# Electricity Procurement Strategies under Supply Disruption and Price Fluctuation

Authors: Jie Tan; Qin Zhong
Journal: Complexity
 (2022)

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## Abstract

Improving the reliability of electricity supply is closely related to the national industrial economy and people’s livelihood. When procuring electricity, the large consumer faces the risk of insufficient electricity supply. Such insufficiency may be caused by the supply disruption of the upstream electricity generator and the fluctuation of electricity prices in the electricity pool. We establish an expected cost model for the large consumer and a revenue model for the electricity generator by introducing robustness and opportunity functions to analyse the impact of supply disruption and price fluctuation on both members. Then, we obtain the optimal reliability level and subsidy rate. Our analytical results reveal the following points: (1) During an electricity price fluctuation, the sufficient and necessary condition for the large consumer to expect high robustness of his own decision-making is to pay a high cost. (2) The high uncertainty of electricity price leads to less revenue for the electricity generator; thus, the electricity generator should perform well in price forecasting. (3) Without disruption risk, the electricity generator is reliable. Furthermore, the electricity pool is unreliable from the perspective of price. However, the electricity supply of the electricity generator is no longer reliable when considering disruption risk, whereas the electricity pool is reliable because the large consumer is tolerant of price fluctuation under this circumstance. Moreover, the impacts of market uncertainty and players’ attributes on the optimal strategies are explored.


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## Body

## 1. Introduction

Many developing countries in Asia and Africa are bestowed with abundant hydrocarbon resources; for example, India and Pakistan (Sudan) reserve the most coal (oil) in the world. However, these countries feature the world’s largest population with denied access to electricity (International Energy Agency [IEA], 2011). This predicament is called “resource rich, energy poor” [1]. The essence lies in the low efficiency of energy utilisation [2]. The lack of electricity increases unemployment and inflation and endangers social and political stability. During an energy crisis, certain countries limit electricity consumption, which leads to an economic recession. For example, Pakistan, which has the world’s 5th largest coal reserves, is severely lacking in electricity in the last few years. In the summer 2013, Pakistan suffered a 6,500 MWh electricity shortage with an estimated total demand of 16,500 MWh. National Electric Power Regulatory Authority reported that load shedding is generally used 9–12 h a day in major cities. Many industrial sectors even face bankruptcy. Particularly, the reducing output of the textile and fertiliser industry is up to 40%–50%, which results in the closure of hundreds of industrial units with an increasing unemployment rate across the country [3]. Moreover, the approximate loss of electricity shortages is estimated 2%–4% of the annual GDP in recent years.The main reason for a large consumer to take part in an electricity market from a variety of resources is to procure its electricity demand at minimum cost and minimum risk. According to the criteria of whether or not to trade through a unified platform, a large consumer would purchase electricity from bilateral contracts and/or an electricity pool.When purchasing electricity from bilateral contracts, a large consumer who procures electricity directly from the electricity generator may face supply disruption risk, leading to large-scale blackouts [4]. In general, natural disasters and system accidents are the direct causes of large-scale blackouts. For example, since January 2021, due to the randomness and intermittency of new energy, several regions in China have adopted measures called “orderly power consumption” and “power rationing.” In July 2016, Lenovo in Wuhan lost at least one million Chinese yuan per day due to the electricity supply disruption caused by a rainstorm. Downstream customers such as Zuk and Motorola were also affected. Oughton et al. [5] showed that the loss caused by electricity supply disruption accounted for 49% of the total macroeconomic revenue in the United States. Such excessive loss has caused an alarm for the electricity supply reliability, thus indicating the urgent need for the improvement in the electricity supply reliability.When purchasing electricity from an electricity pool, a large consumer would face the uncertain risk of the market price. For instance, the average fluctuation range of the electricity price could reach up to 359.8% according to the statistics from the US energy department (2002). The electricity pool is a centralised market for buyers and sellers. All sellers and buyers offer their prices to the pool for trading in the market. Under the mode of electricity pool, the electricity market mainly carries out spot trading. Thus, the equilibrium price of electricity exhibits high fluctuation [6]. Furthermore, the electricity price on the pool fluctuates more sharply compared with that of other products due to the nonstorability of electricity. However, the price should not be too high because electricity is closely related to daily livelihood and economy. Moreover, the price should not be too low, because it will lead to unreliable supply. The electricity market in California pays less attention to its economy, leading to extreme losses. As a result, many power companies were on the verge of bankruptcy. Considering that the electricity price is uncertain and volatile, the electricity procurement cost will be uncertain. Hence, the consumer tries to optimise the procurement problem while controlling the price fluctuation risk. Price fluctuation is usually the focus of supply chain decisions [7, 8].In practice, improving reliability and controlling price fluctuations are common. Firstly, for example, China carries out electricity supply reliability improvement projects in many aspects. By 2017, the number of equipment, facilities, and systems within the reliability management scope of the whole industry has exceeded 92%, and the capacity has exceeded 95%. In 2017, the national average electricity supply reliability rate reached 99.814%, increasing 0.009 percentage points every year. Additionally, the average outage time of users was 16.27 h per household, decreasing by 0.84 h per household every year. Secondly, electricity price is a key point in the electricity market. On the electricity generation side, the on-grid electricity price in China is formed in the range of “benchmark + fluctuation” through a market transaction. The fluctuation is no more than 20%, that is the electricity price is limited. Moreover, China has completed two rounds of electricity transmission and distribution price reform. The electricity price has entered the second supervision period since January 2021.This study considers a supply chain in which a large consumer procures electricity from an electricity generator and an electricity pool simultaneously. In particular, the large consumer who procures electricity directly from the generator faces supply disruption risk, resulting in insufficient electricity supply. In addition, the large consumer provides subsidies to the electricity generator to improve supply reliability. However, electricity procurement from the electricity pool faces the fluctuation risk of electricity prices. The fluctuation of electricity prices also directly leads to the uncertainty of the procurement cost of the large consumer. Specifically, this study tries to answer the following questions in consideration of supply disruption risk and market uncertainty:(1)
Research Question 1: What are the impacts of the players’ risk attitudes on their optimal strategies?(2)
Research Question 2: What is the optimal construction strategy of supply reliability for the electricity generator? What is the optimal subsidy strategy for the large consumer?(3)
Research Question 3: What is the optimal procurement structure between contract procurement and market procurement?To answer these questions, we introduce the target uncertainty level to describe the uncertainty of the electricity market with the robustness function and the opportunity function based on the study by Zare et al. [9]. We then establish an expected revenue model for the electricity generator and a cost model for the large consumer. Furthermore, we obtain the optimal decisions for the large consumer and the electricity generator while considering supply disruption risk and market price fluctuation.Our main contributions are as follows: (1) To our best knowledge, no previous research has explored the electricity supply chain considering both supply disruption and price fluctuation. Price fluctuation is an important feature that sets apart the electricity supply chain from the general supply chain. Short-term fluctuations in electricity prices can be transmitted to different types of energy, leading to rises in energy prices. However, the existing studies about electricity supply reliability only focus on the quantity to meet the demand, ignoring price constraints. Furthermore, contract and market procurement are analysed comprehensively in this study, instead of studying them separately, and then a comparison is made. (2) We introduce the supply reliability construction cost and direct subsidy into the electricity supply chain. In consideration of disruption risk, electricity suppliers need to construct their reliability, such as developing smart technologies and building smart grids. They can design a better operation strategy and/or establish a real-time monitoring system. Thus, the investment of electricity suppliers should not be ignored. Moreover, many studies showed that subsidising suppliers is one of the effective methods to encourage suppliers to improve their supply reliability [10–13]. (3) Similar to Zare et al. [9], we establish an expected revenue model and a cost model to examine the impact of the players’ risk attitude on their decisions. However, supply disruption risks were ignored in their research, and their results may be counterintuitive. Our study shows that electricity supply reliability should include both quantity targets and price constraints. Without disruption risk, the electricity generator is reliable. Moreover, the electricity pool is unreliable from the perspective of price. However, the electricity supply of the electricity generator is no longer reliable when considering disruption risk, whereas the electricity pool is reliable because the large consumer is tolerant of price fluctuations under this circumstance.The rest of this study is organised as follows: In Section2, we review the related literature. In Section 3, we establish and analyse the two models. In Section 4, we conduct a numerical case. Finally, we conclude the study in Section 5.


