IEEE Transaction on Power Systems

Demand Response in a Real-Time Balancing Market clearing with pay-as-bid pricing A. G. Vlachos, Member IEEE, P. N. Biskas, Member IEEE

Abstract— The vast installation of intermittent energy sources (especially wind) has distorted the normal strict pattern of the net demand (demand minus RES production), increasing the importance of real-time balancing markets, which handle efficiently imbalances between supply and demand. In this paper, the incorporation of demand response bids within a real-time balancing market is modeled. The price signal, to which the demand responds, is a price derived from the total cost incurred by increasing or decreasing power of generation units, with a pay-as-bid pricing scheme. The demand price is defined implicitly as a function of the upward and downward supply offers. The proposed balancing market clearing model is formulated as a Mixed Complementarity Problem. All interzonal and intra-zonal DC transmission constraints are incorporated to the problem, thus making it a problem of interregional balancing, and nodal prices are derived from its clearing. The credits/debits to generators for providing balancing energy are balanced in zonal and system level with the debits/credits of elastic and inelastic demand entities. The proposed model can be useful for designing future real-time balancing markets, in view of the forthcoming active participation of price-responsive demand and the significant RES penetration targets set by most countries. Index Terms — Demand response, real-time balancing market, interregional balancing, pay as bid, implicit demand pricing, Mixed Complementarity Problem

Csup

B. Parameters up Price of supply s energy offer, for increasing xs,t up energy quantity xs,t , in dispatch interval t,

( )

( )

dn Csdn xs,t

Cd ( xd ,t )

CAPs TM s RU s RDs Qsup

Qsdn

Qd

t

n g On Og d Dn

Dg s Sn Sg

Tnn'

X nn' LDn,t LDnsched X ssched

Elastic demand entity index Set of demand bids submitted at node n Set of demand bids submitted at node group g

X dsched

Supply entity index Set of supply bids submitted at node n Set of supply bids submitted at node group g

MPnsched

A. G. Vlachos is with the Regulatory Authority for Energy (RAE), Piraeus 132, 11854, Greece (e-mail: [email protected]). P. N. Biskas is with the Department of Electrical & Computer Engineering, Aristotle University of Thessaloniki, 54124 Greece (e-mail: [email protected]).

Price of supply s energy offer, for decreasing dn energy quantity xs,t , in dispatch interval t, defined by a smooth function of the decreased dn energy quantity xs,t , in €/MWh Price of demand d energy bid, for consuming energy quantity xd ,t , in dispatch interval t, defined by a smooth function of demand energy quantity xd ,t , in €/MWh

I. NOMENCLATURE A. Indices and Sets Dispatch interval index; typically equal to 5-min for real-time balancing markets; a typical realtime balancing dispatch horizon (hour) consists of twelve dispatch intervals Node index Node group index Set of nodes connected to node n Set of nodes included in node group g

defined by a smooth function of the increased up energy quantity xs,t , in €/MWh

X so

Available capacity of supply entity s, in MW Technical minimum of supply entity s, in MW Ramp-up limit of supply entity s, in MW/min Ramp-down limit of supply entity s, in MW/min Maximum production increase offered by supply entity s, in MW Maximum production decrease, offered by supply entity s, in MW Maximum demand response offered by elastic demand entity d, in MW Line flow limit from node n to node n΄, in MW Reactance of the line connecting nodes n and n’, in p.u. Load of inelastic demand at node n in dispatch interval t, in MW Load of inelastic demand at node n forecasted at the main scheduling process for the dispatch horizon, in MWh Energy production of supply entity s, scheduled in the main scheduling process, in MWh Load of elastic demand entity d, scheduled in the main scheduling process, in MWh Production of supply entity s at the preceding dispatch interval of the dispatch horizon, in MW Marginal price at node n, defined in the main scheduling process for the dispatch hour, in €/MWh

C. Main variables Adjustment factor for supply bids in node group g Wg ,t in dispatch interval t, in €/MWh Nodal marginal price of node n in dispatch MPn ,t interval t, in €/MWh 1

up xs,t

dn xs,t

xd ,t flnn',t

Cleared production increase of supply entity s in dispatch interval t, with respect to the energy X ssched scheduled in the main scheduling process, in MW Cleared production decrease of supply entity s in dispatch interval t, with respect to the energy X ssched scheduled in the main scheduling process, in MW Cleared demand response of demand entity d in dispatch interval t, in MW Line flow from node n to node n΄, in MW

δ n,t − δ n',t Voltage phase angle difference between nodes n and n’ in dispatch interval t, in rad II. INTRODUCTION The standard design of modern electricity markets throughout the world includes most often OTC bilateral contracts in parallel with a day-ahead market, being either a Power Pool or a pure Power Exchange. Intra-day markets exist mainly in the European countries, allowing the actors to adjust their traded quantities in order to balance their net positions. Last, balancing markets are usually designed to allow the system operators to handle deviations with respect to previous day schedules that are caused by unexpected events in generation, as well as different levels of demand and intermittent sources, resulting from short-term (day-ahead) forecast errors. There are two major classes of balancing markets: (a) Day-ahead balancing markets, which involve the procurement of balancing services in day-ahead basis for the 24 hours of the next day, with upward and downward balancing energy and reserves provided by generators, from which hourly upward and downward prices are derived; the dispatch of balancing power is performed in real-time. Examples of such markets can be found in most European countries (France, Italy, Germany, Spain, Romania, Hungary, etc. [1]). (b) Real-time balancing markets, solved for rolling 5-min dispatch intervals, in which a co-optimization of energy with primary, secondary and tertiary reserve is implemented, from which real-time energy and reserve prices are derived. Most U.S. Regional Transmission Organizations (RTOs) are examples of such markers. These markets are referred to by different names in different systems; e.g., real-time balancing market in PJM [2] and Midwest ISO [3], real-time energy market in New England [4], frequency control ancillary services (FCAS) market in Australia [5], and regulating market in the Nordic system [6]. Many variations of the above two standard designs can be found, depending on the incorporation of transmission system constraints, bidding rules for supply offers, pricing and settlement rules, the possibility to include price-responsive demand, etc. In the following, each of these issues are discussed in detail. A. Zonal/interregional balancing In the U.S. RTOs, the merit order stack with the aggregated supply curve is split into different stacks, one for each zone,

