# Co-optimization of Energy and Reserve with Incentives to Wind Generation:
Case Study

Yves Smeers, Sebastian Martin, and José A. Aguado Y. Smeers is with the Center
for Operations Research and Econometrics (CORE) at Université Catholique de
Louvain (UCL), Belgium (e-mail: yves.smeers@uclouvain.be)S. Martin and J. A.
Aguado are with the Department of Electrical Engineering, University of
Malaga, Malaga, Spain (e-mail<EMAIL_ADDRESS>jaguado@uma.es). Their work was
supported in part by the Spanish Ministry of Economy and Competitiveness
through the project ENE2016-80638-R, and in part by the University of Málaga
(Campus de Excelencia Internacional Andalucía Tech).

###### Abstract

This case study presents an analysis and quantification of the impact of the
lack of co-optimization of energy and reserve in the presence of high
penetration of wind energy. The methodology is developed in a companion paper,
Part I. Two models, with and without co-optimization are confronted. The
modeling of reserve and the incentive to renewable as well as the calibration
of the model are inspired by the Spanish market. A sensitivity analysis is
performed on configurations that differ by generation capacity, ramping
capability, and market parameters (available wind, Feed in Premium to wind,
generators risk aversion, and reserve requirement). The models and the case
study are purely illustrative but the methodology is general.

###### Index Terms:

co-optimization, energy and reserve, complementarity conditions, market
equilibrium

## Notation

Only the terms used in this Part II are included in this section. For a
complete list of terms see Part I.

###  -A Indices and sets

1cm

Dispatchable generators, $g\in G$.

Wind turbines, $w\in WT$.

Index and set for scenarios, $k\in\Omega$.

###  -B Parameters

0.8cm

Upper/lower factor for required up. reserve (p.u.).

Lower bound factor for committed downward reserve respect to the committed
upward reserve (p.u.).

Upward/Downward ramping slope respect to the generation capacity (p.u.).

Slope of gen. cost for dispatch. gen. $g$, (€/MWh).

Premium to the schedu. wind gen., (€/MWh).

Balancing reserve factor for wind turbines, (p.u).

Balancing reserve factor for dispatch. gen., (p.u.).

Constant of the inverse demand function, (€/MWh).

Confidence level for firm Conditional Value at Risk (CVaR), $\Theta\in(0,1)$.

Parameter for ramping availability, $\Lambda\in[0,1]$.

Slope of the inverse demand function (€/(MWh)2).

Level of risk aversion, $\Psi\in[0,1]$, zero is risk neutral.

###  -C Variables

Primal variables 1.22cm

Energy sales of the firm in day-ahead, (MWh).

Committed upward/downward reserve capacity from dispatchable generator $g$,
(MW).

Scheduled generation of dispatchable unit $g$, (MW).

Scheduled generation of wind turbine $l$, (MW).

Dual variables (all in €/MWh) 1cm

Upper bound committed upward/downward reserve.

Lower bound for committed up./down. reserve.

##  I Case Study: Description and Data

The case study is inspired by a phenomenon that affected the dynamics of
European generation in the period 2008-2013 [1] and still persists in moderate
form today [2, 3, 4]. Existing flexible Combined Cycle Gas Turbines (CCGT)
necessary to the system because of their contribution to reliability and
flexibility became unprofitable, with the consequence that special non market
arrangements had to be found to retain them in the system. This situation was
summarized in [5]: “There’s plenty of flexibility, but so far it has no
value”. The statement can be interpreted in two ways: either the system is
awash with flexibility and its short-term price is effectively null, which is
a transient phenomenon; alternatively the market does not price flexibility in
a correct way, which is a matter of market design. We use the models COM (Co-
Optimization) and EQM (Equilibrium Model) developed in Part I to assess
whether co-optimization of energy and reserve would have significantly
affected the cash flow generated by these flexible units. The analysis is
illustrative but the methodology can easily be scaled up and is only limited
by the capabilities of commercial optimization codes to solve the underpinning
two stages stochastic programs.

We structure the analysis around two questions:

  1. 1.

Can one characterize a range of situations where flexibility, expressed in
terms of reserves requirements, has effectively no value and alternatively,
conditions where it has value? If so, can one characterize situations that
retain flexible equipment in the system?

  2. 2.

Does market design (co-optimization) have an impact on the above? And if so,
how does it depend on market parameters such as wind condition $\mu$, Feed in
Premium $FiP$ to wind, generators’ risk aversion $\Psi$, and reserve
requirement $M_{y}$?

This section I of Part II introduces a case study that considers a number of
configurations of generation capacity (High, Low, and Very Low), ramping
capacity (High, Low), and market parameters (wind availability $\mu$, $FiP$,
risk aversion $\Psi$, reserve requirement $M_{y}$). Section II contains a
discussion of the numerical results. The conclusions in Section III close the
paper.

