The effect of variability-mitigating market rules on the operation of wind power plants

Abstract

In power systems with many wind generators, market rules have been slowly changing in order to mitigate or internalize the system costs relating to wind variability. We examine several potential market policies for mitigating the effects of wind variability. For each market policy, we determine the effect that the policy would have on the operation and profitability of wind plants, using time series analysis to estimate the actions of profit-maximizing wind generators acting as price takers. We identify policy scenarios that significantly reduce short-term (30-min) wind fluctuations while having little effect on wind plant revenue. For example, in a scenario where the ramp-rate of wind is limited and ramping violations are assigned a small monetary penalty, a loose ramp rate limit (40 % per 15-min period) can reduce 30-min fluctuations by 35 % while reducing wind plant revenue by only 0.2 %. The novel market-based strategies investigated in this work may enable reductions in the overall system cost of wind integration and can be designed so that both wind generators and system operators are better off than under the status quo.

Appendices

Appendix A: Alternative operational strategies

In every scenario examined above, the wind plants are allowed to purchase energy storage, in the form of a sodium sulfur (NaS) battery. For several reasons, none of the studied scenarios result in wind purchasing energy storage. First, the high capital cost of this device means that only a very value-intensive application will result in profitable operation. Because the focus of this work was to identify market scenarios that would have only minor effects on wind generators, the potential value of storage is small. Second, the use of energy storage was limited to the time-shifting of wind energy, so the extra benefit of charging from outside resources is lost. Third, the value of storage is greater at shorter time-scales [15] and this work used a time step of 15 min. It is possible that the value of storage would increase significantly in markets where the ramping of wind was limited on time-scales shorter than 15 min.

Another strategy that wind generators were allowed to choose was curtailing the wind output slightly to produce an operating reserve that could be used to buffer down-ramping. This strategy only makes sense in the market scenario where wind is penalized for down-ramping, though it was never chosen as a strategy because the value of the lost wind energy was always greater than the value of the operating reserve. The revenue to wind plants is reduced by an average of 3.25 % when the output is curtailed by 1 % of nameplate capacity.⁴ Under the strictest ramp limitation (2 % up-and down-ramp rate, penalty of five times frequency regulation), the value of a 1 % operating reserve is about half of the value of the energy. But under the preferred ramp limitation of 40 % per 15-min time step, the value of the operating reserve is negligible because the ramp limit is normally encountered only during wind curtailment, when wind generators can already control their ramp rate. Thus, curtailment to produce a reserve does not appear to be a good strategy for wind plants under any of the scenarios examined. As with the value of storage, curtailment to produce a reserve might be more valuable if evaluated under shorter time scales, such as the frequency regulation services provided by wind generation in Ireland discussed in the introduction.

1.1 A.1 Curtailment to produce an operating reserve

The “curtailment to produce a reserve” operational strategy is modeled by assuming that a wind plant curtails its power output by a fixed amount (a percentage of nameplate capacity, in MW), in order to create a small operating reserve. When the wind drops off quickly, the wind plant can use the reserve to reduce the observed ramp rate, by increasing the actual power output closer to the potential power output. For example, a 100 MW wind plant could always curtail 1 % of the available wind power in order to buffer sudden drops in the wind. If this wind plant is producing at nameplate capacity, then a 1 % curtailment is 1 MW, and the wind plant’s actual output is 99 MW. If the wind drops suddenly to a level where the wind plant is only able to produce 95 MW, the wind plant can manage the power output change, keeping it to a 4 MW step change (rather than the 5 MW change without the intentional curtailment).

1.2 A.2 Use of energy storage

The energy storage option allows the wind plant to install a sodium sulfur (NaS) battery, which can then be used to either increase wind plant revenue or decrease variability. The NaS battery is modeled after the currently-available PQ modules produced by NGK Insulators, the only established supplier for this technology [22]. Because NaS batteries are commercially available only in a pre-defined modular form as noted above, their power-to-energy ratio is fixed. NaS batteries require a temperature of $\sim$325 $^\circ$C to operate and thus require a continual “maintenance power” to maintain that temperature (accounted for in this model). NaS batteries have a continuous power rating of 0.05 MW, and have a manufacturer-defined pulse power capability (also accounted for in the model) under which they can provide up to four times the normal power rating for 15 min, making their maximum power output 0.2 MW. NaS batteries were chosen as the energy storage technology because they are a relatively established energy storage technology, have an appropriate power to energy ratio for this application, are modular and appropriate to the scale of a wind plant, and have been utilized for wind integration in the past [10, 17, 22]. Table 4 shows the NaS battery properties used in the battery model.

Table 4 NaS battery properties examined and their base-case values

NaS batteries are assumed to be co-located with the wind plant and are operated to maximize revenue. While the batteries could be used with the goal of reducing power fluctuations, an energy storage owner is unlikely to do so unless it is either the most profitable mode of operation or they are directed to by market protocols. To maximize revenue, NaS batteries are charged whenever the apparent energy price to the wind plant (including subsidies and penalties) is below a fixed “charge price”, and discharged whenever the effective energy price is above a fixed “discharge price”. Between the charge and discharge prices, the storage does nothing. Several alternative storage operational strategies were examined, including adjusting the charge/discharge prices as a function of state-of-charge, season, day of the week, or prevailing energy price, but the resulting revenues were similar or lower than those from the simple model. The optimal charge and discharge prices are determined separately for each wind plant in each policy scenario using a genetic algorithm optimization that searches for revenue-maximizing values of the charge and discharge prices.

