1. Introduction
Uncertain and
variable conditions associated with increasing renewable generation in modern power systems introduce prominent challenges in the optimal system operation and necessitate the reinforcement of flexible resources to maintain appropriate levels of reliability. Unlike conventional generating units, the production of renewable energy sources, like wind and solar power, cannot be predicted with perfect accuracy (
uncertainty) even with state-of-the-art forecasting methods [
1,
2,
3,
4,
5], especially as the lead-time between real conditions and relevant forecasts is increased [
6,
7]. Even if renewable production were accurately forecasted, it still varies with time (
variability) depending on weather conditions, and these variations often occur at higher time resolutions [
8,
9,
10] than the ones considered in the market domain where the relevant schedules are produced. The impacts of renewable
uncertainty and
variability have been studied extensively by researchers and industry [
11,
12,
13,
14,
15], universally recognizing the increasing need for power system flexibility, namely sufficient ramping capability provided by conventional generation or possibly other resources in order to follow the unpredictable and steep movements of the net load (load net of renewable production) in real-time conditions. A failure to meet the system flexibility requirements is multifaceted; it can manifest as power balance violations, price spikes and high volatility of electricity prices, frequency deviations and Area Control Error (ACE) augmentation, extensive use of regulation services to resolve the issue in real time or undesirable out-of-market corrections (e.g., committing/keeping additional units online), and often eventually relying on unavoidable curtailments of renewable generation.
To face these reliability challenges in an economically efficient manner with existing power system infrastructure, advanced short-term scheduling strategies have evolved during the past years, enriching the Unit Commitment (UC) paradigm [
16]. Co-optimization of energy and ancillary services in a deterministic modeling framework has been widely utilized by researchers and system operators, to attain improved efficiency and derive price incentives for the actual provision of these services [
17,
18]. In deterministic UC (DUC), the net load is modeled as a single forecast and the associated
uncertainty is handled using ad-hoc reserve requirements, which can be fixed during the course of a day [
19], or vary on a multi-hourly [
20] or hourly [
21,
22] basis. In [
23,
24,
25], the load, conventional and wind generation are considered as uncorrelated variables and the method of convolution is used to determine the reserve amount for different LOLP values; however, the load and wind power
variability is not taken into account. Reference [
26] presents a dynamic reserve quantification method for rolling UC models with variable time resolution, like the one proposed in [
27]; the approach takes into account contingency events, as well as both load and wind power
uncertainty and
variability using the standard deviation measure. In many cases, the literature underlines the need for defining different reserves associated with normal operation of the power system (i.e., operating reserves), like the regulating, load-following and ramping reserves. References [
26,
28,
29,
30,
31] provide a comprehensive review of probabilistic methodologies to quantify requirements for such operating reserves under increased penetration of renewable generation.
Focusing on real-time operations, some United States system operators have lately introduced in their deterministic real-time UC (RTUC) and dispatch (RTD) processes a specific ramping reserve product (CAISO [
32], MISO [
33]). This product, commonly called “flexiramp”, is intended to reduce the frequency of ramp shortages caused by renewable
variability and
uncertainty in the real-time market, while producing sufficient price incentives for the eligible resources to actually provide their ramping capacity. The reduction of ramp shortages and relevant price spikes in RTD upon the introduction of the ramp product in CAISO is demonstrated in [
34]. Navid et al. [
35] analyze the trade-offs between the additional costs of procuring ramp capability, and the respective cost savings achieved in the real-time market. The operational implications of the ramp product on costs and system reliability are further examined by Krad et al. in [
36]; simulations corroborate the reduction in scarcity pricing events caused by insufficient ramping capacity. In [
37], Ela and O’Malley assessed the efficiency and the incentive structure (for providing ramp) of time-coupled (look-ahead) real-time market clearing models, as compared to incorporating ramp products and respective constraints in economic dispatch; look-ahead optimization horizon in real-time markets can prove more efficient in terms of reliability, however it may lack incentives as compared to the utilization of the ramp product. An efficient design of the requirements for the ramp product, which utilizes Monte Carlo simulation, is proposed by Wang et al. in [
38]. References [
32,
33,
34,
35,
36,
37,
38] focus on the incorporation of the ramp product in the real-time markets. A dedicated analysis for a respective provision at the day-ahead stage is proposed in [
31], considering an efficient allocation of the real-time (intra-hourly) system ramping requirements within the coarser (hourly) DUC optimization intervals utilized in day-ahead.