where only bids from within the corresponding zone participate in each stack [7]. The procurement of real-time balancing energy takes place separately in each zone without contributing to congestion on the inter-zonal interfaces. Moreover, any constraint violations can be easily removed by adjusting the real-time energy requirements in the adjoining zones to create the necessary counterflows [7]. In Europe, so far, market coupling of balancing markets has only been implemented within the Nordic market region and between Germany and the Nordic market region (Denmark) [1]. Elsewhere, balancing services are provided nationally, or in the case of Germany within the region of each System Operator (SO). Mutual support between regions is restricted only to emergency situations, such as unexpected power plant failures, and it is not remunerated (the provided energy is returned within a reasonable time-period) [1]. The primary constraint to harmonization of balancing markets in Europe is the significant diversity in their market design [8]-[9]. B. Bidding, pricing and settlement rules There are two settlement price methods: (a) the marginal price principle, and (b) the pay-as-bid principle. Pay-as-bid auctions are also known as “discriminatory auctions” because they pay winners a different price tied to the specific prices offered in their bids. In both methods, the upward and downward balancing prices can coincide or they can be differentiated [10]. Balancing markets applying marginal price settlement include the U.S. RTOs [2]-[3], the Netherlands [11], Australia [5] and the Nordic countries [6]. The pay-asbid pricing is applied in the balancing markets of France, Britain and in many other European countries [12]. Further, in some balancing markets the suppliers are paid when called for the downward direction, whereas in other cases they pay back the SO. For example, in Italy generators submitting decremental bids, when actually lowering their production in real-time, pay the SO. A positive downward bid price is the price the generator is willing to “pay” the system operator in order to decrease its power output. The generator has already sold the power in other markets, so if it reduces its output, it will save its operating costs. Therefore, if it bids at zero for downward regulation, it is actually making an extra profit equal to its operating costs in the regulation market. Thus if it pays the system operator any price lower than its operating costs, it will still make a profit. The downward regulation price can become negative too, in which case the generator is asking the system operator to pay him for lowering his output. However, in all balancing markets incremental bids lead to payments by the SO to the generators. C. Demand response bids Demand response in balancing markets can increase market liquidity and flexibility for balancing services (not just conventional power plants), potentially relieve generation and transmission constraints, reduce the severity of balancing market price spikes, reduce potential market power from supply entities, and lead to lower overall energy prices to all consumers [13]. The potential balancing resources existing in industrial, commercial and household electricity demand are discussed in [14]. At present, however, only an extremely small share of demand side management is actually integrated into balancing 2

markets in Europe, since tight access rules still prevent large potentials of Demand-Side Management (DSM) from engaging in balancing markets [1]. One pertinent criterion to market access is the lead-time and duration of a precommitment to the reserve and balancing markets. Additionally, a reasonable market design must be implemented that allows small units to engage in the market. Germany and the Nordpool countries are the frontrunners in giving incentives for DSM in their balancing markets [1]. Nordpool introduced a harmonization of balance regulation in 2009. The new regulation lowered the bid size to 10 MWh to explicitly encourage non-conventional generation, such as DSM. In 2007 in Germany, no DSM-potentials were prequalified and were thus unable to participate in the balancing market. An improved market design in 2008 allowed DSM technologies to provide balancing services in the minute reserve market [1]. One aspect of the improved market design was the introduction of a day-ahead auctioning of minute reserve capacities and a reduction of the minimum capacities for prequalification to 15 MW. Energy intensive industries made use of their DSM-potentials and provided approximately 20% of the hourly demand for reserve capacities in the tertiary balancing market. On the other hand, in PJM and Midwest ISO real-time balancing markets demand response bids are possible, but they are submitted as energy supply offers for production increase (or equivalently demand curtailment). No bids are allowed for price-responsive demand increase, when significantly low real-time prices are experienced [2]-[3]. D. Present paper contribution In view of the forthcoming active participation of priceresponsive demand and the significant RES penetration targets set by most countries, real-time balancing markets should be adjusted to embed demand response, in order to reap the benefits discussed in the first paragraph of Section II.C above. In this paper, the incorporation of demand response bids within a real-time balancing market is modeled. The price signal, to which the demand responds, is a price derived from the total cost incurred by increasing or decreasing power of generation units, with a pay-as-bid pricing scheme. The demand price is defined implicitly as a function of the upward and downward supply offers. The proposed balancing market clearing model is formulated as a Mixed Complementarity Problem (MCP). All inter-zonal and intra-zonal DC transmission constraints are incorporated to the problem, thus making it a problem of interregional balancing, and nodal prices are derived from its clearing. The credits/debits to generators for providing balancing energy are perfectly balanced in zonal and system level with the debits/credits of elastic and inelastic demand entities. The contribution of this work as compared to the current literature is as follows: a) The problem of a real-time balancing market with pay-asbid pricing for the supply entities, elastic demand response bids and interregional balancing is formulated and solved at one stage. To the best of the authors’ knowledge, there is no current literature referring to such model formulation. b) The model attains interregional (system-wide) balancing in a multi-area market, and full payment balance in regional

