Cross-product manipulation with intertemporal constraints: An equilibrium model

Energy Policy 134 (2019) 110851

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Cross-product manipulation with intertemporal constraints: An equilibrium model

T

Nongchao Guoa, Chiara Lo Preteb,∗ a b

NYISO, USA John and Willie Leone Department of Energy and Mineral Engineering, The Pennsylvania State University, PA 16802, USA

ARTICLE INFO

ABSTRACT

Keywords: Virtual transactions Financial transmission rights Electricity price manipulation Equilibrium models Mathematical program with equilibrium constraints (MPEC)

The use of uneconomic virtual transactions in day-ahead electricity markets with the intent to benefit related financial positions constitutes cross-product manipulation, and has emerged as a policy concern in recent years. Developing analytical frameworks and models to explain the means for achieving sustained day-ahead price manipulation is a challenge. This paper presents a two-stage equilibrium model of day-ahead price manipulation to enhance the value of financial transmission rights (FTRs). We cast the problem as a Stackelberg game between manipulating traders in the day-ahead market (leaders) and generating firms, grid operator and traders without FTRs in the day-ahead and real-time markets (followers). The model accounts for features specific to electricity systems, like intertemporal constraints of power generating units and real-time uncertainty, and considers imperfect competition as a condition allowing manipulation in equilibrium. We simulate hourly financial trading and operations decisions in a small test system for 24 hours. Results suggest that cross-product manipulation is sustained in equilibrium only when both physical and financial participants engage in Cournot competition. Further, as a result of loop flows, price separation between FTR source and sink may be induced by virtual transactions at network locations that are not on the FTR path.

1. Introduction Virtual transactions are purely financial positions that allow market participants to exploit arbitrage opportunities arising when day-ahead electricity prices are predictably higher or lower than expected realtime prices. Specifically, virtual demand (supply) bids allow purchase (sale) of energy in the day-ahead market at a network location, and are settled with a countervailing offer (bid) at the real-time price. Virtual bids clear with physical bids and may set the day-ahead locational marginal price. Empirical evidence suggests that profitable virtual transactions improve price convergence between day-ahead and real-time energy prices (Saravia, 2003; Güler et al., 2010; Jha and Wolak, 2015; Li et al., 2015) and promote the optimal commitment of generation resources in the day-ahead market (Güler et al., 2010; Jha and Wolak, 2015). However, strong interactions between virtual transactions and other elements of the electricity market design may create inefficient incentives and unintended consequences. For example, financial transmission rights (FTRs) are contracts to hedge transmission congestion between two locations (or nodes) in the electric network (termed source

∗

and sink, respectively), and entitle their holders the right to collect a payment when day-ahead congestion arises, inducing price separation between source and sink (Hogan, 1992; Rosellón and Kristiansen, 2013). Since FTRs settle at day-ahead electricity prices, market participants may place unprofitable virtual bids to affect these prices and enhance the FTR value. This creates divergence between day-ahead and real-time prices (Potomac Economics, 2016), and may lead to productive, allocative and transactional inefficiencies (Kyle and Viswanathan, 2008; Ledgerwood and Carpenter, 2012). For example, when day-ahead congestion arises from source to sink of the FTR contract, the holder receives a payment equal to the difference of day-ahead congestion prices between the sink and source nodes, multiplied by the MW award of the contract. Placing virtual demand bids at the FTR sink tends to worsen day-ahead congestion, causing the price differential between source and sink to increase and enhancing the value of the FTR. In addition, unprofitable virtual demand bids diverge day-ahead and expected real-time prices at the sink. Cross-product manipulation involving unprofitable virtual transactions and related financial positions has long been acknowledged (Celebi et al., 2010), but came under renewed scrutiny in recent years, as a result of electricity market ma-

Corresponding author. E-mail address: [email protected] (C. Lo Prete).

https://doi.org/10.1016/j.enpol.2019.06.059 Received 1 March 2019; Received in revised form 12 June 2019; Accepted 27 June 2019 0301-4215/ © 2019 Elsevier Ltd. All rights reserved.

Energy Policy 134 (2019) 110851

N. Guo and C. Lo Prete

Nomenclature

Ft , l Pj (Pj ) PTDFi, l Rj (Rj ) RPi St Tl

Indices f h i j l t ψ ω

generating firm hour node power plant transmission path trader day-ahead scenario real-time scenario

Variables under day-ahead scenario ψ

a i, h c j, h

di , h pi, h

Sets H I ISI ISO J Jf Ji T TN TM

set set set set set set set set set set

of of of of of of of of of of

dect , i, h (inct , i, h ) s j, i, h

hours nodes FTR sink nodes FTR source nodes power plants power plants owned by firm f power plants at node i traders traders without FTR positions manipulating traders with FTR positions

u j, h

wi, h yi, h

i, h

Cj C jSU

(

i, h )

arbitrage sales to node i at hour h commitment cost of plant j at hour h

electric demand at node i and hour h energy price at node i and hour h

virtual energy purchases (sales) of trader t at node i and hour h sales of plant j at node i and hour h commitment status of plant j at hour h

transmission price at node i and hour h transmission services to node i at hour h

