A Real‐Time Information‐Based Demand‐Side Management System

Demand response is a feature to be achieved in the smart grid. In this chapter, we study a few mechanisms to demonstrate the enhanced efficiency in the smart grid with demand response.

6.1 Background and Related Work

6.1.1 Background

Demand response (DR), also known as demand‐side management system [2729], utilizes real‐time information in order to let the power grid generate and consume energy more efficiently while reducing fuel waste. A DR system is widely agreed to be effective at reducing the peak‐to‐average ratio (PAR) of energy consumption [28, 29, 98]. This improvement helps power suppliers reduce the extra fuel costs caused by dramatic and unpredictable margin fluctuations in power generation. Burning less fuel also helps reduce emission of greenhouse gas from those power generators. Moreover, since the control center gets the energy consumption schedule beforehand [83, 99101], renewable sources such as photovoltaics (PV) and wind turbines, which are less stable and less controllable compared than conventional power generators, can support the power grid more efficiently. A higher proportion of such renewable sources will further reduce the burning of fuel by conventional power generators.

In this chapter, we first propose a centralized optimization problem images in order to reduce PAR to its minimum. Although a minimum PAR is obviously beneficial to the environment, it motivates neither power suppliers nor customers. Power suppliers especially must deploy and maintain a more complicated cyber physical system than what AMI can offer to gather and distribute a huge amount of detailed information in real time. Therefore, a monetary incentive is needed to motivate power suppliers. Another centralized optimization problem images is then proposed to reduce the total cost of energy generation cost to power suppliers. Although power suppliers may be willing to adopt the DR system based on images, it is based on direct load control (DLC) [99, 102, 103], which could be defective. In terms of communications, even if the massive centralized problem can be solved efficiently, the transmission overhead will create a huge burden on the communication network and require more advanced technical upgrades as well as more frequent maintenance. Moreover, customers could be reluctant to adopt such a DR system for two reasons. One reason is that the control center takes over the energy consumption scheduling from customers with no clear incentive for them to do so. The other reason is that DLC requires too much private information from customers.

To tackle those issues, we must have a DR system that clearly benefits customers, protects their privacy, and requires much less real‐time information exchange compared with images or images. We formulate a game with two approaches based on smart pricing, which is another major technique applied to the DR system. In one approach, customers get to compute the dynamic price based on their own load schedule, with the total load of the power grid given. In the other approach, the control center computes the price based on the total load of the power grid, and customers get that fixed price schedule that will not be affected by their local scheduling load. In either game theoretical approach, the payoff functions lead customer to more energy cost savings. Therefore, customers are motivated to adopt this DR system. In addition, customers reserve the right to control their power consumption, and by doing so, they keep their information private by submitting only the energy consumption schedule, which is always requested even in the traditional power grid. Moreover, since most of the calculation is performed locally at the customer side, the approaches are mostly distributed instead of centralized. The distributed game theoretical approach largely relieves the transmission overhead. More importantly, we prove that all images, images, and the game theoretical approach with locally computed dynamic smart pricing lead to the same minimum PAR. Therefore, while all parties get enough motivation to participate, the DR system can be deployed in a distributed way.

6.1.2 Related Work

DR in the smart grid has been studied by many researchers recently [2729, 83, 98101, 104106]. However, most of the works focus on one of the parties (e.g. power suppliers when applying DLC or customers when adopting smart pricing) in the system only, without clarifying why others were overlooked. The game theoretical approach and smart pricing have also been widely adopted in most of the studies as efficient approaches. The works most relevant to this paper includes [28, 29, 99]. The authors of [28] proposed a noncooperative game played among residential customers, and a two‐stage Stackelberg game theoretical approach where power suppliers as the leaders tend to maximize their profits and customers as the followers tend to minimize their costs. Since [28] mostly targeted residential customers, the benefits for other parties in the system were not clearly stated, and an impractical situation where the total load goes negative was carefully avoided. In [29], the authors proposed an efficient game theoretical approach for residential customers without a storage unit based on dynamic smart pricing to reduce the PAR. While computational efficiency was demonstrated, the global optimal PAR was not guaranteed by the distributed approach. The authors of [99] are among of the first to minimize PAR by using a distributed game theoretical approach among customers. Similarly, the consideration of a storage unit was reserved for their future work, and the global optimal PAR was not guaranteed.