and system-wide level between supply and demand entities. Thus, there is no need for uplift accounts to attain payment balance for the imbalance settlement. III. MODEL DESCRIPTION AND MATHEMATICAL FORMULATION A. Description of the Balancing Market model In day-ahead, the SO conducts forecasts for load and intermittent sources (RES), in order to formulate a day-ahead schedule. Inevitably, during intraday and real-time operation, the forecasted values are regularly updated in order to accommodate deviations from day-ahead estimations, as dispatching intervals roll in time. The injected energy adjustments, constitute practically the usage of the regulation and reserve margins, that have been accounted in the dayahead scheduling, and, from a market point of view, a physical delivery of the ancillary services products. It is significant to stress that, depending on the market design, the reference main scheduling process may be either the self-scheduling of producers after the last intra-day market session (in most European countries) considering also the intra-zonal congestion, or the day-ahead scheduling in U.S. markets. The concept here is that the balancing problem’s objective is to select the generation adjustments and the elastic demand volumes that match the deviations in the net inelastic demand (inelastic demand minus RES production), with regard to the last main scheduling process (day-ahead scheduling in the U.S. RTOs, day-ahead dispatch in European markets). For clarity purposes, the term “main scheduling process” or “main schedule” will be used hereinafter. Without loss of generality, for the purposes of describing and illustrating the proposed methodology, the following assumptions are adopted in this paper: 1) A five-minutes dispatch interval and a twelve-intervals (hour-ahead) balancing dispatch horizon are considered. 2) Supply entities submit energy deviation bids, i.e. a bid for increasing and a bid for decreasing their energy output, with respect to the main schedule. 3) The nodes of the system are grouped in regulation areas (node groups), and the injected energy adjustments have to be selected according to the suppliers’ bids, in each regulation area. 4) In each node, the total load is defined as the sum of elastic and inelastic demand. 5) The inelastic demand is subject to deviations with respect to the day-ahead forecast, and it constitutes an input to the real-time balancing problem. 6) Supply entities submitting decremental bids, if cleared in real-time, pay the SO. Thus, the formation of balancing prices for demand should accommodate the cost incurred or saved by supply adjustments, considering a pay-as-bid reimbursement scheme. The inclusion of elastic demand in the balancing scheduling problem, adds a conceptual complexity that has to be considered in the price formation. On one hand, supply balancing bids entail the cost that each entity is willing to be extra credited or debited for the adjustments of his scheduled production. On the other hand, elastic demand bids entail the cost that demand entities are willing to pay for the actual 3

elastic demand cleared, thus the price perceived by demand entities should be consistent to their whole energy consumption, rather than to their load “deviations” with respect to the main schedule. Actually, since the elastic demand consumption is derived from the market solution, such entities do not bear the concept of “deviation” between the different stages of scheduling (e.g. “main scheduling process” and “balancing schedule”). Thus, there is no “deviation” for the elastic demand entities between the realtime balancing market and the main schedule (as e.g. with the inelastic demand); there is just their elasticity to the derived market prices. This conceptual difference is essential, and, in order to reach a rational equilibrium, either the supply balancing bids should be transformed to equivalent whole energy prices, or the demand bids should be transformed to balancing deviation offers. At the main scheduling process, the elastic demand is charged (in accordance with the derived day-ahead market prices). Nevertheless, since the elastic demand volumes at the main scheduling process are not final (they may change in the real-time balancing market), any imbalance payments between the main scheduling process and the balancing schedule imposed on the elastic demand should take into account the payments already performed in the day-ahead market. Thus, in order to perceive the total cost of their energy consumption in the balancing process, the elastic demand entities are settled for their total energy consumption, considering the payments already settled in the main scheduling process (based on the respective nodal prices and cleared volumes). The inelastic demand entities’ payments are settled only for their consumption deviation. The total payments by the demand entities must be perfectly balanced, per regulation area, to the total payments that are credited or debited to the supply entities. Consequently, the following payment rules apply: a) The generation should be paid for the total energy scheduled in the main scheduling process. b) The generation should be paid or charged for the total energy deviations (with respect to the main scheduling process) in the real-time balancing schedule. c) The elastic demand should be charged according to final energy schedule (taking into account the bid prices for consumption). d) The fixed load should be charged for the main schedule consumption (in accordance with the derived day-ahead market prices). e) The fixed load should be charged for the imbalance costs caused by the fixed demand deviations (with respect to the main scheduling process). Further, considering up-to-date practices, all existing realtime balancing markets consider deterministic input for intermittent sources and system load; there is no such balancing market, which might consider stochastic fluctuations of the respective variables (even the most mature balancing markets existing in the U.S., namely PJM and MISO [2]-[3]). In that sense, RES and load input depicts the trend of the updated RES injection and system load forecast, for a very short horizon ahead. It should be noted that, for simplicity reasons, in this paper input for fixed load and RES energy is

aggregated in a single inelastic demand curve. B. Mathematical formulation In terms of equilibrium conditions, the problem is formulated mathematically as follows: up dn , xs,t , xd ,t , xb,t , flnn',t , MPn ,t , and Wg ,t subject to Find xs,t the following set of constraints. 1) Definition of prices and payments: The energy adjustments (balancing) price component, MPn ,t , for demand entities is defined as the complement variable of the nodal energy balance equations in each dispatch interval. This variable is the marginal price of each node and has practically the same interpretation as the Lagrange Multipliers of the energy balance constraint, in a classical LP formulation approach. Due to the strict equality complementarity condition, MPn ,t may take either positive or negative values.