Stochastic programming [
39] has gained significant attention as an alternative scheduling strategy for handling the
uncertainty associated with renewable generation. Instead of arranging a single net load forecast and allocating pre-determined amounts of reserves, stochastic UC (SUC) considers a set of possible net load realizations (scenarios) along with their respective probabilities of occurrence, and minimizes the operating cost over all scenarios considered. The driving factor for SUC is that—by actually accounting for different scenario realizations—the expected operating cost over all scenarios can be reduced [
40], as compared to DUC policies which do not consider the potential operating conditions explicitly. This omission in the DUC policies can be further deteriorating, if the actual conditions deviate substantially from the assumptions made when determining the respective reserves.
Various researchers have proposed two-stage SUC formulations, where wind
uncertainty is arranged by either finding the optimal commitment of slow-start units in the first stage so that the system can cope with all possible realizations of wind output at the second (real-time) stage [
41,
42,
43,
44], or explicitly determining the required level of load-following reserves [
45,
46,
47]. Bouffard et al. [
45] were among the first to present a two stage stochastic programming formulation that utilizes explicit decision variables for reserves while considering external reserve bids by the various resources. A similar two-stage formulation is utilized in [
46] by Morales et al. for the quantification and economic valuation of load-following reserves. Reserve procurement at the day-ahead (first) stage is treated as a here-and-now decision, while reserve deployment is a wait-and-see decision determined at the real-time (second) stage, after the scenarios are revealed. Sahin et al. [
47] presented a stochastic model for quantifying the appropriate spinning reserves, which can be provided by both generating units and demand response providers. In [
48], Wang et al. formulated a two-stage SUC model also incorporating demand response, where demand response resources can be scheduled both in the day-ahead and intra-day stage, depending on their relative responsive costs in each stage and their particular operating constraints. A respective security-constrained stochastic approach by Wu et al. [
49] incorporates ramping costs and demonstrates the benefits of applying hourly demand response in managing the increasing renewable
variability. In [
50,
51,
52], rolling stochastic unit-commitment models are presented and tested against their deterministic counterparts, either utilizing coarse (hourly or larger) time intervals [
50] and making aggregations per generating unit technology [
51], or using higher and variable time resolution to achieve more robust results [
52]. Focusing on the utilization of the “flexiramp” product in RTUC [
53] and RTD [
54], Wang and Hobbs compared costs between the deterministic model with ramping reserve requirements as in [
32,
34] and an ideal stochastic model, which endogenously determines the optimal amount of ramp capability to be acquired. Finally, Lee and Baldick [
55] formulated a two-stage stochastic programming economic dispatch model for the determination of the optimal energy and reserve schedules, while adding simplified frequency constraints.
In this paper, we examine both deterministic and stochastic day-ahead UC policies with focus on the determination, allocation and deployment of reserves. A fundamental distinction is proposed between (a) the uncertainty reserve, the procurement of which is intended to arrange the net load forecast errors, and (b) the variability reserve, the explicit procurement of which is intended to reduce the probability for ramp shortages and relevant price spikes in RTD. The mathematical problem formulations proposed for DUC and SUC policies minimize the costs of meeting the hourly net load forecasted in day-ahead, including the costs of uncertainty and variability reserve procurement, as well as the commitment costs. To enhance reliability, the concept of multi-timing scheduling is proposed and applied appropriately in all UC policies, which allows for the determination and optimal allocation of the uncertainty and variability reserves based on an intra-hourly (“real-time”) resolution, when concurrently optimizing energy and the commitment status of the resources over longer scheduling intervals (hours). A modified version of the Greek power system is utilized in the case studies and detailed discussion is provided on the optimal allocation of the day-ahead uncertainty and variability reserves to the available resources, based on the resources’ specific capacity and ramp rate capabilities and their respective economic offers. Finally, in order to better simulate the real operation of the power system and evaluate the attained margins of safety, the UC results (both DUC and SUC) are tested against different RTD regimes, with none or limited look-ahead capability, or with the use of the variability reserve determined by UC, to reveal several implications relative to the nature of RTD.