The operation of storage under perfect information is also examined and compared with the simple model described above. Under the perfect information model, at each time step the operator looks ahead at the wind output and energy prices over the next 24 h. The revenue-maximizing operation of the NaS battery over the next 24 h is calculated, but only the operation in the current step is retained. In other words, an entire day of battery operation is calculated in order to determine the charge/discharge level in a single time step. The operation of the battery is constrained to end the 24-h look-ahead period at the same charge state that it began with, though the boundary effect is insignificant because the NaS battery is able to charge and discharge several times over a 24-h period.

A genetic algorithm was used to determine the “charge price” and “discharge price” that resulted in the highest wind+battery revenue (Fig. 13). Both the charge and discharge price were relatively high, and were consistent across different market policy scenarios. Under the “no rules” scenario, the average charge price was $62/MWh, meaning that the NaS battery would charge whenever the energy price dropped below $62/MWh, and the battery would discharge only when energy price was above $175/MWh. The overall revenue was not very sensitive to changes in these values: a 10 % change in either parameter resulted in less than 1 % change in revenue. The elevated charge price kept the energy storage fully charged most of the time, and the battery was only discharged when the electricity prices were very high. This is because most of the revenue from the storage came during infrequent price spikes, and the optimal strategy was to maintain a high state of charge to capture all the possible revenue from a potential future price spike. This result is similar to Fertig and Apt’s finding that an optimally-dispatched compressed air energy storage system in ERCOT would store energy 91 % of the time and only discharge 3 % of the time, as it attempts to capture all of the potential value of price spikes [13]. Figure 13 provides an example of the battery output under perfect information and the simple “buy below/sell above” model.

Fig. 13

Example of battery operation under perfect information and a simple “buy below/sell above” operation over 60 h. The “sell above” and “buy below” prices used for the simple model are shown in the dashed lines on the top part of the figure. The battery power output is shown in percent, from +100 % (full discharge) to $-$100 % (full charge). Under perfect information, the battery is able to extract value from smaller price changes (such as hour 17) while retaining enough energy for price spikes (hour 23), and charges when electricity price is lowest (hour 32). Under a simple “buy below/sell above” operation, the battery only discharges during relatively high price spikes and tends to recharge to capacity immediately afterwards

Without any wind-related market rules, where it is providing only time-shifting of wind energy, a NaS battery earns revenue equivalent to around 17 % of its annualized cost under a simple “buy below/sell above” operation, resulting in a large net loss. Under very strict rules, such as a 1 % up- and down-ramp limit and a penalty of five times the frequency regulation price, the value of a NaS module increases only a few percent to around 20 % of annualized cost. While there are other costs involved, the primary contributor to annualized cost is the capital cost of the storage, which is $240 K per module or $700/kWh. Given the assumptions and limitations discussed above, NaS batteries only become a profitable investment for the wind plants at a cost of $120–$150 per kWh, even under the stricter scenarios discussed above.

The value of storage improves significantly if the battery is operated under perfect information, knowing the future prices and wind energy. This is due primarily to the ability to take complete advantage of energy price spikes in both the positive and negative direction. Under perfect information and a scenario where wind is not penalized for variability, a NaS battery recovers around 33 % of its annualized cost. This increases slightly to around 38 % under the strictest ramp-rate limitation. Even under perfect information, storage is profitable only if the cost is less than $250/kWh. While more advanced wind and price forecasting could make the operation of energy storage more profitable, most of the increased revenue from the perfect information operation comes from taking full advantage of price spikes, which are very difficult to predict [18, 24, 25, 29, 30].

Appendix B

In the scenarios with penalties for over-ramping or diverging from forecast, the penalties are based on the frequency regulation prices. This is done because frequency regulation prices reflect the willingness of generators to change their output levels, which changes over time. For example, if wind ramps up too quickly, other generators must ramp down to compensate. The regulation down price indicates the payments that a generator requires to perform this ramp-down. If generators are very willing to ramp down, then the regulation down price will be low and the wind plant will not be (and should not be) heavily penalized. Alternately, if wind picks up quickly in a period where generators are unwilling to ramp down, the wind generator will face higher penalties.

It is important to note that while frequency regulation prices are related to the ability of generators to ramp up and down over 15-min time steps, this is not how frequency regulation service is actually used. In the absence of an actual rapid response (5-min) ancillary service, frequency regulation prices are used as a substitute. The energy price is not included in the penalty scheme because any replacement energy is already paid from the market. For example, if a wind plant suddenly drops by 1 MW (over 1 h) and another generator ramps up 1 MW to compensate, the market will pay the prevailing energy price for the replacement MWh to the generator. Because 15-min penalty prices are required, the hourly frequency regulation prices are divided by four to generate four 15-min penalty prices for that hour. Penalties for over-ramping are assessed based on the change since the last time step, rather than changes since the last point where the wind plant was in compliance.