∑

s∈Sn

−

X ssched +

∑

d ∈Dn

∑

s∈Sn

xsup,t −

xd ,t − LDn,t −

∑

s∈Sn

∑

n '∈On

xsdn,t

0, ⊥ MPn,t , ∀n, t flnn ',t =

(1)

A lossless model is considered, thus a DC power flow is used, i.e. the flow between two nodes is expressed as: 1 (2) ⋅ δ n,t − δ n',t flnn',t = X nn' In each dispatch interval, energy adjustments payments debited (downward deviation) or credited (upward deviation) to suppliers should be balanced:    ∑  MPn ,t ⋅  ∑ xd ,t + LDn ,t − LDnsched   = n∈Og   d ∈Dn    (3) ∑ Csup xsup,t ⋅ xsup,t  − ∑ Csdn xsdn,t ⋅ xsdn,t 

(

s∈S g

( )

s∈S g

)

( )

  sched sched  MPn ,t ⋅ ∑ X d  ⊥ Wg ,t , ∀g , t n∈Og  d ∈Dn   The terms in the above equation express the following: The left hand side expresses the payment of elastic and inelastic demand at the balancing market. As aforementioned, elastic demand pays for the whole energy consumed, whereas inelastic demand pays only for the difference with respect to the main scheduling process. The first two terms in the right hand side express the payments of the supply entities for increasing and decreasing production, respectively. The third term on the right hand side expresses the payments already charged to the elastic demand settled at the main scheduling process. Practically, the elastic demand eventually pays for its total energy consumption at the balancing price, MPn ,t .. +

∑

2) Definition of energy volumes: For both increased and decreased volumes of supplied energy three basic constraints are considered: the upper bound of the bid, an inter-temporal ramp limit and a technical limit of the total output. For each set of constraints, a respective complement variable is defined. a) For energy increase, the complement variable of the bid up : limit is denoted as N s,t 4

xsup,t ≤ Qsup

N sup,t , ∀s, t

⊥

up the complement variable of the ramp limit is denoted as Rs,t :

(x where ( x

up s ,t

) (

)

− xsdn,t − xsup,t −1 − xsdn,t −1 ≤ RU s

up s ,t −1

− xsdn,t −1

)

for t=1 equals

(X

⊥ Rsup,t , ∀s, t (5) 0 s

)

− X ssched , and the

complement variable of the technical limit is denoted as Lup s,t : (6) ⊥ Lup s ,t , ∀s, t b) For energy decrease, the complement variable of the bid dn limit is denoted as N s,t : X ssched + xsup,t − xsdn,t ≤ CAPs

xsdn,t ≤ Qsdn

N sdn,t , ∀s, t

⊥

(7)

the complement variable of the ramp limit is denoted as

(x

) (

)

dn Rs,t

:

⊥ Rsdn,t , ∀s, t (8) and the complement variable of the technical minimum is denoted as Ldn s,t : up s ,t −1

− xsdn,t −1 − xsup,t − xsdn,t ≤ RDs

X ssched + xsup,t − xsdn,t ≥ TM s

(9) ⊥ Ldn s ,t , ∀s, t Finally, to avoid irrational simultaneous upward and downward adjustment, the following complementarity condition is included: (10) xsup,t ⋅ xsdn,t = 0 ⊥ Vs ,t , ∀s, t The complementarity condition associated to the nonup is formed as: negative variable xs,t

( )

up up up Wg ,t ⋅ Cs,t xs,t − MPn,t + N s,t − Vs,t up + Rs,t

dn − Rs,t

up dn − Rs,t +1 + Rs,t +1

dn + Lup s,t − Ls,t ≥ 0 ⊥

,

∀s,t

(11)

( )

,

∀s,t

(12)

dn xs,t ≥0

Elastic demand volumes are constrained by the respective bid limit, as follows:

where N d ,t

⊥

(13) N d ,t ∀d ,t , is the respective complement variable. Demand

entities consumption, xd ,t , is cleared at price MPn ,t , and the complementarity condition associated to the non-negative variable xd ,t is formed as:

( )

−Cd ,t xd ,t + MPn,t + N d ,t ≤ 0 ⊥

(15)

 MP − MP + K nn',t − K n' n,t  n',t  n,t = 0 ⊥ δ n,t , ∀ n,t (16) X nn'  n'∈On    where K nn',t , is the respective complement variable of the line

∑

nn' flow limit. The role of Wg ,t variable is explained as follows: In each

node group, supply entities have to be cleared using a bid merit order stack. Nevertheless, except from supply technical limits, line congestions within an area group may also impose an upper limit to the energy injection in each node. As aforementioned, prices MPn,t have practically the same interpretation as the Lagrange Multipliers of the energy balance constraint; furthermore, considering (15) and (16), they are signals of lines congestion and, as in a classical LP formulation, the comparison between nodal prices and energy injection bids, practically embed the congestion effect in bids clearing. However, in the presented model the order of dn and magnitude of MPn,t values is different than the Cs,t up values, and, in order to equilibrate supply bids with nodal Cs,t

marginal prices, the Wg ,t variable is utilized as an adjustment factor of

dn up and Cs,t ; the Wg ,t adjustment is uniformly Cs,t

applied to the supply bids in a specific node group, thus the merit order among supply bids is preserved. Furthermore, the pay-as-bid principle (equation (3)), imposes that suppliers’ surplus is zero, thus the solution equilibrium is driven primarily by the maximization of elastic demand surplus, as essentially makes the problem equivalent to elastic demand payments minimization. Considering the above, the supply

( )

up up surplus, expressed by the terms Wg ,t ⋅ Cs,t xs,t − MPn,t in (11)

dn dn dn −Wg ,t ⋅ Cs,t xs,t + MPn,t + N s,t − Vs,t

xd ,t ≤ Qd ,t

≤ Tnn' ⊥ K nn',t , ∀ n,n' ∈ On ,t

defined by the term −Cd ,t xd ,t + MPn,t in (14); condition (3)

Similarly, the complementarity condition associated to the dn non-negative variable xs,t is formed as:

dn − Lup s,t + Ls,t ≥ 0 ⊥

X nn'

( )

up xs,t ≥0

up up dn dn − Rs,t + Rs,t + Rs,t +1 − Rs,t +1

δ n,t − δ n',t

(4)

xd ,t ≥ 0 , ∀d ,t

(14)

3) Other constraints and equations: Conditions (1)-(14) outline the basic concept for the pay-as-bid real-time balancing market clearing problem. The set of physical constraints considered in this paper is completed by the interzonal and intra-zonal line capacities, as follows:

( )

dn dn and −Wg ,t ⋅ Cs,t xs,t + MPn,t in (12), is essentially fictitious.

