# Theory and analysis

Owing to the large variation in the wind and solar energy, the converter is employed to provide the stable power for normal application. When only one energy source supplies the load, as shown in Fig.1(a), the voltage and frequency of the converter output is adjusted to meet the load specification. In Fig. 1(b), both wind and solar energy supply the same load simultane­ously. In addition to the load requirement, the voltage and frequency of both converter outputs are adjusted such as the two energy sources can supply the load at the same time. In case of the DC-DC converter, only the output voltage of both converters should be adjusted to charge the same load.

In a small hybrid power system, a battery is usually utilized to store the renewable energy to improve the reliability of the system. Moreover, to simplify the power system, the power source charges directly the battery. Figure 2 shows the conventional charging system, in which the rectified DC voltage charges two batteries. In addition to source voltages Ew, E1 and E2, charging currents I1 and I2 are also determined by source resistances rw, r1 and r2 for the wind power and the two batteries, respectively. The output voltage V0 is the summation of V0w, V01 and Vc2 from wind power and batteries E1 and E2, respectively. According to the circuit theory, the equations for V0w, V01 and V02 are as follows:

V01 = EiHH

V02 “ E2( 1 )

V0 = V0. + V01 + V02

As mentioned, Vam, Vo1 and Vo2 are voltages from wind power and the two batteries, respec­tively, which contribute totheoutput voltage ^independently.

The following are possiblechargingsituations.

a. When V0w > V01 = V02, the charging current from wind power charges simultaneously both batteries E1 and E2.

b. When Vto > V01 > V2 the charging currents from both wind power and battery E1 charge battery E2.

c. When V0w > V02 >V01, similar to case (b), the charging currents from both wind power and battery E2 charge batteryEi-

d. When V01 > V0w >V02, wind power has no effect on the circuit, only battery E1 charges battery

e2.

e. When V02> V0w >V01, similar to case (d), – wind power has no effect on the circuit, only E2 charges battery E1.

As seen in above analysis, it is only in case (a) that wind power can charge both batteries at the same time. However, in case (b), when betterу E1 also charges battery E2, the voltage drop of I1 r1 and I2 r2 cause increase in g)2 and decrease in V01 respectively. Finally, when Vm = Vу, the charging coneiricv nnlumsto casn (e).Crtse (c) in similac to cairib),go itaxhibi1= self­

regulating behaviarducing thecharying proceir. C errs(d) ernl (eiara not neamal rVaigtng conditions.

Figure 3(a) shows a hybrid wind and PV power generating system. Ew, Ep, Eb, rw, rp and rb are factors that determine the charging current. Similar to the above conventional charging conditions, the output voltage V0 is made up of Vow, Vop and Vob from the wind generator, solar panel and battery, respectively. The related equations are listed below.

V = E (—b—)

ow w

r

V = E (—b—)

op p rp + rb

V = Eb + V + V

o b ow op

Possible charging conditions are as follows:

a. When Vow > Vop > Eb, both wind and solar energies charge the battery.

b. When Vop > Vow > Eb, both wind and solar energies charge the battery.

c. When Vow > Vop, only wind energy charges the battery.

d. When Vop > Vow, only solar energy charges the battery.

From the above analysis, in cases (a) and (b), there are two energy sources charging a battery at the same time. However, in case (a), the larger current Iw from wind energy may result in a larger internal voltage drop Ib rb of the battery. Therefore, when Vow > Vop, the charging condition becomes case (c), and solar energy cannot be utilized to charge the battery. Case (b) shows the same behavior. Contrary to the conventional charging system, the hybrid charging system exhibits a competition effect, meaning that only the larger power source can dominate the charging system.

Figure 3(b) shows the I-V curves of the charging system. Because the source resistance of the wind generator is much smaller than that of the solar panel, the wind I-V curve reduces slowly with increase in charging current. The source resistance of the battery is also much smaller than that of the wind generator. Therefore, the terminal voltage of the battery Vo increases only slightly with increase in charging current. When the solar I-V curve drops to P, which is equal to the terminal voltage of the battery, the solar energy stops charging the battery.

Figure 3(c) shows the V-T curves of the charging system. Before time To the battery is in under­charge condition, both power sources behave as the current sources with their ratio of output currents proportional to that of generated power levels. For time To to Tf, the source resistance of the solar panel lowers gradually the solar charging current and the battery terminal voltage Vo increases slowly. Finally, at time Tf, only wind power can charge the battery.

To improve the performance of the hybrid power generating system shown above, a switch control is employed. It is connected to the battery circuit as shown in Fig. 4. In this operation mode, both wind and solar energy can be utilized, although only one energy source can charge the battery at any time. Owing to the different characteristics of wind and solar energy, as shown in Eq. (10), we can adjust the charging duty cycle ratio k of the two energy sources to obtain maximum energy in the battery. The equations are listed below.

V = Eb + E (—b—)

0p b P (rb + rp ’

(c)

Figure 3. (a) Small hybrid wind and PV energy charging system. Two power sources charge a battery. Owing to the internal voltage drop caused by impedance of wind, solar and battery power source, only one power source can con­tribute to the charging process. (b) I-V characteristics of the charging system. When the solar I-V curve drops to point P, solar power cannot chargethe battery. (c) Simplified charging curve of the system. Two current sources chargethe battery before time T0. Then, charging speed reduces because of increase in resistance of the solar power circuit. After time Tf, only wind power charges the battery.

To overcome the drawbacks of the hybrid wind and PV charging system shown above, a microprocessor-controlled power generating system, as shown in Fig.5, is proposed. The different charging modes, which vary with the weather conditions to obtain the maximum energy, are shown in Table 1. With both energy sources, the system operates in the independent charging mode. The windcmd solar energycharge batteries£tocmd £bf, respectively. Ifthere is only one energy еауасе, у1ееу^1:ет runsinthd hybrid chargmg mode. giaheyenergyyedece can charge batteries Ebw and Ebp simultaneously. Owing to the instability of wind energy, if both energy sourcee co-exesd, wan decergyexceeds the thyeehoed vrlue, ahe changing syedem runs in the wind-evhaneya mode. tnfhic eaye, not enlycan boCh enercysouscesg nrmployee to improve the reli rbilteyofpowcy syeiem, ihc auctuationsln theamallwie d powernencratlng system can also be rydeaed.

I bw__ |rbwlbp__ I rbp

Figure 5. Microprocessor-controlled wind and PV energy charging system. Both power sources charge the two batter­ies. According to the wind and solar energy conditions, the controller regulates the charging conditions for Ebw and Ebp. There is no power loss in this charging system. When there is only one power source, it can charge both batteries. With both power sources and high wind energy, the excess wind energy charges battery Ebp. The controller improves greatly the reliability of this charging system.

 Energy Source Ebw Ebp ▲ ▲ Wind Energy ▲ it Solas and Wind Energy (lawwind speed) • • Salat and WindEnergy (high wind :peed: ill ▲ • : Independent Charging ▲ : Hybrid Charging Ebp : Solar Battery Ebw : Wind Battery
 Tablel. Microprocessor – controlledchargingmodes, Underindependentcharging condition, thesolarenergyand wind energy charges respectively the corresponding battery. Under hybrid charging condition, bothenergy souryys chargethe twobatteries simultaneously.