## 2. Literature Review

This study is mainly related to three broad streams of literature: supply disruption risk management, electricity price fluctuation, and supply reliability.In the existing literature, numerous countermeasures have been proposed to cope with supply disruptions. For example, pre-disruption tactics focus on improving supply chain resilience, including inventory buffer, backup supply, transportation infrastructures, and supply chain network design [14, 15]. Some contracts and incentives have been studied to improve suppliers’ reliability and to share disruption information [16–18]. From the perspective of post-disruption mitigation, approaches such as coordination contracting, contingent sourcing, and service/production recovery are established to alleviate the negative impacts of supply disruptions [19, 20]. Azad and Hassini [21] considered a supply network consisting of customers and production facilities, in which any facility may be disrupted and may lead to partial failure or complete shutdown of supply facilities. They proposed a model for optimal recovery from major unpredictable disruptions in the supply network. Li et al. [22] compared and selected proactive and reactive strategies for supply disruption management via a cost minimisation model. They proposed a passive-backup strategy and a recovery-backup strategy to guide the mitigation approaches as the disruptions continue. Li et al. [23] discussed the optimal post-disruption decision for customers. They believed that precisely capturing post-disruption demand and designing an effective supply risk mitigation strategy are critical. Our study focuses on improving the supplier’s reliability through subsidy incentives from the perspective of pre-disruption prevention. Ma et al. [24] explained the advertising investment and subsidy behaviours of the manufacturer and the retailer in marketing and provided recommendations for supply chain members to adjust their operations under supply disruption. In addition, a buyer can utilise many procurement strategies to manage supply disruptions proactively or reactively, for instance backup sourcing, contingent sourcing, and supplier diversification/selection, with the splitting of orders among multiple/dual suppliers to reduce the disruption risk proactively or to replenish inventory reactively [25–27].Given that the electricity market mainly carries out on-the-spot transactions under the electricity pool mode, the electricity price usually exhibits high fluctuation [6]. Stochastic probability distributions are often applied to describe the electricity price fluctuation in many fields, such as electricity price forecasting and market risk evaluation. Liu and Guan [28] discussed purchase allocation in day-ahead and real-time markets, in which price fluctuation is modelled by using a stochastic process. Conejo et al. [29] and Conejo and Carrion [30] addressed electricity procurement of large consumers by using a mean-variance methodology. Gabriel et al. [31] analysed the medium-term risk-constrained profit maximisation problem faced by a retailer in which the uncertainties of price are modelled by probability distributions. Considering that the normality assumption has simplified uncertainty modelling in different fields of application, researchers often assume that prices in the electricity market obey the normal distribution [32]. Allen and Ilic [33] supposed that the electricity price during every time interval obeys the normal distribution when dealing with the unit commitment issue of a single electricity supplier. Gao and Zhang [34] assumed that electricity prices obey normal distribution, and the mean value and the mean-square deviation of electricity price in the first time interval of a day in a certain electricity market are obtained. In the electricity market, when the structure of the risk management of electricity suppliers is designed, it is also assumed that electricity prices are associated with fuel prices of electricity generation as random variables obey normal distribution [35]. Zhou et al. [36] showed that electricity prices obey normal distribution approximately when supply-demand relationship is loose. However, some studies found that electricity prices are not supposed to obey the normal distribution. For example, Bai et al. [37] found that electricity prices are supposed to have different probability distributions according to different demands, although this assumption only presents a numerical simulation result without monitoring the date of real electricity markets.Several studies regard the electricity supply reliability. Caralis and Zervos [38] analysed the effect of fan access permeability on generating abundance. Hu et al. [39] studied the influence of wind storage access on wind electricity reliability. Karki et al. (2010) studied the impact of different electricity generation types and showed that resource randomness and resource storage capacity affect electricity supply reliability. Brown [40] established an index system to evaluate the electricity supply reliability and observed that the electricity supply reliability indexes of a distribution network mainly include the average outage frequency and time. This study will model electricity supply reliability from the perspective of both quantity and price. Ebrahimi and Bagheri [41] developed a two-objective mathematical model to maximise the reliability of fossil fuel supply chain. Gurnani and Shi [42] assumed that reliability was the probability that the supplier delivered the agreed quantity on the agreed date and simulated the interaction between the buyer and the unreliable supplier. Krause et al. [12] showed that direct subsidy is effective in improving supply chain reliability. Wang et al. [43] assumed that the manufacturer improves supply reliability through incentives and discussed how the potential spillover effect affects the manufacturer’s motivation to improve supply reliability. Hu et al. [13] proposed that a retailer encourages a supplier to realise capacity recovery by increasing order quantity and/or wholesale price, so as to improve supply reliability. Tang et al. [44] explored that the retailer provides an incentive to the supplier to develop technology strategies that affect supply reliability.