The results demonstrate the enhanced reliability achieved in RTD by applying the multi-timing scheduling concept and explicitly considering the variability reserve in day-ahead. The SUC policies tend to allocate the reserves in lower cost resources (as compared to DUC policies) considering their relative deployment cost, thus leading to cost reductions in RTD. However, SUC may occasionally provide a more ramp-constrained schedule leading to ramp shortage augmentation in RTD. Also, the correlation between the awarded uncertainty reserves in day-ahead UC and the deployed uncertainty reserves (by the awarded resources) in RTD has proven higher in the stochastic cases.
The main contributions of this paper are summarized as follows: (a) an explicit distinction is made between the uncertainty and the variability reserve, both falling into the general category of operating reserves; (b) comparable methodologies and mathematical formulations are developed for the DUC and SUC policies, based on the proposed multi-timing scheduling concept, utilizing a detailed modeling of various generating unit operating states; (c) the two-stage SUC policy incorporates the variability reserve extending previous literature, which mainly focuses on the arrangement of renewable generation uncertainty; (d) a specific proposal is made for the quantification of the uncertainty and variability reserve requirements in the DUC policy; and (e) the mathematical formulation of different real-world RTD modes is presented and utilized for evaluating the UC results, instead of simply interpreting the day-ahead scheduling outcome.
The remaining of this paper is organized as follows:
Section 2 presents the problem formulation of SUC and DUC policies, as well as the structure of different RTD regimes.
Section 3 and
Section 4 describe the case study and the scenario generation technique, respectively, utilized for the scope of this paper. Numerical examples are provided in
Section 5, whereas
Section 6 concludes the paper.
2. Mathematical Problem Formulation
2.1. General Description
The aim of the day-ahead UC phase is to provide the available resources with their optimal commitment status, their hourly energy schedules, and the binding reserve awards which will serve as a tool (for the TSO) to hedge against uncertainty and inherent variability of the net load in real-time conditions. To this end, a fundamental distinction is considered between (a) the uncertainty reserve, the procurement of which is intended to address the net load forecast errors, and (b) the variability reserve, the procurement of which is intended to reduce the probability of ramp (cf. capacity) shortages and relevant price spikes in RTD. Other ancillary services such as contingency reserves, along with possible unexpected outages in RTD, are not considered in this paper to maintain focus on normal operating conditions.
In this context, the UC model (stochastic and deterministic approach) is formulated as a co-optimization problem of energy, uncertainty and variability reserves, and constitutes a Mixed Integer Linear Programming (MILP) model. External bid-costs are considered during cost minimization for the provision of uncertainty and variability reserves, to allow for the commoditization of reserves and sufficiently incentivize flexible resources to develop and provide their fast ramp capability. For simplicity, the resources correspond to conventional thermal and hydro generating units; the inclusion of other possible eligible resources such as storage, renewables and demand response in the proposed models is straightforward. Α detailed modeling of the generating unit start-up and shut-down procedures is utilized at the day-ahead UC stage, which is followed accurately in RTD.
Most notably, the concept of multi-timing scheduling is proposed and applied appropriately in the stochastic and deterministic UC policies. Multi-timing scheduling allows for the determination and optimal allocation of the
uncertainty and
variability reserves based on an intra-hourly (real-time) resolution, when simultaneously optimizing energy and the commitment status of the resources over longer scheduling intervals (hours).