###  I-A Energy demand

The price and energy demand are endogenous and related by a linear inverse
demand function, (1):

$\displaystyle\textrm{Price}=\Gamma_{0}-\Phi_{0}\\!\cdot\\!(\textrm{Energy
Demand in Day-Ahead})$ (1)

where $\Gamma_{0}=209.78$ (€/MWh) and $\Phi_{0}=0.0056$ (€/MW${}^{2}\cdot$h),
based on a calibration on historical data from the Spanish system. The
confidence level for Conditional Value at Risk (CVaR) is $\Theta=0.95$.

###  I-B Generation, Ramping and Market Configurations

TABLE I: Summary of generation configurations |  | High Gen. | Low Gen. | Very Low | $C_{g}$ | $\overline{R}_{g}\\!=\\!\underline{R}_{g}$ |
---|---|---|---|---|---|---|---
|  | $\overline{X}_{g}$ | $\overline{X}_{g}$ | $\overline{X}_{g}$ |  |  |
$g$ |  Tech. | (MW) | (MW) | (MW) | (€/MWh) |  % of $\overline{X}_{g}$ |
1 |  CCGT | 0 | 3274.98 | 1274.98 | 44.31 | 53.33 |
2 |  CCGT | 0 | 2056.58 | 2056.58 | 43.88 | 53.33 |
3 |  CCGT | 10632.7 | 2153.5 | 2153.5 | 43.45 | 53.33 |
4 |  Nuclear | 1519.23 | 1519.23 | 1519.23 | 10.91 | 2.08 |
5 |  Nuclear | 6053.35 | 6053.35 | 6053.35 | 10.29 | 2.08 |
6 |  Coal | 2035.89 | 2035.89 | 2035.89 | 37.5 | 20 |
7 |  Coal | 5119.13 | 5119.13 | 5119.13 | 38.44 | 25 |
8 |  Coal | 1198.12 | 1198.12 | 1198.12 | 19.77 | 25 |
9 |  Coal | 1945.51 | 1945.51 | 1945.51 | 20.24 | 25 |
|  Wind | 22573.00 | 22573.00 | 22573.00 | - | - |
|  Dispatch. | 28503.93 | 25356.29 | 23356.29 | - | - |
|  Total | 51076.93 | 47929.29 | 45929.29 | - | - |

Three configurations of generation capacity are considered and presented in
Table I. Wind capacity (22.57 GW) and the demand function are identical in all
cases. Dispatchable generation capacities take three values: 28.5 GW (High),
25.35 GW (Low), and 23.35 GW (Very Low). These values can be interpreted as
stages in the retirement of CCGT to restore profitability of the remaining
capacity.

The parameter $\Lambda\in[0,1]$ is described in detail in Part I. It is used
for testing the capability of the system to manage forecast errors on wind
generation. $\Lambda$ sets the ramping capacity already committed in the
scheduled generation to move from a period to the next one. For instance, for
the upward reserve the capacity already committed (not available for
flexibility) is $\overline{R}_{g}\\!\cdot\\!\Lambda\\!\cdot\\!x_{g}$. Two
configurations for ramping capability are considered: Low $\Lambda=1$, and
High $\Lambda=0$. $\Lambda$ takes the same value for all dispatchable
generators in each test.

The characteristics of the six possible combinations of generation and ramping
and the number of the figures reporting the results are given in Table II. The
reference situation is taken as Low ramping with Low generation. We also
consider configurations with low generation and high ramping to develop a
story line.

Four parameters further characterize the market configurations: wind condition
$\mu$, $FiP$ to wind, generators’ risk aversion $\Psi\in[0,1]$, and reserve
requirement $M_{y}$ by renewable generation. Eight configurations, listed on
Table III, are considered in the case study. We refer to those configurations
in the figures by using the abbreviated name in the columns’ head in Table
III.