Variables under real-time scenario ω

a i, h c j, h di , h pi, h s j, i , h u j, h wi, h yi, h

Parameters i, h

FTR position of trader t TM on path l min power output (capacity) of plant j power transfer distribution factor at node i on path l ramp-down (ramp-up) limit of plant j reference price for virtual bids at node i collateral of trader t transmission capacity on path l

intercept of day-ahead (real-time) inverse demand at node i and hour h slope of inverse demand at node i and hour h marginal cost of generation for plant j start-up cost of plant j

arbitrage sales to node i at hour h commitment cost of plant j at hour h electric demand at node i and hour h energy price at node i and hour h sales of plant j at node i and hour h commitment status adjustment of plant j at hour h transmission price at node i and hour h transmission services to node i at hour h

manipulation and improving market performance.1 Equilibrium models may also be used to quantify the effect of manipulation on prices, which is required for calculating disgorgement (i.e., repayment of unjust profits from the violation of regulations, orders and tariffs) in FERC enforcement actions. Unlike previous studies on cross-product manipulation in electricity markets (Ledgerwood and Pfeifenberger, 2013; Birge et al., 2018), our work uses equilibrium models. Lo Prete et al. (2019a) adapt a model from cash-settled financial markets to the context of electricity markets, showing that cross-product manipulation is possible under uncertainty and asymmetric information. In a different paper, Lo Prete et al. (2019b) develop a three-stage equilibrium model that represents the manipulating trader's problem in the FTR, dayahead and real-time markets. Given suitable assumptions, the real-time equilibrium can be derived in closed form in a two-node setting, and we may convert the trader's three-stage problem into a two-stage problem in the FTR and day-ahead markets. This solution approach cannot be extended to networks, since it necessitates closed-form solutions for real-time market equilibria that may be derived in a two-node setting, but are generally not available in networked regimes. This paper presents a two-stage, complementarity-based equilibrium model of dayahead price manipulation to enhance the value of financial

nipulation enforcement actions brought by the Federal Energy Regulatory Commission (FERC) (Federal Energy Regulatory, 2012, 2013, 2014a). Several investigations targeted financial market participants that account for a large share of virtual transactions cleared in electricity markets (Federal Energy Regulatory, 2016; California ISO (CAISO), 2016a; Monitoring Analytics, 2016a). Mechanisms and conditions that allow physical load and generation resources to exercise market power in electricity markets are well understood (Newbery, 1995; Borenstein et al., 2002, 2008; Joskow and Kahn, 2002; Wolak, 2003; Puller, 2007; Lo Prete and Hobbs, 2015). Part of the literature has examined market power issues raised by transmission constraints in restructured electricity markets (Cardell et al., 1997; Oren, 1997; Borenstein et al., 2000; Joskow and Tirole, 2000; Joung et al., 2008). However, these studies do not consider crossproduct manipulation involving the role of virtual transactions and related financial positions, or the role of financial market participants in electricity markets. A major challenge is to explain how cross-product manipulation may be sustained over time, absent control over generation and load resources. Predictable differences between dayahead and real-time prices that result from sustained cross-product manipulation should incent market participants to place offsetting virtual positions to profit from arbitrage opportunities and enhance price convergence. What economic conditions (e.g., imperfect competition, transaction costs (Vayanos et al., 2013)) or market design flaws allow cross-product manipulation to persist over time, rather than as an isolated incident? Equilibrium models may provide insights for answering this question (Lo Prete et al., 2019a). If market imperfections and/or design flaws do not support efficient outcomes in equilibrium, the direction and magnitude of their effects should be assessed to evaluate refinements of electricity market design for mitigating

1 Cross-product manipulation may include but is not limited to the use of uneconomic virtual transactions in day-ahead electricity markets. For example, some enforcement actions brought by the FERC involved the use of physical schedules (Federal Energy Regulatory, 2012, 2013) or price indexes (Federal Energy Regulatory, 2017) to benefit sufficiently leveraged related financial positions. It should be noted that the model presented in this paper focuses on cross-product manipulation using virtual transactions to benefit financial transmission rights; other types of cross-product manipulation strategies will be considered in future research.

2

Energy Policy 134 (2019) 110851

N. Guo and C. Lo Prete

transmission rights. We cast the problem as a Stackelberg game between manipulating traders in the day-ahead market (leaders) and generating firms, grid operator and traders without FTRs in the dayahead and real-time markets (followers). FTR positions of the manipulating traders are taken as exogenous in the game. Building on Lo Prete et al. (2019b), we focus on imperfect competition as a condition allowing price manipulation in equilibrium. However, realism of grid representation is enhanced in two important ways. First, instead of considering a single hour of market operations, we model financial trading and operations decisions in the energy markets for 24 h. This enables inclusion of intertemporal constraints that limit a generating unit's ability to produce electricity, like commitment decisions and ramping limits. These constraints complicate the decision problem of the manipulating trader, who should consider the multi-period impacts of her trades on prices (rather than just the impact on one period's price) and the possibility that other market participants take advantage of profitable arbitrage opportunities created by the manipulation. Second, we enhance spatial dimension by extending the analysis to a small network, instead of focusing on the source and sink of the FTR path. Thus, we may account for network externalities stemming from the fact that, when power is transported between two points on the transmission system, it flows through all the lines connecting the two, not just the shortest distance between the two points (“parallel flows”). Our numerical simulations consider a game with one manipulating trader, and the resulting two-stage problem is a mathematical program with equilibrium constraints (MPEC) (Luo et al., 1996). The remainder of the paper proceeds as follows. Section 2 presents the model formulation. Section 3 discusses network characteristics for the simulations, while Section 4 presents the results. Finally, Section 5 addresses policy implications and provides concluding remarks.

