of V h * is resolved for combination of the other α 2 and α 3 .As a result, the obtained minimum value of V h * is plotted on that value of α 1 .On the other α 1 , such minimum V h * value is plotted, and the lowest minimum value can be obtained as the optimum value as shown.It can be seen that the other harmonics are much reduced.The 3 rd , 5 th and 7 th order harmonics do not increase so much.It can be seen that increased quantities are sufficiently suppressed.By using evaluation function, harmonic component can be reduced by 70 to 80 % except V 3 = V 5 = V 7 = 0.

Pursuit of output waveforms using full-bridge circuit
In full-bridge circuit, it is the conventional control strategy to use the 120° conduction wave.In this section, even θ =120° is also varied to obtain the optimum value, and to examine those effects.

Pursuit of optimum value by varying θ =120°
Fig. 5 shows the evaluation function curve to obtain the optimum value where conduction period θ = 120° is varied.In the figure, as θ is varied on the horizontal axis, V h * is also varied and reaches at minimum.Consequently, when θ is shifted from normal θ =120° = 2.094 rad to the right hand side, the optimum value can be obtained at θ =124.1°= 2.166 rad, where the V h * characteristics is improved by 4.4%.Though the effectiveness is insignificant, an improved optimum value can be obtained.By means of increasing the pulsewidth of θ ＝120°, though the triplen harmonics appear a little, the other harmonics are going toward suppression and the relative harmonics is totally reducing.The increased fundamental component contributes an improvement of relative harmonic characteristic.

Pursuit of optimum value by varying θ and α 1
Fig. 7 shows the characteristic to obtain the optimum value by varying and α 1 and θ =120° whose waveform is shown in Fig. 6.Firstly, a certain value of α 1 is arbitrarily given, after that θ is varied to be the minimum value of V h *.The obtained value is plotted as shown.The lowest minimum value becomes optimum one, that is V h * = 0.019 at θ = 122.3°and α 1 ＝0.170.As the conventional method is V h * = 0.026, the characteristic can be improved by 27%.The variation of θ is small 2%, so the effectiveness of improvement due to α 1 is more significant.
Table 2 represents such whole harmonic characteristics, as described above, where θ and α 1 are varied.In the bottom double rows in Table 2, though the triplen harmonics are completely eliminated in the upper row, the other harmonics remain.On the other hand, the harmonics characteristics are suppressed significantly for the optimum waveform method

Pursuit of optimum value by varying θ, α 1 and α 2
Fig. 8 shows harmonic characteristic to obtain the optimum value by varying θ, α 1 and α 2 .As can be seen, after θ is fixed a at 120°, α 1 and α 2 are varied to give V 5 =V 7 = 0, which influence intensely for harmonic characteristics.In such way, t each switching angles can be solved.Secondly, every variables, θ ＝120°, α 1 and α 2 are made varied to obtain minimum V h *.In the figure, these characteristics are plotted with regard to α 1.The minimum and optimum value is given by α 1 ＝ 0.205 rad, α 2 ＝0.301 rad and θ＝0.209 rad, that is V h *=0.008.
With compared to the conventional method of V 5 = V 7 = 0, V h * is improved by 56%.There is little variation with regard to θ = 120°.Table 3 represents to discuss about the harmonic characteristics according to varying three variables of θ, α 1 and α 2 .In third and bottom rows, θ is fixed at 120°and V 5 and V 7 are given by zero (in third row), α 1 and α 2 are varied to obtain the optimum value of V h *.In comparison between two rows, it can be seen that V h * of bottom row can be successfully improved by 55% and more.In the bottom row where three variables α 1 , α 2 and θ are varied simultaneously to obtain the optimum V h *.It can be seen that the identical values are represented between the middle and the bottom row.θ＝ 120°makes triplen harmonics zero and also can contribute optimum waveform method.

Comparison between half-bridge
and full-bridge circuit.

Comparison of evaluation function
In each bottom side and its next upper side rows of Table 1 to 3, the specific order harmonics elimination method and followed optimum waveform method for full bridge circuit are represented in comparison with the results of half bridge circuits.Because the numbers of devices and their switching times are increased in full bridge, both bridges cannot merely compare with regard to their harmonic characteristics.For a case of full bridge, the number of switching in the other side of circuit leg should be also counted.In a similar number of switching, both characteristics are compared.In Table 1, in full bridge (FB), θ is shown as variable instead of α 1 .Fig. 6 shows full bridge waveform having single switching notch α 1 .Table 2 shows a case that the number of switching notch is twice.In FB circuit, that is in double rows at bottom side, two patterns are represented, where upper one is for V 5 = 0 and the other is optimum waveform method.The value of evaluation function in HB is deteriorated about by 70% compared to FB one.On the other hand, in HB, V 7 is reduced about by 20%, however, harmonics like V 3 and V 5 remain in fairly amounts.Table 3 represents in a case of thrice switching.As the conventional method in FB of third row is compared with the optimum waveform in HB, the latter case is deteriorated about by 20%, which would be in permissible level.Furthermore, even though of V 3 = V 5 = V 7 = V 9 = 0 in FB, each harmonics of V 3 , V 5 , V 7, V 9 can be fairly suppressed in HB with optimum switching.Fig. 8 shows comparison results between characteristics of FB and HB due to evaluation function.The bottom row, (j), (k) and (l) show the characteristics of optimum waveform method in FB, which is the most satisfactory characteristic as a matter of course.The next upper side line, (g), (h) and (i) show, specific lower order harmonic elimination method.The characteristic shows a little deteriorated as compared to optimum one.Even the next upper line, (d), (e) and (f) in HB shows the optimum switching.As comparing with conventional switching (a),(b) and (c) in HB, the characteristics is superior.These    Vh*=Vh/V1