TABLE II: Summary of data for generation and ramping configurations Config. | Fig. | Disp. Gen. | Wind Gen. |  Ramp. ($\Lambda$)
---|---|---|---|---
|  | (GW) | (GW) | (p.u.)
HH (High Gen. High Ramp.) | 1 | 28.50 | 22.57 | 0.00
HL (High Gen. Low Ramp.) | 2 | 28.50 | 22.57 | 1.00
LL (Low Gen. Low Ramp.) | 3 | 25.35 | 22.57 | 1.00
VLL (Very Low Gen. Low Ramp.) | 4 | 23.35 | 22.57 | 1.00
VLH (Very Low Gen. High Ramp.) | 5 | 23.35 | 22.57 | 0.00
TABLE III: Summary of values for market configurations | Wind | Wind | $FiP$ | $FiP$ | Risk | Risk | Res. | Res.
---|---|---|---|---|---|---|---|---
| L. | H. | L. | H. | L. | H. | L. | H.
$\mu$, wind (%) | 4.01 | 65.00 | 23.83 | 23.83 | 23.83 | 23.83 | 23.83 | 23.83
$FiP$, (€/MWh) | 30.00 | 30.00 | 0.00 | 80.00 | 30.00 | 30.00 | 0.00 | 80.00
$\Psi$, risk avers. | 0.40 | 0.40 | 0.40 | 0.40 | 0.00 | 1.00 | 0.40 | 0.40
$M_{y}$, (%) | 15.00 | 15.00 | 15.00 | 15.00 | 15.00 | 15.00 | 60.00 | 60.00

###  I-C Reserve Modeling

Reserve is modeled using what we call balancing reserve factors (MW of
reserve/MW scheduled), [6], $M_{x}=0.02$ for conventional generators in all
the configurations, and $M_{y}$ for wind generators. The values of these
parameters are calibrated on the historical observations in the Spanish
market. For wind turbines we consider two cases that reflect the error
forecast due to the time between commitment and real time:

  * •

$M_{y}=0.15$, for short time horizon, around 6 h.

  * •

$M_{y}=0.60$, for long time horizon, around 24 h.

Longer forecasting time horizon imply greater uncertainty and forecast errors.

Using the balancing factors, the reserve required by the Transmission System
Operator (TSO) is given by (2),

$\displaystyle M_{x}\\!{\cdot}\\!\sum_{g\in G}x_{g}+M_{y}{\cdot}\sum_{w\in
WT}y_{w}$ (2)

where $x_{g}$ is the scheduled dispatchable generation by $g$ and $y_{w}$ is
the scheduled wind generation by turbine $l$. The constraints for the upward,
$\sum_{g\in G}ru_{g}$, and downward, $\sum_{g\in G}rd_{g}$, reserves are also
inspired by the Spanish Grid Code, [7]. The upward reserve must remain between
90%, $\underline{A}=0.9$, and 110%, $\overline{A}=1.1$, of the reserve
required by the TSO, (2). The downward reserve must remain between 40%,
$B=0.4$, and 100% of the value of the upward committed reserve. The value for
the committed reserves corresponds here to the sum of the primary and
secondary reserves.

###  I-D Uncertain Parameters

The available wind generation is the only uncertain parameter in the analysis.
The values of $\mu$ and the scenarios are reported in Table IV; all these
values are given as a percentage of the rated wind generation capacity, that
is 22573 MW, as indicated in Table I. We consider the wind variability through
the expected value of wind $\mu$, and also the forecast errors through 12
scenarios for each value of $\mu$. We consider three values of $\mu$ that
correspond to low wind $\mu=4.01\%$, average wind $\mu=23.83\%$, and high wind
$\mu=65.00\%$. All scenarios have the same probability, $\frac{1}{12}\approx
8.33$%. The following describes the construction of the wind scenarios taking
into account the forecast errors.

We use a Beta distribution to model the wind power forecast error. Let the
load factor for wind generation be $q=\frac{\textrm{Power
output}}{\textrm{Rated power}}\in[0,1]$ , then according to [8, 9] this load
factor fits a Beta distribution:
$f(q)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}q^{\alpha-1}\\!\cdot\\!(1-q)^{\beta-1}$,
$q\in[0,1]$, where $\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}$
is a scale factor such as $\int_{0}^{1}f(x)dx=1$, and the parameters $\alpha$
and $\beta$ are directly related with the mean $\mu$ and the standard
deviation $\sigma$ of that distribution:
$\alpha=\mu^{2}\frac{1-\mu}{\sigma^{2}}-\mu$ and
$\beta=\alpha\\!\cdot\\!\left(\frac{1}{\mu}-1\right)$.

The analysis of empirical data shows that $\sigma$ fits a linear function of
$\mu$, $\sigma(\mu)=k_{1}\\!\cdot\\!\mu+k_{2}$, [8, 9, 10], where the
coefficients $k_{1}$ and $k_{2}$ depend mainly on the time horizon and the
geographic dispersion of the wind turbines. Here we use the expression given
in [10] for large scale generation and a time horizon of 24 h, and assume the
same expression for a horizon of 6h: $\sigma=\frac{1}{5}\mu+\frac{1}{50}$ (in
per unit).

