On 21 June I wrote: > The relationship between head variation and reduced efficiency involves a > quartic polynomial. If anyone is interested in the formula they can contact > me > directly.
to which Perran Newman replied: > Does this mean that there are many points of (sub optimum) maximum > and minimum power as the load is varied and that a simple hill climbing > algorithm will not find the true maximum power point ??? > My intention was to address the following issue. If for some particular head (H) a micro-hydro generator is held at its MPP voltage and then the head changes by some fraction, but the voltage remains the same, what is the nature of the reduced output because the system is not allowed to track to its MPP. This is what happens when the voltage is set manually and not allowed to track automatically. Let h be the new head. Then h = H(1 + d) where d is the fractional increase. Then the formula I had in mind was e =(2/((1+d)^0.5) - (1/(1+d)))-1 where e is the fractional change in output. For example if e = -0.02, it means that the output power is 2% less than it would be if the voltage were allowed to adjust to the new MPP. Note that d can be positive or negative, but e is never positive. Now the surds in this formula can be removed and I mistakenly thought that this would lead to a quartic equation - it's actually more complex than this and the algebra becomes quite messy. The form given here can be easily graphed in Excel and be shown to have a single peak at d = 0. This answers Perran's question - yes, a simple hill climbing algorithm will always work. When I get some free time, I will write out a derivation of the formula and provide it those who have asked. bobtransformer wrote: > > Right, the MPP Voltage of the turbine would hardly vary much if at > all. The hydro voltage won't have to vary, or go up, unless > diversion control is absent on the battery side. Otherwise, the > input (hydro) output voltage will have to rise when the batteries get > fully charged, or battery loads go away. This is a separate issue. The MPP voltage has nothing to do with diversion control. I agree that under the conditions you state, the hydro output voltage will rise, but this is because of what is called the "linear series regulation" feature of the controller and not its MPPT ability. Linear series regulation refers to the ability of the controller to control one of the operating variables so that the hydrogenerator delivers just sufficient power as can be safely utilized by the system. This allows the point on the operating curve to range from the MPP (when all power can be utilized) to the freewheeling point (when no power can be utilized). It is a reliable method of control for micro-hydro either to replace or supplement load diversion. Nando makes some interesting observations, including: > > Now that I called your attention: MPPT to the LOAD or MPPT to the GENERATOR > needs to exist. > > MPPT to the LOAD : the Load is varied to Harvest the peak power available > MPPT to the GENERATOR : the Generator is Varied to Harvest the energy PEAK > that the LOAD requires > > In the MPPT to the LOAD case, the generator may have very limited power > capability, much less than the load can Harvest. > In the MPPT to the GENERATOR case, the Generator may have greater power than > the load can Harvest. The controller is able to track the MPP by controlling any one of four variables, i.e., generator voltage (Vgen), generator current (Igen), load voltage (Vload) and load current (Iload). In battery charging applications, Vload is clamped by the battery voltage, but any of the other three can be used. Provided the geometry of the hydrogenerator is not changed (i.e. specific speed stays the same) then as the head (h) varies and with MPP tracking, Vgen varies in proportion to h^0.5, Igen varies in proportion to h and (assuming Vload is clamped) Iload varies in proportion to h^1.5. As an example, if the head is increased by 10%, Vgen increases by 5%, Igen by 10% and Iload increases by 15%. Hence, considering the original issue of the effect of manual setting, Vgen is the best variable to select as it is the one least influenced by changing head. Some years ago an acquaintance of mine used Igen as the controlling variable in an application that had multiple load sites each with its own AERL controller. In this case the purpose was not to provide MPP tracking as such, but rather to control the share of available power that each load centre could draw. For each controller, Igen was set so that the sum of all the Igens matched the MPP Igen. When a load centre did not require its full allocation, the linear series regulation feature of the controllers allowed Vgen to rise thus allowing more power to the other load centres, but still in proportion to their allotted share. Note however that when this happened the system moved well away from its MPP and so overall performance was significantly reduced. Shortly afterwards we were faced with the same problem with two independent households using AERL controllers, taking power from a single hydrogenerator. We chose to control Vgen and by exploiting the small but nevertheless significant transmission cable resistance were able to achieve the same effect as controlling Igen. This method worked well - it's now about eleven years since the system was installed and whilst the turbine itself has undergone extensive modification the original method of control is still in place and in daily use. An advantage of controlling Vgen is that when a load centre does not require its full allocation the system is still held at (or very close to) it MPP so long the remaining load centres can between them take all the available power. Regards, Max Enfield Planetary Power www.planetarypower.com.au Does your company feature in the microhydro business directory at http://microhydropower.net/directory ? If not, please register free of charge and be exposed to the microhydro community world wide! NOTE: The advertisements in this email are added by Yahoogroups who provides us with free email group services. The microhydro-group does not endorse products or support the advertisements in any way. More information on micro hydropower at http://microhydropower.net To unsubscribe: send empty message to [EMAIL PROTECTED] Yahoo! 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