From a mathematical point of view, by assuming (3) being a constraint in a NLP formulation, the Wg ,t variable would be the Lagrange multiplier of that constraint, and the terms

( )

( )

up up dn dn , −Wg ,t ⋅ Cs,t , would be the partial Wg ,t ⋅ Cs,t xs,t xs,t up derivatives of the Lagrangian function with respect to xs,t and dn , respectively. xs,t

In the presented formulation, conditions and variables are coupled in a square system of equations, which in general impose that either the variable or the complementarity condition should be non-zero (positive). The equilibrium conditions incorporated in the problem add a significant complexity, considering (a) the fact that demand prices are computed endogenously within the model based on the pay-asbid reimbursement concept for the supply, and (b) the intertemporal (time-coupling) complementarity conditions (5), (8). The resulting formulation constitutes a Mixed Complementarity Problem (MCP). MCP models inherently do 5

not bear an objective function; they rather comprise only a square set of inequality or equality constraints coupled to respective variables. This structure represents a set of equilibrium conditions that have to be matched. As afoementioned, the presented conditions follow the demand surplus maximization concept, despite the absence of an objective function in that model. Nevertheless, these conditions cannot be reversely expressed as a classical NLP formulation, due to the pay-as-bid pricing rule of supply entities. The direct solution of the system equilibrium conditions by complementarity methods has important computational advantages. MCPs involving thousands of variables, complementarity and equality conditions can be solved even using available general-purpose software, such as a variety of solvers within GAMS [15].

would result in increasing demand clearing prices for all dispatch intervals, causing a decrease of the elastic demand volumes. These remarks can be observed in the following figures. Fig. 1 depicts the cleared elastic demand volumes, summed per group of nodes, whereas Fig. 2 depicts the average (per group of nodes) clearing prices, MPn ,t . In these figures the negative correlation between demand volumes and clearing prices is shown. A graphical overview of the nodal clearing prices MPn,t in the first, sixth and last dispatch interval, is illustrated in Fig. 3, as compared to the nodal prices of the main scheduling process. It should be noted that nodal prices deviations become higher as time (dispatch intervals) evolves, which is rational, 1200

IV. ILLUSTRATIVE IMPLEMENTATIONS

1100

following steps are applied: a) An arbitrary trend (increase or decrease) and respective hourly volume are selected for each entity. For the illustrated case, an increase trend was selected for the majority of the inelastic demand entities, resulting to an system-wide overall increase of the fixed load. b) For each entity a step-wise linear increasing or decreasing curve is formed; each step represents energy demand in the respective dispatch interval. The linear ramp and the first intervals’ energy offset are selected so that the integral of all steps is equal to the hourly horizon volume, selected in the previous step. The total inelastic load per dispatch interval, considered in this illustration, is presented in Table I. Normally, the increased inelastic load is expected to be balanced by increased supply volumes, and subsequently a positive balancing cost is expected, namely the suppliers are credited for their additional production in the system. This

1000

MW

900 800 700 600 500 400 T1

T2

T3

T4

T5

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T7

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Group-2

Group-3

Fig. 1: Cleared elastic demand volumes 70 68 66

€/MWh

64 62 60 58 56 54 52 50 T1

T2

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Dispatch interval Group-1 Average

Group-2 Average

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System Average

Fig. 2: Average clearing prices MPn ,t per node group 85 80 75 70

€/MWh

A. IEEE RTS-96 The IEEE RTS-96 [16] system is used as template for demonstrating the implementations of the presented approach. The system consists of 73 nodes, which are organized in 3 groups, i.e. nodes N101-N124 consist group “G1”, nodes N201-N224 consist group “G2”, and nodes N301-N325 consist group “G3”. The original IEEE RTS-96 network configuration is maintained. A classical LP approach, that maximizes the supply and demand surplus, is utilized, in other to obtain a set of reference values for the X ssched , X dsched and MPnsched parameters. This preprocess resembles a typical day-ahead scheduling. For testing purposes, day-ahead supply energy offers and demand bids are formed as step-wise linear functions. Demand and supply offers are randomly generated. For each node, a fixed load ( LDnsched ) is used to represent the inelastic demand. Regarding the real-time balancing market model, suppliers adjustment offers are formed as one-step bid, for each adjustment direction. Elastic demand entities’ bids are assumed to be the same, as in the main scheduling process. In order to populate the data series of inelastic demand, LDn,t , for each dispatch interval of the hourly horizon, the

