Wind Energy

152 S. Jost et al.
random Poisson network. For small tolerance parameters and also for the
(N −1) analysis based on the average loads, only a relatively small fluctuation
strength is needed to knock out a sizeable fraction (≈ 20%) of the network.
The second model extension is motivated from another wind-power related
picture: a small fraction q =0.1 of (conventional power plant) nodes with large
source capacity scpp face a large fraction 1−q of (repowering wind energy)
nodes with small source strength swind. Instead of (26.7), the source strengths
are then assigned according to the bimodal distribution
p(s) =qδ (s − rscpp)+(1− q)δ (s − swind) . (26.8)
In case of swind = 0, the c.p.p. nodes produce at full capacity scpp with
no reduction (r = 1). The setting scpp = 1/q then insures 〈s〉 = 1 as in
the previous model discussions. With increasing (repowering) swind the c.p.p.
nodes produce less to conserve the overall production (〈s〉 = 1). This fixes the
reduction parameter to r =(1− q)swind. The capacity layout of the network
according to Cn =(1+α)Ln or the (N − 1) analysis is done for swind =0,
which corresponds to the old times when only c.p.p. nodes were produced.
With the introduction of source strengths swind �= 0, small at first but then
further increasing (repowering), again the concern is on the robustness of the
network against cascading overload failure. Figure 26.3b reveals that already
relatively small source strengths suffice to lead to a major network disruption.
Only a further investment into the network in the form of larger tolerance
parameters appears to help.
26.4 Outlook
The (toy) model extensions introduced in the previous section allow room for
further realistic improvements. Only then it makes sense to import and modify
concepts from modern information and communication technologies, like for
example those of [1, 2], and to start building a Power Internet. The latter
would include the distributive and self-organized monitoring and control of
wind farms and the power grid.
References
1. Glauche I., Krause W., Sollacher R., Greiner M. (2004) Phys. A 341:677–701
2. Krause W., Scholz J., Greiner M. (2006) Phys. A 361:707–723
3. Albert R., Barabási L. (2002) Rev. Mod. Phys. 74:47–97
4. Motter A., Lai Y. (2002) Phys. Rev. E 66:065102(R)