pi, h =

i, h

( s j , i, h + s j , i, h ) + a i, h + a i, h ,

i, h

h, i

(1)

j J

where s j, i, h (s j, i, h ) represent the day-ahead (real-time) sales of plant j at

node i and hour h, and ai, h (ai, h ) denote the day-ahead (real-time) arbitrage sales of the system operator (i.e., power bought at the hub and sold at node i to ensure that transmission prices equal nodal price differences (Hobbs, 2001)). Note that our model captures an important feature of two-settlement electricity markets: day-ahead sales represent commitments to sell power for delivery in real time, while real-time sales are residual in that they can only be made if generating capacity is not fully committed day-ahead. Real-time demand uncertainty is introduced through random, scenario-specific intercepts, and purely financial transactions are excluded from real-time demand clearing. Under perfect competition, market participants take prices as exogenous; in contrast, under Cournot competition eq. (1) is substituted into the objective function of each Cournot player, keeping quantities provided by other market participants fixed. (i) Generating firm f chooses real-time power sales from plant j Jf to each location, as well as real-time plant commitment status to maximize profit, subject to generation capacity, minimum output and ramping constraints, and given day-ahead financial commitments. Its real-time optimization problem under perfect competition is presented below. max s j, i, h,

uj, h, c j, h

j Jf h H

+ w (i : j

2. Methodology We consider a game in quantities with risk neutral power generators, a grid operator (ISO), and traders in the day-ahead and realtime energy markets. Each generating firm owns and operates power plants at a network location, but may sell power to other locations. Firms choose the level of hourly day-ahead and real-time power sales from each plant to customers at each node to maximize daily profits in the two-settlement energy market. The ISO provides transmission services to power suppliers, and arbitrages differences in nodal prices by buying MW of power from one node and selling it to another (Hobbs, 2001). Traders choose virtual supply and demand positions (INCs and DECs, respectively) at each node. A subset of traders hold FTR positions settling at the day-ahead prices. In particular, the manipulating traders act as Stackelberg leaders making optimal decisions in the day-ahead market, while correctly anticipating the reactions of other day-ahead and real-time market participants (Stackelberg followers). The game is characterized as a perfect and complete information game with a closed loop information structure, and the resulting equilibrium is subgame perfect (Fudenberg and Tirole, 1991). Next, we present the formulation of the two-stage equilibrium problem.

Ji ), h

(pi, h

i I

i I

s j, i, h

wi, h ) s j, i, h + w (i : j

Cj i I

(s j, i, h + s j, i, h )

Ji ), h

s j, i, h + i I

c j, h

i I

(pi, h

wi, h ) s j, i, h

c j, h

(2)

subject to:

s j, i , h + s j, i , h

u j, h

0,

h, i, j

Jf

(3) (4)

0,

h, j

uj, h + uj, h

1,

h, j

Jf

(5)

c j, h + c j, h

0,

h, j

Jf

(6)

c j, h + c j, h

CjSU (uj, h

( s j , i, h + s j , i, h )

Jf

uj, h

1

+ uj, h

(uj, h + uj, h) Pj ,

uj, h 1),

h, j

h, j

Jf

(7)

Jf

(8)

i I

( s j , i, h + s j , i, h )

(uj, h + uj, h ) Pj ,

h, j

Jf

(9)

i I

(s j, i, h + s j, i, h ) i I

( s j, i , h

1

+ s j, i, h 1)

(uj, h

1

+ uj, h 1) Rj ,

h, j

Jf

i I

(10)

2.1. Lower level problems

( s j , i, h + s j , i, h ) i I

(s j, i , h

1

+ s j, i, h 1)

(uj, h + uj, h) Rj ,

h, j

Jf

i I

(11)

The lower level of the game consists of the optimization problems of the generating firms, ISO and traders without FTR positions in the dayahead and real-time markets. We consider a setting where generating firms and traders without FTRs act competitively, as well as a regime where each player acts à la Cournot with regard to other firms’ sales, but is price-taking with respect to transmission prices. The ISO is modeled as a price-taker.

As noted above, sales by plant j to node i at hour h in the day-ahead market (s j, i, h ) can be adjusted by making residual sales in the real-time market (s j, i, h ). Generating firms pay the ISO for transmission services, and the pricing model adopted here is based on the notion of congestion pricing (Schweppe et al., 1988). At hour h, plants at node i ship their day-ahead (residual real-time) output to the hub node, and get paid the transmission price at their location, w(i :j Ji), h (w(i :j Ji), h ), per unit of output. Next, power output is shipped from the hub to the destination node based on the designated sales. Thus, sales to node i incur a per unit transmission cost of wi, h (wi, h ) in the day-ahead (real-time) market

2.1.1. Real-time market Electricity demand is elastic and determined endogenously assuming an affine specification: 3

Energy Policy 134 (2019) 110851

N. Guo and C. Lo Prete

(Gabriel et al., 2013). In addition to sales decisions, generating firms make unit commitment decisions. In principle, these are binary variables (where 0 indicates no commitment, while 1 represents commitment). However, binary unit commitment in the lower level problems makes the computation of equilibria in two-stage models challenging, because sufficient optimality conditions cannot be derived for problems with discrete variables. The prevalent approach in the literature has been to use relaxed (non-integer) unit commitment variables (Palmintier and Webster, 2016). Following Kazempour and Hobbs (2018a, 2018b), we enforce the tight relaxed version of the unit commitment problem presented in (Kasina, 2017), which defines a tighter constraint set by linking generator commitment status to its ramp capability (eq. (10) and (11)). As with sales schedules, day-ahead commitment of plant j in hour h (uj, h ) may be adjusted upwards in realtime (eq. (4)). In contrast, units that are committed day-ahead cannot be de-committed in real-time (i.e., uj, h cannot be lower than 0). The fixed cost of bringing plant j from 0% to 100% commitment is C jSU . The total commitment cost of plant j in hour h is the sum of day-ahead commitment cost, c j, h , and residual real-time commitment cost, c j, h , and equal to C jSU multiplied by the greater of zero or the change in commitment status between consecutive hours (eq. (7)). Finally, hourly generation from each plant is subject to capacity limits (eq. (8) and (9)) and ramp limits (eqs. (10) and (11)).

