Keywords

1 Introduction

In consideration of global warming and the steep increase of energy prices, various countries have been promoting the introduction of renewable energy generation modes such as photovoltaic (PV) power generation and wind power generation [1]. Because there is generally difficulty in storing the electricity generated using those means, it is necessary to balance demand and supply of electricity simultaneously to stabilize public electrical grid systems. Considering such characteristics of electricity, introduction of renewable energy generations into the current grid system makes it more difficult to stabilize the supply of electricity because some renewable energy generation modes involve output-power fluctuation. Using the smart-grid concept, mutual information exchange among medium-scale electricity suppliers, small decentralized suppliers, and consumers can be realized using information communications technology, which can balance and optimize the supply and demand related to electricity. Moreover, expansion of residential PV systems might enable electricity trade among even small-scale consumers such as households and might play a role in the further stabilization of the grids through household participation in the electricity trade market. Information communications technology helps consumers to give real-time information related to the balance of demand and supply, which is expected to achieve balanced trades by market principals and thereby increase of social surplus. In addition, a technology exists to enable electricity trade among small-scale consumers. Digital Grid, which was advocated by Abe [2], enables identification of who generates how much electricity by attaching information such as an address to units of generated electrical power.

To realize electricity trading, however, we must take several points into consideration. First, as described above, the amount of electricity supply and that of electricity demand must be balanced at any given time. Second, members of the grid are self-interested, meaning that their only purpose of trading electricity is to maximize their profit, which might endanger the grid system stability. Third, electricity is one of the most vital daily necessities which people almost always use incessantly. Therefore, trading mechanisms that compel consumers to follow a complicated process are not desirable.

Recently, the number of studies related to electricity trade is increasing as the introduction of renewable energy for electricity is promoted worldwide. For example, Rudkevich et al. [3] estimated electricity pricing under a market mechanism called Poolco, in which electric power companies bid to maximize their profit; Tanaka [4] simulated the Japanese wholesale electricity market as a transmission-constrained Cournot market. Above all, Vitelingum et al. [5] propose a mechanism based on a continuous double auction for electricity trade in which small-scale consumers can participate. However, few reports describe that kind of electricity trade. Moreover, even the mechanism proposed by Vitelingum et al. is not sufficiently simple for households when considering the features of electricity such as incessant daily use.

In this study, we define “Decentralized Electricity Trading” as “electricity trading in which small-scale consumers who possess their own generator participate not only as consumers but also as producers.”

In these circumstances, we propose two new electricity trading mechanisms which entail simple procedures, and which can stabilize a system even when grid participants are self-interested. To evaluate the mechanisms, we conduct human subject experiments and multi-agent simulations. A model of decision-making by human beings is constructed through subject experiments. We use it for multi-agent simulation as input data.

2 Modeling Decentralized Electricity Trading and Proposed Trading Mechanisms

2.1 Model of Decentralized Electricity Trading

We construct a model of decentralized electricity trading. As Fig. 1 shows, decentralized electricity trading consists of a market, one electric power company, and n consumers who have their own generator and who can generate electricity independently.

Fig. 1
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Model of decentralized electricity trading

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Decentralized Electricity Trading Market. As Fig. 1 shows, in decentralized electricity trading, the electric power company and all consumers trade the generated electricity in this market. This market has a trading mechanism that determines what kind of information consumers must send as an input to trade electricity and how much electricity is traded in the market. The market then determines how to distribute electricity to consumers and the electricity price based on its mechanism.

Electric Power Company. An electric power company exists in the model. Compared with consumers, this electricity trading company has much greater capacity to generate electricity. It takes responsibility for stabilizing the electrical grid system. This company executes actions of two types in decentralized electricity trading.

  • In case too much amount of electricity is generated by consumers, the company purchases the excess electricity for constant price p min.

  • In case too little electricity is generated by consumers, the company sells an amount to alleviate the shortage for constant price p max.

Consumers in the market have no incentive to sell their electricity to other consumers for less than p min, for which they can surely sell their electricity to the electric power company, and also have no incentive to buy other consumers’ electricity for more than p max. In this study, we assume p min = 0 for simplicity. We designate p max as the “electric power company’s electricity sales price.”

Consumers. Consumers send necessary information and electricity they generate to the market. Each of the consumers gains profits through the trade, which is determined by their own demand function for electricity and the amount of electricity they consume through the trade. The purpose of consumers is to maximize their profit.

Consumer’s Reservation Price for Electricity. Each consumer has its own reservation price for electricity per unit. The reservation price for electricity of consumer i (1 ≤ i ≤ n) is determined by min-demand \( q_{i}^{min} , \) max-demand \( q_{i}^{max } \) and the reservation price for min-demand \( p_{i}^{max } . \) The min-demand means the minimum amount of electricity that consumer i consumes irrespective of electricity price. The max-demand means the maximum amount of electricity that consumer i can consume. We assume in this study that all consumers’ reservation prices for the min-demand equal the electric power company’s electricity sales price. We can write the reservation price as Eq. (1) in decentralized electricity trading. p i (q) represents the reservation price of consumer i for the amount of electricity q.

$$ p_{i} (q) = \left\{ {\begin{array}{ll} {p^{max} }& {(0 \le q < q_{i}^{min} )} \hfill \\ { - \frac{{p_{i}^{max} }}{{q_{i}^{max} - q_{i}^{min } }}(q - q_{i}^{max} )} & {(q_{i}^{min} \le q \le q_{i}^{max} )} \hfill \\ \end{array} } \right. $$
(1)

This can be represented as Fig. 2.

