Analyzing Trade in Continuous IntraDay Electricity Market: An AgentBased Modeling Approach
Abstract
:1. Introduction
2. Related Works
3. Principles of Continuous IntraDay Markets
3.1. Market SetUp
3.2. Market Mechanism
4. Continuous Market Clearing
4.1. Continuous Market Operation
Algorithm 1 Run the market 

4.2. Order Processing
4.3. Updating Agents’ Beliefs
4.4. Transaction Confirmation
5. Trading Agents
5.1. Generic Agent
5.1.1. Private Information
5.1.2. Potential Functionalities
(1) Strategy ${S}^{i}\left(to{b}_{t}\right)$
(2) Outage $O({p}^{out},\tilde{c})$
(3) Imbalance Price forecaster $I\left({e}_{i}^{imb}\right)$
(4) Confirm a Transaction Locally
5.2. Dispatchable Agent
5.2.1. Private Information
5.2.2. Potential Functionalities
(1) Strategy ${S}^{i,dis}\left(to{b}_{t}\right)$
Algorithm 2 Steps to decide the orders to be placed 
5.3. Variable Agent
5.3.1. Private Information
5.3.2. Potential Functionalities
(1) Forecasting functionality
 Cosinusoidal forecast:$${e}_{i,t}^{var}=\tilde{C}\xb7cos\left(\frac{t}{\frac{\leftT\right}{2\xb7{e}_{i,t}^{cst}}}\right)$$
 Sinusoidal forecast:$${e}_{i,t}^{var}=\tilde{C}\xb7sin\left(\frac{t}{\frac{\leftT\right}{2\xb7{e}_{i,t}^{cst}}}\right)$$
 Constant offset forecast:$${e}_{i,t}^{var}=\tilde{C}$$$${s}_{i,t}^{private,var}=({s}_{i,t}^{private},{\widehat{p}}_{i,t}^{var}).$$
(2) Strategy ${S}^{i,var}\left(to{b}_{t}\right)$
Algorithm 3 Variable agent strategy 

