3. PLANTEAMIENTO DEL PROBLEMA
3.3. PREGUNTA DE INVESTIGACIÓN
7.1.5. Factores que determinan la Comprensión
This section presents the DUC formulation, in a rough approximation of current GB sys- tem operation. To maintain consistency with chapter 4 and section 6.3, the formulation is described by defining decision variables and constraints at nodes on a scenario tree, where in this case the tree has just a single scenario (Figure 6.1a). The scenario follows the 50th percentile forecast for wind, load and outages, while soft constraints for response and reserve maintain system security. The commitment horizon is 36 hours and the DUC is calculated every 30 minutes (rolling planning), by minimising the operating costs up to the commitment horizon via the following Linear Program:
Minimise
∑
n∈N ∆τ(n)cLSPLS(n) +cFSPFS(n) +cRSPRS(n)+∑
g∈G Cg(n) ! (6.1)subject to a load balance constraint:
Pgen(n) +PLS(n)−PWC(n) =Pnd(n), (6.2) and local constraints for the thermal and storage units. Details of these constraints and the equations governing generation costs Cg are presented in section 4.3. For computa-
tional reasons, it is assumed that all units of a given technology type are identical, and we keep track of the number of units of each technology that are up, down and unavail- able, rather than the status of each individual unit. The integer commitment variables are relaxed to continuous (so that fractions of units can be committed), which was found in section 4.7 to have only a small effect on results while significantly improving run times. The net demand Pnd(n)is taken to be the forecast demand at node n’s timestage less
CHAPTER 6. VALUE OF STOCHASTIC RESERVE POLICIES IN LOW-CARBON POWER SYSTEMS
the forecast wind power. Since the time interval spanned by node n may contain several timesteps, we use the highest demand level within that time interval:
Pnd(n) =−Pwf(k,ℓ(n)) + max i∈I(n)P df(k, i) (6.3) where I(n):= i∈Z:ℓ(n)≤i< ℓ(n) +∆τ(n) ∆t . (6.4)
The optimiser is incentivised to avoid load shedding, response shortfalls and reserve shortfalls by the terms in the inner bracket in Equation (6.1). The VOLL cLS is set to
£30 000/MWh, the unsupplied response penalty cFS to £10 000/MW/h, and the unsup-
plied reserve penalty cRSto £5000/MW/h. The schedules obtained with DUC are insen-
sitive to the choice of these parameters as long as they are significantly greater than the cost of generation and cLS > fgcFS >cRS(so that reserve is never scheduled in preference to response, which is never scheduled while loadshed is occurring).
The shortfalls in response and reserve are defined as nodal decision variables PFS(n)
and PRS(n)in Equation (6.1), and are subject to the following constraints. The shortfall in response cannot be negative and is not less than the excess of the response target over the response provision from part-loaded thermal units, curtailed wind and demand:
PFS(n)≥0 (6.5)
PFS(n)≥ PFT−
∑
g∈GPgF(n)−PFW(n)− fdPd(k+ ℓ(n)). (6.6)
The last term in Equation (6.6) represents the automatic reduction in demand that results from a drop in system frequency, mainly due to the accompanying voltage drop.
The shortfall in reserve cannot be negative and is not less than the excess of the re- serve target over the reserve provision from the thermal units and curtailed wind. The formulation allows for separate targets for total reserve (PRtotT) and for spinning reserve only (PRspinT): PRS(n)≥0 (6.7) PRS(n)≥ PRtotT(n)−
∑
g∈G PgRtot(n)−PRW(n) (6.8) PRS(n)≥ PRspinT−∑
g∈G PgRspin(n)−PRW(n). (6.9)Note that the total reserve target is a function of the time horizon and hence is defined as a nodal value.
The response and reserve provision from each unit group g are defined as decision variables that are subject to the following constraints. The response provision from group
g is limited to a fixed proportion fg (typically 55%) of the spinning headroom in that
CHAPTER 6. VALUE OF STOCHASTIC RESERVE POLICIES IN LOW-CARBON POWER SYSTEMS
vision are mutually exclusive):
PgF(n)≤ fg
Ngup(n)Pgmax−Pg(n)−PgRspin(n)
. (6.10)
There is also an absolute limit to the response that is assumed to be available from any unit, typically around 10% of capacity:
PgF(n)≤PgFmaxNgup(n). (6.11)
The total reserve provision from group g is limited to the spinning headroom in slow- starting units (modelled with a non-zero startup time) or the total unused capacity in fast-starting units (modelled with a zero startup time):
PgRtot(n)≤
Ngup(n)Pgmax−Pg(n), for slow-starting units Nav
g Pgmax−Pg(n), for fast-starting units.
(6.12)
It is normal practice to hold some of the reserve as “spinning reserve”, i.e. as headroom in part-loaded large units (such as coal and CCGT) in addition to any headroom that is earmarked for response; this extra component of the reserve is automatically provided by the market and/or required by the System Operator. Equation (6.9) builds the spinning reserve target from contributions PgRspin(n)defined as
PgRspin(n) =
PgRtot(n), for slow-starting units,
0, for fast-starting units. (6.13)
It is assumed that any curtailed wind can be allocated to response or reserve, with the response element limited to a proportion fwof the total:
PRW(n)≤PWC(n)−PFW(n) (6.14)
PFW(n)≤ fwPWC(n). (6.15)
Note that curtailed wind does not currently provide response services; the requisite tech- nology, market and communications structures would need to be developed to enable curtailed wind to be used for this purpose in the future.
The nodal net demand target is set to the 50th percentile of the (uncertain) total net demand at each node:
Pnd(n) =C−1(0.5; n) (6.16) where the quantile function C−1(·; n)is defined in section 6.5. The response target is set
CHAPTER 6. VALUE OF STOCHASTIC RESERVE POLICIES IN LOW-CARBON POWER SYSTEMS
to the capacity of the largest unit:
PFT=max
g∈G P max
g . (6.17)
The total reserve target is set to the difference between the net demand corresponding to the reserve quantile qresand the nodal net demand target, up to 6ha (hours ahead), which is the startup time for the slowest-starting unit:
PRtotT(n) = C−1(qres; n)−Pnd(n): τ(n)≤6h PRtotT(n6ha): τ(n) >6h (6.18)
where n6ha is the node for which τ(n) = 6h. These requirements constitute a LOLP requirement for reserve and an N-1 requirement for response. In the case study the mini- mum spinning reserve target RSpinTis set to a constant value of 500MW, which is roughly the minimum amount of headroom that is provided in the GB market.