Fig. 2
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Reservation price for electricity of consumer i

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Consumer’s Demand Function. The demand is easily derived from Eq. (1). The potential maximum amount of electricity that the consumer wants to consume is determined according to Eq. (1) if a certain price is given. Figure 3 portrays consumer i’s demand function q i (p) given price p.

Fig. 3
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Demand function for electricity of consumer i

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Consumer’s Profit. Consumers gain profits through electricity trading. The consumer’s profit is divisible into three elements as follows:

  • Profit from consuming electricity

  • Profit from selling electricity

  • Payment for purchasing electricity

Consumer i’s total profit π i can be calculated as Eq. (2) using these elements.

$$ \pi_{i} = \int\limits_{0}^{{q_{i}^{c} }} {p_{i} (q_{i} ){\kern 1pt} \,dq_{i} } + \sum\limits_{j} {pq_{i,j}^{s} } - \sum\limits_{i} {pq_{i,j}^{c} } $$
(2)

The first term represents consumer i’s profit from consuming electricity. Here we assume that a consumer consumes all the electricity the consumer has purchased from the market and does not sell it to other consumers or store it. This profit is calculable with their demand function for electricity and the amount of electricity they consume \( q_{i}^{c} . \) This profit can be depicted as the colored area in Fig. 4.

Fig. 4
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Profit from consuming electricity of consumer i

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The second term represents consumer i’s profit from selling the electricity the consumer generates, which is calculable with the electricity price in the market and the amount of electricity sold in the market. p represents the electricity market price, and \( q_{i,j}^{s} \) represents the amount of electricity that consumer i sells to another consumer j.

The last term represents consumer i’s payment for purchasing electricity, which is calculable with the electricity price in the market, p, and the amount of electricity purchased by consumer i from consumer j, \( q_{i,j}^{c} . \)

Consumers’ purposes for making their decisions in the decentralized electricity trading are to make this total profit as large as possible.

2.2 Proposed Trading Mechanisms

We propose two new trading mechanisms applied to the decentralized electricity trading. These trading mechanisms are devised not only to make the social surplus larger, which is calculated as the sum of consumers’ profit, but also to stabilize the grid system, which means that electricity trading under mechanisms can balance the demand and supply of electricity. The two mechanisms differ from each other in three points as shown below.

  • Kind of input information

  • Tradable amount of electricity

  • Rule of determining the selling order

2.2.1 Mechanism 1: Aggregated Demand–Supply Mechanism

Input and the Amount of Electricity Sent to the Market. Each consumer must input an “Offer Price” in the market under Mechanism 1. The Offer Price is the price at which a consumer wants to sell the electricity the consumer generates. All consumers’ electricity is traded in the market in this mechanism (Fig. 5).

Fig. 5
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Input and the amount of electricity sent to the market under mechanism 1

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Determining the Electricity Price. The electricity price is determined using an aggregate demand curve and aggregate supply curve. The aggregate demand curve is made from demand curves of all consumers, as shown in Fig. 6. The aggregate supply curve is made from the Offer Price and electricity sent from all consumers as shown in Fig. 7. Here, \( p_{k}^{s} \) and \( q_{k}^{g} \) respectively represent the Offer Price and generated electricity output of consumer k, who sends the kth cheapest Offer Price in the market.

Fig. 6
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How to make an aggregate demand curve under mechanism 1

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Fig. 7
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How to make an aggregate supply curve under mechanism 1

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The intersection point of the aggregate demand curve and the aggregate supply curve is determined as the electricity price in the market, which we call a “Trading Price.” All the electricity is traded for that price in the market (Fig. 8).

Fig. 8
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Determining the trading price under mechanism 1

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Order of Selling Electricity. The order of selling electricity is determined by the consumers’ Offer Price. The cheaper an Offer Price consumers input, the earlier they can sell their electricity in the market. For example, a consumer who inputs the cheapest Offer Price can sell electricity first, and a consumer who inputs the second cheapest Offer Price can sell electricity next. A cheaper Offer Price gives a lower probability of not selling all their generated electricity.

2.2.2 Mechanism 2: Residual Electricity Based Mechanism

Input and the Amount of Electricity Sent to the Market. Consumers must input an “Offer Price” and a “Quantity of Electricity to Secure” in the market under Mechanism 2. The Offer Price is the price at which a consumer wants to sell electricity that the consumer generates. The Quantity of Electricity to Secure is the quantity of electricity which a consumer wants to consume from the electricity that is generated. This quantity of electricity is not traded. The rest is traded in the market (Fig. 9).

