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5. Numerical Simulation and Discussion

Table 5 5. Numerical Simulation and Discussion

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the total negotiation sessions), leads to failed negotiations as the agent may choose an incompatible peer. This paper advances the work [1] by proposing a, learning-based intelligent peer selection strategy that increases the quality of the reached agreements in terms of fairness, and the success rate of negotiation. In this paper, the negotiation domain is enhanced to accommodate contracts that potentially is an agreement that may be missing in a limited negotiation domain explored the previous work. Additionally, this paper analyses the P2P interactions for drawing insights regarding emerging cluster of prosumers with compatible strategies. Figure 1: An example of Residential Energy Cooperative (REC) with four prosumers/agents —each comprising a PV panel and a residential battery — are shown on the left side. On the right side, the interactions between two prosumers/agents (prosumer A and prosumer B) in settling energy contracts through P2P negotiation are zoomed-in and illustrated. While the detailed models are described in Section 3, the associated concepts and definitions are put together in Section 4.
the total negotiation sessions), leads to failed negotiations as the agent may choose an incompatible peer. This paper advances the work [1] by proposing a, learning-based intelligent peer selection strategy that increases the quality of the reached agreements in terms of fairness, and the success rate of negotiation. In this paper, the negotiation domain is enhanced to accommodate contracts that potentially is an agreement that may be missing in a limited negotiation domain explored the previous work. Additionally, this paper analyses the P2P interactions for drawing insights regarding emerging cluster of prosumers with compatible strategies. Figure 1: An example of Residential Energy Cooperative (REC) with four prosumers/agents —each comprising a PV panel and a residential battery — are shown on the left side. On the right side, the interactions between two prosumers/agents (prosumer A and prosumer B) in settling energy contracts through P2P negotiation are zoomed-in and illustrated. While the detailed models are described in Section 3, the associated concepts and definitions are put together in Section 4.
Figure 2: Illustration of a contract space of two agents in relation to the definitions. The black dots represent the potential contracts (or agreement (i.e. w), while the Nash (Fair) outcome is shown as a blue dot. The Pareto Frontier hosts the set of contracts that are Pareto efficient [32]. The agent specific aspiration regions and reservation values are highlighted
Figure 2: Illustration of a contract space of two agents in relation to the definitions. The black dots represent the potential contracts (or agreement (i.e. w), while the Nash (Fair) outcome is shown as a blue dot. The Pareto Frontier hosts the set of contracts that are Pareto efficient [32]. The agent specific aspiration regions and reservation values are highlighted
Figure 3: An exemplary issue space representing a negotiation domain with acquired utility. The issues are presented at the axes whereas the utility of the contracts is plotted as a heat- map. The contoured (darker) regions are the aspiration region as they contain the preferred energy contracts with the utility higher than the reservation value.
Figure 3: An exemplary issue space representing a negotiation domain with acquired utility. The issues are presented at the axes whereas the utility of the contracts is plotted as a heat- map. The contoured (darker) regions are the aspiration region as they contain the preferred energy contracts with the utility higher than the reservation value.
Figure 4: Distribution of the target utility of the agent described in Figure 3 with aspira- tion quantile of 80%. The aspiration region is grey-ed out that results in the utility within [-1.0, -1.18].
Figure 4: Distribution of the target utility of the agent described in Figure 3 with aspira- tion quantile of 80%. The aspiration region is grey-ed out that results in the utility within [-1.0, -1.18].
4.4. Toy Example: Energy Contract
4.4. Toy Example: Energy Contract
In addition to the proposed negotiation based strategy, we define a couple of complementary strategies to analyse the comparative efficiencies of the resulting allocations.
In addition to the proposed negotiation based strategy, we define a couple of complementary strategies to analyse the comparative efficiencies of the resulting allocations.
4.5. Efficiency and Fairness
4.5. Efficiency and Fairness
The properties of the strategies are briefed in Table 1. We define the per- formance of an agent achieved by applying a particular strategy. The perfor- mance of the proposed strategy s2 considers the realized energy profile, after periodically negotiating and implementing the agreement. The performance is, therefore, similar to Eq. 9 except it takes into account the realized energy profile and the consequent battery dispatch.
The properties of the strategies are briefed in Table 1. We define the per- formance of an agent achieved by applying a particular strategy. The perfor- mance of the proposed strategy s2 considers the realized energy profile, after periodically negotiating and implementing the agreement. The performance is, therefore, similar to Eq. 9 except it takes into account the realized energy profile and the consequent battery dispatch.
Figure 5: Contract realization between two Agents A and B.
Figure 5: Contract realization between two Agents A and B.
Figure 6: Execution of an agreement. Effects of executing agreements — on net demand and battery dispatch profiles — reached through negotiation between two agents.
