#### written by Anil Lad

**how can we decide on the best solution amongst competing interests?**

From our everyday personal lives to highly complex business projects, trade-offs arise in almost all decision-making processes and understanding how to best manage them is key to finding an optimal solution which satisfies all stakeholders. For large capital-intensive energy projects, where millions of dollars are on the line, an awareness of how competing value drivers affect the attractiveness of various options becomes particularly important.

Qualitatively describing where trade-offs exist in a problem can be a relatively simple task. The ongoing COVID-19 crisis is a case in point; governments must weigh the impact of locking down their countries, to prevent rapid spread of the disease, against the risk of economic recession, which could lead to prolonged periods of high unemployment and have long-term detrimental effects on the health and prosperity of the general population. The difficulty comes in making a choice that fulfils all needs appropriately. Quantifying the effects of each alternative helps, providing decision makers with a clearer vision of all feasible possibilities. This enables them to determine where constraints lie on a spectrum of options, which therefore narrows down the range of potential solutions.

**the A-CAES case study**

This is the exact approach io used when requested to optimise the design of an Advanced Compressed Air Energy Storage (A-CAES) system (see “the case for CAES” for an explanation of how the technology works **[1]**)**.** In this instance, the trade-off was between maximising Round Trip Efficiency (RTE) and minimising total Capital Expenditure per unit of energy stored ($/kWh), whereby increasing RTE came at the expense of a higher $/kWh design. To add to the complexity of the problem, there were multiple control variables which could be used to adjust the performance of the system, each of which had varying impacts on RTE and $/kWh depending on the chosen states of the other degrees of freedom. However, taking a systems approach that accounts for both physical behaviour and cost elements of the technology enabled tangible numerical insights into the trade-offs that exist between RTE and $/kWh.

Figure 1 shows the curve generated by io’s model using multi-objective optimisation techniques (objective function 1: maximise RTE; objective function 2: minimise $/kWh). It is an example of a Pareto Efficiency Curve^{†}, where each solution on the curve represents a point of Pareto optimality i.e. it is impossible to improve one value driver without compromising on the other **[2]**.

Figure 1: Round Trip Efficiency (RTE) vs Capital Expenditure per unit of energy stored ($/kWh)

**how did the model solve the optimisation problem?**

The Differential Evolution algorithm was used to optimise this problem, which works according to the following set of rules **[3]**:

- Produce ‘n’ solutions by randomly assigning values to the control variables between fixed upper and lower bounds. Collectively, these solutions are known as the population and each solution produced is a member of the population.
- For each solution in the population, choose three other random solutions.
- Combine the assigned control variables (vectors) of these three solutions in such a way as to produce another ‘mutant’ set of control variables (a ‘mutant’ vector).
- Randomly assign control variables from the vector of the initial solution in step 2 to the mutant vector to produce a ‘child’ vector.
- Compare the value of function of the initial solution vector to the child vector. If the child vector produces a solution which is better than the initial solution vector, then it is replaced in the population. In this case, a replacement would occur if the RTE is higher and the $/kWh is lower than the initial solution.
- Continue this process for each member of the population
- Repeat this process for ‘x’ number of generations.

Eventually, the model converges to a point where no more solutions can be produced that have both a higher RTE and lower $/kWh than the solution from the preceding generation. This, by definition, leads to the formation of a Pareto Efficiency Curve.

**what conclusions were drawn from the study?**

Assuming the decision maker weights the importance of RTE and $/kWh equally, all solutions on the curve are equally optimal and the chosen solution depends on the constraints of the problem or subjective desires of the decision maker. However, it is clear that moving in either direction away from the knee of the curve (depicted by the point in the red dashed circle) yields diminishing returns:

- / To the right of the knee, every unit change in $/kWh results in a change in RTE that is proportionally smaller.
- / To the left of the knee, every unit change in $/kWh results in a change in RTE that is proportionally greater.

Therefore, given no other information, the best compromise between the trade-offs lies at that point.

Although the qualitative nature of this trade-off was already clear, generating a Pareto Efficiency Curve enabled the client to understand the performance limitations of their system as well as the extent to which efficiency gains can be made before cost begins increasing disproportionately more than RTE. It provided insights on whether their initial expectations were realistic and helped to confirm if budget and RTE targets were fit-for-purpose or if more novel technological solutions needed to be explored to meet stakeholder requirements.

io was also asked to find the lowest cost solution which met a minimum RTE criterion (as accepted by general industry consensus). By re-framing the problem to only minimise cost whilst keeping RTE above the required threshold, io’s model resulted in further cost savings of tens of millions of dollars relative to base case modelling using standard industrial process engineering software.

**final remarks**

With the sudden acceleration of the energy transition in 2020 and the resulting abundance of new clean energy technologies in the market, investors are keen to find projects which can produce returns in line with those seen during the peak of the oil and gas industry. Fierce competition between different energy production solutions means trade-off analysis, and consequently system optimisation, have become ever more important in the race to secure financing. The winners in this new age of energy will likely be those who can conclusively demonstrate they have discovered feasible solutions which optimally balance the needs of all parties involved.

io is a systems engineer or project integrator, and has deep domain expertise in the very early stages of major energy projects, specialised in identifying the key drivers and bringing transparency to decision making. Energy storage is one of io’s six energy transition segments: energy storage, carbon capture usage & storage, hydrogen value chain, net zero facilities, emissions reduction and negative emissions, where io applies its techno-economic and strategy expertise. io has performed projects in green hydrogen, CO_{2} transportation, energy storage, energy efficiency, demanning/electrification of platforms and associated gas utilisation.

† The Pareto Efficiency Curve is named after Vilfredo Pareto, who famously developed the basis behind the 80/20 rule [4]

[1] http://ioconsulting.com/the-case-for-caes-2/

[2] https://stats.oecd.org/glossary/detail.asp?ID=3275