## 3. The Model

We consider a two-echelon supply chain in which a single large consumer purchases electricity from an electricity generator and the electricity pool. Usually, the electricity generating cost consists of the investment in recovery, maintenance, and operation [18]. The generator invests considerable money to build supply reliability. Simultaneously, the large consumer provides subsidies for the cost of the electricity generator to construct its reliability. Our model is based on all-or-nothing disruption, that is no electricity output is supplied if a disruption occurs [45, 46]. In the electricity pool, the price of electricity fluctuates, which is assumed to follow the normal distribution. This assumption has been considered based on the study by Anderson and Davison [47], Zhou et al. [36], and Zare et al. [9]. As shown in Anderson and Davison [47], the price process for electricity is notoriously volatile, and this volatility is nonstationary, showing unpredictable spiking behaviour in a pseudocyclical pattern. In the absence of better bottom-up models for prices during price spikes, the amount of “high” data is insufficient to be able to estimate the choice of anything other than a normal distribution. Bottom-up models, especially those based on matching load and capacity in stack pricing, are incapable of adequately modelling psychologically based price spikes. Observations are also scarce, making the argument for a statistical description more complicated than a normal distribution. The normal distribution of electricity price is used by researchers in many fields, for example electricity price forecasting, market risk evaluation, bidding strategies, and power distribution strategies. In addition, the time-sharing price is adopted and is divided into the peak, middle peak, and low peak periods [9, 48]. The elasticity of electricity demand is extremely small. Thus, we consider that the demand for the large consumer is stable. Figure 1 shows the details, and Table 1 shows the notations for the studied variables.Figure 1
The electricity supply chain system.Table 1
Notations.
ParameterThe large consumer signsn different electricity contracts with the electricity generatorTThe electricity consumption of the large consumer is divided intoT periodsPnThe electricity price of thenth contract signed between the large consumer and the electricity generatorPtThe price oft stage in electricity poolDtThe electricity demand of the large consumer at timetQn,tThe electricity procurement volume of the large consumer from thenth contract in phase tQtThe electricity procured by the large consumer in the electricity pool int stagesl0−1 variable: If contract L is used when purchasing electricity in phase t,then the value is one; otherwise, the value is zerou1The target uncertainty level of the electricity generatoru2The target uncertainty level of the large consumerCThe large consumer’s electricity procurement costRThe electricity revenue of the electricity generatorC¯The mean value of the large consumer’s predicted procurement costR¯The average forecast revenue of the electricity generatorCexpThe large consumer’s expected costRexpThe expected revenue of the electricity generatorTCwThe maintenance cost of the generator to resume operation in case of disruptionTCsThe economic losses of the large consumer in case of disruptionβThe reliability cost coefficient of the electricity generatorDecision variableszThe reliability level of the electricity generatorγThe subsidy proportion of the large consumer to the electricity generator


### 3.1. Expected Cost and Expected Revenue Model under Market Uncertainty

The large consumer procures electricity from the electricity generator and the electricity pool. The market price of electricity exhibits volatility and uncertainty, which lead to the uncertainty of electricity procurement cost and electricity generator’s revenue. In this study, we apply the robustness and opportunity functions to describe the uncertainty of cost and revenue based on the work of Zare et al. [9]; we also establish the expected cost and expected revenue models with market uncertainty under zero disruption risk.


#### 3.1.1. Expected Cost of the Large Consumer

In accordance with the electricity demand and market price, the large consumer’s electricity purchase cost is as follows:(1)C=∑n=1N∑t=1TPnQn,t+∑t=1TPtQt,s.t.(2)Qn,t+Qt=Dt,n=1,…N,t=1,…T,(3)Qn,tC,min∗sl≤Qn,t≤Qn,tC,max∗sl,n=1,…N,t=1,…T.The procurement cost includes contract procurement and market procurement. Equation (2) indicates that the total electricity purchased by the market and the contract must meet the electricity demand in period t. However, the power range and electricity price in different contracts vary. Hence, each contract has the limit of purchasing electricity quantity in different periods in equation (3).The electricity procurement cost of the large consumer obeys an expected distribution because of the substantial fluctuation of electricity prices in the electricity pool. The market electricity price follows the normal distribution, that isPt∼NP⃛t,σ2,t=1,…,T. The expected electricity procurement cost forms a linear relationship with the market price. Thus, the expected electricity procurement cost obeys the normal distribution, that is C∼NC¯,σc2. The mean value of the expected procurement cost is C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt, and the standard deviation is σc in accordance with the mean value of the predicted market price.As mentioned above, the uncertainty of the expected procurement cost caused by the market price uncertainty in the electricity pool can be expressed as follows:(4)Uu2,Cexp=Cexp:Cexp−C¯σC≤u2,u2≥0,where u2 is the uncertain target parameter of the large consumer. According to the definition of the robustness function, when u2 increases, the decision is robust, and the capability to resist the uncertainty is large. Therefore, the maximum value of the expected procurement cost can be expressed as follows:(5)maxEC=maxCexp=C¯+u2σC,where C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt. Equation (5) represents the expected procurement cost of the large consumer under the robustness function, which implies the highest cost for the large consumer-facing uncertainty.


#### 3.1.2. Expected Revenue of the Generator

With one large consumer and one electricity generator in a supply chain, the predicted revenue of the electricity generator equals to the large consumer’s expected purchase cost. Also it follows a normal distribution and can be expressed asR∼NR¯,σc2. The uncertainty of market price in the electricity pool leads to the uncertainty of the large consumer’s expected purchase cost. This event leads to the uncertainty of the predicted revenue of the electricity generator. The uncertainty can be expressed as follows:(6)Uu1,Rexp=Rexp:Rexp−R¯σC≤u1,where u1 is the uncertain target parameter of the electricity generator. According to the definition of the opportunity function, the value of u1 increases, and the benefit is stable. Based on uncertainty, the minimum value of expected revenue can be expressed as follows:(7)minER=minRexp=R¯−u1σC.The above equation represents the expected revenue of the electricity generator with the opportunity function, which indicates that the electricity generator can tolerate the minimum revenue when facing uncertainty. Thus, the generator must accept the lowest revenueR¯−u1σC in the range when setting a certain target uncertainty u1.


### 3.2. Optimal Strategy of Reliability Investment and Subsidy Incentive under the Disruption Risk

When disruption risk occurs, the generator faces the maintenance cost, and the large consumer experiences economic losses with the affected operation. As a follower of the game, the profit function of the generator under the disruption risk is determined by the following:(8)max:π=z∗R¯−u1σc−1−γβz22−1−zTCw,where the first part is the revenue of the generator without the disruption risk. The second part is the cost that the electricity generator needs to invest in building the reliability level z; the cost subsidy proportion of the large consumer to the electricity generator is γ, and the coefficient of the reliability cost is β/2 [13, 44, 49]. The increase in the reliability level that leads to the increased marginal input cost is the essence of the quadratic function. If the growth rate of cost is lower than that of the profit, then the cost and profit are imbalanced, and the improvement in reliability level is always profitable, which is inconsistent with that observed in reality. The third part is the maintenance cost of the generator when disruption risk occurs.According to the reverse induction method, given the optimal reliability level of the electricity generator, the large consumer’s cost function under the disruption risk is as follows:(9)min:TC=z∗∗C¯+u2σc+γβz∗2+1−z∗TCs,where the first part is the procurement cost of the large consumer without the disruption risk. The second part is the cost subsidy of the large consumer to construct the reliability of the electricity generator. The third part is the loss cost of the large consumer when disruption risk occurs.Next, we jointly solve the profit function of the electricity generator and the cost function of the large consumer to obtain the optimal reliability level of the electricity generator and the optimal subsidy ratio of the large consumer.