Table1. Comparison of output harmonics relative to
characteristics appear in order of excellent degree of evaluation function.In the figure, horizontal axis shows the in permissible level order of the number of switching where that begins from once of α 1 or θ twice of α 1 , α 2 or θ and thrice of α 1 , α 2 , α 3 or θ in order of increasing order of the number of switching The characteristics of the evaluation function on the vertical axis, that is harmonic characteristics are improving as the number of switching is increasing.As can be seen, the characteristic of (e) that is the optimum switching by α 1 , α 2 in HB is almost identical or improved with the characteristic in (g) of 120°conduction wave in FB.In a similar, the characteristic of (f) by thrice switching of α 1 , α 2 , α 3 in HB is improved than the results of twice switching α 1 , α 2 or θ in (b) in FB.It can be seen that the characteristics of thrice switching of (f) in HB is almost similar one to thrice switching results in (i) in FB.These reasons can be described as follows; As in FB, the waveform is restricted to almost 120 ° period, the switching angle is also restricted to narrow 120° region.In HB switching, as the number of switching is increasing, the switching angle is expanding toward wide 180º region with switching degree in freedom.

Output waveforms
Fig. 10 shows the output voltage waveforms whose characteristics are previously represented in Fig. 9. Fig. 10(a) shows the optimum voltage waveform in HB.Fig. 10(b) is the voltage waveform in FB which is obtained from the well-known specific harmonic elimination method.That is, the waveform can be obtained by elimination of the 5th and 7th.In addition, the triplen harmonic is eliminated by 120 °phase difference.  .These switching angles α 1 , α 2 , α 3 and the like are represented in the third row in Table 3.By means of verifying these characteristics, the advantage of the proposal optimum switching method by using the HB could be perceived.Thus, in HB, the number of switching is thrice α 1 , α 2 , α 3 , where ｎ＝ 3 per quarter cycle.In addition of polarity switching, the number becomes ｎ+ 1/2 = 3.5.In FB, the number of legs is increased to double, so the switching number becomes also double, that is 2× (n+1/2)= 7.In order to compare with analogous switching times, the number of switching is selected in FB as 2× (ｎ+ 1/2) = 5 whereｎ= 2. These numbers can be counted in the waveforms in Fig. 10.In such a way, with the increased number of switching in FB, the proposed method will be compared and verified.Comparing with the conventional specific harmonic elimination method in FB, even if the number of switching is reduced in HB, the analogous level of harmonic characteristics can be obtained.In addition, comparing with (h) in FB in Fig. 9, where the number of switching is reduced, 2×(ｎ+ 1/2) = 3.Though the number of switching is a little increased in (f) in Fig. 9, the harmonic characteristic is improved a little and an analogous level of harmonic characteristics can be obtained by means of simple construction of half bridge circuit.The effectiveness of the these results could be confirmed and verified by results of V h * = 0.026 in FB in Table 2 and V h * =0.022 in HB in Table 3.

Conclusions
As generating power is restricted in settlement at a narrow space, according lower cost PCS is required.Especially, some inverter constructions including control strategies are proposed and examined.If the PV system is handled as like home apparatuses having attachment plug, the settlement cost can be much reduced.When certain unified specification is introduced and the mass production is promoted for simple PCS, even lower cost apparatus is supplied in the market.In a system interconnection, there are many problems in terms of regulation, so it is an obligation to detect the reverse power flow and the like.However, by means of breaking merely the solar panel circuit, no reverse power settlement of solar panel could be easily accepted.In such a way, various techniques should be considered to avoid severe regulation for protection of utility line.In an interruption, the uninterruptible power supply can not be connected to except the concerned important load line.Consequently, the capacity can be much reduced.In a method of providing exclusive line for interruption, the line is supplied also in normal one.In long term feeding for interruption during night, it is necessary to provide some battery system, which is installed at primary side of transformer of power conditioner.
In roof top solar system, to make PV panel cost low is significant, but in veranda solar, to make power conditioner cost low is much important.In this paper, the compact type power conditioner is presented, which has simple switching.This proposed photovoltaic power conditioner is suitable for comparably small capacity one because of containing harmonics a little.