Sensitivity analysis: the co-optimisation model

Total storage revenues are strongly dependent on model parameters, such as efficiency, variable costs, power and energy capacity. A sensitivity analysis was carried out with respect to these parameters to investigate how their changes influence co-optimised revenues shown in figure 6.10

In the top left of figure 6.10, the impact of round-trip efficiencies is shown in 5% increments, on total revenue, discharge volume, average revenue and the average SOC. Total revenues are approximately a linear function of efficiency only showing slight disproportionate relationships at very low or very high efficiencies. The average revenue function, calculated as total revenues divided by the volume of energy discharged, rises then falls, reaching its maximum around 25% efficiency. This situation arises as two parameters interact: discharge volume and discharge prices. At low discharge volumes due to low round-trip efficiencies, only large price differentials are of interest to the co-optimisation model. At those low efficiency levels, the storage system can only generate arbitrage revenues from extreme price swings. These swings are rare occurrences, hence resulting in a low discharge volume. However, every MWh of energy discharged in this situation yields a high revenue, over £150/MWh at its maximum. Nevertheless, it should be pointed out that because these events are rare, total revenues

still remain relatively low at approximately £1.6 million for a 25% round-trip efficiency system. By comparison, at a 95% round-trip efficiency, the storage system generated about £6.3 million.

The peaking shape of the average revenue function can be explained through the efficiency gain concept stated in section: 5.7.2; as the round-trip efficiency rises, large price differentials yield more revenues due to the higher efficiencies. In this case, the efficiency gain effect is driving the average revenues upwards in the 0-25% efficiency range; at the lowest efficiency level, the storage system can only generate revenues from the highest prices. Further trades (as efficiency rises) occur at lower prices, yet, the average revenue rises due to this efficiency gain effect. For example, an increase in efficiency from 10% to 20% doubles the revenues of existing trades, whereas discharge volume does not increase significantly. As a result, average revenue rises sharply.

The other effect through which efficiency causes revenues to rise, also described previously in section 5.7.2, is the feasibility gain effect whereby smaller price differentials become feasible opportunities for arbitrage, therefore resulting in greater discharge volume. Thus, as efficiency keeps rising, the number of feasible trades increases and therefore discharge volume rises substantially. These feasibility gains, however, are relatively smaller price differentials and therefore as a combined effect causes the average revenue to fall.

In other words, in the low efficiency ranges from 0-30%, the efficiency gain effect dominates the average revenues, however at higher efficiency levels the feasibility gains effect become the dominant driver of revenues. This is evidenced by the orange line in the upper left corner of figure 6.10, representing discharge volume; the latter rises substantially beyond a round-trip efficiency of 35%.

Figure 6.10: Changes in total revenues, discharge volume and average revenue relative to changes in

The top right of figure 6.10 shows the sensitivity of the same output parameters with respect to variable costs. These costs which are incurred both on charging and discharging can be seen to reduce revenues, total discharge volume and average revenues more than proportionately. Revenues are sensitive to variable cost changes though to a lesser extent than efficiency; at a variable cost of zero, total revenues were £4.8 million and at a variable cost of £10/MWh total revenues were £2.9 million. At a variable cost of £20/MWh revenues fell to £2.1 million. On the other hand, average revenue increases as trades from increasingly high price differentials become the only viable source of revenues.

One of the main considerations in evaluating storage’s economic feasibility is its energy capacity since it represents a significant proportion of capital expenditures. Therefore, an appropriate sizing of storage technology is essential and has been investigated with respect to several markets worldwide (Hessami & Bowly 2011; Drury et al. 2011; Kloess & Zach 2014; Sioshansi et al. 2009). The bottom left of figure 6.10 shows the effect of increasing the energy capacity of the storage system expressed in the number of hours of output; at 1 hour of output, 68% of maximum revenues is captured, rising to 81%, 89% and 94% at 2, 3 and 4 hours’ output. By 8 hours, the maximum revenues within a 1-day optimisation horizon are captured, the same effect is observed for total discharge volumes. This implies that on a 1-day optimisation horizon, most of the energy stored is released within 4 hours. Average revenue is very weakly affected as it shows a barely noticeable decrease as energy capacity rises. It is worth pointing out that energy capacity which is sometimes expressed in energy to power ratio is effectively constrained by market liquidity (trading volume or imbalance volume). In this energy capacity analysis, the power capacity was fixed at 50 MW.

As opposed to efficiency, variable costs and energy capacity sensitivities, which all show elements of non-linearity in the form of diminishing returns, power capacity changes bring about almost linear changes in revenues and other parameters. Energy capacity is in this case fixed at 12 hours of output. These occur due to the assumptions; under co-optimisation, power capacity is actually limited by the APX market and BM imbalance volumes. However, additional FFR windows can still generate additional revenues. Average revenues in this case rise since larger power capacities are able to utilise large price variations, increasing their charging and discharging volumes, generating greater profitability.

It is assumed that discharge capacity in the range of 50-500MW is not limited from an FFR perspective. This power capacity sensitivity range lies within the primary frequency response reserve requirement of up to 1800 MW (National Grid. 2015). Further considerations on the probability of FFR tenders being accepted is beyond the scope of this study but become increasingly important the higher the capacity.