To build the scenarios, we divide the range $[0,1]$ for the load factor into
segments and associate each scenario with a segment. Here we consider 12
scenarios, let $k$ be the index for the extreme points of each segment,
$z_{k}\in[0,1]$, then the range $[0,1]$ is discretized using 13 points,
$0=z_{1}<z_{2}<\ldots<z_{13}=1$. The value and the probability of scen. $k$
are:

  1. a)

Value of scenario $k$:
$\mu(k)=\int_{z_{k}}^{z_{k+1}}\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha}\\!\cdot\\!(1-x)^{\beta-1}dx$,
that is the expected value on the segment that defines the scenario.

  2. b)

Probability of scenario $k$,
$pr(k)=\int_{z_{k}}^{z_{k+1}}\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha-1}\\!\cdot\\!(1-x)^{\beta-1}dx$,
integral of the probability density function of the Beta distribution on the
segment associated with the scenario.

The points $0=z_{1}<z_{2}<\ldots<z_{13}=1$ are selected to get segments of
equal probability:
$\frac{1}{12}=\int_{z_{k}}^{z_{k+1}}\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}x^{\alpha-1}\\!\cdot\\!(1-x)^{\beta-1}dx$,
$k=1,2,\ldots,12$.

TABLE IV: Scenarios for available wind (% on rated capacity) Scen. |  $\mu$ (%), (base 22.57 GW) |  Scen. |  $\mu$ (%), (base 22.57 GW)
---|---|---|---
$k$ | 4.01 | 23.83 | 65.00 |  $k$ | 4.01 | 23.83 | 65.00
1 | 0.59 | 12.64 | 35.55 |  7 | 3.66 | 24.09 | 67.81
2 | 1.20 | 16.13 | 46.56 |  8 | 4.27 | 25.60 | 71.13
3 | 1.69 | 18.12 | 52.44 |  9 | 5.00 | 27.27 | 74.52
4 | 2.15 | 19.76 | 56.99 |  10 | 5.93 | 29.24 | 78.18
5 | 2.62 | 21.24 | 60.89 |  11 | 7.27 | 31.86 | 82.46
6 | 3.12 | 22.66 | 64.44 |  12 | 10.57 | 37.34 | 89.05

###  I-E Models Implementation and Solving

COM is a quadratic programming problem with linear constraints, made of 367
equations and 284 variables. As expected it is solved with no difficulty by
standard off the shelf solvers such as CPLEX, CONOPT and MINOS under GAMS
[11]. The computation time is around 0.78 seconds per problem on a machine
with Intel i7-5820K CPU @ 3.30 GHz and 32 GB RAM under Debian 4.19.171-2
x86_64. We crosschecked the model with two alternative formulations using the
Karush-Kuhn-Tucker ( KKT) conditions of COM, and solving it with PATH, also
under GAMS. One formulation with handwritten KKT, and the other provided by
the automatic generation of the dual by the Extended Mathematical Programming
on GAMS. We got the same results with the three formulations.

EQM is a linear complementarity problem that modifies COM’s KKT conditions
(see Part I). This problem misses the perfect arbitraging between reserve and
energy of COM. An interesting question is whether this is reflected in solving
capabilities. And indeed a direct application of PATH (under GAMS) on EQM
failed in some cases while PATH never failed on the corresponding COM
problems. We accordingly used an iterative approach that interacts PATH with a
linear sub-problem calculating the CVaR to update the risk neutral
probabilities at each iteration. This worked in all studied cases, but it is
at this stage a heuristic. Each EQM problem is made of 636 equations and 636
variables, and each linear subproblem for the CVaR contains 14 equations and
13 variables. Computation time to solve each EQM using the iterative approach
is $\approx$ 1.86 sec. using GAMS [11] on a machine with Intel i7-5820K CPU @
3.30 GHz and 32 GB RAM under Debian.

COM is a convex problem that, except for degeneracy, always has an unique
solution. Scalability is not an issue as the (very high) capabilities of LP
commercial codes set the limits. The situation is different for EQM that is
not amenable to optimization. One needs to verify the existence of an
equilibrium and the possibility of multiple solutions; one must also examine
scalability. A full answer to these questions goes beyond the scope of this
paper but the following gives the intuition.

