# Market Values of Variable Renewable Energy Sources

## Energy Value, Capacity Value, Storage, and Reserve Obligation

The deployment of variable renewable energy (VRE) has profound impact on both the power system, the corresponding electricity market, and the society as a whole. Quantifying these impacts is important for both the policy makers and the renewable energy industry. Here we introduce methods to do the task.

# Energy Value

The energy value of VRE installation is the avoided generation costs of CPP due to VRE generation. Assuming a perfect merit order curve exists in the electricity market (i.e., the price is the marginal cost of the marginal CPP, which is a monotonic increasing function of the RL), we can find the MEV per capacity of VRE installed from the equation in the figure below.

As demonstrated above, due to the monotonic nature of the merit order curve, the MEV of VRE always decreases as more VRE capacity is installed; this holds for short term equilibrium (more on that later).

For the AEV of the VRE fleet, we can integrate the MEV for all the capacity installed and then divide the value by the total VRE capacity, as shown in the figure below.

# Capacity Value

The capacity value of installed VRE comes from the RL reduction it contributes to. As shown in the following figure, after installing some solar capacity, the time of peak RL (t*) is shifted from noon to late noon. Eventually, as more solar gets onto the grid, t* will be shifted to dusk time, when the CF of solar approaches 0.

Mathematically speaking, the partial derivative of RL with respect to time is always 0. Exploiting this fact we can deduce how t* evolves as more VRE capacity is installed, as shown in the following figure.

From the relation between t* and installed VRE capacity, we can deduce that the CF of the VRE at t* always decreases as installed VRE capacity increases, as shown in the following figure. Note that discontinuous jumps of CF(t*) can occur, corresponding to another local maxima of the RL time series. These jumps will only further decrease the CF(t*) as more VRE capacity is installed.

Similar to AEV, the ACV can be obtained by integrating the MCV for all the capacity installed and then divide the value by the total VRE capacity. Yet this methodology falls short when two or more distinguishable VRE technologies exist in the power system.

To fairly allocate the contribution of RL reduction due to installation of different types of VRE technologies, we adopt the **Principle of Equipartition of Contribution** here: we assume that at times when DL exceeds peak RL, every unit of VRE output contributes equally for the marginal RL reduction at that moment. The equation for calculating the ACV of a specific technology type can then be obtained as demonstrated in the figure below.

As an example, using the empirical data of the power system in Taiwan on 23 and 24 July, 2020 (when annual peak DL at day and at night occurred), we can conclude that solar currently has a ACV of 41.4%, while wind currently has a ACV of 10.3%. Note that there is still only one offshore windfarm that is providing reliable output data in Taiwan, so the capacity value of wind is probably underestimated here due to more significant local high frequency fluctuations.

# Short Term vs. Long Term Equilibrium

In the short term equilibrium, CPP portfolio is assumed to be the same, thus MC_CPP does not change. The capacity value of VRE only consists of the benefits of increased supply reliability due to less RL.

In the long term equilibrium, CPP portfolio will be altered due to **Principle of Zero Profit**; CPP with less CAPEX but higher variable costs will be favored under the new RLDC. This might result in higher MEV for VRE. On the other hand, the total CPP fleet will be reduced due to less peak RL, which can be translated to the capacity value of VRE under monetary terms.

# A Word on VRE + Storage

As shown from the example calculation above, the available reduction of RL via VRE installation only will be very limited even with large amounts of VRE capacity. Installation of storage along with the deployment of VRE will provide additional capacity value. Since storage units can be regarded as relatively firm and fully dispatchable, the capacity value it can provide will be its maximum discharge power, multiplied by some malfunction coefficient. Meanwhile the storage unit can gain additional energy value by arbitraging the price spread in the electricity market.

When doing a cost-benefit analysis for a marginal unit of storage, the CAPEX per charge / discharge power should be taken into account. In addition, the minimum required discharge time to achieve RL reduction will also be an important factor affecting the CAPEX.

To determine this minimum required discharge time, one may conduct the following procedure:

- Construct two series {p_i} and {n_j}, where i represents the i-th continuous interval for which RL > RL_c and j the j-th continuous interval for which RL < RL_c ; p_i and n_j are the time durations of the continuous intervals.
- Starting from p_2 and the previous corresponding value in {n_j} (n_c), update p_2 <- max(p_1 — n_c*eta, 0) + p_2, and continue this procedure for the rest of the series.
- Once all {p_i} updated, the maximum of the series will be the minimum required discharge time to achieve RL reduction to RL_c.

*(Eta, the efficiency loss during a full charge cycle, will also incur an additional cost due to more electricity demand: an additional demand of (1/eta — 1) per unit of discharge energy will be needed in total. This can nevertheless be considered when calculating the MEV of the storage unit.)*

Below is an example of how the minimum required discharge time for the marginal storage unit should be calculated, with the RL profile of Germany in week 30, 2020. The peak RL was around 36 GW. To reduce the peak to 35 GW for the week, only a few hours of discharge time would be needed. Reducing the peak to 30 GW will require around half a day of discharge time. Reducing the peak to 25 GW will require around two days of discharge time.

VRE, when installed with storage units, might provide additional capacity value to the power system. This can be demonstrated by the following three graphs: in this specific case, VRE and storage together can provide more capacity value than the sum of the capacity value when only one of these technologies is deployed.

# A Word on Fair Reserve Obligation for Retailers

To provide sufficient capacity to meet the long term reserve margin requirements, retailers in the electricity markets are usually given reserve obligation quotas which they must meet by the generators or other flexible resources (virtual power plants, large scale batteries, etc.) they sign contracts with, or by procuring surplus reserve capability from the third party.

A fair allocation of reserve obligation for retailers should also follow the **Principle of Equipartition of Contribution**: the average market share of a retailer during the time intervals which a marginal unit of reserve capacity is used should be the share of the corresponding unit of reserve capacity that retailer is responsible for. The total reserve obligation for that retailer can then be obtained by integrating the shares of the responsibility along the DLDC, as shown in the figure below.