65 60 55 50 45 40 35 101

201

301

325

Nodes Dispatch Interval-1

Dispatch Interval-6

Dispatch Interval-12

Main Schedule

Fig. 3: Nodal clearing prices MPn ,t

6

considering that increasing load induces more congestion in the network, and consequently higher divergence in the nodal prices. Fig. 4 presents the supply entities upward volumes (summed for each group of nodes). These upward volumes represent the supplier adjustments with respect to their main scheduling process. Fig. 5 presents the total production that balances total demand in each dispatch interval. This total production is practically the sum of the main schedule volumes plus the supply volumes adjustments in each dispatch interval. These figures implicitly depict the ramping of production, which is practically equal to the difference in the volumes between two subsequent dispatch intervals. It should be noted that steeper or abnormal adjustments that may appear, in the first few intervals, are due to the assumed initial conditions of the system ( LDn,t =0 , X so ) at the interval preceding the balancing horizon. In these intervals, some supply entities may exhibit a limited downward adjustment. Fig. 6 illustrates the payments credited to suppliers, for upward increase, in each group of nodes. It should be noted that suppliers payments are settled considering a pay-as bid rule, and practically exhibit the cost of the required adjustments, which is subsequently distributed in the demand entities, according to the rule defined in (3). Fig. 7 depicts the respective payments charged to demand entities. Table I summarizes the energy balance per dispatch interval, whereas Table II summarizes the payments balance at system level per dispatch interval. The first column depicts the sum already charged to elastic demand at the main scheduling process. The third column expresses the elastic demand credits for decreasing its volume, due to its response to the higher 250

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150

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50

0 T1

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Dispatch interval Supply Group-1

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3,500 € 3,000 € 2,500 € 2,000 € 1,500 € 1,000 € 500 € 0€ T1

T2

T3

Supply Group-1

MW

3800 3600 3400 T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

Dispatch interval Supply Group-1

Supply Group-2

Fig. 5: Supply entities total volumes per node group

Supply Group-3

T7

T8

T9

T10

T11

T12

Supply Group-2

Supply Group-3

6,000 € 5,000 € 4,000 € 3,000 € 2,000 € 1,000 € 0€ T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

Dispatch interval Elastic Demand Group-1 Inelastic Demand Group-1

Elastic Demand Group-2 Inelastic Demand Group-2

Elastic Demand Group-3 Inelastic Demand Group-3

Fig. 7: Demand entities payments per node group

nodal prices. The inelastic load charges for its upward deviation are shown in the fourth column. The supplies credits for their upward production are shown in the last column of Table II. The sum of the elastic demand payments for its consumption (shown in the second column of Table II with a negative sign) is calculated by the subtraction of the main schedule charges minus the balancing markets credits. It should be noted that there is a payment balance in the last three columns of Table II. The resulting payments indicate a rational concept: the disturbance caused by the inelastic demand imposes (a) supply adjustments and (b) elastic demand re-scheduling, and a TABLE I ENERGY BALANCE PER DISPATCH INTERVAL (UPWARD DEVIATION CASE)

4400

4000

T6

Fig. 6: Supply entities payments for upward increase

Dispatch interval

4200

T5

Dispatch interval

Fig. 4: Supply entities upward volumes per node group 4600

T4

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

Elastic demand (MW) 3,064 3,089 2,999 2,894 2,790 2,686 2,577 2,464 2,356 2,242 2,126 2,011

Inelastic load (MW) 8,703 8,850 8,997 9,144 9,291 9,438 9,585 9,732 9,879 10,026 10,173 10,320

Suppliers production (MW) 11,767 11,939 11,996 12,038 12,081 12,124 12,162 12,196 12,235 12,268 12,299 12,331

7

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

Elastic demand main schedule settlement charge (€) 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604

Elastic demand total settlement charge (€) 14,947 14,911 14,664 14,293 13,963 13,651 13,284 12,803 12,391 11,905 11,364 10,785

Elastic demand imbalance settlement credit (€) 657 693 940 1,311 1,641 1,953 2,320 2,801 3,213 3,699 4,240 4,819

Inelastic Suppliers load imbalance imbalance settlement settlement credit (€) charge (€) -2,455 1,798 -3,171 2,479 -3,950 3,010 -4,752 3,441 -5,593 3,952 -6,472 4,519 -7,360 5,040 -8,296 5,495 -9,243 6,030 -10,184 6,484 -11,149 6,909 -12,192 7,372

TABLE III ENERGY BALANCE PER DISPATCH INTERVAL (DOWNWARD DEVIATION CASE) Dispatch interval T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

Elastic Demand (MW) 3,624 3,665 3,655 3,675 3,711 3,724 3,736 3,754 3,764 3,776 3,783 3,784

Inelastic Suppliers load production (MW) (MW) 7,765 7,606 7,447 7,288 7,129 6,970 6,811 6,652 6,493 6,334 6,175 6,016

11,389 11,271 11,102 10,963 10,840 10,694 10,547 10,406 10,257 10,110 9,958 9,800

TABLE IV ENERGY PAYMENTS PER DISPATCH INTERVAL (DOWNWARD DEVIATION CASE) Disp atch inter val

Elastic demand main schedule settlement charge (€)

Elastic demand total settlement charge(€)

Elastic demand imbalance settlement credit (€)

Inelastic load imbalance settlement credit (€)

Suppliers imbalance settlement charge (€)

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604 15,604

15,417 15,289 14,944 14,773 14,659 14,451 14,217 14,013 13,658 13,342 12,977 12,461

187 315 660 831 945 1,153 1,387 1,591 1,946 2,262 2,627 3,143

1,850 2,447 3,037 3,604 4,104 4,608 5,107 5,582 5,950 6,339 6,686 6,906

-2,038 -2,762 -3,697 -4,435 -5,049 -5,762 -6,494 -7,173 -7,895 -8,600 -9,313 -10,049

to the main schedule settlement is covered either by the inelastic load debits (in case of upward deviation) or by the supply entities’ debits (in case of downward deviation). B. Greek power system The presented approach has been tested also with the Greek power system. Using historical data of the system load and Renewable Energy Sources (RES) injections per minute for the whole year 2012, the hour with the sharper upward net load (system load minus RES injections) increase (08:0009:00 on Monday 30/07/2012) has been selected for demonstration purposes. The minute-data have been integrated in five-minutes intervals, and assigned to the load buses. For demonstration purposes, the load volumes in each node, have been split to inelastic (about 66%) and elastic (about 34%) entities; for the latter, several price-quantity steps have been constructed. Regarding generation units offers, the estimated variable cost has been used as a basis for constructing the respective energy offers (used in the main schedule), as well as for the upward and downward deviation offers (used in the real-time balancing market). Fig. 8 illustrates the upward supply volumes per unit category (units are grouped based on their fuel) and per dispatch interval, along with the system average clearing prices ( MPn ,t ), derived by the solution of the real-time balancing market, and corresponding to the right axis of the graph. 500

