of studies on system effects
Annex 3.A6. Comparison of methodology: Residual load duration curves vs MILP
As discussed in Chapter 2, modelling the electricity system is a complex undertaking which requires the adoption of sophisticated tools. Most of the recent publications in this area rely on capacity planning and unit commitment models which are formulated as mixed-integer linear programmes (MILP). GenX, the tool used for the present study, falls in to such a category of numerical tools. While these models constitute the current reference for such analyses, it may be interesting to compare some of the results of this study with those that would have been obtained using a less sophisticated representation of the electricity system based on residual load duration curves (RLDC). In this context, the curtailment of VRE resources and their value factor have been calculated for the main region using a RLDC method. The results are presented in the following figures: Figure 69 compares the curtailment of VRE in the main region for the two penetration levels of 50% and 75%, while Figure 70 shows the value factor of solar PV and onshore wind at different penetration levels.
Figure 69. Curtailment of VRE using MILP and RLDC modelling approaches
Calculations based on the method of RLDC are much simpler and require much lower numerical resources than models based on MILP. On the other hand, as a consequence of the much simpler and less sophisticated representation of the electric power system, methods based on the RLDC are unable to correctly represent some of the characteristics of the system, in particular:
i. storage reserves, including flexible hydroelectric capacities: these plants are either not modelled or their modelled dispatch is based on their realised generation;
ii. interconnections and electricity flows between two regions: in most of the cases RLDC models solely a single region represented as a copper plate;
iii. operational constraints of all generation capacities are not represented; it is therefore implicitly assumed that all power plants modelled have infinite flexibility.
0 20 40 60 80 100 120 140 160 180
1 1001 2001 3001 4001 5001 6001 7001 8001
VRE generation (GW)
Utilisation time (hours)
75% VRE: Maximal production 75% VRE: Effective production - MILP 50% VRE: Effective production - RLDC 50% VRE: Maximal production 50% VRE: Effective production - MILP 50% VRE: Effective production - RLDC
0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000
In comparison to a MILP formulation, the first two elements tend to underestimate the flexibility present in the system which increases the challenges for VRE integration; this simplified approach suggests a larger curtailment of VRE resources and a lower market price for VRE generation (and thus a lower value factor). On the other hand, not taking into account the operational constraints of thermal power plants reduces the integration challenge and therefore has an opposite effect on the two observables analysed here.
With respect to the VRE curtailment, it is interesting to observe that, in the 50% VRE scenario, these “shortcomings” compensate each other, and the estimated level of VRE curtailment is very similar using the two models. The error increases at higher VRE penetration levels, with the methods based on RLDC suggesting a larger curtailment rate of VRE than that obtained with more accurate simulations based on MILP. Interestingly and more surprisingly, the value factors of VRE are very similar when obtained with the MILP and the RLDC approaches: quantitative results are similar and show the same downward trend.
Clearly, compensation between different effects also plays a major role in explaining such a convergence of results.
Figure 70. Value factor of wind and PV generation in the main region
The results shown above should not be interpreted as a suggestion to adopt one modelling technique over another, nor should they be viewed as a rigorous benchmark of the two methodologies. These conclusions are valid only for the observables analysed here (VRE curtailment and their value factor), do not necessarily apply to other characteristics of the system and may be not be valid for other systems. There are also many other aspects that can be analysed only with a MILP calculation but are not accessible via a RLDC approach. However, the methods based on RLDC curves appear sufficiently robust to provide reliable results, at least as a first approximation.
0%
20%
40%
60%
80%
100%
120%
0% 10% 20% 30% 40% 50%
Value factor of electricity generated (% of base price)
VRE penetration level (%)
Wind - MILP Wind -RLDC
Solar PV - MILP Solar PV -RLDC
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