pi, h =

yi, h , ai, h

s.t.

ai, h = 0,

max s j , i , h,

PTDFi, l (yi, h + yi, h + ai, h + ai, h )

Tl ,

h, l

i I

PTDFi, l (yi, h + yi, h + ai, h + ai, h )

Tl ,

h, l

0

(s j, i, h + s j, i, h), j Ji i I

h, i

(pi, h

wi,h ) s j, i, h + w (i : j

wi, h ) sj, i,h + w (i : j

h, i , j

uj, h

1,

0,

Ji ), h

Ji ), h

s j, i, h

Cj

i I

s j, i, h

c j, h

+

i I

i I

s j , i, h

Cj i I

s j , i, h

c j, h

(18)

Jf

(19)

h, j

h, j

C jSU (uj, h

c j, h

Jf

(20)

Jf

(21)

uj, h 1),

h, j

s j , i, h

uj, h Pj ,

h, j

Jf

s j , i, h

uj, h Pj ,

h, j

Jf

Jf

(22) (23)

i I

(24)

i I

s j , i, h i I

s j , i, h

1

u j, h

s j , i, h

1

uj, h Rj ,

1

Rj ,

h, j

Jf

(25)

i I

s j , i, h

h, j

Jf

(26)

i I

Note that f's day-ahead power sales are constrained to be positive, while real-time sales may be negative to allow for buying back dayahead positions in real-time. Day-ahead commitment variables may take any value between 0 and 1 (eq. (20)). The day-ahead commitment cost of plant j is non-negative (eq. (21)), and equal to C jSU multiplied by the greater of zero or the change in commitment status between consecutive hours (eq. (22)). Finally, hourly day-ahead schedules are subject to capacity limits (eq. (23) and (24)) and ramp limits (eqs. (25) and (26)). (ii) The day-ahead problem faced by each trader t

max inct , i, h, h H

i I

[(pi, h

pi, h ) inct , i, h + (pi, h

s.t. inct , i, h

0, dect , i, h

RPi (inct , i, h + dect , i, h ) h H i I

TN is:

pi, h ) dect , i, h] (27)

dect , i, h

(iv) Balancing of supply and demand at each hour and node follows from eq. (1). Thus, the only market clearing condition is for the provision of transmission services: at each node i and hour h, the MW of transmission delivery provided from the hub should equal net sales, given by the difference between sales of all generators to node i and sales of generators located at i to all nodes:

(s j, i, h + sj, i, h )

i I

0,

c j, h

Eq. (13) ensures matching of arbitrage power bought and sold by the ISO. Eqs. (14) and (15) constrain the sum of day-ahead and realtime transmission services and arbitrage quantities to be equal to physical power flows delivered in real-time and satisfy transmission capacity constraints.

j J

(pi,h

s j , i, h

(15)

i I

yi, h + yi, h =

j Jf h H

subject to:

(14)

i I

h, i

u j , h, c j , h

(13)

i I

dect , i, h) ,

(i) Generating firm f chooses sales s j, i, h (i.e., commitments to sell power at the day-ahead price for delivery in real-time) and makes commitment decisions to maximize day-ahead and expected real-time profit, subject to unit constraints:

(12)

h H i I

(inct , i, h t T

(17)

i I

wi, h yi, h + pi, h ai, h

s j, i, h + ai, h +

i, h j J

(ii) Traders do not solve a real-time optimization problem, because virtual transactions are settled against real-time prices. (iii) The ISO allocates transmission capacity to maximize the value that the market receives from the transmission assets. To this end, the ISO sells hourly transmission services from the hub node to node i, yi, h , to power suppliers at wit, , and performs spatial arbitrage using sales ai, h , subject to network constraints. Conditional on dayahead transmission services and arbitrage sales, the problem formulation is:

max

i, h

0,

h, i St ,

(28) (29)

The trader chooses hourly virtual demand (DEC) and supply (INC) positions at each node, and profits from arbitrage opportunities created by price differences between day-ahead and real-time markets. Eq. (29) represents the credit requirement for virtual bidding in several ISO markets (Li et al., 2015). Specifically, ISOs determine a reference price at each location, and the sum of virtual supply and demand bids at that location, multiplied by the reference price, cannot exceed the collateral established by the market participant with the ISO (St ). Note that traders in the lower level problems do not hold FTR positions.

(16)

2.2. Day-ahead market

(iii) The day-ahead problem of the ISO is similar to the one defined for the real-time market:

Day-ahead demand for electricity is also elastic and assumed linear: 4

Energy Policy 134 (2019) 110851

N. Guo and C. Lo Prete

max

wi, h yi, h + pi, h ai, h

yi, h , ai, h

s.t.

position and day-ahead congestion in the direction specified in the contract (i.e., from source to sink), the trader receives a per MW payment equal to the difference between the day-ahead prices at the sink and source. If congestion is in the opposite direction of the contract, the trader pays the difference in day-ahead prices.3 It should be noted that the ability to enhance the FTR value gives the trader an incentive to submit more virtual demand bids at the sink than she would, absent the contract. This increases the day-ahead price at the sink and tends to worsen day-ahead congestion, increasing the price differential between source and sink and enhancing the FTR value.