#### 3.2.1. Optimal Reliability Level

The first derivative of the revenue function of the generator onz is equal to zero. Hence, the expression of the optimal reliability level of the generator with respect to the subsidy ratio γ is as follows:(10)z∗=minC¯−u1σc+TCw1−γβ,1.We can obtain the optimal reliability level of the generator by substitutingz∗ into the cost function of the large customer.Proposition 1.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the generator and the large consumer, the optimal reliability level of the electricity generator is computed as follows:(11)z∗=TCs+C¯−u1σc+TCw/2−C¯+u2σc,βC¯−u1σc−2C¯+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,C¯−u1σc+TCwβ，C¯−u1σc≤β−TCw3C¯−u1σc+2u2σc≥2TCs−TCw,1,others.Proof.
Whenz∗=C¯−u1σc+TCw/1−γβ, we can obtain γ=1−C¯−u1σc+TCw/z∗β. We can obtain z∗≥C¯−u1σc+TCw/β because 0≤γ≤1. Simultaneously, we can obtain the following equation by substituting the expression on γ into the cost function of a large consumer and setting the first derivative on z to zero:(12)Z=TCs+C¯−u1σc+TCw/2−C¯+u2σcβ.
Moreover, (a) when1≥C¯−u1σc+TCw/1−γβ≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β, the optimal reliability of the generator is C¯−u1σc+TCw/1−γβ. (b) When 1≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥C¯−u1σc+TCw/1−γβ, the optimal reliability of the generator is TCs+C¯−u1σc+TCw/2−C¯+u2σc/β. (c) When C¯−u1σc+TCw/1−γβ≥1 or TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥1, the optimal reliability of the generator is 1.
In Proposition 1, the cost coefficientβ (or β/2) represents the difficulty experienced by the electricity generator in building supply reliability. When β is large, the difficulty is high and the optimal reliability level is low. When β is small, the difficulty is low and the optimal reliability level is high. Moreover, z∗ increases on TCw and TCs. This result shows that when the maintenance cost of the electricity generator is high, the electricity generator invests cost to build reliability to resist the risk of disruption. When the loss cost of the large consumer is high, the large consumer offers additional subsidies to improve the reliability of the electricity supply. Further analysis of the influence of u1 and u2 on the optimal reliability level shows that the target uncertainty level of the large consumer and the generator negatively affects the optimal reliability of the generator. These results are attributed to two reasons. On the one hand, with the high target uncertainty level of the electricity generator resulting in low expected revenue, the electricity generator assumes reducing revenue and invests less on reliability construction cost when the reliability level drops. On the other hand, with the high target uncertainty level of the large consumer leading to a high expected cost, the large consumer assumes that the procurement cost is high and thereby reduces the subsidy of the reliability construction cost. By contrast, the electricity generator naturally reduces the investment in reliability construction.


#### 3.2.2. Optimal Subsidy

Applying the reverse induction method, when the optimal reliability level of the electricity generator is determined, the large consumer makes subsidy decisions on the basis of the different reliability levels to encourage the electricity generator to build the electricity supply reliability and reduce the risk of supply disruption.Proposition 2.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the electricity generator and the large consumer, the optimal subsidy ratio for the large consumer is as follows:(13)γ∗=1−C¯−u1σc+TCwβ，C¯−u1σc−2C¯+u2σc≥2β−TCw−2TCs,1−C¯−u1σc+TCwTCs+C¯−u1σc+TCw/2−C¯+u2σc，C¯−u1σc−2C+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,0,other.Proof.
According to the optimal reliability level of the generator in Proposition 1, substitutingz∗ into γ=1−C¯−u1σc+TCw/z∗β, we can obtain the optimal subsidy proportion of the large consumer.Proposition 3.
shows that the optimal subsidy proportionγ∗ decreases on u2 and increases on TCs. This result shows that when the level of the target uncertainty of the large consumer and the expected procurement cost are high, the subsidy for the reliability cost of the electricity generator reduces. When disruption occurs, the loss of the large consumer is high. Hence, the large consumer likely expands subsidies to the electricity generator to improve the reliability of the electricity supply and ensure electricity procurement.Arrangingγ∗, we can obtain γ∗=4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1. Notably, 4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1.≥1>0. Thus, γ∗ increases on u1 and decreases TCw. This result shows that the generator, with the high target uncertainty level and the low expected revenue, may reduce the investment cost of building the reliability. The large consumer increases the proportion of subsidies to encourage the electricity generator to supply electricity better and more reliably to reduce the probability of electricity supply disruption. When the maintenance cost of the electricity generator is high, the electricity generator pays attention to the reliability construction and increases the cost investment. The large consumer observes this situation and hence appropriately decreases incentive subsidies.


## 3.1. Expected Cost and Expected Revenue Model under Market Uncertainty

The large consumer procures electricity from the electricity generator and the electricity pool. The market price of electricity exhibits volatility and uncertainty, which lead to the uncertainty of electricity procurement cost and electricity generator’s revenue. In this study, we apply the robustness and opportunity functions to describe the uncertainty of cost and revenue based on the work of Zare et al. [9]; we also establish the expected cost and expected revenue models with market uncertainty under zero disruption risk.


### 3.1.1. Expected Cost of the Large Consumer

In accordance with the electricity demand and market price, the large consumer’s electricity purchase cost is as follows:(1)C=∑n=1N∑t=1TPnQn,t+∑t=1TPtQt,s.t.(2)Qn,t+Qt=Dt,n=1,…N,t=1,…T,(3)Qn,tC,min∗sl≤Qn,t≤Qn,tC,max∗sl,n=1,…N,t=1,…T.The procurement cost includes contract procurement and market procurement. Equation (2) indicates that the total electricity purchased by the market and the contract must meet the electricity demand in period t. However, the power range and electricity price in different contracts vary. Hence, each contract has the limit of purchasing electricity quantity in different periods in equation (3).The electricity procurement cost of the large consumer obeys an expected distribution because of the substantial fluctuation of electricity prices in the electricity pool. The market electricity price follows the normal distribution, that isPt∼NP⃛t,σ2,t=1,…,T. The expected electricity procurement cost forms a linear relationship with the market price. Thus, the expected electricity procurement cost obeys the normal distribution, that is C∼NC¯,σc2. The mean value of the expected procurement cost is C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt, and the standard deviation is σc in accordance with the mean value of the predicted market price.As mentioned above, the uncertainty of the expected procurement cost caused by the market price uncertainty in the electricity pool can be expressed as follows:(4)Uu2,Cexp=Cexp:Cexp−C¯σC≤u2,u2≥0,where u2 is the uncertain target parameter of the large consumer. According to the definition of the robustness function, when u2 increases, the decision is robust, and the capability to resist the uncertainty is large. Therefore, the maximum value of the expected procurement cost can be expressed as follows:(5)maxEC=maxCexp=C¯+u2σC,where C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt. Equation (5) represents the expected procurement cost of the large consumer under the robustness function, which implies the highest cost for the large consumer-facing uncertainty.