Figure 1 depicts the fundamental concept of determining the system
uncertainty and
variability reserve requirements (either inherently in the SUC policy, or exogenously in the DUC policy) in the above context. As can be seen, the
uncertainty reserve is aimed to cover the net load forecast errors, namely the possible mismatches between the hourly (
h) net load level forecasted day-ahead and the net load realized in each instance (
t) of RTD, while the
variability reserve is aimed to cover the net load variations between successive intervals (
t) in RTD, with each variation being assigned as a respective requirement to the preceding real-time interval.
We thereby maintain the legitimate simplicity of the hourly commitment and scheduling solutions during the day-ahead stage. However, the utilization of real-time information and the coordination with the time resolution of RTD when procuring the respective reserves (a) brings more accuracy and efficiency on the system scheduled flexibility, by securing a dedicated capacity and ramping headroom per each specific real-time interval; (b) enhances incentives for the provision of fast (real-time) ramp capability at the scheduling stage, and thereof; (c) optimally arranges the increased net load variations in RTD associated with high penetration levels of renewable generation.
2.2. Stochastic Unit Commitment (SUC)
The structure of the SUC model is divided into two stages (two-stage stochastic programming). The first stage describes the day-ahead scheduling decisions (optimal commitment, hourly energy schedules, uncertainty and variability reserve awards), while the second considers various possible realizations of the power system operation through a set of net load scenarios, in order to determine the optimal reserve awards of the first stage in an accurate and economic (in terms of actual deployment) manner. Since the second stage models real-time operation, and in order to attain advanced flexibility features in the scheduling results, the utilization of finer time resolution is proposed at this stage, coordinated with the time-step of the RTD function, which addresses both the increased intra-hourly forecast errors (uncertainty) and the steep intra-hourly system ramping requirements (variability) that may occur during RTD.
2.2.1. Objective Function
The TSO total cost (1) to be minimized over the scheduling period consists of (in order of appearance of the various terms): (a) the resources’ commitment (start-up and shut-down) costs; (b) the hourly procurement (as-bid) costs of energy; (c)
uncertainty and (d)
variability reserves at the first stage, as well as; (e) the intra-hourly deployment cost of the
uncertainty reserve, along with the load shedding and wind spillage cost, at the second stage, weighted by the respective probability of each net load scenario:
The term is used to account for the intra-hourly resolution considered at the second stage of the SUC model, for example it is equal to ¼ in case a quarterly resolution is applied.
2.2.2. Day-Ahead Market Constraints (1st Stage)
The constraints utilized in the first stage of the SUC model are scenario independent and apply to each hourly interval
h of the daily scheduling horizon. The following set (2)–(6) models the generating unit operating states of synchronization (2), stepwise soak (3) based on hourly energy soak steps (4) as pre-defined by the producer, and stepwise desynchronization (5) following a linear decrease rate (6). For an analytical description of these constraints the reader is referred to [
56].
Inequalities (7) and (8) denote the minimum up and down time constraints of the generating units, respectively,
while (9)–(13) describe the logical relations of the commitment binary variables.
In (14) and (15), the hourly day-ahead energy schedule of each unit (
) is coordinated with the respective upward and downward
uncertainty reserve, within the unit technical limits in every operating state (i.e., synchronization, soak, normal dispatch or desynchronization). Apparently, the
uncertainty reserve can be allocated only during the phase of normal dispatch (i.e., unit operation between its technical minimum and maximum limit). The last term in the right-hand side of (14) is used to equalize the output of a unit with its technical minimum production at the hour prior to the desynchronization process, and is omitted for units with desynchronization time less than one hour.
In (16), the hourly energy schedule of a unit is derived from the cleared quantities of all steps
k of the associated unit offer, while in (17) the cleared quantity of each step is limited by the offered size of the step.