6. Pricing Strategies
6.1. Generic Strategy
6.2. Naive Strategy
6.3. Modified Trader AA Strategy
 The competitive equilibrium price estimate $\widehat{p}$ is computed at each step as the mean value of K past transactions according to:$$\begin{array}{c}{\widehat{\pi}}_{t}=\frac{1}{K}\sum _{k=1}^{K}{\pi}_{k}\end{array}$$
 The aggressiveness a is updated as$$\begin{array}{c}{a}_{t+1}={a}_{t}+\beta \xb7({\delta}^{p}{a}_{t}),\end{array}$$
 The target price parameter $\theta $ is only updated when a transaction takes place, while the magnitude of the update depends on the market volatility $\nu $ through function $\overline{\theta}\left(\nu \right)$. The updated parameters are given by$$\begin{array}{c}{\theta}_{t+1}={\theta}_{t}+{\beta}_{1}\xb7(\overline{\theta}\left(\nu \right){\theta}_{t}),\end{array}$$
 The target price ${\tau}_{t}$ at each step t is computed as a function of the aggressiveness level a, the estimated equilibrium price ${\widehat{\pi}}_{t}$ and the limit prices to buy/sell (${l}_{t}^{sell}$, ${l}_{t}^{buy}$). Compactly, it writes:$${\tau}_{t}={g}_{{\theta}_{t}}({l}_{t}^{sell},{l}_{t}^{buy},{\widehat{\pi}}_{t},{a}_{t}),$$
7. Imbalance Settlement
7.1. Impact on System Regulation
8. Test Case, Results and Discussion
8.1. Test Case SetUp
8.1.1. Trading Agents Configuration
8.1.2. Market Operator Configuration
8.2. Evaluating the Effect of Different Pricing Strategies
8.3. Comparing the Response to Capacity Outages
 Case I: all the agents follow the naive strategy;
 Case II: only the agent that suffers the outage follows an MTAA strategy while all the other agents are naive;
 Case III: all agents adopt the MTAA strategy except the one that suffers the outage;
 Case IV: all agents follow the MTAA strategy.
8.4. Evaluating the Effect of the Imbalance Price Information Asymmetry
8.4.1. Effect of Information Asymmetry on the Wind Agent
8.4.2. Effect of Information Asymmetry on the Flexible Agent
8.5. Discussion
9. Conclusions
 The proposed ABM provides a formalized tool to study the behavior of agents (market players) under different CID market settings;
 The MTAA strategy presented in this work outperforms the benchmark (i.e., a naive strategy) in terms of revenue and coping after outages;
 Information asymmetry among agents regarding the imbalance prices influences the transaction prices in the CID market, favoring those agents with more information.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Abbreviations  
$AA$  Adaptive aggressiveness 
$ABM$  Agentbased model 
$CDA$  Continuous double auction 
$CID$  Continuous intraday 
$DA$  Day ahead 
$FCFS$  Firstcome–firstserve 
$ID$  Intraday 
$ISP$  Imbalance settlement period 
$LOB$  Limit order book 
$MO$  Market operator 
$MTAA$  Modified trader adaptive aggressiveness 
$RES$  Renewable energy sources 
$TOB$  Top of the order book 
$WPP$  Wind power producer 
$XBID$  Crossborder intraday 
Indices  
i  Agent that participates in the CID market 
t  Time 
j  Order number 
Parameters  
${t}_{open}^{{H}_{1}}$  Gate opening time for intraday trade for hourly product ${H}_{1}$ 
${t}_{close}^{{H}_{1}}$  Gate closing time for intraday trade for hourly product ${}_{1}^{H}$ 
${t}_{delivery}^{{H}_{1}}$  Start time of the physical delivery for hourly product ${H}_{1}$ 
${t}_{settle}^{{H}_{1}}$  End time of the physical delivery for hourly product ${}_{1}^{H}$ 
$\tilde{T}$  CID trading horizon for a specific CID product 
$\Delta t$  Discretization step for the trading horizon 
N  Total number of agents participating in the CID market 
${\pi}^{DA}$  Dayahead price 
${p}_{i}^{da}$  Position of an agent i after DA market clearing 
${C}_{i,{t}_{open}}$  Effective capacity of agent i at time ${t}_{open}$ 
n  Number of orders placed by an agent in CID market 
${e}_{i}^{imb}$  Factor to represent the deviation of the forecast with respect tothe real 
imbalance price  
${\pi}^{imb,+}$  Real positive imbalance price 
${\pi}^{imb,}$  Real negative imbalance price 
${\pi}^{up}$  Upregulation price 
${\pi}^{down}$  Downregulation price 
${\underline{C}}_{i}$  Minimum stable load of a dispatchable agent i 
$\alpha $  A step factor to update limit prices 
${l}_{i,0}^{buy}$  Initial limit of an agent to buy 
${l}_{i,0}^{sell}$  Initial limit of an agent to sell 
$\tilde{C}$  Amplitude/offset of the forecast error 
${e}_{i,t}^{cst}$  Parameter to define the shape of forecast of agent i at time t 
${D}_{i,t}$  Frequency of arrival of new forecasts 
${p}_{i}^{var}$  The actual production/consumption of a variable agent 
R  Parameter indicating the size and sign of regulation volume to counteract 
the system imbalance  
k  Probability of having a positive imbalance 
f  Imbalance influence factor 
Variables  
Binary Variables  
Y  Binary variable that indicates if the system was up or downregulating 