### 3.1.2. Expected Revenue of the Generator

With one large consumer and one electricity generator in a supply chain, the predicted revenue of the electricity generator equals to the large consumer’s expected purchase cost. Also it follows a normal distribution and can be expressed asR∼NR¯,σc2. The uncertainty of market price in the electricity pool leads to the uncertainty of the large consumer’s expected purchase cost. This event leads to the uncertainty of the predicted revenue of the electricity generator. The uncertainty can be expressed as follows:(6)Uu1,Rexp=Rexp:Rexp−R¯σC≤u1,where u1 is the uncertain target parameter of the electricity generator. According to the definition of the opportunity function, the value of u1 increases, and the benefit is stable. Based on uncertainty, the minimum value of expected revenue can be expressed as follows:(7)minER=minRexp=R¯−u1σC.The above equation represents the expected revenue of the electricity generator with the opportunity function, which indicates that the electricity generator can tolerate the minimum revenue when facing uncertainty. Thus, the generator must accept the lowest revenueR¯−u1σC in the range when setting a certain target uncertainty u1.


## 3.1.1. Expected Cost of the Large Consumer

In accordance with the electricity demand and market price, the large consumer’s electricity purchase cost is as follows:(1)C=∑n=1N∑t=1TPnQn,t+∑t=1TPtQt,s.t.(2)Qn,t+Qt=Dt,n=1,…N,t=1,…T,(3)Qn,tC,min∗sl≤Qn,t≤Qn,tC,max∗sl,n=1,…N,t=1,…T.The procurement cost includes contract procurement and market procurement. Equation (2) indicates that the total electricity purchased by the market and the contract must meet the electricity demand in period t. However, the power range and electricity price in different contracts vary. Hence, each contract has the limit of purchasing electricity quantity in different periods in equation (3).The electricity procurement cost of the large consumer obeys an expected distribution because of the substantial fluctuation of electricity prices in the electricity pool. The market electricity price follows the normal distribution, that isPt∼NP⃛t,σ2,t=1,…,T. The expected electricity procurement cost forms a linear relationship with the market price. Thus, the expected electricity procurement cost obeys the normal distribution, that is C∼NC¯,σc2. The mean value of the expected procurement cost is C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt, and the standard deviation is σc in accordance with the mean value of the predicted market price.As mentioned above, the uncertainty of the expected procurement cost caused by the market price uncertainty in the electricity pool can be expressed as follows:(4)Uu2,Cexp=Cexp:Cexp−C¯σC≤u2,u2≥0,where u2 is the uncertain target parameter of the large consumer. According to the definition of the robustness function, when u2 increases, the decision is robust, and the capability to resist the uncertainty is large. Therefore, the maximum value of the expected procurement cost can be expressed as follows:(5)maxEC=maxCexp=C¯+u2σC,where C¯=∑n=1N∑t=1TPnQn,t+∑t=1Tp¯tQt. Equation (5) represents the expected procurement cost of the large consumer under the robustness function, which implies the highest cost for the large consumer-facing uncertainty.


## 3.1.2. Expected Revenue of the Generator

With one large consumer and one electricity generator in a supply chain, the predicted revenue of the electricity generator equals to the large consumer’s expected purchase cost. Also it follows a normal distribution and can be expressed asR∼NR¯,σc2. The uncertainty of market price in the electricity pool leads to the uncertainty of the large consumer’s expected purchase cost. This event leads to the uncertainty of the predicted revenue of the electricity generator. The uncertainty can be expressed as follows:(6)Uu1,Rexp=Rexp:Rexp−R¯σC≤u1,where u1 is the uncertain target parameter of the electricity generator. According to the definition of the opportunity function, the value of u1 increases, and the benefit is stable. Based on uncertainty, the minimum value of expected revenue can be expressed as follows:(7)minER=minRexp=R¯−u1σC.The above equation represents the expected revenue of the electricity generator with the opportunity function, which indicates that the electricity generator can tolerate the minimum revenue when facing uncertainty. Thus, the generator must accept the lowest revenueR¯−u1σC in the range when setting a certain target uncertainty u1.


## 3.2. Optimal Strategy of Reliability Investment and Subsidy Incentive under the Disruption Risk

When disruption risk occurs, the generator faces the maintenance cost, and the large consumer experiences economic losses with the affected operation. As a follower of the game, the profit function of the generator under the disruption risk is determined by the following:(8)max:π=z∗R¯−u1σc−1−γβz22−1−zTCw,where the first part is the revenue of the generator without the disruption risk. The second part is the cost that the electricity generator needs to invest in building the reliability level z; the cost subsidy proportion of the large consumer to the electricity generator is γ, and the coefficient of the reliability cost is β/2 [13, 44, 49]. The increase in the reliability level that leads to the increased marginal input cost is the essence of the quadratic function. If the growth rate of cost is lower than that of the profit, then the cost and profit are imbalanced, and the improvement in reliability level is always profitable, which is inconsistent with that observed in reality. The third part is the maintenance cost of the generator when disruption risk occurs.According to the reverse induction method, given the optimal reliability level of the electricity generator, the large consumer’s cost function under the disruption risk is as follows:(9)min:TC=z∗∗C¯+u2σc+γβz∗2+1−z∗TCs,where the first part is the procurement cost of the large consumer without the disruption risk. The second part is the cost subsidy of the large consumer to construct the reliability of the electricity generator. The third part is the loss cost of the large consumer when disruption risk occurs.Next, we jointly solve the profit function of the electricity generator and the cost function of the large consumer to obtain the optimal reliability level of the electricity generator and the optimal subsidy ratio of the large consumer.