Constraints (18) and (19) enforce the ramp rate limits on the unit power output between consecutive hourly (
) time intervals. The last terms in the right-hand side of (18) and (19) relax the ramp limits during the synchronization, soak and desynchronization phases.
Finally, in power balance Equation (20) the energy procured from all conventional generating units covers the hourly net load forecasted at the day-ahead stage.
Within the scope of this paper, renewable generation is represented by wind production, which is assumed to be a regulated (non-competitive) activity given dispatch priority, as is currently the case for existing wind plants in most energy systems around the world. Thus, wind producers do not submit offers in the market and the forecasted wind generation is considered as negative demand in (20). However, there is the possibility for wind generation to be spilled at extreme scenarios considered in the second stage of the SUC model (see power balance Equation (31)).
2.2.3. Real-Time Operation Constraints (2nd Stage)
The multi-timing scheduling concept requires that the second stage of the SUC model (a) considers the realization of a number of possible net load scenarios s based on the finer (intra-hourly) time resolution t applying in RTD; (b) calculates the optimal uncertainty and variability reserve quantities that are actually deployed in each real-time interval t and scenario s; and thereby (c) determines the respective hourly uncertainty and variability reserves to be allocated to the various resources at the day-ahead (first) stage.
More specifically, in equality (21), the upward (downward)
uncertainty reserve deployed is essentially the incremental (decremental) energy procured by unit
i in scenario
s and real-time interval
t, over the unit day-ahead schedule (
) for the corresponding hour
h. The resulting real-time schedule
is placed within the unit technical limits in every operating state, in constraints (22) and (23). Note the special handling for the coordination of the real-time (
t) variables with the respective hourly (
h) variables in the formulation of (21)–(23) (i.e., these constraints apply
and simultaneously
).
Note also, that by summing each side of (21) for all units
i, the term in the left-hand side essentially provides the real-time net load for scenario
s and time interval
t, the first term of the right-hand side provides the hourly net load forecasted at the day-ahead stage, while the two latter terms provide the respective system
uncertainty reserve requirements in each direction, respectively, for the given scenario
s and real-time interval
t. That is, the
uncertainty reserve requirements per scenario
s are determined as the difference between the real-time net load and the respective hourly net load forecasted at the day-ahead stage, in line with the relevant description provided in
Figure 1.
Accordingly, in (24), the
variability reserve deployed by unit
i in each real-time interval
t − 1 is essentially the variation of the unit’s power output
between the successive intervals
t − 1 and
t, for a given scenario
s. In case of positive variations, upward
variability reserve is deployed, and vice versa. The
variability reserve deployed is in turn limited by the unit ramp capability over the length of the real-time interval (
) in (25) and (26) for the upward and downward direction, respectively.
Note again, that by summing each side of (24) for all units
i, the left-hand side provides the net load variations between successive real-time intervals
t in each scenario
s, while the right-hand side provides the corresponding system
variability reserve requirements; each net load variation (i.e., between
t − 1 and
t) is assigned as a respective requirement to the preceding real-time interval (i.e.,
t − 1), in line with the relevant description provided in
Figure 1.
In order for the hourly
uncertainty and
variability reserves of the first stage to be calculated over all (independent of the) scenarios considered at the second stage, the linking constraints (27) and (28) are applied. In (27), the largest
uncertainty reserve deployed by unit
i among all real-time intervals
t belonging to hour
h, and among all scenarios
s of the second stage, defines the respective hourly
uncertainty reserve award of that unit for the given hour
h. A similar approach is also applicable for the
variability reserve in (28). In this case, the hourly (first-stage)
variability reserve award of a unit (right-hand side of (28)) is defined based on the largest algebraic summation of the
variability reserves deployed by that unit within the given hour
h, among all scenarios
s of the second stage. In this context, the unit is remunerated through the hourly
variability reserve award for all real-time variations of its power output expected to realize within said hour in RTD (since the TSO has hedged its position against all real-time variations of the net load, respectively), acquiring stronger incentives to provide its ramp capability in real-time conditions.