(30)

h H i I

ai, h = 0,

(31)

i I

PTDFi, l (yi, h + ai, h)

Tl ,

h, l

(32)

i I

PTDFi, l (yi, h + ai, h)

Tl ,

h, l

(33)

i I

Importantly, since the day-ahead market only creates a financial obligation to buy or sell power in real-time, no power actually flows on transmission line l in the day-ahead market. Instead, in the day-ahead stage the ISO sells transmission services and chooses arbitrage quantities at each node i for delivery in real-time.

3. Data We simulate financial trading and operations decisions in the energy markets for 24 h on a small electric network with three nodes (A, B and C) connected by lines with equal reactance (Fig. 1). Market participants include three generating firms (1, 2 and 3), one manipulating trader with FTRs (4), and one trader without FTRs (5). We solve the resulting MPEC under five scenarios described below. Under each scenario, we first collect the KKT and market clearing conditions for all players into a single mixed complementarity problem (MCP), and solve the MCP using PATH. The MCP solution provides the starting points of the MPEC simulations with KNITRO 10.0. Parameter values are presented in Table 1. Each generating firm owns and operates one power plant at a node, but may sell power to other nodes. Marginal costs, start-up costs, and generation capacity are for a representative coal-fired unit (Plant 1 at node A), natural gas combined cycle unit (Plant 2 at node B) and gas turbine unit (Plant 3 at node C) (Herrero et al., 2018). We assume that units have no minimum output level and can ramp up to full capacity in 1 h, as in (Kazempour and Hobbs, 2018b). Reference prices for virtual positions at each node represent the 95th percentile value of the normal distribution of the absolute difference between hourly RT and DA LMP (Li et al., 2015; California ISO (CAISO), 2016b; PJM Interconnection, 2017); we obtain the mean of the distribution from an initial simulation run in which reference prices are close to 2017 prices in the California ISO, and its standard deviation from historical CAISO DA and RT price differences in 2017 (California ISO (CAISO), 2017b). Given the network parameters in Table 1, we determine the FTR size (in MW) that satisfies simultaneous feasibility (PJM Interconnection, 2018a).4 The slope of the inverse demand functions is set to 0.1, while the hourly intercepts are calibrated to ensure that day-ahead load is positive at each node and subject to uncertainty in real time.

(iv) Finally, the market clearing condition for day-ahead transmission services is similar to the one defined for the real-time market, and given by:

yi, h =

s j , i, h j J

s j , i, h ,

h, i

(34)

j Ji i I

2.3. Upper level problem When making optimal decisions in the day-ahead market, manipulating trader t TM is assumed to correctly anticipate how the generating firms, ISO and traders without FTR positions will adjust their decisions in response to changes in financial positions taken by t. Thus, our model represents a Stackelberg game between one or more manipulating traders in the day-ahead market (leaders) and the generating firms, ISO and traders without FTR positions in the day-ahead and realtime markets (followers). FTR positions are taken as exogenous in the game, unlike (Lo Prete et al., 2019b).2 The problem of each manipulating trader is a mathematical program with equilibrium constraints; with two or more manipulating traders, the problem becomes an equilibrium problem with equilibrium constraints (EPEC) representing the interaction of several Stackelberg leaders, each of whom solves a MPEC (Luo et al., 1996; Su, 2005). Mathematically, correctly anticipating the follower reactions is achieved by including the sufficient equilibrium conditions of the day-ahead and real-time market problems as constraints in the trader's problem. Thus, the MPEC of each manipulating trader t TM is:

max

inct , i, h, dect , i, h

+ Ft , l (pi

s.t.

h H ISI , h

inct , i, h

i I

pi

[(pi, h

ISO, h

pi, h ) inct , i, h + (pi, h

)

0, dect , i, h

RPi (inct , i, h + dect , i, h )

pi, h ) dect , i, h]

4. Results (35)

0,

h, i

St ,

h H i I

Day

ahead KKT and Market Clearing Conditions

Real

time KKT and Market Clearing Conditions

We examine five scenarios that differ with respect to the assumed behavior of market participants and FTR path. Key equilibrium outcomes and metrics for comparison across scenarios are presented in Fig. 2 and Table 2. Scenario 1 assumes that all Stackelberg followers are price-takers

(36) (37)

3 In electricity markets, FTR revenues are equal to the difference between the day-ahead congestion components of the nodal prices at the sink and source of the contract. Absent transmission losses, as in our model, the difference between electricity prices equals the difference between congestion prices. 4 System operators run simultaneous feasibility tests to ensure revenue adequacy (i.e., total congestion charges collected from day-ahead markets are sufficient to cover FTR payments). When running the test, ISOs model FTRs as generation at source point and load at sink point, and conduct DC power flow analysis to evaluate if the FTR positions satisfy or violate network constraints (PJM Interconnection, 2018a). To illustrate, let the FTR path be from A to C in Fig. 1. Assuming equal reactances for all lines, two thirds of the FTR position sourcing at A flow on line AC , which has a thermal limit of 100 MW. Thus, the maximum FTR position that may be established while satisfying simultaneous feasibility is F4, AC = 150 MW.

where KKT refers to Karush-Kuhn-Tucker, Ft , l represents the size of a FTR contract held by t TM on path l, and pi ISO, h and pi ISI , h are the nodal prices at the FTR source and sink, respectively. Given a long FTR 2

This choice is motivated by computational challenges associated with threestage equilibrium models (Lo Prete et al., 2019b). However, taking FTRs as exogenous does not seem overly restrictive, because these positions are established well in advance of energy markets, e.g. through quarterly or annual auctions held by the ISOs (California ISO (CAISO), 2017a). 5

