4.2. Opportunity Cost for Wind Providing Ramp Products
In Case 1 and Case 2, the prices for wind providing energy and the ramp-up product are the same. Therefore, when wind curtails the power output to provide the ramp-up product, it will receive the same amount of revenues from providing the ramp-up product. In current markets, wind power will receive some subsidies for its power production, like emission free credits. Therefore, the opportunity cost for providing the ramp-up product with wind curtailment included the lost subsidies.
For instance, if there is a subsidy of $5/MW for wind power, in Case 1 the opportunity cost of the curtailed 15 MW of wind power would be $5 × 15 = $75 in which $5 is the subsidy price. Although, some markets have a higher subsidy price for wind, this subsidy is prone to decline due to the cost of wind decreasing. Because the wind power is forecasted to ramp up in the next interval, the 5 MW wind ramp-up (185–180 MW) will lead to a revenue of $30 × 5 = $150 from providing the ramp-up product. The opportunity cost would be $75 − $150 = −$75, which means there is a net-profit for wind by providing the ramp-up product. Therefore, when both wind and load ramp up, wind power can lead to more money being earned by providing the ramp-up product, even if it commits more capacity towards the ramping-up product (under the given cost and subsidy assumptions). In Case 2, because wind power is forecasted to ramp down in the next interval, the wind curtails 25 MW to provide a 20 MW ramp-up capability for the system’s next interval ramp-up requirement. The opportunity cost is $(30 + 5) × 25 − $20 × 30 = $275, meaning wind would lose money for providing the ramp-up product in this case.
However, the opportunity cost to provide the ramp-down product is not as intuitive as that of the ramp-up product. In Case 3 and Case 4, the wind still generates the maximum available power at current interval to provide the ramp-down product. But in the next interval, the wind power output should ramp down. For instance, in Case 3, wind should hold the power output at 110 MW (180 MW − 70 MW) for the next interval. Therefore, if wind has an available power output of more than 110 MW in the next interval, there will be a curtailment loss for wind in the next interval. Then, the opportunity cost is like that of the ramp-up product. In Case 3, the wind curtailment for the next interval is 75 MW (185 MW − 110 MW). In Case 4, the curtailment is 65 MW (175 MW − 110 MW). The price for the ramp-down product is 0, which means that there is no revenue for providing the ramp-down product. So, the opportunity cost is 75 MW multiplied by the LMP in the next interval plus the subsidy price. Therefore, when both wind and load ramp down, the opportunity cost for wind providing the ramp-down product is less than it is when the wind ramps up and the load ramps down because the potential wind curtailment is lower in the former case.
For both the ramp-up and ramp-down products, when the wind ramp direction coincides with the load ramp direction, the opportunity cost for wind providing the ramp products is less than that when the wind ramp direction is opposite of the load ramp direction.
4.3. Ramp Price for Wind Ramping Products
In this subsection, wind offer prices for ramp products are developed, such that wind can recover the opportunity cost and participate more actively in the ramp market.
In Case 1, when the wind ramps up, the total revenue to provide the ramp-up product can be formulated as
where
is the total profit for providing the ramp-up product;
is the current interval energy LMP;
is the offer price for the ramp-up product;
is the wind forecast ramp-up capacity;
is the subsidy price received by wind for the energy; and
is the total capacity for the ramp-up product provided by the wind.
Then, when
wind power can earn a positive profit through providing a ramp-up product.
In Case 2, when the wind ramps down, the total revenue is
where
is the wind forecast ramp-down capacity.
Then, when
wind power can earn a positive profit by providing the ramp-up product.
For the ramp-up product, because the potential opportunity cost is caused by the wind curtailment at the current time interval, and because this cost is already included in the objective function in (5), if the ramp-up offer price is given by (109) or (111), the wind power opportunity cost for providing the ramp-up product can be recovered. Then, the strategic offering model can endogenously optimize the wind power output and the ramp-up capacity to maximize its profit.