Existence of a solution to EQM can be proved by a homotopy argument, [12]. One
can show that a solution of COM is a solution of a modified EQM, and that the
EQM that one wants to solve can be obtained by a continuous transformation of
COM. A standard reasoning of degree theory will then imply that the uniqueness
of the solution of COM implies a finite number of isolated solutions of EQM.
These mathematical properties have an economic interpretation. As argued in
Part I, COM differs from EQM by the fact that co-optimization takes into
account the opportunity cost on reserves of decisions of energy. The
continuous transformation of COM into EQM amounts to progressively decrease
the impact of this opportunity cost. Multiplicity of solution also has an
economic interpretation: co-optimization tries to minimize the excess demand
(positive or negative) by a search of both energy and reserve prices. It is
easy to show that this excess demand is a “monotone” (that is well behaved)
mapping of these energy and reserve prices. We argued in Part I that the
separation of energy and reserve (dropping co-optimization) implies that one
needs to find a zero of the excess demand by only playing with reserve prices,
and letting the market find the corresponding energy production and price
through a separate auction. The problem is that the obtained excess demand of
reserve is not necessarily monotone (can be badly behaved) in the price of
reserve, which is the source of a multiplicity of solutions. This has
consequences on scalability. There is now a lot of experience (that originated
in Hogan’s work on project independence in the seventies [13]) in solving
these problems by sequences of optimizations problems. Except for the need to
resort to an iterative procedure, scalability is only restricted by the
possibilities offered by commercial codes. But this remains a heuristic.

A final question is whether multiplicity of solution can occur in practice. As
argued later in the case study multiplicity of solutions can indeed occur.
Former European Union (EU) experience with the separation of the clearing
energy and transmission showed that awkward situations could happen in
practice where the clearing of transmission and energy were incompatible
(transmission rights and energy flows were in opposite directions). This
pattern already reappeared with the recent separation of energy transmission
between the UK and the EU due to Brexit. The analysis and interpretation of
multiplicity of solutions goes beyond this paper.

##  II Case Study: Results and Discussion

Samples of results for the eight configurations listed on Table III are
depicted in Figs. 1 to 5. The configurations differ by the parameters ($\mu$,
$FiP$, $\Psi$, $M_{y}$) and are referred to by the column names in Table III.
To facilitate comparisons results are expressed in percentage of a base value,
as explained below. COM and EQM results are respectively represented in
continuous and dashed lines in each figure. The selected results and the base
values are listed and briefly described below:

  1. 1.

(Demand Day-Ahead)111Names in parenthesis refer to the figures. with base
value 30120.39 MWh.

  2. 2.

(Equil. price), with base value 78.15 €/MWh, that corresponds to the highest
equilibrium price for the Low Generation configurations. Using that base
value, the maximum value of variable cost for generators,
$\max_{g}\\{C_{g}\\}$, is around 55.5%. This means a (Equil. price) lower than
55.5% is an incentive for plant retiring.

  3. 3.

(Gross welf.), gross welfare, with base value 3552878.90 €. It is computed as
the objective function for COM both for COM and EQM.

  4. 4.

(Net welf.), net welfare, with the same base value as (Gross welf.), is
obtained by subtracting the $FiP$ payment, $\sum_{w\in
WT}y_{w}\\!\cdot\\!FiP$, from the (Gross welf.).

  5. 5.

(Consum. pay.): consumer payment for energy,
$(\Gamma_{0}-\Phi_{0}\\!\cdot\\!d)\\!\cdot\\!d$, with base value 1837531.10 €.
This payment goes to the generator.

  6. 6.

(Reser. cap. pay.): payment for committed reserve capacities, $\sum_{g\in
G}(ru_{g}\\!\cdot\\!(\overline{\kappa}-\overline{\gamma})+rd_{g}\\!\cdot\\!(\underline{\kappa}-\underline{\gamma}))$,
with base value 1837531.10 € , the same as for the (Consum. pay.), so both
percentages can be added to get a global payment.

Because reserve is a service managed by the TSO in EQM, this payment goes from
the consumer to the TSO, when it needs to incentivize the generator to provide
reserve. Because the Spanish system includes an upper bound on reserve, we
also introduce penalties, $\overline{\gamma}$ and $\underline{\gamma}$, on the
generator in order to induce it to remain within these bounds. In that case,
these penalties are levied by the TSO and rebated to the consumer as a
reduction of fixed access charges.

A tentative motivation for the TSO’s upper bound for reserve is briefly
discussed here. Because of zero marginal cost, margins accruing from wind
generation are higher than those from fossil fuel plants. This effect is
further enhanced by the $FiP$. There is thus an incentive to bid wind instead
of fossil plants in Day-Ahead (DA). The Real Time (RT) correction in case of
discrepancies between DA forecast and RT realization mitigates this incentive,
but to an extent that is difficult to foresee ex ante. There may thus remain
an incentive to bid wind higher than expectation and to keep fossil capacities
for reserve. The TSO may want to restrict this practice: it can do so by
setting a reserve requirement and adding some interval (from 90 to 110%) of
that value for the generator to choose. This $[90,110]$% is referred to as the
TSO’s interval in the following.