With regard to the additional cost of deployment of the
uncertainty reserve at the second stage, the right-hand side of (29) determines the quantity deployed (positive if upward reserve is deployed, and vice versa) per step
k of the associated energy offer, and the relevant cost of deployment (energy cost) is considered in the last term of the objective function (1). Note that a similar deployment (energy) cost for the
variability reserve shall not explicitly be defined in (1), put it differently, the deployment of the
variability reserve refers to the variations of the unit output between consecutive real-time intervals and not to the actual energy level in each specific interval. Inequalities (30) calculate the remaining margins (in both directions) for
uncertainty reserve deployment per step
k of the unit energy offer, as compared to the energy procured by that unit at the first stage (
).
Finally, (31) enforces the power balance equation at the second stage of the SUC model, where the possibility for load shedding and wind spillage in extreme scenarios is also considered.
2.3. Deterministic Unit Commitment (DUC)
In contrast to the SUC model, which determines the day-ahead
uncertainty and
variability reserve awards inherently (i.e., through the consideration of different possible net load scenarios at the second stage and the linking constraints), the DUC model calculates the optimal reserve allocation through pre-determined reserve requirements defined rather exogenously. That is, the DUC model is similar to the one presented in
Section 2.2, but with the following exceptions: (a) constraints (21)–(31) pertaining to the second stage of the SUC model are replaced by (32), (33) and (38)–(42) presented hereinafter; and (b) the last term of the objective function (1) (regarding the deployment cost of the
uncertainty reserve) is apparently omitted. Then, the DUC problem formulation is as follows:
Constraints (32) and (33) ensure that the total contribution in each type of reserve meets the associated system requirements:
The multi-timing scheduling concept in the DUC policy requires that the reserve requirements are determined as per the following formulas (34)–(37) utilizing real-time information for both types of reserves (
uncertainty and
variability), according to the relevant description of
Figure 1. In (34)/(35), the largest difference between the hourly net load forecasted at the day-ahead stage and the real-time net load (considering all corresponding intervals
t and scenarios
s) determines the upward/downward
uncertainty reserve requirement for hour
h. Accordingly, in (36)/(37), the largest variation of the net load between successive real-time intervals
t and
t + 1 (considering all scenarios
s) determines the upward/downward
variability reserve requirement for real-time interval
t.
Note that the load and wind power dataset utilized for the quantification of the deterministic reserves essentially comprises the same real-time scenarios
s also considered in the stochastic approach (second stage), for homogeneity purposes. Nevertheless, the same methodology (34)–(37) can also be implemented on the initial (historic) load and wind power dataset utilized for the creation of scenarios (
Section 4), replacing the Max criterion by a certain percentile (e.g., 99%) of the respective error/variation probability distributions. In any case, the herein approach provides an accurate method of quantifying the deterministic reserves, which is comparable to the respective SUC functionality at the second stage, as compared to utilizing trial-based values [
41] or simplified/heuristic approaches for determining the reserve requirements (e.g., a constant requirement representing a certain fraction of the peak load [
43], or the 3 + 5 rule [
12]), or not imposing reserve requirements in the DUC policy at all.
Moreover, the
variability reserve requirements are explicitly determined in (36) and (37) per real-time interval
t, and allocated to the eligible resources based on their real-time ramp capability through the following constraints (38) and (39). These constraints are similar to (25) and (26) of the SUC model, and are used to allocate the
variability reserve to faster resources in case of increased intra-hourly net load variations expected in RTD:
The respective hourly
variability reserve award of each unit is then calculated in (40) (similarly to constraint (28) of the SUC model):
Finally, the following constraints (41) and (42) are additionally enforced in the DUC model, in order to delimit the upward and downward
variability reserve award of a unit in the range
.
