5. Models constructed within this research
This section aims to present the methodological side of this research. The structure of the general profitability model that underlines all the (other) models built within this research is described in the following subsection. Following the practices of traditional investment analysis, this model is supplemented with sensitivity analyses to provide insights into the Russian RE mechanism effects on investment profitability.
The next two subsections present the implementation of the DMM method and the new extension to enhance the decision-making support achieved from the simulation-based technique. The last subsection documents the model built with the fuzzy pay-off method.
These three models utilize the RO valuation logic and aim to provide a deeper understanding of RE investment profitability under the Russian RE support mechanism.
5.1. General profitability model
The investment model used is realized in a spreadsheet environment, Excel®, and follows a traditional logic of the capital budgeting: estimating cash-flows, discounting them, and arriving at NPV and other profitability indicators. The model is based on a stylized RE investment for all the three technology types supported by the Russian mechanism, wind, solar PV, and small hydropower. A distinct feature of the model is that it includes an implementation of the calculation procedure of the RE remuneration provided by the Russian RE capacity mechanism. The outline of the model is illustrated by Figure 7.
Figure 7. Outline of the RE investment model
Project outflows include capital expenses (CapEx), operational expenses (OpEx), and financial expenses reflected in the discount rate. They are influenced accordingly by the project planned CapEx, inflation, and interest rates. A (generic) project studied has two sources of revenue: i) electricity sales that depend on the market electricity price and electricity production (or capacity factor); ii) revenue from the RE capacity delivery contract.
The formation of the capacity price is based on all of the factors listed above, and on the local
5 . Models constructed within this research 25 content of the power plant equipment. A summary of the key variables used and the underlying assumptions are presented in Table 2.
Table 2. List of key input variables
Variable Source Assumption
Electricity price
Average day-ahead market prices in Russia
Forecasted with linear regression, based on historical data, or assumed to be uniformly distributed between extreme values.
Inflation Russian consumer price index
Forecasted with linear regression, based on historical data, or assumed to be uniformly distributed between
Assumed fixed. To illustrate the capacity price influence on project profitability under changing market interest, a separate sensitivity analysis of project IRR to local risk-free rate is performed in Publication III.
Capacity factor
Normative levels set by the support mechanism
The base value is set equal to the high level in accordance with the Russian legislation, the variation is checked with sensitivity analysis, or assumed to be uniformly distributed, from 30% to 120% of the base value.
CapEx Normative CapEx limit Assumed to be equal to the set limit. Effects of CapEx variation are demonstrated with sensitivity analysis or assumed to have a uniform distribution between 80% and 150% of the base value.
OpEx Normative value set by the support mechanism
The effects of OpEx variations are checked with sensitivity analysis. Because of low importance, excluded from the list of key variables in later models an assumed to be fixed.
Capacity price
Calculation based on legislative procedure
The inputs to the capacity price calculation are the same as the inputs to the project cash-flow calculation.
Russian10-year government bond yield is used as a reference interest rate, in accordance with the legislation.
Local
Sensitivity analysis of the project NPV with regards to seven factors is performed, namely:
electricity price, inflation, CapEx, OpEx, capacity factor, discount rate, and the local risk-free rate. All the factors´ values are tested through the range ±50% with a 10% step.
5.2. Monte Carlo simulation model
The Monte Carlo simulation is based on the investment model already described above. The simulation has been implemented in Matlab Simulink® and illustrated with a block-diagram, see Figure 8.
26 5 . Models constructed within this research
Figure 8. Block diagram of the Monte Carlo simulation model
The blocks on the left of the diagram represent the key input variables. The model also allows running simulations for all three types of RE technologies, defined by the variable
‘technology’. Going from left to right, the inputs are transformed into the format needed for computation, and multiplied by random coefficients that create uniform distributions for the input variables. The orange block contains the capacity price calculation, whereas the blue block computes the project NPV. The resulting NPV vector (result of each simulation run) is
“sent” to the Matlab workspace, in which the resulting probability distribution is constructed from the set of results. The Monte Carlo simulation performs 100,000 runs. Different scenarios can be generated by adjusting the random coefficients, and/or by switching inputs to the fixed values.
5.3. The new extension to the simulation model (created new method)
The new decision-support approach for simulation-based methods, created within this research, enables the decomposition of the created probability distribution into a number of sub-distributions. The sub-distributions consist of (in this case NPV) results created with set (user determined) combinations of variable value sub-ranges. This way the sub-distributions
“tell the story” of where one will end up if one is able to “lock-in” on a sub-range of an uncertain variable (to reduce uncertainty) and does not have to face the whole uncertainty (whole range of possible outcomes).
For the purpose of this research, and to create sensible and in reality important sub-ranges, selected key variables (project-internal factors) were identified: local content, capital costs, and capacity factor. In this context the sub-ranges of the identified variables are (quite naturally) given by the Russian RE support mechanism features. The local content requirement is either “fulfilled” or “not fulfilled” and capital costs are divided into two subsets: “within the limit” and “over the limit”. Range of the capacity factor is divided into
5 . Models constructed within this research 27 three subsets, associated with production levels, “high”, “medium”, and “low”, and are set by the support mechanism.
The creation of the sub-distributions is done during the (normal) Monte Carlo simulation, by having MATLAB record, not only the NPV result from the simulation, but also the key variable combination that was randomly drawn and that resulted in the NPV outcome. This is put into practice by introduction of a scenario recording block that works by using the ‘if-then’ principle. In this context, twelve possible sub-range combinations of the key (uncertain) variables are used. The new scenario recording block and its links with the rest of the model are highlighted on Figure 9.
Figure 9. Block diagram of the extended Monte Carlo simulation model. The scenario recording block and links to and from it are highlighted.
The Matlab function, responsible for the creation of the probability distribution of the NPV, is adjusted in a way that it color-codes the created distribution, according to the scenario (variable sub-range combination) underlying each NPV result of the distribution. The resulting distribution allows matching NPV outcomes to key variable states. This enables the user to extract more relevant information for decision-making from the “same simulation”. In addition, separate distributions that correspond to each scenario (sub-range combination) and their descriptive statistics, including RO value, can be obtained, and studied further.
5.4. Pay-off method implementation
The pay-off method is realized with Excel® on top of the created spreadsheet investment model. The triangular pay-off distribution is built, based on three scenarios, where minimum possible (pessimistic) and maximum possible (optimistic) scenarios take the extreme values
28 5 . Models constructed within this research of the uncertain input variables (defined in Table 2) and the realistic (best guess) scenario takes the base case values.
The pay-off method application is repeated for several cases. In the Russian RE mechanism context, the overall pay-off distribution is first divided into three triangular fuzzy NPVs that reflect three different levels of electricity production performance (“high”, “medium”, and
“low”) set by the legislation, with all other factors unchanged and equally uncertain. In the following iteration the capital expenses are assumed to be “within the limit”, and the localization requirement is expected to be fulfilled - this is repeated for all three levels of electricity production. In total, seven cases of uncertain factor combinations are illustrated with pay-off distributions, in order to make sensible conclusions, with respect to the support mechanism effects on investment profitability (presented in Publication IV).