The common EU wisdom is that the electricity market is a commodity (energy)
matter and that services (here reserve) are an other business. This is
reflected in the separation of the Power eXchanges and TSOs. Market conditions
where energy prices are insufficient for remunerating plants that are
necessary for the functioning of the system, suggest exploring whether
services (reserve) provided by the generators could constitute an other
valuable source of revenue. This underpins the case study with the subsidiary
question of whether co-optimization of energy and reserve could modify the
value of the reserves. Three different situations can be identified: i)
Reserve is available as an abundant byproduct of generation and hence has “no
value”; ii) Reserve is excessive, it hits the upper value of the TSO’s
interval, and has a negative value. Increasing the upper bound to a level
where it is no longer binding will extend the range where it has “no value”;
and iii) The case of most interest is when reserve is effectively a scarce
resource; it hits the lower value (90%) of the TSO’s interval and should be
remunerated.

(a)

(b)

Figure 1: Results for High generation and High ramping (HH). COM is in
continuous line and EQM is in dashed line.

###  II-A High Generation Capacity (28.5 GW) and High Ramping Capability
($\Lambda=0$): HH (Fig 1)

This case (HH) fully reflects the 2013 statement “There’s plenty of
flexibility but so far it has no value” [5]. Electricity prices (Equil. price)
are lower or equal to the highest fuel cost of the CCGT in most cases and
hence will also not cover the fixed operating costs of all plants222Verifying
that statement would require a full profile of wind availability (multi-
period) and hence a more developed model, our statement is thus only a
judgmental comparison.. The problem is structural and due to a legacy of
flexible generation capacity that exceeds the need for reserve and generation.
This is a short-term problem as the excess capacity will eventually retire.
But it creates a stranded asset issue that needs to be managed: one needs an
ordered exit in order to avoid a simultaneous dismantling of all the excess
capacity. In contrast, and assuming that the unprofitable plants are retained
through some special contractual arrangement, the consumer benefits from the
disequilibrium: its bill (Consum. pay.) is low and it receives a rebate on
access charges (Reser. cap. pay.), this can obviously not last. The supply of
reserve is excessive in almost all configurations with just a few cases where
it remains within the TSO’s interval. The following elaborates on this general
situation: it applies to both COM and EQM.

Reserves hit the upper bound of the TSO’s interval and are thus excessive in
five configurations. They are signaled by negative Reserve Capacity payments
(Reser. cap. pay.).

The three other configurations have zero reserve capacity payment with their
reserve remaining within the TSO’s interval. They occur in case of risk
aversion (Risk H.) and high reserve requirement, $M_{y}=60$%, which
corresponds to an imprecise DA forecast of RT wind (Res. H. and Res. L.).

The low electricity price and the excessive level of the reserve are two faces
of a same coin, with the financial consequence that the latter reinforces the
impact of the former.

COM and EQM only show small differences: demand in DA is higher and energy
price (Equil. price) lower in a few COM configurations. Reserve is also more
efficiently used in COM as shown by smaller payment from generators (Reser.
cap. pay.) to TSO reflecting less excessive reserve. (Gross welf.) are a bit
higher in EQM, but (Net welf.) are identical. Existing differences are real
but small. The striking feature of the situation is the dramatic
disequilibrium in the generation system, that indeed prevailed in Europe
before massive capacity impairment.

###  II-B High Generation Capacity (28.5 GW) and Low Ramping Capability
($\Lambda=1$): HL (Fig. 2)

This case (LH) slightly differs from the previous one (HH). It changes the
value of energy and reserves and moderately increases the differences between
the results of EQM and COM that remain limited to the same items: electricity
demand, equilibrium price and reserve capacity payment. Electricity price
(Equil. price) increases compared to HH but remains generally too low to cover
both fuel costs and fixed operating costs, except when demand for reserve
increases because of imprecise forecast (high $M_{y}$ cases in Res. H. and
Res. L.) or low wind (Wind. L.). Low wind reduces demand because it implies
higher fossil generation, with the aggravation that low ramping also
contributes to the reduction of demand in DA (92.92% in HL compared to 95.08%
in HH). This is neither a scarcity of capacity nor a market power effect: it
is more profitable to use capacity for reserve of wind generation than
directly for fossil generation. Recall that hindering that pattern has been
mentioned above as one possible justification of the upper bound of the TSO’s
interval ([90,110]% reserve requirement).

(a)

(b)

Figure 2: Results for High generation and Low ramping (HL). COM is in
continuous line and EQM is in dashed line.