${y}_{i,t}$  Order side of an order posted by agent i at time t 
Positive Variables  
${g}_{i,t}^{down}$  The volume that a dispatchable agent i can buy at t 
${g}_{i,t}^{up}$  The volume that a dispatchable agent i can sell at t 
${C}_{i,t}$  Effective capacity of an agent i at time t 
${v}_{i,t}$  Volume of an order posted by agent i at time t 
${v}_{i,t}^{rem}$  Remainder volume from order i at time t 
${v}_{i,t}^{match}$  Matched volume from order i at time t 
$bb{v}_{t}$  Best bid volume at time t 
$ba{v}_{t}$  Best ask volume at time t 
${v}^{match}$  Volumes matched in a transaction 
Continuous Variables  
${r}_{i,t}$  Cumulative revenues collected by an agent i at each timestep t of the 
trading process  
${\pi}_{i,t}$  Price of an order posted by agent i at time t 
$bb{p}_{t}$  Best buy price at time t 
$ba{p}_{t}$  Best ask price at time t 
$vwap{b}_{t}$  Volume weightedaverage price in the bid side at t 
$vwap{a}_{t}$  Volume weightedaverage price in the ask side at t 
${\pi}^{match}$  Price at which orders are matched 
${p}_{i,t}^{mar}$  The net volume of energy traded by agent i until timestep t 
${\delta}_{i,t}$  Imbalance of an agent i at time t 
${\widehat{\pi}}_{i,t}^{imb,}$  Recent prediction of negative imbalance price by agent i at time t 
${\widehat{\pi}}_{i,t}^{imb,+}$  Recent prediction of positive imbalance price by agent i at time t 
${\Delta}_{i}$  Final imbalance of an agent i 
${l}_{i,t}^{buy}$  Maximum price that an agent i is willing to pay to buy at time t 
${l}_{i,t}^{sell}$  Minimum price at which an agent i can sell at time t 
${p}_{i,t}^{mar}$  The market position at the closing time of the CID market 
${\widehat{p}}_{i,t}^{var}$  The recent forecast of uncertain production/consumption at t 
${e}_{t}^{var}$  Error component that relates the forecasted and actual production/ 
consumption of variable agents  
$bb{p}_{t}^{prev}$  Best bid price of the previous step 
$ba{p}_{t}^{prev}$  Best ask price of the previous step 
$bb{v}_{t}^{prev}$  Best bid volume of the previous step 
$ba{v}_{t}^{prev}$  Best ask volume of the previous step 
${r}_{n}^{sip}$  Single imbalance pricing settlement amount 
${r}_{n}^{dip,up}$  Dual imbalance pricing amount under upregulation 
${r}_{n}^{dip,down}$  Dual imbalance pricing amount under downregulation 
${\Delta}^{market}$  The cumulative imbalance caused by agents trading in the CID market 
Compilation of Variables  
$o{b}_{t}$  Order book that contains outstanding bids and asks at time t 
${o}_{i,t}$  Order posted by an agent i at time t 
$to{b}_{t}$  Top of the order book at time t 
Sets  
I  Set of agents participating in the CID market 
T  Set of timesteps available for trading in CID market 
${\mathcal{P}}^{sell}$  Set of candidate prices in naive strategy 
$o{b}_{i,t}^{local}$  A private ledger by agent i to track its outstanding orders in the CID 
market at timestep t  
${s}_{i,t}^{private}$  Set of private information available to agent i at time t 
${s}_{i,t}^{private,dis}$  Set of private information available to a dispatchable agent i at time t 
Outage Parameters  
${p}^{out}$  Probability of outage 
$\tilde{c}$  Outage percentage 
Naive Strategy Parameters and Variables  
${\pi}^{range}$  Size of price range considered in naive strategy 
m  The number of evenly spaced parts of price range in naive strategy 
${\pi}_{min}^{buy}$  Minimum price value at which a naive agent can buy 
${\pi}_{max}^{buy}$  Maximum price value for a naive agent to buy 
${\pi}_{min}^{sell}$  Minimum price value at which a naive agent can sell 
${\pi}_{max}^{sell}$  Maximum price value for a naive agent to sell 
${\mathcal{P}}^{sell}$  Set containing the candidate prices for ask orders 
${\mathcal{P}}^{buy}$  Set containing the candidate prices for bid orders 
$\Delta \pi $  Price step 
MTAA Strategy Parameters and Variables  
${\pi}_{min}$  Userdefined minimum price value for MTAA strategy 
${\pi}_{max}$  Userdefined maximum price in the MTAA strategy 
${\pi}_{i,t}^{ask}$  Price of an ask order determined by MTAA strategy for agent i at time t 
${\pi}_{i,t}^{bid}$  Price of a bid order determined by MTAA strategy for agent i at time t 
${a}_{i}$  Aggressiveness of agent i 
${\tau}_{i}$  Target price for an agent i 
$\theta $  Parameter that relates r with $\tau $ 
$\widehat{\pi}$  Competitive equilibrium price 
$\beta $  Stepsize parameter to update aggressiveness 
$\nu $  Market volatility 
${\mathcal{P}}^{sell}\left({V}_{j}\right)$  Set of price values of ask orders as a function of proportion of order volume 
${\mathcal{P}}^{buy}\left({V}_{j}\right)$  Set of price values of bid orders as a function of proportion of order volume 
Operators  
$max$  Maximum operator 
$min$  Minimum operator 
Appendix A. Algorithms
Algorithm A1 Order processing 

