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goal is to level the total load of all users instead of just one type of user. The company and each type of user would have a utility function reflecting its overall profit/cost. The utility functions are listed below, where wu, is for the utility company; ur, u2p, and war are for residential, commercial, and industrial users, respectively: ind f(Z) is the cost due to fluctuation of total user loads. spx, 3Br, and sp, are satisfaction functions for residential, com- nercial and industrial users, respectively. These functions have lifferent parameters based on the characteristics of the users, uid may take different forms other than (4) if necessary. In his paper, we employ the same satisfaction function as in the single-user-type case with different parameters, and the users’ yptimal responses to prices are in a form similar to (16), with lifferent parameters € and 7. The optimal responses of different vnes of users can be obtained as follows:

Figure 4 goal is to level the total load of all users instead of just one type of user. The company and each type of user would have a utility function reflecting its overall profit/cost. The utility functions are listed below, where wu, is for the utility company; ur, u2p, and war are for residential, commercial, and industrial users, respectively: ind f(Z) is the cost due to fluctuation of total user loads. spx, 3Br, and sp, are satisfaction functions for residential, com- nercial and industrial users, respectively. These functions have lifferent parameters based on the characteristics of the users, uid may take different forms other than (4) if necessary. In his paper, we employ the same satisfaction function as in the single-user-type case with different parameters, and the users’ yptimal responses to prices are in a form similar to (16), with lifferent parameters € and 7. The optimal responses of different vnes of users can be obtained as follows:

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Fig. 1. 5, with different parameters a, and 3; (with unit d;). increases faster as the actual load decreases. If the actual load is greater than the user demand, the function value is negative, meaning the users are satisfied. The decrease of the function value, however, slows down as the actual load continues to in- crease, because the users will not be “infinitely” more satisfied when they use more electricity. When the actual load equals the user demand, the function value is zero. Therefore the satisfac- tion function s;(l,,d,) should meet the following conditions:
Fig. 1. 5, with different parameters a, and 3; (with unit d;). increases faster as the actual load decreases. If the actual load is greater than the user demand, the function value is negative, meaning the users are satisfied. The decrease of the function value, however, slows down as the actual load continues to in- crease, because the users will not be “infinitely” more satisfied when they use more electricity. When the actual load equals the user demand, the function value is zero. Therefore the satisfac- tion function s;(l,,d,) should meet the following conditions:
The goal is to maximize the utility functions wu; and w2 under certain constraints. The optimization problem is formulated as The constraints are used to regulate the activity of the utility company and the users. The first constraint is on the actual user load. Due to the nature of electricity markets, electricity prices have to be regulated [16]. In order to guarantee the minimum load /;,min required by users, the utility company should not set the price too high . Also, the actual load cannot exceed min{d% max; Jmax}, Which is the minimum between the max- imum possible user load dg max at time period k and the max- imum generation limit gx max. This constraint means that even though users want to increase their use of electricity at a specific time period & when the price is low, there is a limit on how much they could increase it. Also, the actual user load always has to be less than the generation capacity of the system. The second constraint guarantees that the sales price is always greater than or equal to the marginal generation cost. The utility function of users is the negative of the cost function, 1.e.,
The goal is to maximize the utility functions wu; and w2 under certain constraints. The optimization problem is formulated as The constraints are used to regulate the activity of the utility company and the users. The first constraint is on the actual user load. Due to the nature of electricity markets, electricity prices have to be regulated [16]. In order to guarantee the minimum load /;,min required by users, the utility company should not set the price too high . Also, the actual load cannot exceed min{d% max; Jmax}, Which is the minimum between the max- imum possible user load dg max at time period k and the max- imum generation limit gx max. This constraint means that even though users want to increase their use of electricity at a specific time period & when the price is low, there is a limit on how much they could increase it. Also, the actual user load always has to be less than the generation capacity of the system. The second constraint guarantees that the sales price is always greater than or equal to the marginal generation cost. The utility function of users is the negative of the cost function, 1.e.,
Fig. 2. Illustration of the matrix A. Black denotes 1, light grey denotes —1, and white denotes 0. (a) Matrix A for flat pricing. (b) Matrix A for TOU block pricing.
Fig. 2. Illustration of the matrix A. Black denotes 1, light grey denotes —1, and white denotes 0. (a) Matrix A for flat pricing. (b) Matrix A for TOU block pricing.
Fig. 3. Comparison of prices and loads between flat pricing and GT-TOU pricing.
Fig. 3. Comparison of prices and loads between flat pricing and GT-TOU pricing.
COMPARISON OF THREE PRICING STRATEGIES IN SINGLE-USER-TYPE SCENARIO. TOTAL NOMINAL DEMAND IS 1700.10 GWh Fig. 4. Comparison of company profit and user benefit in the scenarios of flat pricing and GT-TOU pricing as yx changes.
COMPARISON OF THREE PRICING STRATEGIES IN SINGLE-USER-TYPE SCENARIO. TOTAL NOMINAL DEMAND IS 1700.10 GWh Fig. 4. Comparison of company profit and user benefit in the scenarios of flat pricing and GT-TOU pricing as yx changes.
Fig. 5. Comparison of total load and average unit price in the scenarios of flat pricing and GT-TOU pricing as j: changes.
Fig. 5. Comparison of total load and average unit price in the scenarios of flat pricing and GT-TOU pricing as j: changes.
Fig. 6. Parameter ¢, for different types of users used in the numerica examples.
Fig. 6. Parameter ¢, for different types of users used in the numerica examples.
Fig. 8. Loads of different types of users before and after applying GT-TOU pricing. Fig. 7. Comparison of GT-TOU prices with flat prices for multiple user types.
Fig. 8. Loads of different types of users before and after applying GT-TOU pricing. Fig. 7. Comparison of GT-TOU prices with flat prices for multiple user types.
COMPARISON OF USER LOAD AND PRICE IN A MULTIPLE-USER-TYPE SCENARIO. TOTAL NOMINAL DEMAND IS 1700.10 GWh high-energy-consumption procedures to hours when the elec- tricity price is low. In this way they can substantially reduce the average unit electricity price. As illustrated in Fig. 9, after applying the GT-TOU pricing strategy, the total electricity con- sumption of these three types of users is much more leveled. The peak total load is reduced by about 10.24%. TABLE V
COMPARISON OF USER LOAD AND PRICE IN A MULTIPLE-USER-TYPE SCENARIO. TOTAL NOMINAL DEMAND IS 1700.10 GWh high-energy-consumption procedures to hours when the elec- tricity price is low. In this way they can substantially reduce the average unit electricity price. As illustrated in Fig. 9, after applying the GT-TOU pricing strategy, the total electricity con- sumption of these three types of users is much more leveled. The peak total load is reduced by about 10.24%. TABLE V
COMPARISON OF COMPANY PROFIT AND USER UTILITY LEVEL IN A MULTIPLE-USER-TYPE SCENARIO
COMPARISON OF COMPANY PROFIT AND USER UTILITY LEVEL IN A MULTIPLE-USER-TYPE SCENARIO
Fig. 9. Comparison of total load before and after GT-TOU pricing.
Fig. 9. Comparison of total load before and after GT-TOU pricing.
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