### 3.2.1. Optimal Reliability Level

The first derivative of the revenue function of the generator onz is equal to zero. Hence, the expression of the optimal reliability level of the generator with respect to the subsidy ratio γ is as follows:(10)z∗=minC¯−u1σc+TCw1−γβ,1.We can obtain the optimal reliability level of the generator by substitutingz∗ into the cost function of the large customer.Proposition 1.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the generator and the large consumer, the optimal reliability level of the electricity generator is computed as follows:(11)z∗=TCs+C¯−u1σc+TCw/2−C¯+u2σc,βC¯−u1σc−2C¯+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,C¯−u1σc+TCwβ，C¯−u1σc≤β−TCw3C¯−u1σc+2u2σc≥2TCs−TCw,1,others.Proof.
Whenz∗=C¯−u1σc+TCw/1−γβ, we can obtain γ=1−C¯−u1σc+TCw/z∗β. We can obtain z∗≥C¯−u1σc+TCw/β because 0≤γ≤1. Simultaneously, we can obtain the following equation by substituting the expression on γ into the cost function of a large consumer and setting the first derivative on z to zero:(12)Z=TCs+C¯−u1σc+TCw/2−C¯+u2σcβ.
Moreover, (a) when1≥C¯−u1σc+TCw/1−γβ≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β, the optimal reliability of the generator is C¯−u1σc+TCw/1−γβ. (b) When 1≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥C¯−u1σc+TCw/1−γβ, the optimal reliability of the generator is TCs+C¯−u1σc+TCw/2−C¯+u2σc/β. (c) When C¯−u1σc+TCw/1−γβ≥1 or TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥1, the optimal reliability of the generator is 1.
In Proposition 1, the cost coefficientβ (or β/2) represents the difficulty experienced by the electricity generator in building supply reliability. When β is large, the difficulty is high and the optimal reliability level is low. When β is small, the difficulty is low and the optimal reliability level is high. Moreover, z∗ increases on TCw and TCs. This result shows that when the maintenance cost of the electricity generator is high, the electricity generator invests cost to build reliability to resist the risk of disruption. When the loss cost of the large consumer is high, the large consumer offers additional subsidies to improve the reliability of the electricity supply. Further analysis of the influence of u1 and u2 on the optimal reliability level shows that the target uncertainty level of the large consumer and the generator negatively affects the optimal reliability of the generator. These results are attributed to two reasons. On the one hand, with the high target uncertainty level of the electricity generator resulting in low expected revenue, the electricity generator assumes reducing revenue and invests less on reliability construction cost when the reliability level drops. On the other hand, with the high target uncertainty level of the large consumer leading to a high expected cost, the large consumer assumes that the procurement cost is high and thereby reduces the subsidy of the reliability construction cost. By contrast, the electricity generator naturally reduces the investment in reliability construction.


### 3.2.2. Optimal Subsidy

Applying the reverse induction method, when the optimal reliability level of the electricity generator is determined, the large consumer makes subsidy decisions on the basis of the different reliability levels to encourage the electricity generator to build the electricity supply reliability and reduce the risk of supply disruption.Proposition 2.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the electricity generator and the large consumer, the optimal subsidy ratio for the large consumer is as follows:(13)γ∗=1−C¯−u1σc+TCwβ，C¯−u1σc−2C¯+u2σc≥2β−TCw−2TCs,1−C¯−u1σc+TCwTCs+C¯−u1σc+TCw/2−C¯+u2σc，C¯−u1σc−2C+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,0,other.Proof.
According to the optimal reliability level of the generator in Proposition 1, substitutingz∗ into γ=1−C¯−u1σc+TCw/z∗β, we can obtain the optimal subsidy proportion of the large consumer.Proposition 3.
shows that the optimal subsidy proportionγ∗ decreases on u2 and increases on TCs. This result shows that when the level of the target uncertainty of the large consumer and the expected procurement cost are high, the subsidy for the reliability cost of the electricity generator reduces. When disruption occurs, the loss of the large consumer is high. Hence, the large consumer likely expands subsidies to the electricity generator to improve the reliability of the electricity supply and ensure electricity procurement.Arrangingγ∗, we can obtain γ∗=4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1. Notably, 4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1.≥1>0. Thus, γ∗ increases on u1 and decreases TCw. This result shows that the generator, with the high target uncertainty level and the low expected revenue, may reduce the investment cost of building the reliability. The large consumer increases the proportion of subsidies to encourage the electricity generator to supply electricity better and more reliably to reduce the probability of electricity supply disruption. When the maintenance cost of the electricity generator is high, the electricity generator pays attention to the reliability construction and increases the cost investment. The large consumer observes this situation and hence appropriately decreases incentive subsidies.


## 3.2.1. Optimal Reliability Level

The first derivative of the revenue function of the generator onz is equal to zero. Hence, the expression of the optimal reliability level of the generator with respect to the subsidy ratio γ is as follows:(10)z∗=minC¯−u1σc+TCw1−γβ,1.We can obtain the optimal reliability level of the generator by substitutingz∗ into the cost function of the large customer.Proposition 1.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the generator and the large consumer, the optimal reliability level of the electricity generator is computed as follows:(11)z∗=TCs+C¯−u1σc+TCw/2−C¯+u2σc,βC¯−u1σc−2C¯+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,C¯−u1σc+TCwβ，C¯−u1σc≤β−TCw3C¯−u1σc+2u2σc≥2TCs−TCw,1,others.Proof.
Whenz∗=C¯−u1σc+TCw/1−γβ, we can obtain γ=1−C¯−u1σc+TCw/z∗β. We can obtain z∗≥C¯−u1σc+TCw/β because 0≤γ≤1. Simultaneously, we can obtain the following equation by substituting the expression on γ into the cost function of a large consumer and setting the first derivative on z to zero:(12)Z=TCs+C¯−u1σc+TCw/2−C¯+u2σcβ.
Moreover, (a) when1≥C¯−u1σc+TCw/1−γβ≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β, the optimal reliability of the generator is C¯−u1σc+TCw/1−γβ. (b) When 1≥TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥C¯−u1σc+TCw/1−γβ, the optimal reliability of the generator is TCs+C¯−u1σc+TCw/2−C¯+u2σc/β. (c) When C¯−u1σc+TCw/1−γβ≥1 or TCs+C¯−u1σc+TCw/2−C¯+u2σc/β≥1, the optimal reliability of the generator is 1.
In Proposition 1, the cost coefficientβ (or β/2) represents the difficulty experienced by the electricity generator in building supply reliability. When β is large, the difficulty is high and the optimal reliability level is low. When β is small, the difficulty is low and the optimal reliability level is high. Moreover, z∗ increases on TCw and TCs. This result shows that when the maintenance cost of the electricity generator is high, the electricity generator invests cost to build reliability to resist the risk of disruption. When the loss cost of the large consumer is high, the large consumer offers additional subsidies to improve the reliability of the electricity supply. Further analysis of the influence of u1 and u2 on the optimal reliability level shows that the target uncertainty level of the large consumer and the generator negatively affects the optimal reliability of the generator. These results are attributed to two reasons. On the one hand, with the high target uncertainty level of the electricity generator resulting in low expected revenue, the electricity generator assumes reducing revenue and invests less on reliability construction cost when the reliability level drops. On the other hand, with the high target uncertainty level of the large consumer leading to a high expected cost, the large consumer assumes that the procurement cost is high and thereby reduces the subsidy of the reliability construction cost. By contrast, the electricity generator naturally reduces the investment in reliability construction.