We summarize the main contributions as follows:

  • In order to benefit the entire society and the environment, we propose a DLC‐based centralized approach to minimizing PAR.
  • In order to show the benefits to the power suppliers, we propose another DLC‐based centralized approach that minimizes the cost of power generation, and the power generation cost model considers all sources, including conventional, nonexpanding green energy, and expanding renewable energy sources.
  • In order to motivate customers to adopt the DR system and protect their privacy, we propose smart pricing based game theoretical approaches that can maximize savings for customers adopting such a DR system. The game theoretical approaches are mostly distributed, and thus they alleviate the communication burden of the network.
  • We prove that the proposed DLC‐based approach and one of the smart‐pricing‐based distributed game theoretical approaches yield the same optimal solution (minimum PAR); therefore the distributed game theoretical approach can be applied in real situations while all parties observe clear benefits from the DR system.
  • We provide extensive numerical analysis and simulation results to demonstrate our analysis. We also compare several distributed approaches in order to find the best way to deploy the DR system.

6.2 System Model

6.2.1 The Demand‐Side Power Management System

The DR system under consideration mainly consists of three parts: the control center, power suppliers, and customers, as illustrated in Figure 6.1. Power generators include all major types, from fuel‐consuming conventional power generators to renewable power generators. For simplicity, a micro grid that can be attached to or detached from the power grid is not considered, and customers do not have power generators. The control center is mainly responsible for power distribution. It also gathers data (e.g. energy consumption) and distributes control information (e.g. price, tariff, and emergency control signal). The information is available because of a two‐way communication network in the DR system. At each customer site, there is a smart meter that is responsible for reporting the power consumption and possible scheduling to the control center through the communication network. It is also responsible for receiving price, tariff, and other control information from the control center.

Diagrammatic illustration of demand-side power management system.

Figure 6.1 Demand‐side power management system.

According to [107], major customers in the United States include residential, business, and industrial ones as shown in Figure 6.2. Those customers have different characteristics when consuming electric energy. For example, residential customers may consume power mostly from afternoon through midnight, business customers consume energy mostly during office hours, while industrial customers may have a longer peak consumption schedule because of continuous shifts by different work groups. The deployment of energy storage units and the use of plug‐in hybrid vehicles (PHEV) are increasing rapidly. Such devices/appliances will increase energy consumption and change the current peak time schedule. For example, it is reasonable to assume that most customers will charge their PHEV during the night. For simplicity, the PHEV is considered as a hybrid of a normal energy‐consuming appliance and an energy storage unit in the studied DR system.

Grid illustration of bars showing the power sale to the customers in the United States.

Figure 6.2 Power sale to the customers in United States.

6.2.2 Mathematical Modeling

Table 6.1 lists the key notations of sets and variables we use throughout the rest of this chapter. Let images be the set of all customers, where images is the total number of customers. Although the DR system can be modeled for any arbitrary time period to satisfy the assumptions, we consider a daily model in this work without loss of generality. Let one day be divided into several uniform time intervals, denoted as images.

Table 6.1 Key sets and variables.

imagesset of customers
imagesset of time intervals
imagesdaily energy consumption scheduling
imagesset of total cost for each time interval
imagesset of unit price for each time interval
Local (for customerimages)
imagesset of appliances
imagesdaily energy scheduling set of images
imagesEnergy requirement set
imageson/off operating scheduling set of images
imagesdischarging scheduling of storage unit
imagescharging scheduling of storage unit
imagesdaily energy consumption scheduling set

Each customer images has a set of appliances images, where images. Each appliance (e.g. images) has a daily energy consumption scheduling set images, which records the energy needed or consumed during each time interval. Moreover, each appliance images also has a predetermined energy requirement images for a time period (assuming one day for simplicity). Therefore, for images, it must satisfy

where images is a column vector of images and images calculates the transposition. Appliance images has an on/off operating scheduling set images, where 1 indicates that images is allowed to operate, whereas 0 indicates an off status for images. The on/off operating schedule can model the operating status more precisely than the model using an operating time period, which is more widely adopted [28, 29, 99]. For example, with an on/off operating schedule, it is possible to model a two‐hour pause in an air‐conditioning (AC) system. However, if it is modeled by the operating time period, the time period must be divided into three corelated sessions with extra constraints. With the on/off operating scheduling set images, Eq. (6.1) can be rewritten into


For an appliance that needs to be used several times daily (e.g. a coffee machine), it can be modeled as multiple independent appliances with corresponding energy requirements and on/off schedules. For this reason, we want to emphasize that images may not necessarily be the exact number of appliances of customer images but the number that counts independent appliances.

