*3.1. Conceptual Design*

The proposed hybrid three-tier model combines all three types of energy models reviewed earlier. Its concept is depicted in Figure 1. Block A is composed of an operational power system model. This block contains hourly demand load curves and power generation profiles of different technologies; projects hourly electricity prices; and comprises weather and other uncertainties with relevant diurnal, weekly, and seasonal variations in demand and supply. With hourly projections, this block is responsible for computing system reliability measures at every hour. Block A feeds its information to Block B, where investment incentives are created and investment decisions are made. Here, the support instrument for renewable energy sources is based on system reliability and can be designed and tested. If the amount of remuneration from renewable energy sources is calculated based on their contribution to system reliability, it affects the profitability of the renewable energy technology with different power generation profiles differently. Thus, the investment incentives are created and translated based on the investors' behavior. The resultant investment decisions affect the composition of the system's technology mix, which is cap-

tured using a long-term energy system model component, Block C. The technology mix, in turn, affects the hourly power generation modeled in Block A. Thus, the cycle repeats. The environmental footprint of the system is calculated within Block A based on the simulated data of the system operations. which is captured using a long-term energy system model component, Block C. The technology mix, in turn, affects the hourly power generation modeled in Block A. Thus, the cycle repeats. The environmental footprint of the system is calculated within Block A based on the simulated data of the system operations.

**Figure 1.** Concept of the hybrid three-tier model. **Figure 1.** Concept of the hybrid three-tier model.

The model should be run for two main scenarios: The model should be run for two main scenarios:


The difference in technology mix evolution for these two scenarios showcase the relevance of renewable energy support via a reliability-based instrument for a particular region. If a region possesses spatial and temporal complementarity of its renewable energy sources, then new investments in renewable energy sources can be optimized to favor system reliability. This, in turn, results in a reduced overall backup capacity or storage solutions needed. Overall, such a system would cover its peak demand with a smaller installed capacity and, thus, less incurred costs, compared with scenario #2, where renewable energy sources are supported in a conventional way. The difference in technology mix evolution for these two scenarios showcase the relevance of renewable energy support via a reliability-based instrument for a particular region. If a region possesses spatial and temporal complementarity of its renewable energy sources, then new investments in renewable energy sources can be optimized to favor system reliability. This, in turn, results in a reduced overall backup capacity or storage solutions needed. Overall, such a system would cover its peak demand with a smaller installed capacity and, thus, less incurred costs, compared with scenario #2, where renewable energy sources are supported in a conventional way.

Continuing the list of scenarios, the model can analyze the effects of different policy mix arrangements and technological solutions available, though not considered in this Continuing the list of scenarios, the model can analyze the effects of different policy mix arrangements and technological solutions available, though not considered in this paper:


### 6. Storage and demand-response development effects for scenarios #1–4. *3.2. A Stylized Example*

gas-fired power plants [46] (Table 2).

#### *3.2. A stylized Example*  3.2.1. Assumptions

3.2.1. Assumptions A stylized example is used to demonstrate the model's functioning on a high level of abstraction in an intuitively understandable way. We chose a region with high potentials for solar energy resources; therefore, the numbers for technology-specific estimates, such as the capacity factor and levelized cost of electricity, are taken based on California's data for 2018 [45], and as the lifetime of flexible generation, we use the estimated lifetime of A stylized example is used to demonstrate the model's functioning on a high level of abstraction in an intuitively understandable way. We chose a region with high potentials for solar energy resources; therefore, the numbers for technology-specific estimates, such as the capacity factor and levelized cost of electricity, are taken based on California's data for 2018 [45], and as the lifetime of flexible generation, we use the estimated lifetime of gas-fired power plants [46] (Table 2).


In the system, 20 GW-based load facilities and 5 GW flexible generation are assumed

**Table 2.** Technology-specific assumptions. **Table 2.** Technology-specific assumptions.

*Sustainability* **2021**, *13*, x FOR PEER REVIEW 8 of 18

In the system, 20 GW-based load facilities and 5 GW flexible generation are assumed to exist. The intraday load profile is a classic textbook example with two consumption peaks: morning and evening. It is assumed to vary between 20 and 45 GW (Figure 2a). Such demand levels correspond to a region with electricity consumption similar to California [47]. The one-day profile is assumed to be representative of the whole year. The day-ahead electricity market prices are set proportional to the demand (Figure 2a). The missing supply is deemed to be covered by renewable energy sources, solar and wind power, and extra flexible generation, if needed, is auctioned by the regulator. The solar and wind power generation profiles are sketched to resemble the most common situation, with the sun peaking during the day and winds prevailing at nighttime (Figure 2b). The power profiles are presented for 1 MWh generation per day overall for each technology. to exist. The intraday load profile is a classic textbook example with two consumption peaks: morning and evening. It is assumed to vary between 20 and 45 GW (Figure 2a). Such demand levels correspond to a region with electricity consumption similar to California [47]. The one-day profile is assumed to be representative of the whole year. The day-ahead electricity market prices are set proportional to the demand (Figure 2a). The missing supply is deemed to be covered by renewable energy sources, solar and wind power, and extra flexible generation, if needed, is auctioned by the regulator. The solar and wind power generation profiles are sketched to resemble the most common situation, with the sun peaking during the day and winds prevailing at nighttime (Figure 2b). The power profiles are presented for 1 MWh generation per day overall for each technology.