## 3.2.2. Optimal Subsidy

Applying the reverse induction method, when the optimal reliability level of the electricity generator is determined, the large consumer makes subsidy decisions on the basis of the different reliability levels to encourage the electricity generator to build the electricity supply reliability and reduce the risk of supply disruption.Proposition 2.
Given the average forecast price of the electricity market, the electricity demand of the large consumer, and the target uncertainty level of the electricity generator and the large consumer, the optimal subsidy ratio for the large consumer is as follows:(13)γ∗=1−C¯−u1σc+TCwβ，C¯−u1σc−2C¯+u2σc≥2β−TCw−2TCs,1−C¯−u1σc+TCwTCs+C¯−u1σc+TCw/2−C¯+u2σc，C¯−u1σc−2C+u2σc≤2β−TCw−2TCs3C¯−u1σc+2u2σc≤2TCs−TCw,0,other.Proof.
According to the optimal reliability level of the generator in Proposition 1, substitutingz∗ into γ=1−C¯−u1σc+TCw/z∗β, we can obtain the optimal subsidy proportion of the large consumer.Proposition 3.
shows that the optimal subsidy proportionγ∗ decreases on u2 and increases on TCs. This result shows that when the level of the target uncertainty of the large consumer and the expected procurement cost are high, the subsidy for the reliability cost of the electricity generator reduces. When disruption occurs, the loss of the large consumer is high. Hence, the large consumer likely expands subsidies to the electricity generator to improve the reliability of the electricity supply and ensure electricity procurement.Arrangingγ∗, we can obtain γ∗=4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1. Notably, 4TCs−4C¯+u2σc/2TCs+C¯−u1σc+TCw−2C¯+u2σc−1.≥1>0. Thus, γ∗ increases on u1 and decreases TCw. This result shows that the generator, with the high target uncertainty level and the low expected revenue, may reduce the investment cost of building the reliability. The large consumer increases the proportion of subsidies to encourage the electricity generator to supply electricity better and more reliably to reduce the probability of electricity supply disruption. When the maintenance cost of the electricity generator is high, the electricity generator pays attention to the reliability construction and increases the cost investment. The large consumer observes this situation and hence appropriately decreases incentive subsidies.


## 4. Numerical Experiments

In this study, we study the dual-source procurement strategy consisting of the contract procurement and the market procurement. The transaction environment contains two uncertainties: disruption risk and market price fluctuation. In this section, the above models are analysed by conducting numerical cases. The main focus is on how to determine the optimal strategies to purchase and sell electricity. Specifically, we explore the impact of the proportion of the contract electricity purchase quantity on the cost of the large consumer and on the profit of the electricity generator. We divide 24 h a day into three stages according to the classification methods of Zare et al. [9] and Nojavan et al. [48]. These stages include the peak, medium peak, and low peak periods of electricity consumption. Each phase consists of 8 h (not necessarily eight consecutive hours), as shown in Table 2. The time span is the next week, 21 stages (i.e., 3 times 7) in total. Figure 2 shows the electricity consumption of each stage. The market prices differ in various peak periods. On the same day, the prices in peak, middle peak, and low peak periods are the highest, second, and lowest, respectively. The electricity market price in the following week can be predicted in accordance with the historical electricity price (Figure 3). The large consumer and the electricity generator sign two different electricity contracts first, and different electricity prices are considered, as shown in Table 3.Table 2
Periods of electricity consumptions.
PhaseTime SegmentLow peak period1, 2, 3, 4, 5, 6, 7, 8Middle peak period9, 10, 15, 16, 17, 18, 23, 24Peak period11, 12, 13, 14, 19, 20, 21, 22Figure 2
The electricity consumption distribution of the large consumer in the next week.Figure 3
The market price forecast in the next week.Table 3
The electricity contracts.
Contract numberMinimum electricity (MW)Maximum electricity (MW)Price (Yuan/MWh)11825322253545The values of the parameters are as follows:β=3×106, u1=10, u2=10, TCs=8×106, TCw=3×106, and σc=1.24×103. The proportion of the contracted electricity purchase quantity to the total electricity purchase quantity is ∑t=1T∑n=1NQn,t/∑t=1TDt with T=21,N=2 Similarly, the proportion of the market electricity purchase quantity is 1−∑t=1T∑n=1NQn,t/∑t=1TDt. The impacts of the cost of large consumer and the profit of electricity generator on the proportion of contract procurement quantity are obtained. Furthermore, we investigate whether the large consumer’s cost and the electricity generator’s revenue are always beneficial in improving the proportion of the contract procurement quantity. To enhance the robustness of numerical experiments, we set three different values for each parameter (with fixed β=3×106 and σc=1.24×103) to represent low, medium, and high levels, respectively.


### 4.1. The Optimal Procurement Structure

In this part, we analyse the optimal strategies between contract procurement and market procurement.Figure4 shows that the cost of the large consumer always increases in proportion to the quantity of electricity procurement under the contract for different u2 (i.e., the uncertain target parameter of large consumer). That is, the cost of the large consumer can be harmed by the contract procurement. This finding shows that the large consumer should reduce the contract procurement in the case of electricity supply disruption risk and electricity market uncertainty. Moreover, the large consumer should increase the procurement quantities in the market trading platform, which seems to be the opposite of the management enlightenment in Section 3.1.1.Figure 4
The impact of the proportion of the contract procurement quantity on the large consumer’s cost.The essence of these two conclusions is the same, that is the large consumer should purchase electricity from a reliable source. Without disruption risk, the large consumer should apply contract procurement. From the perspective of electricity supply, the electricity generator and the market trading platform are reliable for the large consumer. However, from the perspective of electricity price, when the price of the electricity generator is stable and the price on the market trading platform is uncertain, the large consumer should pay extra “tolerance cost.” Therefore, the large consumer should procure electricity from a reliable electricity generator. When considering supply disruption risk, the electricity supply of the electricity generator is no longer reliable. When purchasing electricity from the electricity generator, large consumers need to invest in the unreliable electricity generator with cost subsidies, which aggravate their cost burden. Moreover, large consumers are seriously influenced by profit when the electricity supply is interrupted. The robustness function also sets the tolerance level of the uncertainty for the large consumer in advance. The large consumer can eliminate the influence of uncertain electricity price through the appropriate “tolerated cost,” indicating that the uncertain market electricity procurement cost is converted into certainty. Therefore, purchasing electricity from the market trading platform with a reliable electricity supply and less procurement cost is profitable for the large consumer.Figure5 shows that increasing the proportion of the contract electricity procurement could expand the profits of the electricity generator. The additional use of the contract electricity procurement implies the expanded order of the electricity generator. Such order incentives the electricity generator, which can benefit from extra profits. At the same time, facing interruption risk, if the electricity generator expects the large customer to keep or expand the order, then the electricity generator signing the contract should transfer part of the profits to the large customer. Moreover, the generator should invest additional costs in the reliability construction, such as developing smart technologies and establishing a real-time monitoring system, to construct a reliable supply.Figure 5
The impact of the proportion of the contract procurement quantity on the electricity generator’s revenue.