The reserve behavior is mostly analogous to the one in HH, Fig. 1, but a bit
tighter. This is due to the lower flexibility that reduces the contribution of
capacity to reserve. Generally speaking, reserve remains in the “no value”
area with (Reser. cap. pay.) negative or zero. An exception occurs with high
requirement for reserve capacity (Res.L and Res.H) and risk aversion high
(Risk H.) where (Reser. cap. pay.) is zero or positive. Reserve is now higher
or equal to the lower bound of the TSO’s interval. The energy price (Equil.
price) in high reserve demand (Res. H. and Res. L.) comfortably exceeds the
fuel cost of the plants, which should make them able to cover their fixed
operating costs. The same is true in low wind (Wind. L.). The more efficient
use of reserve in COM than in EQM observed in HH is mostly confirmed with
reserve being now positive with high reserved demand (Res. H.), except for one
case that deserves a particular attention. Configuration (Res. L.) with high
demand for reserve shows a reserve capacity payment higher in COM than in EQM,
which is an anomaly with respect to all other results.

We conducted a deeper investigation of (Res. L.), using a homotopy reasoning
from configuration (FiP. L.) to (Res. L.). This amounts to parameterize the
problem from the low to the high demand for reserve, $M_{y}=15$% $\rightarrow$
$M_{y}=60$%, (all other parameters remaining equal). The results show a
discontinuous behavior for a demand of reserve $M_{y}$ around 46.5% where PATH
switches from an isolated equilibrium to an other one where it remains till
$M_{y}=60$%. Note that the results remain within basic principles, in other
words EQM does not dominate COM in terms of welfare, which would have
contradicted basic economics. It is simply an illustration that the lack of
co-optimization, that is the separate clearing of energy and reserve, creates
uncertainty (and counter intuitive behaviors) in the outcome of the market and
that these are worth further exploration.

The general conclusion of these two cases (HH and HL), high generation with
high/low ramping, is that except in the configurations of high reserve demand,
and low wind one should expect some generation capacity to be retired in order
to restore financial sustainability. The next cases examine this situation.

###  II-C Low Generation Capacity (25.35 GW) and Low Ramping Capability
($\Lambda=1$): LL (Fig. 3)

A reduction of capacity is the expected logical consequence of the loss of
profitability of generation observed in Figs. 1 (HH) and 2 (HL). This
reduction should in principle increase the price of energy, as well as the
revenue accruing from, now possibly scarce, reserves. This is effectively what
happens in (LL), at least for energy: the price (Equil. price) is now
sufficiently higher than the 55.5% benchmark to suggest that it can support
fuel and fixed operating costs. Inducing investment is obviously another
matter. The only exception to this general finding occurs with high wind (Wind
H.) where energy price is still a low 52.65%. Reserve also look better even
though generally remaining abundant as observed by the profile of reserve
capacity payment (Res cap. pay), which remain negative or zero in six
configurations, some of them associated to excessive reserves. Positive values
occur for high reserve demand (Res. H. and Res. L.): the reserve capacity in
those cases is effectively a payment from the consumer to the TSO, and
eventually to the generator that contributes to the value of the plant.

Other phenomena are worth mentioning. The payment for excessive reserve that
reduces the value of capacities decreases compared to the case with higher
generation capacity (HL): excess reserve diminishes when excess generation
capacity decreases. Similarly the positive value of the reserve capacity
increases the contribution to the plants profit, with (Reser. cap. pay.)
becoming a non negligible fraction of the revenue of the plants when the
demand for reserve is high (Res. L. and Res. H.). Also EQM and COM now perform
differently, with COM significantly reducing the cost of reserve capacity.
This has consequences on the electricity price and the payment for services by
the consumers (both lower in COM than in EQM), implying a (modestly) higher
welfare in COM. Co-optimization of energy and reserve thus appears useful if
the demand for reserve is high. This suggests further reducing the capacity to
test a possibly general scarcity of reserves, what is discussed next.

(a)

(b)

Figure 3: Results for Low generation and Low ramping (LL). COM is in
continuous line and EQM is in dashed line.

###  II-D Very Low Generation Capacity (23.35 GW) and Low ($\Lambda=1$): VLL
(Fig. 4) /High ($\Lambda=0$) Ramp. Capa.: VLH (Fig. 5)

We conclude with two cases of a further reduction of capacity, both with very
low dispatchable generation (23.35 GW), one with low ramping (VLL) Fig. 4, the
other with high ramping (VLH) Fig. 5. Most of the phenomena observed in Fig. 4
for VLL are similar to those discussed for LL, Fig. 3, just a bit stronger.
The price of energy (Equil. price) increases and the negative value of reserve
capacity payment (Reser. cap. pay.) persists, but decreases in the
configurations (Wind L.) and (Risk L.). Reserve thus remains non constraining
in these cases. The co-optimization of energy and reserve in COM improves the
efficiency of the market by avoiding diverting too much capacity from energy
to reserve. Also the share of reserve drastically increases in importance in
the remuneration of plants with significant differences of efficiency between
EQM and COM.