**Figure 2.** Initial load profile, available power, and hourly day-ahead market prices (**a**) and assumed solar and wind power profiles (**b**). **Figure 2.** Initial load profile, available power, and hourly day-ahead market prices (**a**) and assumed solar and wind power profiles (**b**).

An investment decision is based on profitability by comparing the cost (LCOE) per megawatt hour and revenue per megawatt hour comparison. If the revenue exceeds the cost, the decision to invest is made. The model is entirely deterministic; therefore, there is no uncertainty and, hence, value to postpone investment. That is why profitability is defined by the deterministic net present value (benefits minus costs) rather than real options. However, industrial players behave in accordance with the real options theory [30]; therefore, it is imperative to integrate the real options framework when uncertainty is included into the model, as in the hybrid model discussed above [31]. The LCOE assumptions are presented in Table 2. The revenue is composed of the market sales (with prices depicted in Figure 2, right) and a premium. An investment decision is based on profitability by comparing the cost (LCOE) per megawatt hour and revenue per megawatt hour comparison. If the revenue exceeds the cost, the decision to invest is made. The model is entirely deterministic; therefore, there is no uncertainty and, hence, value to postpone investment. That is why profitability is defined by the deterministic net present value (benefits minus costs) rather than real options. However, industrial players behave in accordance with the real options theory [30]; therefore, it is imperative to integrate the real options framework when uncertainty is included into the model, as in the hybrid model discussed above [31]. The LCOE assumptions are presented in Table 2. The revenue is composed of the market sales (with prices depicted in Figure 2b) and a premium.

A premium is modeled in two different scenarios. The YELLOW scenario is modeled with a classic fixed premium of 20 USD/MWh on top of electricity prices. The premium remains constant and does not depend on the hour of the day or any other factors. In the GREEN scenario, we present an experimental reliability-based premium. At the core of many reliability indicators is a probability of lost load (electricity supply not meeting demand) [32]. Since our conceptual model is entirely deterministic, no probabilities. Thus, A premium is modeled in two different scenarios. The YELLOW scenario is modeled with a classic fixed premium of 20 USD/MWh on top of electricity prices. The premium remains constant and does not depend on the hour of the day or any other factors. In the GREEN scenario, we present an experimental reliability-based premium. At the core of many reliability indicators is a probability of lost load (electricity supply not meeting demand) [32]. Since our conceptual model is entirely deterministic, no probabilities. Thus,

our lost load *LL* is calculated simply as the demand *D* minus the available supply *S* for each hour of the day *h*.

$$LL\_h = D\_h - \mathcal{S}\_h.\tag{1}$$

Then, we set the ceiling of the premium *Pmax* at 40 USD/MWh. We compute the hourly premium as a fraction of the maximum premium corresponding to the hourly lost load compared with the maximum lost load of the day.

$$P\_{\hbar} = P\_{\text{max}} \ast \frac{LL\_{\hbar}}{LL\_{\text{max}}}.\tag{2}$$

Thus, when the need for power at a particular hour is greater, the reliability premium is higher. The hourly profile of the reliability premium, in turn, defines the profitability of technologies with different generation profiles. The need for reliability is translated into an investment incentive.

This is a simplified calculation of the reliability-based premium for the current stylized case with a fully deterministic model. In reality, many variable and stochastic factors should be taken into account, including weather, electricity demand, operating profiles of power plants, etc. With those factors taken into account, the premium should be based not on a deterministic indicator but on one of the proper indicators for a 'useful' capacity, for example, based on the loss of load probability, as discussed in Section 2.2. A detailed analysis of existing approaches to calculating the contribution of renewable energy sources to system reliability is presented in [17].

For the GREEN scenario, the auction is run in two phases. First, the reliability premium is calculated based on the current reliability situation (Figure 2a), and the most profitable technology type is selected. Then, the reliability indicator *LL<sup>h</sup>* is recalculated, taking into account the generation profile of the selected technology. The reliability premium *P<sup>h</sup>* is recalculated as well, taking into account the updated reliability indicator. The updated premium then may change the profitability of different technologies.