### 4.2. The Impact of the Players’ Risk Attitude

Figure4 shows that a higher value of u2 leads to higher expected procurement cost of the large consumer. Thus, if large consumers want to ensure that their decisions are fully robust as expected, then they must face the “worst case” and pay the highest cost. Evidently, the expected procurement cost of the large consumer comprises the average forecast market price, electricity demand, contract procurement price, and quantity and uncertainty. The value of u2 is high, which denotes that the uncertainty and the expected procurement cost of the large consumer are high. Thus, certain management implications are obtained. Firstly, if the large consumer expects its decision-making to be robust, then it must pay a high cost. Thus, if the large consumer pays high cost, then its decision-making exhibits high robustness. Moreover, without disruption risk, the large consumer should purchase additional electricity from a reliable source, such as contract procurement, and attempt to avoid purchasing electricity from the electricity pool. The large consumer should also implement long-term planning and establish a sustained and stable strategic cooperation relationship with the upstream electricity generator.Figure5 shows that, when the value of u1 is high, the expected revenue of the generator is low. This result is due to the potential revenue loss (relative to the average expected revenue) when the uncertainty is high. Thus, the electricity generator should accurately master and forecast the market price to narrow the uncertainty and to strive for the most stable expected revenue.


## 4.1. The Optimal Procurement Structure

In this part, we analyse the optimal strategies between contract procurement and market procurement.Figure4 shows that the cost of the large consumer always increases in proportion to the quantity of electricity procurement under the contract for different u2 (i.e., the uncertain target parameter of large consumer). That is, the cost of the large consumer can be harmed by the contract procurement. This finding shows that the large consumer should reduce the contract procurement in the case of electricity supply disruption risk and electricity market uncertainty. Moreover, the large consumer should increase the procurement quantities in the market trading platform, which seems to be the opposite of the management enlightenment in Section 3.1.1.Figure 4
The impact of the proportion of the contract procurement quantity on the large consumer’s cost.The essence of these two conclusions is the same, that is the large consumer should purchase electricity from a reliable source. Without disruption risk, the large consumer should apply contract procurement. From the perspective of electricity supply, the electricity generator and the market trading platform are reliable for the large consumer. However, from the perspective of electricity price, when the price of the electricity generator is stable and the price on the market trading platform is uncertain, the large consumer should pay extra “tolerance cost.” Therefore, the large consumer should procure electricity from a reliable electricity generator. When considering supply disruption risk, the electricity supply of the electricity generator is no longer reliable. When purchasing electricity from the electricity generator, large consumers need to invest in the unreliable electricity generator with cost subsidies, which aggravate their cost burden. Moreover, large consumers are seriously influenced by profit when the electricity supply is interrupted. The robustness function also sets the tolerance level of the uncertainty for the large consumer in advance. The large consumer can eliminate the influence of uncertain electricity price through the appropriate “tolerated cost,” indicating that the uncertain market electricity procurement cost is converted into certainty. Therefore, purchasing electricity from the market trading platform with a reliable electricity supply and less procurement cost is profitable for the large consumer.Figure5 shows that increasing the proportion of the contract electricity procurement could expand the profits of the electricity generator. The additional use of the contract electricity procurement implies the expanded order of the electricity generator. Such order incentives the electricity generator, which can benefit from extra profits. At the same time, facing interruption risk, if the electricity generator expects the large customer to keep or expand the order, then the electricity generator signing the contract should transfer part of the profits to the large customer. Moreover, the generator should invest additional costs in the reliability construction, such as developing smart technologies and establishing a real-time monitoring system, to construct a reliable supply.Figure 5
The impact of the proportion of the contract procurement quantity on the electricity generator’s revenue.


## 4.2. The Impact of the Players’ Risk Attitude

Figure4 shows that a higher value of u2 leads to higher expected procurement cost of the large consumer. Thus, if large consumers want to ensure that their decisions are fully robust as expected, then they must face the “worst case” and pay the highest cost. Evidently, the expected procurement cost of the large consumer comprises the average forecast market price, electricity demand, contract procurement price, and quantity and uncertainty. The value of u2 is high, which denotes that the uncertainty and the expected procurement cost of the large consumer are high. Thus, certain management implications are obtained. Firstly, if the large consumer expects its decision-making to be robust, then it must pay a high cost. Thus, if the large consumer pays high cost, then its decision-making exhibits high robustness. Moreover, without disruption risk, the large consumer should purchase additional electricity from a reliable source, such as contract procurement, and attempt to avoid purchasing electricity from the electricity pool. The large consumer should also implement long-term planning and establish a sustained and stable strategic cooperation relationship with the upstream electricity generator.Figure5 shows that, when the value of u1 is high, the expected revenue of the generator is low. This result is due to the potential revenue loss (relative to the average expected revenue) when the uncertainty is high. Thus, the electricity generator should accurately master and forecast the market price to narrow the uncertainty and to strive for the most stable expected revenue.


## 5. Conclusion

Considering the unreliable supply of electricity quantity and the fluctuation of electricity prices, the large consumer’s electricity procurement strategy becomes extremely difficult. Unlike previous studies, the present research explores electricity procurement strategies considering both electricity supply disruption risk and market price fluctuation. The quadratic function describes the construction cost of the electricity supply reliability, and the robustness function and opportunity function describe the market price fluctuation. With these functions, we discuss the electricity transaction problems of the large consumer and the electricity generator. Results show that, firstly, the large consumer should purchase electricity from a reliable source without disruption risk, such as contract procurement. Moreover, they must attempt to avoid purchasing electricity from the electricity pool. In the case of electricity supply disruption risk and electricity market uncertainty, however, the large consumer should reduce contract procurement and increase procurement quantities on the market trading platform. Secondly, the high loss cost of the large consumer or the high maintenance cost of the electricity generator can promote the reliability level of the electricity supply enlargement. However, the uncertainty of the market price negatively affects the reliability level. Thirdly, the loss cost of the large consumer can promote subsidies, but the maintenance cost of the electricity generator can weaken the willingness of the large consumer to be subsidised directly. The tolerance of uncertainty of the large consumer can weaken the direct subsidy, whereas the tolerance of uncertainty of the electricity generator can promote the subsidy incentive of the large consumer.For future research, this study can be extended in the following directions. In this study, we consider a supply chain consisting only of a generator and a large consumer. Market competition among multiple generators is excluded. However, in reality, competition among multiple generators will inevitably improve the voice of the large consumer. As a result, the proportion of direct subsidies and the procurement strategies can be affected. This notion should be considered in future studies. Information asymmetry is also interesting to consider. In this research, we consider that the information of the generator and that of the large consumer are completely symmetric. However, both parties may keep their own prediction information about the future electricity market price to themselves. They may even send egoistic signals to mislead the other party. Thus, how to play the game under private information is another direction of future research.



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*Source: 9303478-2022-06-10.xml*