One relevant question regarding implementation of a ramp rate limit that has a large effect on both revenue and fluctuations is whether a wind plant’s output should be tied to the most recent non-violation power output or if it should be tied only to the output in the prior time step. If the output of a wind plant is tied to the last point at which it did not violate the ramp limit, then a wind generator is penalized for any energy delivered above the original ramp-up profile. Alternately, the wind generator output can be related only to the energy output in the previous step, and is thus charged an over-ramp penalty in only one time step (the difference in the two potential rules is illustrated more clearly in Fig. 14). This latter version of the rule is more forgiving towards over-ramping, and we find that it also results in much lower penalty charges to wind plants while having approximately the same effect on variability. From the system perspective, there is little reason to tie a wind generator’s current power output to past power outputs (except the immediately past output). Throughout this work, the ramping constraints are tied only to the immediately prior power output, as this is better for both wind generators and the electricity system.

Fig. 14

Example output of a wind plant under two alternative ramping rules when only up-ramping is limited. The dashed blue line shows the output of a wind plant when the allowed power output is based on a fixed ramp-up from the last time step that did not violate the ramp limit. Under this rule, the wind plant is constrained to the ramp-up that starts around minute 200, and goes to full power output whenever the price of energy minus the penalty cost results in profit for the wind generator (around minutes 225, 450, and 500), but returns to the original line when energy price is no longer higher than the penalty. This can cause significant short-term variability, as wind output goes back and forth between the allowed ramp-up and maximum energy output. The solid red line shows the output of a wind plant when the allowed power output is the previous power output plus a limited up-ramp. When the wind plant violates the ramp limit at minute 225, it only pays the violation penalty during that time step and is no longer coupled to the original ramp-up line

Appendix C

1.1 C.1 The effect of different ramp rate limitations

It is natural to expect that using a much tighter ramp limitation should decrease variability significantly, though this was not found to be the case in the ramp rate-limited market scenarios that we studied. Figure 15 illustrates why a tighter ramp rate may result in little or no additional reduction in variability. Under any ramp rate limit, the wind plant will occasionally determine that the value of the available wind energy is greater than the penalty for violating the ramp rate, and ramp up to full power output. Under a tighter ramp limit, the power output of the wind plant will often be further from full output, resulting in a larger change in power output when the wind plants ramps up to full power. In general, using a tighter ramp limit results in fewer but sharper power output changes. Figure 15 is for a wind plant facing only an up-ramp limit, but the effect is very similar for a market scenario where wind plants have both up- and down-ramp limits.

Fig. 15

Example wind power output under no ramping limit, an up-ramp limit of 1 % per 15-min time step, and an upramp limit of 20 % per 15-min step, showing why a tighter ramp rate limit can result in higher short-term fluctuations. At 180 min, the tighter ramp limit results in a much smaller change in power output than the 20 % ramp limit or no limit, as expected. At the point around minute 300 of this example, the 1 % ramp limit produces a sharper change in power output than the 20 % ramp limit. Under both ramp rates, the wind plant finds that the value of the available wind energy is greater than the penalty payment and decides to produce at minute 300, but under a 1 % ramp rate the power output comes up from a much lower level. A similar sharp change can be seen for the wind plant under a 1 % ramp limit around minute 400, while the 20 % ramp rate scenario results in a more gradual increase

1.2 C.2 Underforecasting results

Figure 16 shows the average reduction in revenue and RMSE of wind plants under different deadband and penalty levels when underforecasting is permitted. When underforecasting is allowed, the situation is very different than when it is not permitted, as tighter deadband values with low penalties are best able to improve adherence to forecast while having little effect on wind revenue. This is because most wind plants use some amount of underforecasting and are better able to match a slightly diminished wind forecast. With underforecasting permitted, the improvements in RMSE are much better that when it is not permitted, resulting in a reduction in RMSE from 26 to 18 % with a wind plant revenue loss of around 1 %.

Fig. 16

Average change in revenue and RMSE of the collection of 16 wind plants under a market scenario where wind generators are penalized for diverging from the 6-h forecast and wind generators are permitted to report a smaller-than-actual capacity (underforecasting). RMSE is expressed as percent of the actual nameplate capacity

Figure 17 shows the RMSE and change in revenue for each wind plant in a market scenario where wind generators are penalized for diverging more than 10 % from the 6-hour forecast and underforecasting is permitted. The RMSE values for the 16 wind plants range over a factor of two, though small improvements are apparent for individual wind plants as the penalty is increased. The change in revenue is much less variable, though that variability increases as the penalty is increased. This is due to the natural ability of certain wind plants to better adhere to forecast.

Fig. 17

Change in revenue and RMSE for 16 wind plants under a market scenario where wind generators are penalized for diverging from the 6-h forecast and wind generators are permitted to report a smaller-than-actual capacity (underforecasting). The results shown are for a deadband of 10 %, similar to the left-most line in Fig. 2, though these RMSE values are for individual wind plants rather than the collection of wind plants. RMSE is expressed as percent of the actual nameplate capacity