The utilization of the downward uncertainty reserve in a counteractive manner to the upward variability reserve in the left-hand side of (41) is motivated by the following possible outcome noticed in the SUC model respectively: a unit is scheduled at its maximum level in a given hour at the first stage, in parallel receives a downward uncertainty reserve award for that hour (obtained due to a low scenario at the second stage), while at the same time the unit receives an upward variability award (i.e., the unit was ramping up in said low scenario at the second stage). That is, in case the low scenario actually materializes in real time, the unit is expected to be producing at a lower level, thereby also being able to ramp-up in the given hour. A respective concept also applies to constraint (42) for the downward direction.
2.4. Real-Time Dispatch (RTD)
The RTD function is utilized in this paper in order to evaluate the scheduling results of any UC policy (stochastic and deterministic approach). Elsewhere, the literature often determines the expected cost in real-time operation directly from the solution of the SUC model (cost of each scenario at the second stage multiplied by the respective probability of occurrence), e.g., [
46], or by implementing additional Monte Carlo simulations for a number of net load realizations, each one solved one-shot for the whole scheduling horizon based on the commitments produced by the UC process, e.g., [
41]. In order to replicate more accurately the RTD applications in real world and reveal some implications relative to the nature of the RTD regime used, the deterministic RTD, herein, is simulated as a rolling dispatch procedure (i.e., solved sequentially for each real-time interval), with none or limited [
57] look-ahead capability, or with the use of the
variability reserve [
32,
33,
34,
35] determined by the UC application. The baseline RTD mathematical formulation is the following:
For each subsequent RTD execution, the energy, load shedding and wind spillage costs are minimized in the objective function (43) over the given dispatch horizon . In the constraints following objective (43), the value of all variables denoted with an upper dash, like the commitment status, has already been determined by the UC solution and is not re-optimized in RTD. In that respect, (44) describes the actual deployment of the uncertainty reserve by each unit in RTD as compared to its hourly day-ahead energy schedule, (45) and (46) impose the unit power output limits in every operating state, (47) and (48) enforce the ramping constraints, (49) and (50) determine the unit output based on the maximum offered quantity per step of the associated energy offer, while (51) describes the power balance equation. The latter constraints (52)–(55) are used only in the RTD mode RTD_SI_Var (explained below) to consider the variability reserve as an alternative way of “looking ahead” in RTD.
In this context, five RTD modes are used to evaluate the UC outcome, as follows:
RTD_SI (model (43)–(51)): RTD economically dispatches the committed resources for each subsequent real-time interval without future expectation of the net load (single-interval or blind mode); set essentially comprises only one element, i.e., the current interval.
RTD_LA_1 (model (43)–(51)): RTD economically dispatches the committed resources for each subsequent real-time interval, while also looking ahead to the following interval. In each clearance, the dispatch solution for the first interval is binding, while the solution for the look-ahead interval is only advisory.
RTD_LA_4 (model (43)–(51)): Similar to RTD_LA_1, however the look-ahead horizon is extended to four real-time intervals.
RTD_SI_Var (model (43), (44), (47)–(55)): Similarly to RTD_SI, a single-interval dispatch is implemented, however the
variability reserve awards determined by the UC application are used in (52)–(55) to keep the dispatch schedule of the eligible resources “away” from their technical maximum (52) (or minimum (53)) limit in previous RTD intervals, so as they can provide their upward (or downward) ramping headroom in future intervals, when mostly needed. The
variability reserve product has been introduced along with
variability reserve requirements in RTD by the CAISO [
32,
34] and the MISO [
33,
35] in a similar way. The new product, commonly called “flexiramp”, is intended to establish sufficient ramping margins between consecutive time intervals of the optimization process and thereby reduce the frequency of temporary ramp shortages in the real-time market, while also producing a sufficient revenue for economic resources being held back in previous RTD intervals in order to provide their ramping capacity towards future intervals. Note that when a similar situation takes place by implementing multi-interval (look-ahead) RTD (instead of utilizing the
variability reserve), for example when the generation of an economic unit is held back from its maximum limit in the current real-time interval due to the need to provide upward ramping towards the following (look-ahead) interval, the resource suffers from a lost revenue in the first interval which is never settled upon, thereby receiving weaker incentives to actually provide the required flexibility [
37]. It is that price-incentivizing structure that brings an increasing interest to the use of the flexiramp product. The only difference, herein, is that the
variability reserve requirements are not re-allocated in RTD. Instead, the
variability reserve variable of each unit in the left-hand side of (52) and (53) is determined by the respective day-ahead UC award through (54) and (55). We thereby examine the pure impact of the UC pre-determined
variability reserve quantities on the outcome of RTD. The only case that the
variability reserve quantity of a unit in a given interval is not fulfilled by the respective UC award is when such quantity is actually dispatched in order to avoid a power balance violation in the current interval, rather than being secured to meet the expected
variability in future intervals. This is achieved in RTD_SI_Var by imposing a lower penalty price on
variability reserve deficits incurred in (54) and (55) (see the last term of objective (43)), as compared to the penalty prices imposed for load shedding and wind spillage.