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on line AC (thus creating congestion in each day-ahead realization, as can be seen in Table 2) to make the best use of transmission assets. In addition to the forward premium, we compare equilibrium outcomes across scenarios based on the average procurement cost of electricity, consumer surplus and social welfare in the network. The average procurement cost of electricity is the total cost of purchasing power in the energy markets divided by total energy consumption in the network. Social welfare is measured by the sum of surpluses for all market participants (Joskow et al., 1989), which are calculated based on the equilibrium outcomes of the game. Producer surplus is the sum of profits (i.e., revenues minus generation, commitment and transmission costs) for all generating firms. Trader surplus is the sum of profits for virtual bids and FTR positions (if any) for all traders. Finally, we obtain day-ahead net consumer surplus at each node by integrating the inverse demand function from zero to total day-ahead demand at that node, minus day-ahead energy costs. If real-time demand is higher than the day-ahead schedule at a node, we add real-time net consumer surplus, which is calculated by integrating the real-time inverse demand function from the day-ahead load to the real-time load (Fig. 4). If real-time demand is lower than the day-ahead schedule at a node, we adjust day-ahead surplus downwards to reflect the fact that consumers would not enjoy part of this surplus in real-time. Further, since day-ahead purchases that are not converted into physical positions must be sold back in real-time in a two-settlement system, we add the revenue from these real-time sales to the adjusted day-ahead consumer surplus to obtain total consumer surplus (Fig. 5). Relative to other less competitive scenarios, consumer surplus and social welfare are maximized in Scenario 1, while the average procurement cost of electricity is minimized. Scenario 2 assumes that generating firms are Cournot with respect to other firms' sales and financial positions, while trader 5 is a price-taker. Trader 4 continues to hold a 150 MW FTR from A to C. Generation, consumer surplus and social welfare are lower, while average procurement cost and producer surplus are higher, compared to Scenario 1. However, trader 5 adds liquidity to the market and is able to close the gap between day-ahead and expected real-time prices at each node. As a result, the forward premium is still zero (Fig. 2), and we observe no price manipulation of the type considered in FERC's recent enforcement actions (e.g. (Federal Energy Regulatory, 2014a)). In Scenario 3, we assume that all Stackelberg followers except the ISO are Cournot with regard to other firms’ sales and financial positions, but price-taking with respect to transmission prices. Trader 4 holds a FTR from A to C, as in the previous scenarios. In this case, crossproduct manipulation is sustained in equilibrium. Two points are worth emphasizing. First, the trader holding the FTR places unprofitable virtual demand positions at the contract sink at every hour, although dayahead prices are higher than expected real-time prices. This results in daily losses of -$3,872 at node C, which are offset by larger profits on the FTR position ($67,665): as in the two-node setting (Lo Prete et al., 2019b), sufficient leverage in FTR positions provides an incentive to use uneconomic behavior for moving day-ahead prices to benefit those related positions. Second, day-ahead and expected real-time prices diverge at all nodes, with an average forward premium ranging from 0.67 $/MWh at A to 2.55 $/MWh at C. Consumer surplus and social welfare decrease, while the average procurement cost of electricity in the network increases, relative to the previous scenarios. In order to examine the effects of cross-product manipulation on equilibrium outcomes, we compare Scenario 3 against a benchmark where trader 4 no longer has a FTR position, holding all other assumptions constant (Scenario 4). This comparison is useful to examine the effect of cross-product manipulation on prices, which is required for calculating disgorgement. To this end, changes in simulated prices with and without uneconomic virtual bidding may provide a measure of the price impact of manipulation, in a similar vein to methods for measuring unilateral market power ex ante (Helman, 2006). Absent the FTR position, trader 4 has no motive to bid uneconomically at C, and in fact

Fig. 1. Three-node network and market players. Table 1 Parameter values. C1 ($/MWh)

C2 ($/MWh)

C3 ($/MWh) C1SU ($)

C2SU ($) C3SU ($)

P1 (MW) P2 (MW) P3 (MW) P1 = P2 = P3 (MW)

26

R1 = R1 (MW)

400

60

70,000

R3 = R3 (MW) TAB = TBC (MW)

100

10,000

TAC (MW)

100

5,000

RPA ($/MWh)

5.50

400 300 100 0

RPB ($/MWh) RPC ($/MWh) S4 = S5 ($) F4,AC = F4,AB (MW)

5.23 5.66 30,000 150

40

R2 = R2 (MW)

300

120

Fig. 2. Average day-ahead and real-time prices in Scenarios 1-5.

with respect to energy and transmission prices, and trader 4 holds a FTR from A to C. The trader's equilibrium strategy consists in placing INCs at node A and DECs at node C in an attempt to move day-ahead prices in a direction that enhances the value of her FTR position. Yet, day-ahead prices converge to their expected real-time level, and the forward premium (i.e., the average difference between day-ahead and expected real-time price over 24 h) is equal to zero at every node (Fig. 2). It is worth noting that generation capacity and credit requirement constraints are rarely binding. Fig. 3 presents the hourly generation profile in Scenario 1: the coal-fired plant runs close to full capacity (315 MW) at all times, the NGCC plant is fully dispatched in hours 12–13 and 18–21, and runs close to capacity in most other hours, and the gas turbine only runs at limited capacity to satisfy peak load. Similarly, trader 5 uses most (but not all) of its daily collateral to place INCs and DECs at the three nodes, hence credit requirement constraints are not binding. Despite the absence of arbitrage profits on the energy market, trader 4's FTR position is profitable because the ISO maximizes scheduled flows 6