When images is operating, its energy consumption is bounded by images and images, and mathematically


Besides the appliances, let each customer (images) be equipped with an energy storage unit with a design capacity of images. For simplicity, we assume that the storage unit has images discharging/charging efficiency, and the energy can be distributed for all the appliances within the power grid with images efficiency. In other words, the energy in storage units can support the appliances of customers themselves as well as be sold to the power grid. Let images be the discharging scheduling set, and let images be the charging scheduling set. Like appliance energy consumption, the discharging/charging energy in each time interval is bounded by the safety thresholds images/images, which are expressed as


To be more precise, the storage unit should not discharge and charge at the same time for efficiency, so we have

where “images” is the entrywise/Hadamard product, and images is the column vector with all images. Eq. (6.6) will help convert the storage unit model into a lossy one easily.

Let images be the set of remaining energy at the beginning of each time interval,


where images is the initial remaining capacity. Let images be the designed capacity of the storage unit; then


Let the daily energy consumption schedule for customer images be images. With the previous modeling, we now have


For the whole DR system, the global load schedule images is calculated as

6.2.3 Energy Cost and Unit Price

Based on [108], power suppliers are categorized into three types: conventional generators using fossil fuels (e.g.coal), nonexpandable green sources (hydroelectric, nuclear), and expandable renewable sources (PV fields, wind farms). The net capacity of those generators/sources is shown in Figure 6.3. Conventional generators are still the major energy producers; however their proportion is decreasing. The proportion of nonexpandable generators is slowly decreasing since the total amount of energy is increasing. Although the proportion of expandable renewable energy is low, it is increasing at a faster pace. Therefore, we need to take into consideration all three categories of power suppliers for a more precise modeling.

  • Fuel‐consuming conventional generators. A quadratic cost function is widely adopted for these generators [2729, 98, 99] as
  • Nonexpandable green sources. Assuming that the energy produced is predetermined by the fixed facilities, the total cost can be viewed as a fixed cost images plus a linear cost with respect to power transmission capacity as
  • Expandable renewable sources. Since most of their cost comes from the management of the facilities [109], by assuming the facilities can be on/off based on the load requirement, the total cost is increasing with respect to the load requirement. However it increases slower than that of the conventional generators [110], especially when carbon tax [111] applies. Therefore we adopt the following cost model for expandable renewable sources.
Grid illustration showing the existing net capacity by energy source and producer type.

Figure 6.3 Existing net capacity by energy source and producer type [108].

Source: Data from http://www.eia.gov/electricity/annual/html/epa_03_01_a.html

Taking into consideration the proportions of all the generators/sources, the overall energy cost is modeled as


where images, images and images are the proportions of the three power suppliers respectively, and images. Let images be the set of total costs for each time interval. At the customer side, the unit price (images per kWh) is more important than the total cost. For simplicity, let the energy be generated uniformly during a time period; the unit price is then calculated as

Finally let images be the set of unit prices for each time interval.

6.3 Centralized DR Approaches

6.3.1 Minimize Peak‐to‐Average Ratio

One of the ultimate goals of applying DR is to reduce the peak‐to‐average ratio, which raises the first problem:


Note that although the existence of an optimal solution always stands, the uniqueness of the solution only stands when images is considered as the variable set, because multiple solutions to Eq. (6.11) may exist with a given images. Although minimizing PAR is a desirable objective, it may not be convincing enough for power suppliers or customers to adopt such a DR system. For this reason, we further formulate another problem that has a monetary incentive as part of its objective function.

6.3.2 Minimize Total Cost of Power Generation

In the electricity energy market, power generators/sources are not yet fully competitive with each other, since some of the technologies are still too expensive to apply and they operate based on a government subsidy [112]. Moreover, sophisticated regulatory mechanisms are needed to avoid arbitrarily high prices produced by monopolies and rigid electric energy demand. Therefore, we focus on a cost‐oriented instead of a profit‐oriented objective. In short, images minimizes the total cost to the power suppliers, such that


Let function images. Then the optimal solution to images can be found by solving the necessary and sufficient conditions of KKT [113].

Note that solution presented in Eq. (6.21) is unique with respect to images, and it may have multiple solutions with respect to the detailed energy consumption scheduling patterns to all the appliances.