Fig. 9
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Input and amount of electricity sent to the market under mechanism 2

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How to Determine the Electricity Price. The electricity price is determined by the aggregate demand curve and aggregate supply curve from which secured amounts are removed. The aggregate demand curve is made from the demand curve. The Quantity of Electricity to Secure of all consumers is shown as Fig. 10. The aggregate supply curve is produced from the Offer Price, Quantity of Electricity to Secure, and electricity sent from all consumers as shown in Fig. 11.

Fig. 10
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How to make the aggregate demand curve under mechanism 2

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Fig. 11
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How to make the aggregate supply curve under mechanism 2

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The intersection point of the aggregate demand curve and the aggregate supply curve determines the Trading Price in the market. All electricity is traded with that price in the market (Fig. 12).

Fig. 12
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How to determine the trading price under mechanism 2

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Order of Selling Electricity. The order of selling electricity is determined by the consumer’s Offer Price, as shown in Mechanism 1. The lower the consumers set their Offer Price, the earlier they can sell their electricity.

3 Experiments with Human Subjects

We conducted experiments with human subjects to analyze how human beings make their decisions in the decentralized electricity trading under each of two mechanisms. Though perfect rationality is assumed in economic theory, human beings do not always make their decisions rationally, which should be considered when we evaluate how stable the mechanisms are. The experiments are based on the experimental economics methodology [6, 7]. Subjects were promised a monetary reward according to the payoff earned in experiments. The experiments were conducted with 54 subjects on December 3 and 14, 2011.

3.1 Experimental Settings

We fixed the number of consumers in the market as three. 27 subjects joined each day. Thereby, the subjects are divided into nine groups. Consumers of three types are assumed and are set to each subject respectively in a group. Each type has a different min-demand and generated electricity output, as Table 1 shows.

Table 1 Consumer parameters
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Subjects made their decisions based on their parameters and profits they were able to gain through trading electricity. They knew their own parameters and profits, but they could not know the others’.

3.2 Experimental Results

We were able to elicit models of decision-making by human subjects from the experiments. The model we elicited is the following.

  • Subjects make their decisions based on decision change and profit change from the previous trade. The decision change shows whether consumers make values of input larger, smaller, or no change them; the profit change shows whether the consumer’s profit becomes larger, smaller, or shows no change.

  • Subjects make their decisions for the next trade based on a combination of their decision change and profit change from the previous trade. Whether they make the values of input larger, smaller, or do not change them for the next trade is determined stochastically according to a probability derived from the experiments.

Tables 2 and 3 portray the probability elicited from the result of the experiments. These results are used in the next section as the decision-making model of agents.

Table 2 Consumer parameters
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Table 3 Model of decision-making by human beings under mechanism 2
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4 Multi-Agent Simulation Considering Decision-Making by Humans

We conducted a multi-agent simulation in which agents’ decisions were based on the model elicited in the experiments with human subjects in the former section. We evaluated the two mechanisms proposed in Sect. 2 in terms of stability of the grid system and social surplus.

4.1 Parameters

We set up the parameters used in the simulations as follows:

  • The number of agents n is 100.

  • Max-demand of each consumer is 100.

  • Min-demand of each consumer is between 10 and 50 in intervals of 10.

  • The generated electricity output of each consumer is between 10 and 200 at intervals of 10.

  • The min-demands and electricity outputs are uniformly distributed, meaning that all consumers have a different set of min-demand and electricity output.

4.2 Simulation Results

Table 4 presents the simulation results. We use the variance of each consumer’s decisions as an index of how stable the grid system under each of the mechanisms is. Variances are average values of 100 trials. Values of social surplus are the moving average values of the prior 200 steps in 100 trials. Each trial has 1000 steps.

Table 4 Simulation results
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As Table 4 shows, Mechanism 2 achieves smaller values of variance in both the Offer Price and Trading Price compared with Mechanism 1. The low variance indicates stability in the mechanism because it means consumers in the market do not change their values of input frequently. It can therefore be said that Mechanism 2 makes the electricity trading more stable than Mechanism 1 does. In addition, as Table 4 and Fig. 13 show, social surplus in the market under Mechanism 2 is larger. Moreover, it is apparent in Fig. 13 that the high social surplus is realized in early steps under Mechanism 2. We infer that consumers can obtain profits to some extent without fail because they are sure to consume some amount of electricity as the Quantity of Electricity to Secure under Mechanism 2. We conclude that Mechanism 2 is better than Mechanism 1 not only in terms of grid system stability but also in terms of social surplus.

Fig. 13
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Social surplus transition of mechanism 1 and mechanism 2

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5 Conclusion

Electricity trade in which small-scale consumers such as households participate, which we call Decentralized Electricity Trading, is regarded as realizable in the near future. This paper proposes new trading mechanisms applied to decentralized electricity trading and is evaluated using an integrated approach with experiments using human subjects and multi-agent simulation. Results show that, when considering irrationality in decision-making by human beings, Mechanism 2, by which consumers secure the electricity they use beforehand and by which the rest is traded in the market, achieves a good result in terms of grid system stability and social surplus. Considering the fact that balancing demand and supply with robustness is desired to make large profit, which Makris et al. [8] mention in their research, we think the methods used in this research are also useful in manufacture.