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Table 2 Results. Scenarios Behavior

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

Firms 1,2,3

Competitive

Cournot

Cournot

Cournot

Cournot

Trader 5

Competitive

Competitive

Cournot

Cournot

Cournot

AC

AC

AC

-

AB

7,557.07 5,777.85 234.01 -55,104 -10,000 -1,840 -196,484 -231,114 -14,041 884 954.93 200.95 -38.35 0 0 0 76,620 76,620 76,620 66,540 27,824 63,524 157,888 84,744 -2 243,514 0.00 0.00 0.00 43.81 0% 66.67% 100%

6,468.84 4,967.12 198.96 -47,169 -8,531 -1,577 -168,190 -198,685 -11,938 48,264 1,389.24 973.98 -255.06 0 0 0 61,337 61,337 61,337 43,969 19,405 59,915 123,289 66,260 0 237,813 0.00 0.00 0.00 46.78 0% 58.33% 95.83%

6,496.56 5,229.68 255.63 -47,372 -8,809 -2,062 -168,911 -209,187 -15,338 51,675 2,431.10 1,538.10 -1,325.06 1,568 2,653 -3,872 67,665 68,014 70,668 39,526 10,278 46,271 96,075 73,197 -1 223,949 0.67 1.74 2.55 48.39 0% 66.67% 95.83%

6,680.52 5,132.61 209.57 -48,711 -8,809 -1,674 -173,694 -205,304 -12,574 53,894 1,385.22 1,645.36 -120.16 2,860 2,527 11 0 5,398 7,053 33,186 10,832 58,274 102,292 61,391 -2 224,628 2.04 1.56 0.15 47.69 0% 58.33% 95.83%

6,537.60 5,279.87 209.57 -47,673 -8,996 -1,674 -169,978 -211,195 -12,574 53,826 2,161.56 1,088.14 -421.76 1,837 2,086 -558 28,532 31,897 33,944 37,844 9,826 55,407 103,077 63,143 4 225,462 0.98 2.39 0.73 47.25 0% 58.33% 95.83%

Trader 4's FTR Position Generation (MW) Commitment Cost ($) Generation Cost ($) Producer Surplus ($) (a) Net Virtual Sales of Trader 4 (MW) Profit for Trader 4 ($)

Trader Surplus ($) (c) Consumer Surplus ($) Consumer Surplus ($) Consumer Surplus ($) Consumer Surplus ($) (d) ISO Day-ahead Surplus ($) (e) ISO Real-time Surplus ($) (f) Social Welfare ($) (a-b + c + d + e + f) Forward Premium ($/MWh) Average Procurement Cost ($/MWh) Frequency of Day-ahead Transmission Congestion

Plant Plant Plant Plant Plant Plant Plant Plant Plant

1 2 3 1 2 3 1 2 3

Node A Node B Node C Node A Node B Node C FTR (b) Total Node A Node B Node C

Node A Node B Node C Line AB Line BC Line AC

Note: We subtract the FTR revenue from social welfare to avoid double counting, since day-ahead congestion revenues represent a transfer to FTR holders.

Fig. 4. Net consumer surplus in the two-settlement market, when real-time demand is higher than day-ahead demand.

in Scenario 3, more units are committed to meet demand, including the expensive generator at node C; on the contrary, more INCs at node A in Scenario 3 imply that fewer physical resources are needed at that node, explaining Plant 1's lower commitment. The intermediate cost plant is dispatched more often in Scenario 3, but commitment cost is unchanged. It should be noted that these changes in generation patterns raise the average cost of electricity to the consumers by 1.5% in Scenario 3, relative to Scenario 4. Our last set of results (Scenario 5) assumes that all Stackelberg followers except the ISO are Cournot with regard to other firms’ sales and financial positions, but price-taking with respect to transmission prices, and trader 4 holds a FTR position on path AB. As in Scenario 3, the trader places unprofitable DECs at node C, although position size and related losses are smaller. However, in this case C is not the sink of the

Fig. 3. Hourly generation profile in Scenario 1.

few DECs at that node maximize her arbitrage profits. Cross-product manipulation increases the day-ahead price at the FTR sink by 4%, relative to the benchmark. It is worth noting that no uneconomic positions are ever taken at nodes A and B, but prices at these nodes are affected, as a result of the change in equilibrium positions of the manipulating trader. The comparison between Scenario 3 and Scenario 4 also yields useful insights with regard to the effects of manipulation on the optimal commitment and dispatch of generation resources. When cross-product manipulation is in the works, commitment and dispatch costs are lower for the cheapest plant (Plant 1) and higher for the most expensive unit (Plant 3) (Table 2). As a result of larger DECs at node C 7

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Fig. 5. Net consumer surplus in the two-settlement market, when real-time demand is lower than day-ahead demand.

