Analyzing spot prices in a context with high penetration of variable energy resources: the
role of the pricing rules
Andrea Veiga, Instituto de Investigación Tecnológica, Universidad Pontificia Comillas, Madrid, Spain, Phone: +34915422800,
<Andrea.Veiga@iit.upcomillas.es >
Pablo Rodilla, Instituto de Investigación Tecnológica, Phone: +34915422800, <Pablo.Rodilla@iit.upcomillas.es>
Carlos Batlle, Instituto de Investigación Tecnológica, also with the MIT Energy Initiative, Cambridge, MA, US
Phone: +34915406306, <Carlos.Batlle@iit.upcomillas.es>
Overview
A large penetration of highly variable, less dispatchable and hardly predictable energy resources (referred as Variable Energy
Resources, VER) is expected to significantly change the way electric power systems are operated. These changes in operation
will eventually lead to changes in production costs, and thus also to changes in short-term prices.
From the point of view of the economic side, the changes that VER can introduce in the scheduling regime of the rest of the
generating facilities in the system can have a key impact both in the short and in the long term. In this paper, we focus on
assessing how spot prices can be affected by the penetration of VER. We first qualitatively analyze how the operating cost of
some conventional thermal units increase due to increasing cycling operation. This effect is particularly acute in systems in
which storage facilities are scarce, since VER can change to a large extent the scheduling regime of the rest of the generating
facilities in the system, increasing the need of cycling them. The VER intermittency together with this resulting alteration of the
operation of the plants (in particular, the increase in the number of starts or in the number of hours producing at lower
efficiency) may lead to significantly different market price patterns.
The size of this change will depend on the pricing mechanism implemented in the system. In this paper, we focus on assessing
the different market outcomes that could be expected in this new context when two alternative pricing rules are considered: on
the one hand, a linear (non-discriminatory) pricing rule (where prices are assumed to ensure the recovering of operation costs to
all units), and on the other hand, a non-linear pricing rule that needs the inclusion of discriminatory side-payments on a
differentiated per unit basis for the uniform prices defined are not capable of ensure the full recovery of all operating costs.
We argue that, due to the increased impact of the non-convex costs of conventional thermal plants, the growing large
deployment of VER increases the differences between the two aforementioned pricing contexts in terms of both the demand
payments and the income perceived by the generating units. In order to illustrate and support the discussion, we present a case
example where we compare the market results (in both pricing contexts) obtained in two scenarios; a baseline scenario with no
VER and an scenario characterized by a massive penetration of solar photovoltaic.
Methods
Since our objective is to evaluate the impact of the pricing mechanism implemented in the presence of large amounts of VER
(in our particular case solar photovoltaic) on the market results, it is crucial to count on a model able to properly capture the
cycling-related costs. To do so, we have resorted to a short-term unit commitment model that not only takes into account the
traditional sources of cost but also represents in detail the not-so-well-known cost associated to the Maintenance Interval
Function (MIF), a source of cost highly related to the cycling operation. This MIF mainly depends on the number of starts and
the number of firing hours (two variables that serve to roughly characterize the operation regime of a plant). This extended unit
commitment model provides the detailed scheduling and the hourly marginal costs. Once these marginal costs are known, we
evaluate ex-post the side-payments (corresponding to the non-linear pricing rule) and uplifts (for the case of the linear one) that
guarantee that all the scheduled units fully recover their non-convex costs.
We present a real-size case example in order to illustrate our research findings. We analyze the market outcomes to be expected
for both pricing rules for two different scenarios, without and with a large presence of solar photovoltaic. The system
considered is fully thermal, i.e. the net demand (obtained after subtracting the hourly solar photovoltaic profile and the hourly
nuclear production) has to be supplied with the conventional thermal plants. For the sake of clarity, in the case example only
photovoltaic and CCGT plants have been considered.
Results
We argue that a large penetration of solar photovoltaic increases the differences between the two alternatives to calculate
market prices. This is an important result, because this yields not only to different payments for consumers in the short-term,
but also will affect the capacity expansion in the long-term, since the income the different generating units perceive in the
market are different in each particular design.
Side payments in the non-linear pricing context
The marginal costs represent the prices that remunerate the hourly production of all generators. In this case example, the
marginal cost in each hour is equal to the variable cost of a ccgt plant due to the simplicity of the system considered. However,
these marginal costs do not include non-convex costs such as no-load costs and start-up costs. This is the reason why additional
payments may be necessary so as to ensure the recovery of total production costs.
In Figure 1 (right), each position of the x-axis represents a different thermal plant and the corresponding y-value the sidepayment it would receive under the discriminatory pricing rule. It can be seen how in the case with solar photovoltaic the
average side payment (9.44 $/MWh) is higher than in the case without solar photovoltaic (7.70 $/MWh). This is because, as we
analyze in the paper, the start-up adder component is higher when solar enters in the system due to the fact that it increases the
need of cycling conventional thermal generating units.
Uplifts in the linear pricing context
As a consequence of the change in the net load shape solar photovoltaic introduces and in the hourly period in which the peak
load situates, we can see in Figure 1 (left) how the uplifts are set in different hourly periods. The additional remuneration these
uplifts provide is larger in the case of solar photovoltaic (w/ pv) due to the cycling costs increase in the presence of solar.
$/MWh
160
140
$
120
120000
w/o pv
w/ pv
80000
100
80
w/o pv
60
w/ pv
40000
40
20
0
0
1
3
5
7
9
11
13
15
17
19
21
23
Hours
CCGT
NUCLEAR
Figure 1. Uplifts added to hourly prices (left) and side payments required by each one of the units considered (right)
Remuneration of a base-load unit in each pricing context
We next focus on the income perceived by a base-load unit operating at a constant base-load regime. In the next table we have
gathered the resulting income in the four cases (depending on the solar PV scenario and the pricing rule considered) for one
1000 MW nuclear power plant.
Table i. Average price for a base-load plant depending on the solar PV production and pricing rule scenario
$/MWh
Linear pricing
Discriminatory
Difference in %
With solar PV
63.58
49.55
28.31
Without solar PV
62.16
49.55
25.44
We can see how the difference between the discriminatory pricing rule and the linear pricing rule is larger in the case with large
VER penetration. As we have repeatedly insisted, increasing VER increases start-up costs, and these start-up costs are
perceived by all units in the linear pricing scheme.
Conclusions
In this paper, we analyze the influence of the pricing rule implemented (linear pricing or non-discriminatory pricing) in the
market results. By means of an illustrative stylized case example we argue that a large penetration of solar increases the
differences between the two alternatives to calculate market prices. The selection of the pricing mechanisms not only results in
different payments for consumers (which are lower in the non-discriminatory context) but also will affect the future generation
mix, since in real systems, the income perceived by the different generating technologies will be different in each particular
context.
Main references
Baldick, R., Helman, U., Hobbs, B. F., and O’Neill, R. P., 2005. “Design of Efficient Generation Markets”. Proceedings of the
IEEE, vol. 93, n. 11, pp. 1998-2012, November 2005.
O’Neill, R. P., Sotkiewicz, P. M., Hobbs, B. F., Rothkopf, M. H.., Stewart, W. R., 2005. Efficient market-clearing prices in
markets with nonconvexities. European Journal of Operation Research, vol. 164, iss. 1, pp. 269–285.
Schweppe, F. C, M. C. Caramanis, R. D. Tabors and R. E. Bohn (1988). Spot pricing of electricity. ISBN 0-89838-260-2,
Kluwer Academic Publishers, Boston, MA, 1988.