Although power suppliers may be willing to adopt a DR system according to images so that they can reduce their total cost, it still has three major issues to solve for either images or images. Customer privacy is the first issue. Since both images and images are executed exclusively at the control center side (often regarded as DLC schemes), all customers must submit detailed information to the control center and willingly let the control center schedule their power usage. The incentive for the customers to adopt a DR system is the second issue. Although a DR system smooths PAR and reduces the total cost, it is not clear whether customers can benefit from images or images or not. Third, both images and images are centralized optimization problems, which can get quite complicated and computation‐intensive to solve. Even if the problems can be solved efficiently, the huge overhead of raw data gathering puts too much burden on the communication network. Therefore, we need a distributed DR system that also protects the customers by letting them control their own appliances.

6.4 Game Theoretical Approaches

6.4.1 Formulated Game

Smart pricing is another widely adopted cost strategy in order to attract customers' interest. Moreover, a game theoretical approach is an efficient way to solve a problem in a distributed fashion with some limited sharing of information. Therefore, we formulate a noncooperative game images, where images is the strategy set (all possible load scheduling patterns) of player (customer hereafter for consistency) images (the notation of a customer is changed from images to images, which is more generic for game theoretical approach), and images is the payoff function of customer images, which is

where images is a flat‐rate price vector if a smart pricing strategy is not applied. This payoff function shows the saving of a customer from adopting this particular DR system. Intuitively, if adopting a DR system reduces their cost, customers are willing to participate. In this game, each customer calculates a best response images with a given images such that

The best response in Eq. (6.30) is the same as calculating


Note that Eq. (6.31) has a specific meaning for its incentive, which is to find the set of load scheduling patterns that maximize the energy cost saving for customer images by adopting a DR system.

Since each customer has relatively stable daily energy consumption levels, that is, images, the flat‐rate price yields a constant cost for each customer. Therefore, the problem in Eq. (6.31) equals the one as follows:


6.4.2 Game Theoretical Approach 1: Locally Computed Smart Pricing

In this approach, we assume that each customer submits an initial load schedule images to the control center and then the control center broadcasts the initial total load schedule images to the customers. In this approach, the price computing function in Eq. (6.16) is known to all customers. Then each customer will be able to compute the smart pricing schedule as


Let images. Customer images will need to solve the following problem to find images,


Let function images, and images be the total energy requirement for customer images. Then the optimal solution to images can be found by solving the necessary and sufficient conditions of KKT [113].

Algorithm 6.1 is proposed to approach the NE of images.


Theorem 6.2 demonstrates that images not only favors the customers but also minimizes the total cost and thus favors power suppliers as well. So images minimizes PAR according to theorem 6.1. However, the control center may not want to release the price‐calculating function to customers. We then propose another approach based on a precalculated fixed‐price schedule.

6.4.3 Game Theoretical Approach 2: Semifixed Smart Pricing

In this approach, each customer images also submits an initial load schedule images; however, the price function is hidden from customers. Only the control center is able to calculate the fixed price vector with each images as


Then each customer images will solve the following problem to find images,


Note that images is a linear optimization problem, which can be solved with a unique solution. However, the NE for images is not guaranteed, since the objective function is no longer strictly concave.

6.4.4 Mixed Approach: Mixed images and images

The mixed approach is to apply both images and images approaches based on the properties of customers. As mentioned earlier, images reveals the price function to the customers, which may not favor the control center. The total load is also given to all customers. However, customers who use a significant proportion of energy may not want to reveal such private information. images does not have those issues but it does not guarantee the optimal solution of images or images. In the mixed approach, large‐energy‐consumption customers adopt images (e.g. business and industrial customers), and regular‐energy‐consumption customers (e.g. residential customers) adopt images. In the numerical analysis and simulation section, we will show that the mixed approach converges to the minimum PAR in practice.

6.5 Precision and Truthfulness of the Proposed DR System

Because customers could have exceptional energy consumption, a one‐time scheduling approach [28, 29, 99] can hardly be followed strictly. In order to increase the precision of the proposed DR system, the system should run at the beginning of each time interval for the rest of the day. The control center and the computing device of each customer (e.g. the smart meter) should save the previous status and subtract it from the constraints when calculating the load scheduling for the rest of the day. With the DR system following schedule, and since the payment is collected after each time interval based on the real energy usage in that interval, for images, images and images, the minimum PAR, the minimum total cost, and the maximum local saving will be achieved only when customers report the load schedules truthfully. The conclusion is quite intuitive because lying about the load will keep customers from reaching the optimal solution. Therefore, the truthfulness of the proposed DR systems should be guaranteed.