(Xu and Baldick, 2007; Mercadal, 2018)) should be closely monitored, because this condition likely facilitates the exercise of cross-product manipulation. More research is needed on analytical frameworks and economic models to identify conditions and potential flaws in the current design of electricity markets that create inefficient incentives and unintended consequences. In addition to suggesting prospective reforms in market rules, models may be useful to determine the material effect of manipulation on prices, as illustrated in our analysis. As an example of market imperfections creating limits to arbitrage in electricity markets, consider transaction costs. Virtual transactions pay transaction costs in the form of daily uplift charges, in $ per MW cleared. Uplift payments are made to generation resources that are committed and dispatched by the ISOs, but are not able to recover their total production costs (including start-up costs) through electricity prices (Federal Energy Regulatory, 2014b). These additional payments ensure revenue sufficiency and are determined ex post on a zonal basis (Helman et al., 2008). Market participants face uncertainty in the level and variability of uplift charges when submitting virtual bids in the energy auctions, and uplift charges may be assigned asymmetrically to virtual demand and supply positions. For instance, in PJM cleared INCs pay real-time uplift charges, while cleared DECs pay both day-ahead and real-time uplift charges (PJM Interconnection, 2015; Monitoring Analytics, 2016b). Asymmetric transaction costs make one type of virtual transactions more expensive, and may give rise to price manipulation opportunities. In addition to elements of market design, there may be asymmetries in the risk associated with virtual transactions. Some market participants may perceive INCs as riskier than DECs, because they are settled with purchases in the real-time market, and real-time prices tend to be more volatile than day-ahead prices. On the other hand, DECs (which are settled with real-time sales) may be riskier if renewable penetration is higher and negative real-time prices occur frequently. It is unclear whether these asymmetries are significant and how they affect the ability to sustain cross-product manipulation. As a second policy implication, our analysis shows that the ability to increase price separation between FTR source and sink is a requirement for the exercise of cross-product manipulation. Importantly, price separation may be induced by virtual transactions clearing at network locations that are not on the FTR path. As a case in point, PJM established a FTR forfeiture rule to prevent market participants from intentionally misusing virtual transactions to increase source-sink price separation, and thus FTR payouts (PJM Interconnection, 2018a; PJM Interconnection, 2018b). Under the rule, FTR profits are forfeited when the holder's net virtual transaction portfolio enhances the value of the FTR contract and results in a higher price difference between source and sink in the day-ahead market than in the real-time market. In addition, the virtual transaction portfolio flow on a day-ahead binding constraint must exceed the physical limit of the constraint by the greater of 0.1 MW or 10%: this criterion is added to eliminate virtual bids that do not have a large impact on price separation between source and sink (Hayik, 2018). It is worth noting that, while PJM used to extend the forfeiture rule to buses that are “at or near delivery or receipt buses of the FTR” (PJM Interconnection, 2016), the language of the

FTR. As a result of loop flows, price separation between source and sink of the FTR may be induced by transmission congestion on a line other than the contract path. This yields congestion revenues for the FTR holder, even though the contract path is not congested (PJM Interconnection, 2012). In our simulation, the FTR path AB is never congested, but day-ahead congestion on lines AC and BC creates price separation between the end points of these lines, making the FTR position profitable. Cross-product manipulation increases the premium at the sink relative to the benchmark (Scenario 4), but the effect is lower in magnitude relative to Scenario 3. 5. Conclusions and policy implications The use of uneconomic virtual transactions in day-ahead electricity markets with the intent to benefit related financial positions has emerged as a policy concern in recent years. Developing analytical frameworks and models to explain the means for achieving day-ahead price manipulation that persists over time, rather than being an isolated incident, is a challenge. We contribute to the literature by presenting a two-stage, complementarity-based equilibrium model of day-ahead electricity price manipulation to enhance the value of financial transmission rights under real-time uncertainty. We cast the problem as a Stackelberg game between one or more manipulating traders in the day-ahead market (leaders) and generating firms, ISO and traders without FTRs in the day-ahead and real-time markets (followers). FTR positions of the manipulating traders are exogenous in the game. The model builds on our past work in a two-node setting (Lo Prete et al., 2019b) by enhancing realism of grid representation both at the temporal and spatial level. We simulate hourly financial trading and operations decisions for 24 h on a three-node network, assuming one manipulating trader. Results suggest that imperfect competition in energy markets enables cross-product manipulation in equilibrium. Given sufficient leverage in FTR positions, uneconomic behavior for crossproduct manipulation is sustained in equilibrium only when both physical and financial market participants engage in Cournot competition. This result generalizes our previous findings in a one-period model to a more complex setting where the multi-period impacts of virtual transactions on day-ahead prices must be taken into account. Cross-product manipulation through unprofitable virtual transactions at the FTR sink creates divergence between day-ahead and real-time prices and affects the commitment and dispatch of generation resources, increasing costs to serve electric demand. Our simulations also show that uneconomic bidding may take place at nodes that are not on the FTR path. The reason is that, when loop flows are introduced, dayahead price separation between source and sink of the FTR may be induced by congestion on transmission lines other than the contract path. Our analysis has important policy implications. First, day-ahead price manipulation through uneconomic financial positions can be sustained at network locations where both physical and financial participants act non-competitively. This suggests that locations where suppliers have a unilateral incentive to exercise market power (as measured by low transmission-constrained residual demand elasticity 8

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tariff and FTR manual has recently been revised, and physical proximity to source and sink is no longer required. Further, FTR profits are forfeited even when the 10% virtual test is triggered on a different dayahead constraint than the FTR contract path (VECO Power Trading, 2018). The California ISO has a similar monitoring rule for cross-product manipulation (California ISO (CAISO), 2016c). Other system operators, like NYISO, do not adopt claw back rules, but have measures in place for monitoring and mitigating virtual transactions. For example, NYISO applies position limits if persistent price differences between day-ahead and real-time markets are observed at a given location and it is determined that virtual transactions contributed to this price divergence (New York ISO (NYISO) Tariffs, 2019). Designing tests to identify and detect uneconomic behavior associated with cross-product manipulation would help system operators, market monitors and enforcement activities to distinguish between manipulative and efficient transactions, and represents an interesting area for future research.

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