Another approach to mitigate undesirable effects of the new RES is to tackle them locally, at distribution grid level. This approach relies in particular on active demand response (ADR) [67]. We want to assess the maximal effect that ADR can have on the results we presented in the chapter. How ADR is concretely implemented is out of the scope of the present work, we simply add an effective contribution to the national residual load that models the sum of all active demand response contributions. With ADR, the residual load is given by
R(t ) = L(t) + δL(t) − Ppv(t ) − Pwind(t ) − Pmrun= R0(t ) + δL(t), (3.10) where changes in the load profile due to ADR are included inδL(t) and R0is the residual load without ADR, as in Eq. (3.1). ADR can be deployed for various reasons, for instance to reduce electricity costs of end users or to mitigate load fluctuations on the distribution network. In both instances, ADR tends to reduce variations in the residual load, and we incorporate this goal in an optimizing procedure which we briefly describe. For the sake of simplicity, we do not incorporate specific load constraints such as comfort temperature intervals for ADR with thermostatically controlled loads. The only constraint on the ADR profile is
¯
3.5. Conclusion
whereδLmaxis the maximal ADR power. We further assume that the annual consumption remains unchanged,
tf
Z
ti
δL(t)dt = 0. (3.12)
Recent estimates of the potential of ADR indicate that only a fraction of the total consumption can be shifted, tf Z ti ¯ ¯δL(t)¯¯dt ≤ 2σ tf Z ti L(t )dt , (3.13)
withσ ' 0.01 giving the maximal fraction of the total consumption that can been shifted, while the maximal ADR powerδLmaxis about 10 % of the maximal load Lmax(roughly corresponding to 7 GW in Germany) [67]. These numbers may seem rather small, however they have been obtained assuming a broad load participation in ADR [67].
Our procedure is to compute the ADR profile that minimizes the fluctuations of the residual load,
min
δL £Var(R)¤ = minδL £Var(L
+− L−+ R
0)¤ , (3.14)
where we defined L±(t ) = max£0,±δL(t)¤. We linearly increase σ and δLmax/Lmaxfrom 0 in 2015 toσ = 0.01 and δLmax/Lmax= 0.1 in 2025. Because we neglect specific load constraints on ADR, our results likely overestimate the impact of ADR on the residual load, and therefore on electricity prices.
Fig. 3.13 (a) shows the effect of ADR on the revenues of a PS plant. ADR being a form of storage, it competes with PS and reduces its revenues, however, the effect is rather moderate, with 2020 revenues still exceeding those of 2005. Fig. 3.13 (b) shows the revenues of a conventional dam hydroelectric plant, which are even less affected by ADR than those of the PS plant.
3.5 Conclusion
Our interest in this Chapter was to investigate how the increasing penetration of new RES affect electricity prices in Europe. We showed that day-ahead electricity price is strongly correlated with residual loads in most European countries. From this observation we built an effective price based solely on the residual load. With this physico-economic indicator we investigated the revenues of different electricity producers.
• Residual load and day-ahead electricity prices are strongly correlated in Europe. • A simple physico-economic indicator can be used to investigate the future electricity
prices.
• New RES drag electricity prices down, PV particularly decreases the volatility of electric- ity prices.
• The insufficient withdrawal of must-run productions plunges the revenues of flexible sources. 2005 2007 2009 2011 2013 2015 2017 2019 0.7 0.8 0.9 1 1.1 1.2 1.3 Normalized revenue 2005 2007 2009 2011 2013 2015 2017 2019 0.85 0.9 0.95 1 1.05 1.1 1.15 Normalized revenue (a) (b)
Figure 3.13 –(a) Revenues of a PS plant in Germany with (dashed) and without (plain) ADR. (b) Revenues of a conventional dam hydroelectric plant in Germany with (dashed) and without (plain) ADR. ADR linearly evolves from zero in 2015 to its maximal potential in 2025, withδLmax= 7[GW] and σ = 0.01 [67].
Part II
The roles of inertia, primary control
and grid geometry on disturbances in
transmission grids
4
Disturbance propagation in large
transmission grids
The rotational inertia of conventional generators helps the system to be resilient against contingencies. The substitution of thermal generators by inertialess new RES may jeopardize power system stability in particular within the first few seconds after the occurrence of a fault. In this chapter, we investigate the propagation of disturbances in large transmission grids following abrupt power losses. To that purpose, we construct a dynamical model of the Continental European transmission grid, its elaboration is detailed in Section 4.1. We investigate the system disturbance following abrupt power losses in Section 4.2. We show that for a given amount of lost power the magnitude of the following disturbance strongly depends on the fault location. Furthermore we show that the strongest disturbance magnitudes are related to the buses located in the “Fiedler areas” which consist in the buses with large squared Fiedler components. The Fiedler vector is the eigenvector corresponding to the smallest non-zero eigenvalue of the network Laplacian. In Section 4.3, we investigate the influence of the placement of inertia by removing the inertia of certain generators. We show that the resilience of the grid against contingencies strongly depends on where inertia was removed. The system is more prompt to be disturbed when inertia is reduced in the “Fiedler areas”. To confirm our conclusions, we alternatively use a model of the Texas ERCOT transmission grid [68], where we obtain inertia and damping coefficients using the same procedure as for the European model. The model and most of the results presented in this chapter were published in Ref. [69].
4.1 A dynamical model of the continental European transmission
grid
For our investigation on disturbances in large transmission grids, we need detailed information on them. In this section, we elaborate our dynamical model of the continental European transmission grid1.
There are only few publicly available models of part or all of the synchronous grid of continen- tal Europe. To the best of our knowledge, the first one was released by Zhou and Bialek [70] and later upgraded to incorporate the Balkans [71]. Other models include ELMOD [72], PE- GASE [35, 34] and PyPSA-Eur [37]. These models are intended for power flow computations and they have not been extended to dynamical simulations. Furthermore, except PyPSA-Eur, they lack bus geolocalization which makes the interpretation of the results tedious. None of those model can be used straightforwardly for dynamical investigations, this motivated us to develop our own model.
Similar elaboration procedures to the one presented in this work were used in Refs. [70, 72, 73]. A similar model has recently been constructed, whose parameters do not seem to be publicly available [73].