6.6 Numerical and Simulation Results

6.6.1 Settings

Assume that power suppliers are available to support customers with any energy requirement. The control center is able to gather information from and distribute it to the power suppliers and the customers in real time (e.g. images). The customers are categorized into residential, business, and industrial types. Without loss of generality, we assume that the daily energy consumption of the customers follows the proportions obtained from the data in Figure 6.2. Specifically, as shown in Figure 6.4, residential customers consist of three types (i.e. families in big houses, families in townhouses, and families in apartments), each with 55 kilowatt‐hours, 41 kilowatt‐hours, and 33 kilowatt‐hours daily average energy consumption respectively. Each residential customer type has 50 customers. Business customers have two types (i.e. day‐time based business and shopping malls), each with 2400 kilowatt‐hours and 2700 kilowatt‐hours daily average energy consumption respectively, and each type has one customer. Industrial customers have two types (i.e. nonstop shift‐based manufacturers and day‐time based industry), each with 2100 kilowatt‐hours and 2500 kilowatt‐hours daily average energy consumption respectively, and each type has one customer. Note that the settings for the customers are flexible as long as the total energy consumption of each category follows the practical data.

Bar illustration showing the daily energy consumption of the customers.

Figure 6.4 Daily consumption of customers.

The granularity of time intervals is important to the DR system. As shown in Figure 6.5 and Figure 6.6, when images, the total load of the power grid is constant throughout the day, while it fluctuates when images.

Grid illustration showing the total load of the power grid solution to P1 with |T| = 24.

Figure 6.5 Solution to images with images.

Grid illustration showing the total load of the power grid solution to P1 with |T| = 8.

Figure 6.6 Solution to images with images.

Some of the detailed initial settings for residential customers are shown in Table 6.2. We assume that each storage unit is able to hold images of the daily power usage, each family has 2 PHEVs for type 1 and type 2 residential customers, and customers living in apartments have 1 PHEV each. Each PHEV holds 9 kilowatt‐hours of electricity. The power usage and rough schedules for other appliances are estimates based on day‐to‐day experiences. For simplicity, the on/off schedule is shown as start/end times. Note that some of the appliances are shown as multiple ones to make the modeling more precise; for example, AC for residential users is shown as ventilation all day and fully operating in the afternoon.

Table 6.2 Residential settings for the case study.

App imagesimagesimagesimagesStartEnd
Dish washerimages0images20,20,2024,23,22

6.6.2 Comparison of images, images and images

In this subsection, we evaluate the three DR mechanisms, including the two centralized ones and the game theoretical approach where smart pricing is computed locally. Figure 6.7 shows that the images, images, and images all reach the same optimal result with respect to the total load. However, each customer receives a different load scheduling. This is observed in all three DR systems.

Grid illustration showing the load schedules by P1, P2, and GA1.

Figure 6.7 Load schedules by images, images and images.

To better illustrate the results from the three DR mechanisms, more detailed results for residential customers are shown in Figure 6.8. Specifically, Figure 6.8(a), Figure 6.8(c), and Figure 6.8(c) show the results for three types of residential customers respectively. For each type of residential customer, the results are given for eight hours only. Note that images leads to a negative load for some customers, as shown in Figure 6.8(c). In the smart grid, some customers sell extra energy from their storage unit when the price is high to maximize their savings.

Three grid illustrations showing the load of different types of residential customers during the time of a day.

Figure 6.8 Load of different types of residential customers.

Similarly, load schedules for business customers are shown in Figure 6.9. Load schedules for industrial customers are shown in Figure 6.10.

Grid illustrations showing the load of different types (Type 1 and Type 2) of business customers during the time of a day.

Figure 6.9 Load of different types of business customers.

Grid illustrations showing the load of different types (Type 1 and Type 2) of industrial customers during the time of a day.

Figure 6.10 Load of different types of industrial customers.

6.6.3 Comparison of Different Distributed Approaches

Figure 6.11 shows the load scheduling results of images, images, mixed images, and a distributed approach when all customers intend to minimize their local PAR. From the simulation results, we can see that both images and mixed images converge to the optimal PAR, while neither images nor min local PAR minimizes PAR.

Grid illustration showing the load scheduling from different distributed approaches during the time of a day.

Figure 6.11 Load scheduling from different distributed approaches.