Figure 6: Execution of an agreement. Effects of executing agreements — on net demand and battery dispatch profiles — reached through negotiation between two agents.
Figure 7: Outcome space: The Agreement is reached at the 1560-th round of negotiation sessions between the agents. An exemplary outcome space of agent A and agent B with marginal cumulative distributions of their utilities are shown. The Nash solution, agreement and No-deal solution are plotted to illustrate their relative distances and agents’ capability to find a deal very close to the Nash solution under the proposed negotiation based strategy.
Figure 7: Outcome space: The Agreement is reached at the 1560-th round of negotiation sessions between the agents. An exemplary outcome space of agent A and agent B with marginal cumulative distributions of their utilities are shown. The Nash solution, agreement and No-deal solution are plotted to illustrate their relative distances and agents’ capability to find a deal very close to the Nash solution under the proposed negotiation based strategy.
the negotiation based strategy are fairer than that of a non-negotiation based strategy.
the negotiation based strategy are fairer than that of a non-negotiation based strategy.
Figure 8: Issue space: The negotiation domain with the juxtaposed aspiration regions bounded by contour lines for both agents. The negotiation traces, represented by the coloured scatters, depict the behaviour of the agents with the opponents as both of them converge to the agreement. The gradients in the traces represent the trace order - the darker ones are with the higher utility, which the perspective agents follow to reach the agreement.
Figure 8: Issue space: The negotiation domain with the juxtaposed aspiration regions bounded by contour lines for both agents. The negotiation traces, represented by the coloured scatters, depict the behaviour of the agents with the opponents as both of them converge to the agreement. The gradients in the traces represent the trace order - the darker ones are with the higher utility, which the perspective agents follow to reach the agreement.
Figure 9: Distributions of the Euclidean distance to the Nash solution from the agreements and the no-deal solutions in the outcome space and estimations of corresponding Gaussian kernel densities. The majority resulting agreements are locating themselves closer to the Nash solutions, hence confirm the fairness of the energy allocations.
Figure 9: Distributions of the Euclidean distance to the Nash solution from the agreements and the no-deal solutions in the outcome space and estimations of corresponding Gaussian kernel densities. The majority resulting agreements are locating themselves closer to the Nash solutions, hence confirm the fairness of the energy allocations.
Figure 10: Agents utility improvement of individual control strategy (horizontal) and negoti- ation and control strategy (vertical) over no flexibility baseline. Agents are above the dashed equal improvements line, hence our newly proposed strategy dominates individual control, while also improving relative fairness (nw,,|5, © 1.38 - 1019 > NW,,|s9 © 3-35 - 101”).
Figure 10: Agents utility improvement of individual control strategy (horizontal) and negoti- ation and control strategy (vertical) over no flexibility baseline. Agents are above the dashed equal improvements line, hence our newly proposed strategy dominates individual control, while also improving relative fairness (nw,,|5, © 1.38 - 1019 > NW,,|s9 © 3-35 - 101”).
Figure 11: Hourly distribution of the (agreed) energy volumes to be exchanged (q*) compiled over 7 days. Evidently, the agents are more flexible around the sunny hours and tend to exchange a larger volume of energy during these periods.
Figure 11: Hourly distribution of the (agreed) energy volumes to be exchanged (q*) compiled over 7 days. Evidently, the agents are more flexible around the sunny hours and tend to exchange a larger volume of energy during these periods.
Figure 12: Distribution of (absolute) peak exchange — inside the REC and aggregated over all P2P exchange in every 15 minutes — over 7 days of simulation period. The P2P negotiation and resulting exchange does not congest the physical network excessively. Relatively higher ramp of congestions could be noticeable during the sunny periods.
Figure 12: Distribution of (absolute) peak exchange — inside the REC and aggregated over all P2P exchange in every 15 minutes — over 7 days of simulation period. The P2P negotiation and resulting exchange does not congest the physical network excessively. Relatively higher ramp of congestions could be noticeable during the sunny periods.
Figure 13: Comparison of peak power distribution at PCC between the proposed Negotiation and control strategy and Individual control strategy. The representative distribution of Ne- gotiation and control strategy considers the return of the energy loan as well. The resulting exchanges do not excessively congest the physical network in terms of peak power compared to that of Individual control.
Figure 13: Comparison of peak power distribution at PCC between the proposed Negotiation and control strategy and Individual control strategy. The representative distribution of Ne- gotiation and control strategy considers the return of the energy loan as well. The resulting exchanges do not excessively congest the physical network in terms of peak power compared to that of Individual control.
Figure 14: Improvements in agents utility over the comparative strategies in an REC of 10( prosumers.
Figure 14: Improvements in agents utility over the comparative strategies in an REC of 10( prosumers.
Related topics:
BusinessEngineeringComputer ScienceEconomicsEnvironmental EconomicsMarket DesignAutomated Negotiation
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