7. Value of wind forecast accuracy and flexibility enhancements in wind-integrated
8.2. Further Work
8.2.2. Simulation length requirements
Run times have been tolerable in the case studies reported in this thesis despite the long simulations that were found to be necessary, because of the simplicity of the systems that have been simulated. More complicated systems could impose a much greater computa- tional burden. For example, run times will be severely affected by the larger number of decision variables in a multi-bus formulation, because of the greater number of scenarios, the larger number of generator groups, and the power flow equations.
Although run times can be shortened by increasing the number of cores used, it may still be necessary to perform shorter simulations than have been used for the case studies in this thesis, if more complex systems are to be analysed. The need for long simulations is mainly due to the extreme spikiness of the operating costs as a result of the very high VOLL (£30 000/MWh) compared with marginal generation costs (£40–£60/MWh). If the VOLL is assumed to be lower—£3000/MWh, say—then statistically significant results will be achievable with shorter simulations.
Variance reduction techniques have been attempted during the course of this project in order to reduce the simulation length required, but have not been reported in the technical chapters. Two techniques have been tried: Importance Sampling (IS) [134] and Child Node Valuation. The IS method was applied to generating the wind realisations used in the simulation, rather than the scenarios in the scenario tree. In simulations with IS, a large number of week-long wind samples were used, rather than a small number of year-long ones. A very large population of samples (1 000 000) were pre-generated by the wind model, and a much smaller subset were chosen such that the variance of the op- erating cost was minimised assuming that the costs are a linear function of the delivered wind energy. In order to compensate for the biased sampling, the operating cost for each sample must be debiased by multiplying by a weighting factor. The interested reader is referred to Appendix D for an explanation of the method.
Although IS was found to be effective in reducing the variance of operating costs due to the variability in delivered wind energy, we are more interested in the relative operating costs between two different systems (e.g. with and without storage), or modes of operation (e.g. deterministic versus stochastic). IS was much less effective at reducing
CHAPTER 8. CONCLUDING REMARKS AND FURTHER WORK
the variance of these differences, which cannot be approximated as simple functions of the wind energy. Another problem with IS is that we may be interested in more than just the operating cost: for example, we may wish to estimate the expected number of CCGT startups. However, IS targets a single element of the simulation results, in this case the operating cost, for variance reduction, but does nothing for the other properties whose variance may indeed be amplified by the biased sampling.
Another technique that was tried was an original idea that we have termed Child Node Valuation, which attempts to use some of the information from the SUC that is otherwise discarded by the rolling planning process. Let c(n; k)be the operating cost per hour at node n from the SUC solution calculated at timestep k, i.e.
c(n; k) =cLSPLS(n) + 1
∆τ(n) g
∑
∈GCg(n) at timestep k. (8.1)If Child Node Valuation is not used, then the estimate for the expected operating cost per hour over a sample with Nk timesteps is the average operating cost at the root node
nr(Root Node Valuation):
ˆc= 1 Nk Nk−1
∑
k=0 c(nr; k). (8.2)An alternative estimate for the expected operating cost is to use the solution for deeper nodes in the scenario tree, with a common relative start time τ (Child Node Valuation):
ˆc= 1 Nk Nk−1
∑
k=0∑
n∈Nτ π(n)c(n; k). (8.3) whereNτ ={n∈ N : τ(n) =τ}.In general, Equation (8.3) will yield less variance than (8.2), because it effectively includes a range of samples at each timestep. Typically one can use τ = 1h: it is best to use nodes that are close to the root node, since the solutions near the leaves will be biased due to the limited horizons visible to these nodes. Child Node Valuation is particularly effective at reducing the variance from loadshed costs, which are smoothed out by the low probability weightings that apply in scenarios in which loadshed occurs.
Unfortunately, Child Node Valuation consistently underestimates operating costs when used with a scenario tree with a fan structure, typically by about 5%. This can be attributed to the lack of awareness of uncertainty at the child nodes, since scenarios are purely deterministic after the root node, which causes spinning reserve requirements to be zero at these nodes. The biasing can be mitigated by using trees with further branch- ing at deeper timestages, but this in turn increases run time requirements so that the advantages of using variance reduction are undermined.
For these reasons, and because of the reduction in transparency that accompanies the use of variance reduction, such techniques have not been presented in the technical
CHAPTER 8. CONCLUDING REMARKS AND FURTHER WORK
chapters of this thesis. However, they may need to be revisited if more computationally intensive systems are analysed.