In fact, images performs the worst in the simulation when all customers are considered. Because of the fixed smart price, customers will shift their load to the time intervals with low prices without considering the consequences of doing so. When all customers do so, the time intervals with a relative low previous load will be scheduled with a higher load, and the price will go up. Then customers will shift back based on the updated price schedule. The simulation also indicates that images alone fluctuates between these two states without converging to the NE. Figure 6.12 shows the two states of the total load schedule by images for the first eight time intervals. Figure 6.13, Figure 6.14, and Figure 6.15 show the average load schedules by images and mixed images for the first type of customers in each category. It appears that images schedules a smoother load for each customer, because residential customers have better assessments of the cost changes based on their updated schedule with images. When applying mixed GA, although each customer does not affect the price much, they together still cause a major impact. Therefore, both business and industrial customers must schedule their loads with more fluctuation to adapt to the residential load.

Grid illustration showing the two states of total load schedule by GA2 during the time of a day.

Figure 6.12images illustration.

Grid illustration showing the load achieved by GA for type 1 residential customers during the time of a day.

Figure 6.13 Load achieved by images for type images residential customers.

Grid illustration showing the load achieved by GA for type 1 business customers during the time of a day.

Figure 6.14 Load achieved by images for type images business customers.

Grid illustration showing the load achieved by GA for type 1 industrial customers during the time of a day.

Figure 6.15 Load achieved by images for type images industrial customers.

Figure 6.16 shows that both images and mixed images converge quickly to the NE. In game theoretical approaches, the uplink to the network transmits the load schedule of each customer to the control center, and the control center broadcasts the total load schedule to all customers. Although it requires multiple iterations, it also requires much less data transmission compared with the centralized approach, which needs much more detailed data from the customers, and the scheduled appliance load must be delivered to each customer individually. Moreover, it is worth mentioning that energy providers may not want to declare the true cost function to all the customers in practice. With the adoption of mixed GA, only a few customers are required to know the cost function, and some confidential agreements can be made.

Grid illustration showing the convergence of GA1 and mixed GA.

Figure 6.16 Convergence of images and mixed images.

6.6.4 The Impact from Energy Storage Unit

Whether to include energy storage units in the smart grid may contribute to DR in the smart grid. From Figure 6.17 we can see that the total load schedule is no longer a straight line without the assistance of storage units. Therefore, storage units on the customers' side will certainly improve the efficiency of DR mechanisms. In theory, if the capacity of the energy storage units is unlimited, the smart grid would have enough buffer to store all electricity that is overgenerated, especially that from renewable power sources. In practice, customer may use electric vehicles as energy storage units in the future.

Grid illustration showing the load schedule without storage units during the time of a day.

Figure 6.17 Load schedule without storage units.

Without energy storage units, the PAR for the power grid would be higher, as shown in Figure 6.18. However, storage units may not necessarily help reduce the PAR for each customer individually.

Illustration of bars on a grid showing the impact of storage units on peak-to-average ratio (PAR).

Figure 6.18 Impact of storage units on PAR.

6.6.5 The Impact from Increasing Renewable Energy

In the future, the smart grid will integrate more renewable energy sources. Based on the data shown Figure 6.3, we can estimate the different power suppliers up to the year 2020. As shown in Figure 6.19, renewable energy sources will be more than 20% of the smart grid.

Grid illustration showing an estimation of different power suppliers.

Figure 6.19 An estimate of different power suppliers.

Based on these estimates, the total energy cost to te customers in 2014, 2018, and 2020 is shown in Figure 6.20. Clearly, the expansion of renewable energy would help to reduce energy costs.

Grid illustration of bars showing the corresponding total cost estimations for future years.

Figure 6.20 Corresponding total cost estimates for future years.

6.7 Summary

In this chapter, we studied demand response in the smart grid. In order to motivate and benefit all parties, including society (the environment), power suppliers, and customers, we proposed several approaches for the DR system. First, images directly minimizes PAR. Second, a DLC‐based cost minimization approach images motivates the power suppliers. However, both images and images fail to protect the privacy of customers, and their communication overhead is too high for deployment in a real‐time system. We proposed two further smart pricing‐based game theoretical approaches images and images to address the shortcomings of images and images. We successfully proved that both images and images, in which each customer calculates the dynamic price locally, reach the solution to images (min PAR). In the numerical analysis and the simulations, we further demonstrated the results and compared the performance of several distributed approaches.

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