RTD_Oneshot (model (43)–(51)): RTD economically dispatches the committed resources in an one-shot solution for the whole daily scheduling horizon, for comparison purposes; set essentially comprises all real-time intervals of the daily horizon.
3. Case Study
The proposed UC policies are tested using a modified version of the Greek interconnected power system for the daily scheduling period of 31 March 2014. A summary of the conventional generating unit techno-economic characteristics is presented on
Table 1. The basic modifications concern (a) a reduction in the hydro installed capacity—which is actually utilized mainly for peak-shaving reasons in Greece—from approximately 3 GW to 300 MW; (b) an increase in the Open Cycle Gas Turbine (OCGT) generating potential from approximately 150 MW to triple its size; and (c) a reduction in the ramping capability of the various resources by approximately 70%. The aim of the reductions is to create a more constrained case in terms of reliability in real-time operation, since the Greek generation fleet is currently flexible enough to absorb the inherent
uncertainty and
variability of the load and the wind generation typically existing in Greece. It should be stressed however, that the available generating potential is enough to cover the peak load of this case study, as well as the peak load of the Greek interconnected power system during 2014, which was equal to 9263 MW. Note also that the constrained case created affects negatively the solution times (
Section 5.3), especially regarding the SUC approach.
The energy offers are based on incremental steps above the units’ minimum variable costs. The offers for uncertainty reserve reflect the unit opportunity costs (foregone energy revenues), thus they increase inversely to the respective energy offers, while the offers for variability reserve increase in accordance with the unit ramping capability. The load shedding and the wind spillage cost are set to the typical value of 1000 €/MWh, while the variability reserve deficit cost in RTD is set to the lower value of 200 €/MWh.
Four UC policies are executed for comparison purposes:
SUC_15: The SUC model is executed with a 15-min real-time resolution t at the second stage.
SUC_60: The SUC model is executed with a 60-min real-time resolution t at the second stage (uniform hourly resolution throughout the model).
DUC_15: The DUC model is executed with a 15-min real-time resolution t, wherever set t is applicable (i.e., in DUC constraints or in the determination of the reserve requirements (34)–(37)).
DUC_60: The DUC model is executed with a 60-min real-time resolution t (uniform hourly resolution throughout the model); for example, the reserve requirements (34)–(37) are determined based on hourly net load averages (day-ahead forecasts and realizations per scenario), and the variability reserves are allocated to the various resources in (38) and (39) based on their hourly ramp capability.
Each UC policy (SUC_15, SUC_60, DUC_15, DUC_60) is tested against all RTD modes (RTD_SI, RTD_LA_1, RTD_LA_4, RTD_SI_Var, RTD_Oneshot), with each RTD mode having a 15-min time-step and solved for any separate net load scenario considered in UC. The results focus on uncertainty and variability reserve allocation, total expected costs, power balance violations (load shedding or wind spillage), and certain features relative to the functionality of the RTD mode executed.