47.50

450

47.00

400

46.50

350

46.00

300 45.50 250 45.00 200

€/MWh

Disp atch inter val

the elastic demand re-scheduling. Practically elastic demand “perceives” a counter-back payment for decreasing its volume. A similar remark holds in the case of decreasing inelastic demand. Tables III and IV summarize the attained results. The suppliers are charged for their downward adjustment, and this amount is credited to demand entities. Inelastic demand receives a payment, but this “relief” is less than the credit of suppliers. Elastic demand receives also a payment, although it increases its consumption. This result is due to the fact that the balancing prices are much lower than the prices in the main scheduling process, so the elastic demand will eventually be cleared by the balancing process at higher volume with a lower overall payment, as compared to the main schedule. It should be noted that in both cases (upward and downward inelastic demand deviation) the elastic demand eventually pays for the total energy consumed at the balancing price, MPn ,t , and the difference of this payment with respect

MW

TABLE II ENERGY PAYMENTS PER DISPATCH INTERVAL (UPWARD DEVIATION CASE)

44.50

150 100

44.00

50

43.50

0

43.00 T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

Dispatch interval

recalculation of their payments. Thus, the actors causing the disturbance pay for the supply upward production cost and for

LIG

GAS

System Average Price

Fig. 8: Supply entities upward volumes and average clearing prices MPn ,t

8

TABLE V ENERGY BALANCE PER DISPATCH INTERVAL Dispatch interval T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

Elastic demand (MW) 2435 2410 2403 2392 2380 2373 2367 2355 2324 2301 2286 2255

Inelastic load (MW) 4958 5004 5039 5070 5099 5165 5211 5243 5294 5338 5377 5433

Finally, in order to evaluate the model’s efficiency and scalability, the model is also tested on a 365-bus system (by replicating five times the IEEE RTS-96 and adjusting appropriately the respective data), with 480 supply entities, 255 elastic demand entities and 255 fixed load entities. The resulting problem size is about 161,000 equations and variables, and the density is about 0.002%. The reported solver CPU time is 7.8 minutes; this performance is acceptance in terms of a real-time balancing market that runs every hour during the dispatch day.

Suppliers production (MW) 7393 7414 7442 7463 7478 7538 7579 7598 7618 7639 7662 7688

V. CONCLUSIONS

TABLE VI ENERGY PAYMENTS PER DISPATCH INTERVAL Disp atch inter val

Elastic demand main schedule settlement charge (€)

Elastic demand total settlement charge (€)

Elastic demand imbalance settlement (€)

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12

9,041 9,041 9,041 9,041 9,041 9,041 9,041 9,041 9,041 9,041 9,041 9,041

9,037 8,956 8,961 8,952 8,931 9,027 9,085 9,078 8,996 8,943 8,927 8,855

4 85 80 89 110 13 -44 -37 44 97 114 186

Inelastic Suppliers load imbalance imbalance settlement settlement credit (€) charge (€) -747 -921 -1,054 -1,174 -1,284 -1,555 -1,746 -1,876 -2,079 -2,261 -2,422 -2,656

743 836 974 1,086 1,175 1,541 1,790 1,913 2,034 2,163 2,309 2,470

Table V summarizes the energy balance per dispatch interval. It is evident that the elastic demand decreases due to the raising real-time prices. Table VI summarizes the payments balance at system level per dispatch interval. The suppliers (generating units) are paid for their increased production, and the elastic demand pays or is paid back the difference between the final settlement and the main scheduling charge. The inelastic demand pays (due to the positive consumption deviation); this payment covers both the suppliers and the elastic demand. C. Computational and Feasibility Issues The illustrative cases have been implemented and solved in GAMS [15] using the PATH solver, running on a notebook PC, with Intel Pentium M processor at 1.73 GHz, 1.5 GB RAM. Convergence tolerance was set to 1e-06. Regarding the IEEE RTS-96, the order of magnitude of the model’s size is 32,600 equations and variables, and the density is about 0.01%. The reported solver CPU time was 9.6 seconds. Regarding the test case of the Greek power system, the resulting problem size is about 85,896 equations and variables, and the density is about 3.4E-5. The reported solver CPU time is 41 seconds.