For the ramp-down product, although the lower bound of the offer price can be formulated via a similar method as (109) and (111) in order to recover the opportunity cost in the next time interval, this can change the generation dispatch at the current time interval and lead to a suboptimal solution for wind power scheduling at the current interval. For instance,
Table 4 shows the results with a fixed ramp-down offer price (
$40/MW for the ramp-down product) and without the fixed offer price for wind power (the lower limit is
$0/MW for the ramp-down product).
Figure 4 demonstrates the generation dispatch under the two scenarios.
Table 4 shows that although setting the ramp-down offer price can increase the clearing price for the ramp-down product, it also reduces the energy LMP, which leads to less total profit for the current time interval. When the ramp-down product offer price is 0, the system can schedule more ramp-down capacity from wind power. Therefore, expensive generation, such as Gen4, is not scheduled. However, the generation dispatch shown in
Figure 4 demonstrates that with this fixed
$40/MW wind offer price for the ramp-down product, the expensive Gen4 increases its power output to provide the ramp-down product. The total ramp-down capability is 50 MW, but the ramp-down requirement is 70 MW. Therefore, the system LMP changes, and the wind power profit is less.
The opportunity cost for the ramp-down product is the potential wind curtailment cost in the next time interval, which is not explicitly included in the objective function in (5).
In Case 3, when the wind ramps up while providing the ramp-down product, the revenue is
where
is the next interval energy LMP forecast value.
In Case 4, the revenue is
With the objective function modeled in (112) and (113), when providing the ramp-down products, the wind can optimize its power and ramp-down capacity to maximize its profit at the current time interval. But, the opportunity cost for providing the ramp-down product is still not recovered in this objective function. To compensate for the wind power’s service of the ramp-down capacity and to maintain market efficiency, some out-of-market measurements should be provided.
Note that , , , and are the ISO’s economic dispatch results, which means that the wind power producer will not know the exact values of these variables before the strategic offer model is solved. Therefore, they should offer the ramp-up product prices based on the forecast of these variables from the historical data.
The wind dispatch with the ramp-up offer price lower limit and new objective function for the ramp-down product are shown in
Table 5 and
Table 6. For Case 1, because the wind ramps up with the same load ramp direction, the ramp-up product price is still 0. For Case 2, the wind ramp-up price is
$13.75/MW, as shown in Equation (28). Therefore, the clearing price for the ramp-up product increases to
$43.75/MW, which recovers the opportunity cost of curtailing wind to provide the ramp-up product. For Case 3 and Case 4, compared to
Table 2 and
Table 4,
Table 5 shows that when considering the potential wind curtailment opportunity cost, the wind schedules less ramp-down capacity, and the clearing price for the ramp-down product increases. The increment for the ramp-down product price does not significantly reduce the energy LMP; therefore, the profit at the current interval is reduced only slightly. Considering the potential wind curtailment cost in the next time interval, in Case 3, the opportunity cost is
$24.475 × 40 =
$974, as shown in
Table 5. Here
$40/MWh is the forecast LMP
$35/MWh in the next interval (from
Table 4 and
Table 6, this forecast is reasonable) plus the
$5/MWh subsidy. In
Table 2 and
Table 4, the opportunity cost of providing the ramp-down product in Case 3 is
$70 × 40 =
$2800 and
$30 × 40 =
$1200 (Not fixed, Case 3 in
Table 4), respectively. Obviously, the opportunity cost of providing the ramp-down product is reduced significantly in
Table 5. As shown in
Table 3,
Table 4, and
Table 6, all the cases can be solved within one second which demonstrates that the computational burden of the proposed model is not high.
Figure 5 shows that the generation dispatch varies with the system’s ramp requirement. Compared to the ramp-up requirement, in the ramp-down scenarios, such as Case 3 and Case 4, the expensive generators, such as Gen4, increase their power output to provide ramp-down capacity. Therefore, the ramping requirement changes the generation dispatch and the LMP. If there is a shortage in ramping resources, the dispatch and LMP will be distorted from the reasonable values.