A striking result is that these effects disappear with a high ramping capacity
as shown in Fig. 5 for VLH. The valuation of reserves and the role of market
design are now completely different. The price of electricity (Equil. price)
remains high enough to support fuel and fixed operating cost of the plants:
this is a result of the lower capacity. But reserves loose all their values
and return to the pattern depicted in Fig. 1 for HH. The (Reser. cap. pay.)
becomes highly negative in the configurations for different wind (Wind L.,
Wind H.), $FiP$ (FiP L., FiP H.), and risk neutral generators (Risk L.), and
close to zero (or zero) with high risk aversion (Risk H.) and high reserve
requirements (Res. L., Res. H.). This suggests a very unstable market for
reserve, at least in this model.

(a)

(b)

Figure 4: Results for Very Low generation and Low ramping (VLL). COM is in
continuous line and EQM is in dashed line.

Figure 5: Results for Very Low generation and High ramping (VLH). COM is in
continuous line and EQM is in dashed line.

##  III Conclusion

The dramatic impact of wind penetration on power markets is now well
recognized. Wind decreases the price of the commodity and damages the
economics of conventional and flexible generators. While this may seem like a
good step towards the energy transition, this creates stranded costs for plant
owners. It also raises an issue of vulnerability of the energy market if
flexible capacity is suddenly retired from the system, because it can no
longer cover its fixed operating costs, and alternatives are not yet
available. The phenomenon is now well understood; it was most flagrant in the
period 2008-2013 in the EU, and recent documents show that it is still
rampant. Possibly less understood is the extent to which the demand for
reserve by the TSO for accommodating wind, can create a countervailing demand
for services that could mitigate or substitute the pressure coming from low
energy prices whether in the residual conventional system or its replacement.
Still less understood might be the possible impact of market design on that
countervailing demand. More specifically in this paper, the EU develops a
strong renewable policy in a regime of separation of energy and services.
Because there exists clear arbitrage possibilities between energy and reserve
a relevant objective is to try to characterize the demand for reserve services
in the current evolution of reduced fossil generation and whether the EU
separation of energy and reserve has an impact on that demand compared to a
co-optimization design.

This work attempts to provide some insight on this issue. Leaving aside
transmission we construct two models that embed energy and reserve in two
market organizations: EQM keeps energy and reserve separate and COM co-
optimizes them. The models are not meant to represent a particular market, but
try of satisfy some degree of realism by taking inspiration from a European
situation. The analysis is conducted by referring to the (costly) evolution of
fossil generation since the beginning of this century and in particular in the
period 2008-2013.

We find that there is no pricing power in reserve when generation capacity is
important and fossil plants are unable to cover their fixed and variable
operating costs on the energy market. Market design (COM or EQM) is also
irrelevant. But a high demand for reserve due to wind combined with a
reduction of economically redundant generation capacity restores plant
profitability, reveals the value of reserve and the relevance of co-
optimization at least in a basic situation of little flexibility capability.
The revenue accruing from reserve significantly contribute to the viability of
flexible plants in COM and EQM, but because of a more efficiently use of
reserves COM decreases the price to the consumer and increases demand and
welfare. But these advantages look fragile to an increase of reserve
capability. Increasing the reserve potential of existing plant could quickly
decrease their value both in COM and EQM and be possibly self defeating for an
investor.

This result obviously requires further analysis. This should be combined with
the relaxation of important simplifications made in the representation of the
EU system idiosyncrasies that could only be removed at the cost of
considerable technical difficulties. This will be treated in a future work.

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Yves Smeers received the M.S. and Ph.D. degrees from Carnegie Mellon
University, Pittsburgh, PA, in 1971 and 1972, respectively.
He is currently a Professor Emeritus and a member of the Center for Operations
Research and Econometrics, at Université Catholique de Louvain, Louvain-la-
Neuve, Belgium.
---
Sebastián Martín (S’08, M’14) was born in Málaga, Spain, in 1980. He graduated
from University of Granada, Spain, as Civil Engineer in 2003. He received an
Industrial Engineer and a PhD degrees from University of Málaga, Spain, in
2007 and 2014 respectively.
He is currently a teaching assistant at the University of Málaga. His research
interests include: optimization theory, methodologies for teaching, and
economics of electric energy systems.
---
José Antonio Aguado (M’01) received the Ingeniero Eléctrico and Ph.D. degrees
from the University of Málaga, Málaga, Spain, in 1997 and 2001, respectively.
Currently, he is full Professor and Head of the Department of Electrical
Engineering at the University of Málaga. His research interests include
operation and planning of smart grids and numerical optimization techniques.
---