Algorithm A2 Match 

Algorithm A3 Update LOB 

Algorithm A4 Update posted order 

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$\mathit{Wind}1$  $\mathit{Wind}2$  $\mathit{Flex}1$  $\mathit{Flex}2$  $\mathit{Ther}1$  $\mathit{Ther}2$  

$\overline{{C}_{i}}$  (MWh)  2500  2400  2500  2400  1000  1000 
${p}_{da}$  (MWh)  1500  1400  −1500  −1500  700  700 
${\widehat{p}}_{0}^{var}$  (MWh)  1600  1800  −1800  −1900  
${p}^{var}$  (MWh)  1700  1600  −2400  −2300  
${l}^{sell}$  (EUR/MWh)  10  10  30  30  80  80 
${l}^{buy}$  (EUR/MWh)  150  150  150  150  15  20 
$\widehat{p}$  (EUR/MWh)  20  40  100  100  50  50 
${e}^{cst}$  ()  4  4  4  4  
$\alpha $  ()  0.5  
${e}^{imb}$  ()  20 
Scenario  

Agent  Wind AA  Consumer AA  Thermal AA  All AA 
$Wind1$  79.20  64.48  84.41  68.16 
$Wind2$  70.51  61.76  89.67  61.09 
$Flex1$  −106.76  −61.26  −105.50  −71.75 
$Flex2$  −94.39  −55.26  −92.81  −69.15 
$Ther1$  54.03  20.86  35.96  26.80 
$Ther2$  36.40  8.41  27.26  23.84 
(%) Time  Case I  Case II  Case III  Case IV  

${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  
Bef.  Af.  (%)  Bef.  Af.  (%)  Bef.  Af.  (%)  Bef.  Af.  (%)  
25%  65  70  7.69  58  62  6.89  69  86  24.63  77  77.8  1.04 
50%  40  47  17.5  25  35  40  68  90  32.35  74.5  75  0.67 
75%  20  25  25  20  85  325  65  85  30.76  76.5  77.5  1.30 
(%) Time  Case I  Case II  Case III  Case IV  

${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  ${\mathit{\pi}}_{\mathit{tr}}$  ${\mathit{\pi}}_{\mathit{tr}}$  $\Delta $  
Bef.  Af.  (%)  Bef.  Af.  (%)  Bef.  Af.  (%)  Bef.  Af.  (%)  
25%  65  165  153.8  57.5  70  21.7  15  165  1000  76.8  77.5  0.91 
50%  45  165  266.6  18  80  344.4  15  165  1000  65  67  3.07 
75%  20  165  725  17  87  411.7  15  165  1000  40  47  17.5 
Parameter  Units  Wind1  

${e}^{imb}$  EUR/MWh  0.0  50.0  100.0  150.0  200.0  250.0 
${\pi}_{tr}^{open}$  EUR/MWh  80.5  80.5  84.0  80.0  80.0  82.0 
${\pi}_{tr}^{close}$  EUR/MWh  73.0  73.0  15.0  14.0  13.0  12.0 
$\Delta {\pi}_{tr}$  %  −9.32  −9.32  −82.14  −82.50  −83.75  −85.37 
Parameter  Units  Flex1  

${e}^{imb}$  EUR/MWh  0.0  50.0  150.0  250.0  300.0 
${\pi}_{tr}^{open}$  EUR/MWh  80.0  91.0  73.0  63.0  66.0 
${\pi}_{tr}^{close}$  EUR/MWh  77.0  80.0  80.1  69.2  80.0 
$\Delta {\pi}_{tr}$  %  −3.75  −1.23  9.72  9.84  21.21 
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Shinde, P.; Boukas, I.; Radu, D.; Manuel de Villena, M.; Amelin, M. Analyzing Trade in Continuous IntraDay Electricity Market: An AgentBased Modeling Approach. Energies 2021, 14, 3860. https://doi.org/10.3390/en14133860
Shinde P, Boukas I, Radu D, Manuel de Villena M, Amelin M. Analyzing Trade in Continuous IntraDay Electricity Market: An AgentBased Modeling Approach. Energies. 2021; 14(13):3860. https://doi.org/10.3390/en14133860
Chicago/Turabian StyleShinde, Priyanka, Ioannis Boukas, David Radu, Miguel Manuel de Villena, and Mikael Amelin. 2021. "Analyzing Trade in Continuous IntraDay Electricity Market: An AgentBased Modeling Approach" Energies 14, no. 13: 3860. https://doi.org/10.3390/en14133860