Efficient balancing markets allow security of supply to be ensured at the least cost and can deliver environmental benefits by reducing the need for back-up generation. This target is further enhanced by incorporating demand response in the real-time balancing markets, meaning that customers change their operating patterns to aid system balancing. Moreover, interregional balancing has significant advantages over national balancing, since larger regions reduce the overall demand for balancing and reduce costs for providing balancing power through a broader portfolio of power plants and additional sources for balancing power. The model described in this paper incorporates both demand response bids and interregional balancing within a real-time balancing market with pay-as-bid pricing for supply entities. The scope of the presented real-time balancing market is to obtain the elastic demand volumes that would be cleared – based on the respective priced bids – considering a very short term load and RES forecast (hour-ahead) and that the supply balancing bids will be paid under a pay-as-bid settlement rule. The attained results are consistent with the theory of Ramsey-Boiteux pricing, under which the inelastic demand should be settled with a higher overall price as compared to the elastic demand, which constitutes the basic feature of “price discrimination” in electricity tariffication. It should be noted that a generic framework for the solution of the real-time balancing market has been presented in this paper, in which load representatives may participate according to the price signals they acquire from the market and according to the commercial packages contracted with their end customers. This generic framework is valid independently of any regulatory-defined demand response threshold (in MW), which may allow certain group(s) of customers to engage in demand response activities. Such threshold in realworld markets is usually dependent on (a) the scale of deregulation of the market, (b) the maturity of the participants (both large/medium industries and load representatives), and (c) the existing smart grid (metering, communication, data management) infrastructure in the respective country. The greater the extent of deregulation, the maturity of the market participants and the existence of such infrastructure, the lower would be the threshold defined by the regulatory authority. Nevertheless, the proposed method can be applied equally well for all potential customer groups that would be willing to engage in such activities. The proposed model has a broad scope of applications that may be of interest to system and market operators, electricity market designers and economists. The authors’ goal is to 9

extend the current work by introducing enhanced pricing rules in the proposed model, incorporating other side-payments (e.g. for RES feed-in tariffs) within the implicit price formation of the demand entities. VI. ACKNOWLEDGEMENT The authors are thankful to ENTSO-E for providing the UCTE network data, from which the reduced Greek transmission system has been deducted, and to the Greek Independent Power Transmission Operator (ADMIE S.A.) for providing the system load and Renewable Energy Sources (RES) injections per minute for the whole year 2012. VII. REFERENCES [1]

[2]

[3]

[4] [5]

[6] [7]

[8]

[9]

[10]

[11] [12]

[13]

[14]

[15] [16]

F. Borggrefe, K. Neuhoff, “Balancing and Intraday Market Design: Options for Wind Integration”, Climate Policy Initiative, January 2011. [Online]. Available: http://climatepolicyinitiative.org/wp-content/ uploads/2011/12/Intraday-and-wind-integration-paper.pdf. PJM Manual 11, Energy & Ancillary Services Market Operations, PJM, 2012. [Online]. Available: www.pjm.com/~/media/documents/manuals/ m11.ashx. Midwest ISO, “Energy and Operating Reserve Markets – Business Practices Manual”, January 2012. [Online]. Available: https://www. midwestiso.org/_layouts/MISO/ECM/Redirect.aspx?ID=19178. Market Operations, ISO New England, Inc., Apr. 2006. [Online].Available: http://www.iso-ne.com. “Operating procedure: Frequency control ancillary services,” National Electricity Market Management Company (NEMMCO), Jul. 2005. [Online]. Available: http://www.nemmco.com.au. Nordic Grid Code 2004, Nordel, Jun. 2004. [Online]. Available: http://www.nordel.org. A. Papalexopoulos, H. Singh, “Alternative design options for a realtime balancing market”, 22nd IEEE Power Engineering Society International Conference on Innovative Computing for Power, pp. 272 – 277, 2001. L. Vandezande, L. Meeus, R. Belmans, M. Saguan, J.M. Glachant, “Well-functioning balancing markets: A prerequisite for wind power integration”, Energy Policy, vol. 38, pp. 3146–3154, 2010. “Study of the interactions and dependencies of Balancing Markets, Intraday Trade and Automatically Activated Reserves”, Katholique University of Leuven, Technical Report, February 2009. [Online]. Available: http://ec.europa.eu/energy/gas_electricity/studies/doc/electri city/2009_balancing_markets.pdf. M. Olsson, L. Soder, “Modeling real-time balancing power market prices using combined SARIMA and Markov processes”, IEEE Transactions on Power Systems, vol. 23, no. 2, May 2008. The Imbalance Pricing System as at 01-01-2001, revised per 26-102005, TenneT, Oct. 2005. [Online]. Available: http://www.tennet.nl. K. Verhaegen, L. Meeus and R. Belmans, “Development of balancing in the Internal Electricity market in Europe”, Technical Report. [Online]. Available: www.esat.kuleuven.be/electa/publications/ fulltexts/pub_1527.pdf. S.D. Braithwait, K. Eakin, “The role of demand response in electric power market design”, Edison Electric Institute, Technical Report, October 2002. [Online]. Available: D. Feng, “New real-time market facilitating demand-side resources for system balancing”, 2011 IEEE Power and Energy Society General Meeting, pp. 1-6, July 2011. General Algebraic Modeling System. [Online]. Available: www.gams.com. Reliability Test System Task Force of the Application of Probability Methods Subcommittee, “The IEEE Reliability Test System-1996,” IEEE Trans. Power Syst., vol. 14, no. 3, pp. 1010–1020, Aug. 1999.

of Athens, Greece, in 1996 and 2001 respectively. From 1997 to 2003 worked as consultant to various projects. From 2004 is with the scientific staff of the Regulatory Authority of Energy (RAE) in Greece. His research interests cover electrical power systems operations, security & control, production scheduling and real time dispatch, transmission network expansion, energy management systems, and computer applications for power systems modeling and simulation.

Pandelis Biskas received his Dipl. Eng. degree from the Department of Electrical Engineering, Aristotle University, Thessaloniki, in 1999, and his Ph.D, in 2003 from the same university. He also performed his Post Doc research from March 2004 till August 2005 in the same university. From March 2005 till July 2009 he was a power system specialist at the Hellenic Transmission System Operator (HTSO), Market Operation Department. Currently, he is a Lecturer at the Aristotle University of Thessaloniki, in the Department of Electrical and Computer Engineering. His research interests are in power system operation & control, in electricity market operational and regulatory issues, and in transmission pricing.

VIII. BIOGRAFIES Andreas Vlachos received his Dipl. of electrical and computer engineering and the Ph.D. degree in engineering from the National Technical University

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